text
stringlengths 14
5.77M
| meta
dict | __index_level_0__
int64 0
9.97k
⌀ |
|---|---|---|
\section{Introduction}
{ With the deployment of a massive number of devices, IoT networks are envisioned to enable a plethora of real-time applications involving features like local decision making and/or remote monitoring and control using some sensory mechanisms. For example, IoT networks can play a vital role in the efficient detection and management of natural disasters by deploying multiple sensors over a large area (potentially observing multiple physical processes). In such a scenario, some designated aggregator sensors (or cluster heads) may process the locally collected information from the nearby sensors and forward timely updates to some central unit through cellular BSs for further processing and the subsequent dissemination of the evacuation plans when needed. For such applications, the IoT devices may need to handle different data traffic streams for different destinations, where each stream has different performance objectives, such as rate, latency, or information freshness. }
To account for the heterogeneity of wireless data traffic and multiple functionalities of IoT devices, the interplay between the performance objectives of different data streams becomes an interesting topic. For example, the transmitter of an IoT device can be shared among two different traffic flows, one aiming at maximizing the system throughput by allowing direct D2D communication, and the other one related to monitoring some events in the environment. The D2D communications between nearby IoT devices can be useful for the efficient utilization of their available limited energy sources. For instance, the spatial correlation in the data measurements collected by nearby devices can be exploited for performing their communication tasks in a cooperative manner, thereby reducing the total energy required to execute these tasks. On the other hand, the IoT devices may frequently generate status updates regarding some stochastic processes being observed and send them to the BSs. The objective of updating the information status is to keep the information as fresh as possible, which can be characterized by the Age of information (AoI) \cite{abd2018role,kaul2012real}.
Motivated by the interplay between different IoT applications, we develop a novel analytical framework that allows for a comprehensive analysis of the large-scale IoT networks while integrating both the throughput-oriented D2D traffic and the age-oriented traffic from IoT
devices to BSs into a unified network design.
\subsection{Related Work}
We utilize the concept of AoI to quantify the freshness of information at the BSs regarding random processes monitored by IoT devices \cite{abd2018role}. The authors of \cite{kaul2012real} first introduced AoI for a simple queuing-theoretic model and derived a closed-form expression for the temporal mean (average over infinite period of time) of AoI. Using this result, it was demonstrated in \cite{kaul2012real} that the optimal rate at which the source should generate its update packets in order to minimize the average AoI is different from the optimal rates that either maximize throughput or minimize delay. A series of works then focused on extending the results of \cite{kaul2012real} by characterizing the temporal mean of AoI or other age-related metrics for different variations of queue disciplines \cite{kosta2017age_mono}. These early queuing-theoretic works have inspired the use of AoI or similar age-related metrics to quantify the freshness of information in a variety of communication networks that deal with time sensitive information including, D2D communications \cite{buyukates2019age,D2d_caching,bastopcu2020information} and IoT networks \cite{gu2019timely,abd2018average,AbdElmagid2019Globecom_b,zhou2018joint,Stamatakis_2020,abd2019tcom,AbdElmagid_joint,li2019minimizing,li2020age_a,AbdElmagid2019Globecom_a,Hasan2020,abbas2020joint,ferdowsi2020neural,wang2020minimizing}. The interplay/trade-off between throughput and AoI was also investigated in \cite{ABedewy2016,kadota_throughput,Kosta_Nikos,Gopal_Kaul} for wireless networks with heterogeneous traffic. The prime objective of the works in \cite{buyukates2019age,D2d_caching,bastopcu2020information,gu2019timely,abd2018average,AbdElmagid2019Globecom_b,zhou2018joint,Stamatakis_2020,abd2019tcom,AbdElmagid_joint,li2019minimizing,li2020age_a,AbdElmagid2019Globecom_a,Hasan2020,abbas2020joint,ferdowsi2020neural,wang2020minimizing,ABedewy2016,kadota_throughput,Kosta_Nikos,Gopal_Kaul} was to obtain optimal transmission policies that minimize the temporal mean of AoI or some other age-related metrics for fixed network topologies, referred to as AoI-optimal polices, by
applying different tools from optimization theory.
While the aforementioned works provide a thorough understanding of the temporal statistics of AoI, they are fundamentally limited in their ability to provide insights about the spatial disparity in the AoI performance that is inherently present in wireless networks. This is primarily because each receiver perceives a different signal and interference environments, which cannot be studied using approaches considered in the above works. Once the spatial dimension is explicitly modeled, we can argue that the temporal mean of a performance metric (seen over the complete ensemble of the fading gains), such as transmission rate, delay, or AoI, observed by a receiving device becomes a location-specific quantity. This, in turn, introduces the spatial disparity in the quality of service (QoS) experienced by various wireless links spread across the network. Therefore, it is important to accurately model the spatial distribution of wireless devices to analyze the impact of spatial variations on the achievable QoS.
In recent years, stochastic geometry has emerged as a powerful tool for modeling the spatial distribution of wireless nodes. Most of the early works in this area have focused on characterizing the coverage probability (equivalently, the fraction of devices for which the received signal-to-interference-and-noise ratio (SINR) is above some predefined threshold) in a variety of wireless network settings, such as cellular networks \cite{AndBacJ2011}, heterogeneous networks \cite{DhiGanJ2012} and ad-hoc networks \cite{Baccelli_Aloha2006}.
While this spatio-temporally averaged coverage probability provides useful insight into the network design, it is not sufficient to study the spatial disparity in the link-level performance of the network as discussed above. To overcome this shortcoming, the distribution of location-specific successful transmission probability, termed {\em meta distribution}, was recently introduced in \cite{Haenggi_Meta} to infer useful information like {\em ``the percentage of devices in the network experiencing success probability above some threshold for a given predefined ${\rm SINR}$ value"}. In particular, the moments of the meta distribution were derived for the bipolar Poisson network in \cite{Haenggi_Meta}, and for the Poisson cellular networks in \cite{Haenggi_Meta} and \cite{Wang_2018}.
However, these stochastic geometry based models are usually agnostic to the traffic variations since they mostly rely on the assumption of saturated queues, i.e., each wireless node always has information to transmit whenever it is scheduled to access the channel. To relax this assumption and allow the traffic aware performance analysis of cellular networks, a semi-analytical framework was developed in
\cite{Blaszczyszyn} and \cite{blaszczyszyn2016spatial} by combining tools from queueing theory (for transmission scheduling) and stochastic geometry (for modeling spatial dimension and hence signal propagation). Further, \cite{Abishek_BirthDeathProcess} studied the spatial birth-death process of randomly arriving wireless links while capturing their stochastic interactions in both space (through interference) and time (through random traffic). A quick glance through the analyses of \cite{Blaszczyszyn,blaszczyszyn2016spatial,Abishek_BirthDeathProcess} is sufficient to realize that the spatio-temporal performance analysis of of wireless networks is challenging because of: i) the interference-induced correlation between the evolution of queues associated with the transmitting devices, and ii) the temporal variation of the interference field seen by a receiving devices resulting from the stochastic transmission scheduling policy of the transmitting devices.
It is worth noting that the prime focus of the works in \cite{Blaszczyszyn,blaszczyszyn2016spatial,Abishek_BirthDeathProcess} was on performing the spatio-temporal analysis of conventional performance metrics such as transmission rate and delay. On the other hand, the application of stochastic geometry to perform the spatio-temporal analysis of AoI has been only considered in a handful of recent works \cite{hu2018age,yang2020optimizing,mankar2020stochastic,emara2019spatiotemporal}.
In particular, the authors of \cite{hu2018age,yang2020optimizing,mankar2020stochastic} presented the spatio-temporal analysis of AoI in the context of D2D networks by modeling the D2D links as a bipolar PPP. Specifically, they derived bounds on the spatio-temporal mean AoI \cite{hu2018age}, the spatio-temporal mean peak AoI \cite{yang2020optimizing}, and the spatial distribution of the temporal mean peak AoI \cite{mankar2020stochastic}, by incorporating system modifications to deal with the issue of correlated queues. Besides, the authors of \cite{emara2019spatiotemporal} derived the spatio-temporal mean peak AoI in the context of cellular-based IoT networks while modeling the locations of the BSs and the IoT devices using independent PPPs. Note that since the works in \cite{hu2018age,yang2020optimizing,emara2019spatiotemporal} were focused on characterizing the spatio-temporal mean of AoI or peak AoI, their analyses did not account for the spatial AoI disparity. In contrast to these works that considered AoI as the only performance quantifying metric, this paper presents a joint spatio-temporal analysis of AoI and throughput for cellular-based IoT networks with heterogeneous traffic as discussed next.
\subsection{Contributions}
We present a novel stochastic geometry-based analysis of the cellular-based IoT networks which includes: i) the D2D communications between IoT devices, and ii) the transmission of status updates from the IoT devices to the BSs regarding some independent random processes they are sensing.
{ Each BS is assumed to schedule the transmission of a status update uniformly at random from one of its associated devices, while the other devices (i.e., the ones that are not scheduled for status updates) are considered to transmit regular D2D messages at a fixed rate using Aloha protocol. }
The locations of the IoT devices are assumed to follow a bipolar PPP whereas the locations of the BSs follow an independent PPP. To improve the delivery rate of the status update transmissions, we assume that each IoT device employs a power control method which is also an important aspect of uplink communications. Further, we consider a generalized system setup wherein the transmission of status updates from the IoT devices within a certain distance from their serving BSs is allowed, leading to the JM tessellation based topology of cellular-based IoT networks as will be formally defined in Section \ref{sec:SysModel} {(please refer to \cite{Priyo_2019_FPR} for more details)}. This is particularly useful to capture the fact that the maximum transmission power of IoT devices is limited in practice. This construction will allow us to account for the correlation between the locations of IoT devices with status updates and the locations of their serving BSs. For this setup, we employ AoI and transmission rate as the key metrics for characterizing the performance of the status update links and D2D links, respectively. The contributions of this paper are briefly summarized below.
\begin{enumerate}
\item The mean success probability for the D2D links and the moments of the conditional success probability for the status update links are derived.
\item Moments of the scheduling probability of a status update link are derived while assuming that each BS schedules its associated IoT devices uniformly at random.
\item Next, we derive the achievable transmission rate for the typical D2D link using its mean success probability. Further, the spatial moments of the temporal mean AoI of the status update links are derived using the moments of the conditional success probability and scheduling probability.
\item Our simulation results verify the analytical findings. Next, using numerical results, we highlight the impact of the power control on the achievable D2D network throughput and the spatio-temporal mean AoI for different system design parameters.
\end{enumerate}
To the best of our knowledge, this paper is the first to develop a joint stochastic geometry-based analysis of AoI and throughput for cellular-based IoT networks while capturing the spatial disparity in the AoI performance of the status update links.
\section{System Model}
\label{sec:SysModel}
We consider a cellular-based IoT network wherein the IoT devices can exchange messages in a D2D fashion and also send status updates regarding some random processes to their associated BSs.
The D2D links of IoT devices are assumed to be randomly distributed according to a homogeneous bipolar PPP wherein the transmitting IoT devices form a PPP $\Phi_{\rm d }$ with intensity $\lambda_{\rm d}$. Their designated receiving IoT devices are independently located at distance $R_{\rm d}$ in uniformly random directions. The locations of the BSs are also assumed to follow an independent homogeneous PPP $\Phi_{\rm b}$ with intensity $\lambda_{\rm b}$.
The status updates from the IoT devices contain timestamped measurements of their associated random processes observed in their vicinity. To support variety of real-time applications, the IoT devices are generally deployed to monitor different types of physical random processes. Therefore, we assume that the random processes associated with different IoT devices are independent of each other. The power control is an important aspect of the uplink transmissions in cellular networks for achieving improved transmission rates.
Therefore, we assume that the IoT devices send status updates to their nearest BSs using a distance-proportional fractional power control scheme.
Specifically, the IoT device at distance $R_{\rm b}$ from its serving BS transmits the status update with power $P=p_{\rm b}R_{\rm b}^{\alpha\epsilon}$ where $p_{\rm b}$ is the baseline transmit power, $\epsilon\in[0,1]$ is the power control fraction, and $\alpha$ is the path-loss exponent. Note that $\epsilon=0$ corresponds to the fixed power transmission case (i.e., IoT devices transmit at the fixed power $p_{\rm b}$), and $\epsilon=1$ corresponds to the full power control case (i.e., BSs receive the signals at the fixed power $p_{\rm b}$). The transmission from the devices with high serving link distances naturally require high transmission powers which may not be possible when the transmission power is limited. For instance, the transmissions of the devices with serving link distances greater than ${\mathcal{J}}=(P_{\rm \max}/p_{\rm b})^\frac{1}{\alpha\epsilon}$ may fail when the maximum available transmission power is $P_{\rm \max}$. Therefore, we consider that the cellular-based status update links can be supported for the IoT devices within distance ${\mathcal{J}}$ from their serving BSs using this power control scheme. As a result, the IoT devices associated with a given BS at ${\bf x}\in\Phi_{\rm b}$ must lie within the intersection ${\mathcal{V}}_\mathbf{x}={\mathcal{B}}_\mathbf{x}({\mathcal{J}})\cap V_\mathbf{x}$, where ${\mathcal{B}}_\mathbf{x}({\mathcal{J}})$ is the ball of radius ${\mathcal{J}}$ centred at $\mathbf{x}$ and $V_\mathbf{x}$ is the Poisson Voronoi (PV) cell which is given by
$$V_{\bf x}=\{{\bf y}\in\mathbb{R}^2:\|{\bf x}-{\bf y}\|\leq \|{\bf z}-{\bf y}\|, {\bf z}\in \Phi_{\rm b}\}.$$
The set of collection of cells $\{{\mathcal{V}}_\mathbf{x}\}_{\mathbf{x}\in\Phi_{\rm b}}$ forms a JM tessellation \cite{moller_1992}. This JM cell based construction provides an attractive way of clustering the mobile users based on their performance in a random geometric setting. For example, the authors of \cite{Priyo_2019_FPR} applied a similar construction to differentiate between the cell center and cell edge users in the cellular networks.
\begin{table*}
\centering
{\caption{ Summary of notations }
\label{table:Syatem_Variable}
{\small \begin{tabular}{ |c |c|c|c| }
\hline
Point processes of BSs and IoT devices & $\Phi_{\rm b}$ and $\Phi_{\rm d}$ & Transmission rate of D2D links & ${\rm T_d}$ \\ \hline
BS and IoT device densities & $\lambda_{\rm b}$ and $\lambda_{\rm d}$ & Cond. mean AoI & $\Delta(\mathbf{y},\Phi)$ \\ \hline
Cellular and D2D link distances & $R_{\rm b}$ and $R_{\rm d}$ & $n$-th moment of cond. mean AoI & $\Delta_n$ \\ \hline
Radius of JM cell & ${\mathcal{J}}$ & Success prob. of D2D link & ${\rm P_d}$\\ \hline
PV and JM cells of BS $\mathbf{x}$ & $V_{\mathbf{x}}$ and ${\mathcal{V}}_{\mathbf{x}}$& Cond. success prob. of update link & ${\rm P_b}(\mathbf{y},\Phi)$\\ \hline
D2D link and uplink baseline tx. powers & $p_{\rm d}$ and $p_{\rm b}$ & Moment of Cond. success prob. & $M_b$\\ \hline
Maximum transmission power of device & $P_{\rm max}$ & Mean JM cell area & $\bar{{\mathcal{V}}}_o^1$ \\ \hline
D2D link medium access probability & $q_{\rm d}$ & Second moment of JM cell area & $\bar{{\mathcal{V}}}_o^2$ \\ \hline
Path-loss exponent & $\alpha$ & Number of users in JM cell ${\mathcal{V}}_o$ & $N_{{\mathcal{V}}_o}$ \\ \hline
Power control fraction & $\epsilon$ & Cond. update scheduling prob. & $\zeta_{\rm b}(\mathbf{y},\Phi)$\\ \hline
$\mathtt{SIR}$ thresholds & $\beta_{\rm b}$ and $\beta_{\rm d}$ & Transmission probability of D2D message & $q_{\rm d}$ \\ \hline
Channel bandwidth & ${\rm B}$ & & \\ \hline
\end{tabular}}}
\end{table*}
\subsection{ Transmission Scheduling}
{ The IoT devices are assumed to transmit information packets, containing either regular messages or status updates, in a synchronized time-slotted manner over the same frequency. Thus, the considered system provides co-channel access (or, underlay transmission) for the D2D and cellular-enabled status update links. We will also provide the analysis for the orthogonal channel access (or, overlay transmission) where the types of links (D2D and status updates) are assumed to communicate over orthogonal frequency bands.}
Each BS is assumed to schedule its associated IoT devices for the status update transmission in a uniformly random fashion to avoid the intra-cell interference.
{Such a random scheduling policy allows for mathematical tractability and is also meaningful from the perspective of fair resource allocation.}
{ To ensure the timely delivery of status updates, the devices are assumed to give higher priority to the status update transmissions over the regular message transmissions.} Thus, the IoT devices transmit their status updates whenever they are scheduled by their associated BSs. Further, we consider that the IoT devices that are not scheduled for the status updates choose to transmit regular packets on D2D links with probability $q_{\rm d}$ in a given time slot to alleviate the inter-D2D-link interference. Fig. \ref{fig:System_Model} shows a representative realization of the system model discussed above.
\begin{figure}[h]
\centering
\includegraphics[clip, trim=0cm 0cm 0cm .4cm, width=.48\textwidth]{SysModel_v1.pdf}
\caption{A typical realization of the cellular-based IoT network.}
\label{fig:System_Model}
\end{figure}
\subsection{Signal-to-Interference Ratio}
Let $\Psi_{\rm b}\subseteq\Phi_{\rm d}$ and $\Psi_{\rm d}\subseteq\Phi_{\rm d}$ denote the sets of the locations of active IoT devices transmitting status updates and regular D2D messages, respectively. Note that { $\Psi_{\rm b}\cap\Psi_{\rm d}=\emptyset$}. By this construction, we have
\begin{align*}
\Psi_{\rm b}=\{U({\mathcal{V}}_{\bf x}\cap\Phi_{\rm d}):{\bf x}\in\Phi_{\rm b}\}
\end{align*}
where $U(A)$ represents a point selected uniformly at random from set $A$. We assume $\lambda_{\rm d}\gg\lambda_{\rm b}$ to avoid ${\mathcal{V}}_{\bf x}\cap\Phi_{\rm d}=\emptyset$ for $\forall {\bf x}\in\Phi_{\rm b}$ with a high probability. This assumption is quite suitable for the IoT network as it requires cellular connectivity to massive number of sensors deployed in the field.
From Slivnyak's theorem, we know that conditioning on a point of PPP at ${\bf x}$ is equivalent to adding the point ${\bf x}$ to the PPP. Therefore, without loss of generality, we can place the typical BS of the BS PPP $\Phi_{\rm b}\cup\{o\}$ at the origin $o$ and thus the PV cell $V_{o}$ (or JM cell ${\mathcal{V}}_o$) represents the typical cell in the tessellation. Further, using the stationarity of PPP, we can deduce that the points within the set ${\mathcal{V}}_{\bf x}\cap\Phi_{\rm d}$ are uniformly distributed in ${\mathcal{V}}_{\bf x}$. Thus, we will focus our AoI analysis for an updating device that is distributed uniformly at random in ${\mathcal{V}}_o$. This construction facilitates the AoI analysis of the status updates from the perspective of the typical BS which is significantly different than the perspective of the typical IoT device which is expected to reside in the bigger PV (or JM) cells (refer to \cite{mankar2020TypicalCell} for more details).
Let ${\bf y}\sim U({\mathcal{V}}_o)$ denote the location of an IoT device scheduled for the status update transmission, and $R_{\rm b}=\|{\bf y}\|$ denote its distance from the typical BS placed at $o$.
We consider the interference-limited scenario. The signal-to-interference ratio (${\rm SIR}$) received at the typical BS on the status update link from the IoT device at $\mathbf{y}$ is
\begin{align*}
&{\rm SIR_{\rm b}}=\frac{h_\mathbf{y} R_{\rm b}^{\alpha(\epsilon-1)}p_{\rm b}}{I_{\rm b} },
\end{align*}
where
$$I_{{\rm b}}=\sum_{{\bf x}\in\Phi_{\rm d}} h_{\bf x}\|{\bf x}\|^{-\alpha}\left[p_{\rm d}\mathds{1}({\bf x}\in\Psi_{\rm d}) + p_{\rm b}D_{\mathbf{x}}^{\alpha\epsilon}\mathds{1}({\bf x}\in\tilde{\Psi}_{\rm b})\right],$$
$\tilde{\Psi}_{\rm b}=\Psi_{\rm b}\setminus\{\bf y\}$, $p_{\rm d}$ denotes the fixed power of regular message transmissions on the D2D links, $D_\mathbf{x}$ denotes the distance of the IoT device at $\mathbf{x}$ from its serving BS, and $h_{\bf x}$ denotes the fading coefficient associated with the link from the IoT device at ${\bf x}$. Assuming independent Rayleigh fading, we model $\{h_{\bf x}\}$ as independent unit mean exponential random variables.
Similar to the typical BS viewpoint discussed above, we perform the D2D network throughput analysis from the perspective of the typical designated receiving IoT device placed at $o$ by including an additional transmitting IoT device at $\mathbf{z}\equiv(R_{\rm d},0)$ (paired with the typical designated receiver) to the PPP $\Phi_{\rm d}$. Thus, the ${\rm SIR}$ received at this typical designated IoT receiver becomes
\begin{align*}
&{\rm SIR_{\rm d}}=\frac{h_\mathbf{z} R_{\rm d}^{-\alpha}p_{\rm d}}{I_{\rm d}},
\end{align*}
where
$$I_{{\rm d}}=\sum_{{\bf x}\in\Phi_{\rm d}} h_{\bf x}\|{\bf x}\|^{-\alpha}[p_{\rm d}\mathds{1}({\bf x}\in\Psi_{\rm d}) + D_\mathbf{x}^{\alpha\epsilon}p_{\rm b}\mathds{1}({\bf x}\in\Psi_{\rm b})].$$
\subsection{Performance Metrics}
\label{subsec:Performance_Metrics}
For the system setting discussed above, our focus is on characterizing the transmission rate for the typical D2D link and the spatial disparity in the AoI performance metric measured at the BSs.
We assume that the D2D links employ a fixed rate transmission strategy (also termed {\em outage strategy} \cite{Biglieri}) and have saturated queues (i.e., the devices always have a packet to transmit). The transmission rate of the typical D2D link is
\begin{align}
{\rm T_d}={\rm B}\zeta_{\rm d}\log_2(1+\beta_{\rm d}){\rm P_d},
\label{eq:D2D_TxRate}
\end{align}
where $\zeta_{\rm d}$ and ${\rm P_d}$ are the fraction of transmission time and the successful transmission probability of the typical D2D link, respectively, and ${\rm B}$ is the channel bandwidth.
For the status update transmission, the IoT devices are assumed to generate/sample status updates using {\em generate-at-will} policy \cite{abd2018role}. This policy implies that a device generates a fresh status update for the transmission when it is scheduled. Hence, this policy does not require the ACK/NACK protocol or retransmissions since it always transmits a fresh status update regardless of whether the previous transmission was successful or not.
We employ AoI to characterize the performance of the timely delivery of the status updates from the IoT devices to their BSs.
The AoI of status updates received at a BS is defined by the time elapsed from the generation of the latest received status update \cite{kaul2012real}. Thus, the AoI measured by the BS related to the status updates from its associated device placed at ${\bf y}\in {\mathcal{V}}_o$ during time slot $k$ is
\begin{equation}
A_{\bf y}(k)=k-S_{{\bf y},k},
\end{equation}
where $S_{{\bf y},k}$ is the timestamp of the generation of the latest received update from the device ${\bf y}$ before time slot $k$.
Since the status updates are generated just before their transmissions, the AoI drops to one whenever a successful transmission occurs.
The temporal mean AoI of status updates from the device $\mathbf{y}\in{\mathcal{V}}_o$ that is measured by the typical BS solely depends on its scheduling probability $\zeta_{\rm b}(\mathbf{y},\Phi)={N_{{\mathcal{V}}_o}}^{-1}$ and successful transmission probability ${\rm P_b}(\mathbf{y},\Phi)$ where $\Phi=\Phi_{\rm d}\cup\Phi_{\rm b}$ and ${N_{{\mathcal{V}}_o}}$ is the number of devices in ${\mathcal{V}}_o$.
Unlike the transmission rate metric given in \eqref{eq:D2D_TxRate}, the AoI is a {{\em nonlinear function}} of these probabilities (which will be evident in Section \ref{sec:AoI_Througput}). Therefore, the knowledge of the joint distribution of these conditional probabilities is essential to analysis the spatial distribution of the temporal mean AoI.
{For the exact joint analysis of the success probability and scheduling probability for the typical device at $\mathbf{y}\in {\mathcal{V}}_o$, the key step is to derive the distribution of the area of ${\mathcal{V}}_o$ given $\mathbf{y}\in {\mathcal{V}}_o$. However, it is reasonable to deduce that this exact analysis will be challenging since even the distribution of the area of the typical cell $V_o$ (which is a much simpler case) is empirically determined \cite{tanemura2003statistical}. In addition, analyzing scheduling probability jointly with the conditional success probability will introduce additional complexity. Therefore, we will derive the scheduling probability of the device at $\mathbf{y}$ by relaxing the condition $\mathbf{y}\in {\mathcal{V}}_o$ and perform the AoI analysis under the following widely accepted assumption (e.g., please refer to \cite{Zhong_2017,ElSawy_CelluarIoT_2017,Praful_NOMA,gharbieh2017spatiotemporal}).
\begin{assumption}
\label{assumption}
The cell load $N_{{\mathcal{V}}_o}$ and the conditional successful transmission probability ${\rm P_d}(\mathbf{y},\Phi)$ are independent of each other.
\end{assumption}}
{ In order to verify Assumption 1, we compare simulation results of the distribution of conditional (temporal) mean AoI obtained through the Monte-Carlo simulations with joint and independent (i.e., Assumption 1) samplings of $N_{{\mathcal{V}}_o}$ and ${\rm P_b}(\mathbf{y},\Phi)$. As will be derived in Section V, the conditional mean AoI of user at $\mathbf{y}$ is given by $\Delta(\mathbf{y},\Phi)=\frac{N_{{\mathcal{V}}_o}}{{\rm P_d}(\mathbf{y},\Phi)}$. Fig. \ref{fig:Assumption_1} provides a visual verification of the accuracy of Assumption 1 for the AoI analysis using simulation results. }
\begin{figure}[h]
\centering
\includegraphics[width=.4\textwidth]{Assumpt1_Verfication.pdf}
\caption{Distribution of conditional mean AoI for $\lambda_{\rm b}=10^{-4}$, $\lambda_{\rm d}=40\lambda_{\rm b}$, $\alpha=4$, $\epsilon=0$, and $q_{\rm d}=0$.}
\label{fig:Assumption_1}
\end{figure}
Now, we present the analysis of success probabilities of the update and D2D links in the following section which will be used to derive the AoI and D2D network throughput in Section \ref{sec:AoI_Througput}.
\section{Success Probability Analysis}
\label{sec:SuccessProb}
In this section, we first derive the success probability for the regular message transmissions over D2D links.
Next, we present the analysis of the distribution of conditional success probability for the status update transmissions over device-BS links.
\subsection{Success Probability of D2D Transmission}
\label{subsec:SucceProb_d}
The probability of successful transmission of a regular message for the typical designated D2D receiver can be determined as
\begin{align*}
{\rm P_d}&=\mathbb{P}[\mathtt{SIR}_{\rm d}>\beta_{\rm d}],\\
&=\mathbb{P}\left[h_\mathbf{z}>\beta_{\rm d}R_{\rm d}^\alpha I_{{\rm d}} /p_{\rm d}\right],\\
&=\mathbb{E}_{I_{{\rm d}}}\left[\exp\left(-\beta_{\rm d}R_{\rm d}^\alpha I_{{\rm d}}/p_{\rm d}\right)\right].
\end{align*}
As $I_{\rm d}$ is the aggregate interference generated from the transmissions of regular messages and status updates, we require the joint distributions of point processes $\Psi_{\rm d}$ and $\Psi_{\rm b}$ to derive the success probability ${\rm P_d}$. However, the exact characterization of this joint distribution is challenging because $\Psi_{\rm b}$ further depends on the BS PPP $\Phi_{\rm b}$.
Since $\Psi_{\rm b}$ has exactly one device residing in each cell ${\mathcal{V}}_\mathbf{x}$, one can interpret $\Psi_{\rm b}$ as the dependent thinning of the PPP $\Phi_{\rm d}$ for given $\Phi_{\rm b}$. Despite this dependent thinning, the process of the remaining points in $\Phi_{\rm d}^\prime=\Phi_{\rm d}\setminus\Psi_{\rm b}$ can be closely approximated using a homogeneous PPP with density $\lambda_{\rm d}^\prime=\lambda_{\rm d}-\lambda_{\rm b}$ because of the assumption $\lambda_{\rm d}\gg\lambda_{\rm b}$. Thus, $\Psi_{\rm d}$ can be directly interpreted as the unconditional thinning of $\Phi_{\rm d}^\prime$ with probability $p_{\rm d}$, hence $\Psi_{\rm d}$ can be modeled as a PPP with density $q_{\rm d}\lambda_{\rm d}^\prime$.
Besides, the exact characterization of $\Psi_{\rm b}$ is difficult because of the dependent thinning mentioned above.
On the other hand, one can observe that the density of $\Psi_{\rm b}$ can be approximated with $\lambda_{\rm b}$ as $\Psi_{\rm b}$ contains exactly one device in each ${\mathcal{V}}_\mathbf{x}$. In fact, we have observed that the complementary cumulative distribution function ($\mathtt{CDF}$) of distance from a fixed point, say $o$, to the nearest point in $\Psi_{\rm b }$ closely follows $\exp(-\pi\lambda_{\rm b}r^2)$ which is the {\em void probability} of BS point process $\Phi_{\rm b}$. Thus, it is reasonable to approximate $\Psi_{\rm b}$ with a homogeneous PPP of density $\lambda_{\rm b}$.
Based on the above observations and to aid the analytical tractability, we consider that the point processes $\Psi_{\rm b }$ and $\Psi_{\rm d}$ are independent of each other. The net interference power received at the typical receiver can be segregated as $I_{{\rm d}}=I_{\Psi_{\rm d}} + I_{{\Psi}_{\rm b}}$
where
$$I_{\Psi_{\rm d}}=\sum_{{\bf x}\in\Psi_{\rm d}}h_{\bf x}\|{\bf x}\|^{-\alpha}p_{\rm d} \text{~and~}I_{\Psi_{\rm b}}=\sum_{{\bf x}\in\Psi_{\rm b}}h_{\bf x}\|{\bf x}\|^{-\alpha}D_{\mathbf{x}}^{\alpha\epsilon}p_{\rm b}.$$
Since $\Psi_{\rm d}$ and $\Psi_{\rm b}$ are considered to be independent, we can evaluate the success probability as
\begin{align*}
{\rm P_d}&={\cal L}_{I_{\Psi_{\rm d}}}(\beta_{\rm d}R_{\rm d}^\alpha/p_{\rm d}){\cal L}_{I_{\Psi_{\rm b}}}(\beta_{\rm d}R_{\rm d}^\alpha/p_{\rm d}),\numberthis\label{eq:SuccessProba_LT}
\end{align*}
where ${\cal L}_{X}(\cdot)$ is the Laplace transform (LT) of random variable $X$. The LT of $I_{\Psi_{\rm d}}$ is
\begin{align*}
{\cal L}_{I_{\Psi_{\rm d}}}(s)&=\mathbb{E}_{\Psi_{\rm d}}\prod_{{\bf x}\in\Psi_{\rm d}}\mathbb{E}_{h_{\bf x}}\exp\left(-s p_{\rm d}h_{\bf x}\|{\bf x}\|^{-\alpha}\right),\\
&=\mathbb{E}_{\Psi_{\rm d}}\prod_{{\bf x}\in\Psi_{\rm d}}{\frac{1}{1+s p_{\rm d}\|{\bf x}\|^{-\alpha}}},
\end{align*}
where the first equality follows due to the assumption of independent fading coefficients.
Further, using the probability generating functional ($\mathtt{PGFL}$) of the PPP $\Psi_{\rm d}$, we can obtain
\begin{align*}
{\cal L}_{I_{\Psi_{\rm d}}}(s)&=\exp\bigg(-2\pi q_{\rm d}\lambda_{\rm d}^\prime \int_{0}^\infty \frac{1}{1+(sp_{\rm d})^{-1}r^\alpha}r{\rm d}r \bigg),\\
&=\exp\bigg(-\pi q_{\rm d}\lambda_{\rm d}^\prime \frac{(sp_{\rm d})^\delta}{{\rm sinc}(\delta)} \bigg),\numberthis\label{eq:LT_Pd_Id}
\end{align*}
where $\delta=\frac{2}{\alpha}$. Now, we obtain the LT of $I_{\Psi_{\rm b}}$ as
\begin{align*}
{\cal L}_{I_{\Psi_{\rm b}}}(s)&=\mathbb{E}_{\Psi_{\rm b},D_\mathbf{x}}\prod_{{\bf x}\in\Psi_{\rm b}}\mathbb{E}_{h_{\bf x}}\exp\left(-s h_{\bf x}p_{\rm b}D_\mathbf{x}^{\alpha\epsilon}\|{\bf x}\|^{-\alpha}\right),\\
&=\mathbb{E}_{\Psi_{\rm b},D_\mathbf{x}}\prod_{{\bf x}\in\Psi_{\rm b}}\frac{1}{1+s p_{\rm b}D_\mathbf{x}^{\alpha\epsilon}\|{\bf x}\|^{-\alpha}}.
\end{align*}
Recall that $D_\mathbf{x}$ denotes the device-BS link distance, i.e., the distance from the device (with status update) to nearest BS. The link distance $D_\mathbf{x}$ is naturally smaller than ${\mathcal{J}}$ since the devices associated with BS $\mathbf{x}$ are essentially located within ${\mathcal{V}}_\mathbf{x}$.
Therefore, the probability density function ($\mathtt{pdf}$) of the link distance $D_\mathbf{x}$ of a randomly selected device $\mathbf{x}$ becomes
\begin{align}
f_{D_\mathbf{x}}(u)=\frac{1}{F({\mathcal{J}})} 2\pi \lambda_{\rm b}u\exp(-\pi \lambda_{\rm b}u^2), \label{eq:Distance_Distribution}
\end{align}
for $0\leq u\leq {\mathcal{J}}$
where $F({\mathcal{J}})=1-\exp(-\pi \lambda_{\rm b}{\mathcal{J}}^2)$. Thus
\begin{align*}
{\cal L}_{I_{\Psi_{\rm b}}}(s)&=\mathbb{E}_{\Psi_{\rm b}}\prod_{{\bf x}\in\Psi_{\rm b}}F({\mathcal{J}})^{-1}\int_0^{\mathcal{J}} \frac{2\pi \lambda_{\rm b}u\exp(-\pi \lambda_{\rm b}u^2)}{(1+s p_{\rm b}u^{\alpha\epsilon}\|{\bf x}\|^{-\alpha})}{\rm d}u.
\end{align*}
Next, using $\mathtt{PGFL}$ of PPP approximation of $\Psi_{\rm b}$, we get ${\cal L}_{I_{\Psi_{\rm b}}}(s)$
\begin{align*}
&=\exp\left(-\lambda_{\rm b}\int_{\mathbb{R}^2} \left[1-\int_0^{\mathcal{J}} \frac{2\pi \lambda_{\rm b}u\exp(-\pi \lambda_{\rm b}u^2)}{F({\mathcal{J}})(1+s p_{\rm b}u^{\alpha\epsilon}\|\mathbf{x}\|^{-\alpha})}{\rm d}u\right]{\rm d}\mathbf{x}\right),\\
&=\exp\left(-\lambda_{\rm b}\int_{\mathbb{R}^2} \int_0^{\mathcal{J}} \frac{2\pi \lambda_{\rm b}u\exp(-\pi \lambda_{\rm b}u^2)}{F({\mathcal{J}})(1+(s p_{\rm b})^{-1}u^{-\alpha\epsilon}\|\mathbf{x}\|^{\alpha})}{\rm d}u{\rm d}\mathbf{x}\right),\\
&=\exp\left(-2\pi\lambda_{\rm b}\int_0^\infty \int_0^{\mathcal{J}} \frac{2\pi \lambda_{\rm b}uv\exp(-\pi \lambda_{\rm b}u^2)}{F({\mathcal{J}})(1+(sp_{\rm b})^{-1}u^{-\alpha\epsilon}v^{\alpha})}{\rm d}u {\rm d}v\right),\\
&=\exp\left(-\frac{\pi\lambda_{\rm b}}{F({\mathcal{J}})}\frac{(sp_{\rm b})^\delta}{{\rm sinc}(\delta)}\int_0^{\mathcal{J}} 2\pi \lambda_{\rm b}u^{1+2\epsilon}\exp(-\pi \lambda_{\rm b}u^2){\rm d}u\right),\\
&=\exp\left(-\frac{\pi\lambda_{\rm b}}{F({\mathcal{J}})}\frac{(sp_{\rm b})^\delta}{{\rm sinc}(\delta)}\frac{\gamma(1+\epsilon,\pi \lambda_{\rm b}{\mathcal{J}}^2)}{(\pi\lambda_{\rm b})^\epsilon}\right),\numberthis\label{eq:LT_Pd_Ib_1}
\end{align*}
where $\gamma(\cdot,\cdot)$ is a lower incomplete gamma function.
Finally, by substituting the LTs of both $I_{\Psi_{\rm d}}$ (given in \eqref{eq:LT_Pd_Id}) and $I_{\Psi_{\rm b}}$ (given in \eqref{eq:LT_Pd_Ib_1}) at $s=\beta_{\rm d}R_{\rm d}^\alpha/p_{\rm d}$ in
\eqref{eq:SuccessProba_LT}, we obtain the success probability of regular transmission as presented in the following theorem.
\begin{thm}
\label{thm:SuccessProba_pd}
For a given $\epsilon$, the success probability of the typical D2D link is ${\rm P_d}=$
\begin{align*}
\exp\bigg(-\pi q_{\rm d}\lambda_{\rm d}^\prime \frac{\beta_{\rm d}^\delta R_{\rm d}^2}{{\rm sinc}(\delta)} -\pi\lambda_{\rm b}\frac{(\beta_{\rm d}p_{\rm b}/p_{\rm d})^\delta R_{\rm d}^2}{{\rm sinc}(\delta)}\frac{\gamma(1+\epsilon,\pi \lambda_{\rm b}{\mathcal{J}}^2)}{(\pi\lambda_{\rm b})^\epsilon F({\mathcal{J}})}\bigg).\numberthis\label{eq:SuccessProba_pd}
\end{align*}
\end{thm}
For no power control, i.e., $\epsilon=0$, \eqref{eq:SuccessProba_pd} is simplified in the following lemma.
\begin{cor}
For $\epsilon=0$, the success probability of the typical D2D link is
\begin{align*}
{\rm P_d}&=\exp\bigg(-\pi q_{\rm d}\lambda_{\rm d}^\prime \frac{\beta_{\rm d}^\delta R_{\rm d}^2}{{\rm sinc}(\delta)} -\pi \lambda_{\rm b} \frac{(\beta_{\rm d}p_{\rm b}/p_{\rm d})^\delta R_{\rm d}^2}{{\rm sinc}(\delta)} \bigg).\numberthis\label{eq:SuccessProba_pd_epi_0}
\end{align*}
\end{cor}
\begin{proof}
For $\epsilon=0$, ${\rm P_d}$ given in \eqref{eq:SuccessProba_pd_epi_0} follows by substituting $\gamma(1,x)=1-\exp(-x)$ in \eqref{eq:SuccessProba_pd}.
\end{proof}
{\begin{cor}
Under orthogonal access, the success probability of the typical D2D link is
\begin{align*}
{\rm \tilde{P}_d}&=\exp\bigg(-\pi q_{\rm d}\lambda_{\rm d}^\prime \frac{\beta_{\rm d}^\delta R_{\rm d}^2}{{\rm sinc}(\delta)} \bigg).\numberthis\label{eq:SuccessProba_pd_ortho}
\end{align*}
\end{cor}
\begin{proof}
The proof follows by setting the density $\lambda_{\rm b}$ of interfering update links to zero in \eqref{eq:SuccessProba_pd}.
\end{proof}}
\subsection{Success Probability of the Status Update Transmission}
\label{subsec:SucceProb_a}
The success probability of the status update transmission is defined as the probability that ${\rm SIR_b}$ is above a threshold $\beta_{\rm b}$. Similar to the analysis presented in Section \ref{subsec:SucceProb_d}, this success probability can be derived by averaging over the space. However, this spatially averaged success probability is not very useful to characterize the performance of non-linear metrics, such as AoI, as will be evident in Section \ref{sec:AoI_Througput}. For this reason, the distribution of the conditional success probability, termed {\em meta distribution} \cite{Haenggi_Meta}, is required. Since the meta distribution is difficult to determine directly \cite{Haenggi_Meta}, our first goal is to derive its moments.
Given $\Phi=\Phi_{\rm d}\cup\Phi_{\rm b}$, the conditional success probability of status update from the IoT device at ${\mathbf{y}}\in {\mathcal{V}}_o$ is
\begin{align*}
{\rm P_b}(\mathbf{y},\Phi)&=\mathbb{P}[{\rm SIR_b}>\beta_{\rm b}|\Phi]=\exp\left(-\beta_{\rm b}R_{\rm b}^{\alpha(1-\epsilon)} I_{\rm b}/p_{\rm b} \right).
\end{align*}
While $\mathbf{y}$ is already included in $\Phi$, we explicitly condition ${\rm P_b}$ on $\mathbf{y}$ to indicate that the IoT device at $\mathbf{y}$ is scheduled for the status update transmission.
Given $\Phi$, the conditional success probability depends on the evolution of the point process $\Phi_{\rm d}$ whose devices are randomly scheduled for the status update and D2D message transmissions. However, given the complexity of characterizing point process of interfering devices (transmitting status updates) even for a fixed time instance, as presented in \cite{Priyo_2019_FPR,user-point}, it is reasonable to presume that the exact characterization of evolution of $\Phi_{\rm d}$ is even more challenging. Therefore, we perform the conditional success probability analysis while considering the interference powers received from the IoT devices transmitting regular messages and status updates are independent across the transmission slots.
Therefore, it is safe to assume that devices scheduled for status update transmissions and regular message transmissions are drawn from independent point processes.
Since each BS is assumed to schedule its associated users uniformly at random, the probability that an IoT device at $\mathbf{z}\in {\mathcal{V}}_{\mathbf{x}}$ transmits the status update in a given slot is
\begin{align}
\label{eq:StatusUpdate_Link_scheduling_Probabilityf}
\zeta_{\rm b}(\mathbf{z}|\Phi)=N_{{\mathcal{V}}_\mathbf{x}}^{-1},\text{~for~}\mathbf{x}\in\Phi_{\rm b},
\end{align}
where $N_{{\mathcal{V}}_\mathbf{x}}$ is the number of IoT devices in set $\Phi_{\rm d}\cap{\mathcal{V}}_\mathbf{x}$.
The IoT devices that are not scheduled for status update transmission are assumed to transmit regular messages with probability $q_{\rm d}$.
Hence, we consider that the IoT device $\mathbf{z}\in\Phi_{\rm d}$ transmits regular messages with probability
\begin{align*}
\zeta_{\rm d}&=q_{\rm d} \mathbb{P}\left[\mathbf{z}\notin \bigcup\nolimits_{\mathbf{x}\in\Phi_{\rm b}} {\mathcal{V}}_\mathbf{x}\right]\\
&+ q_{\rm d}\mathbb{E}\left[(1-\zeta_{\rm b}(\mathbf{z}|\Phi))|\mathbf{z}\in \bigcup\nolimits_{\mathbf{x}\in\Phi_{\rm b}} {\mathcal{V}}_\mathbf{x}\right]\mathbb{P}\left[\mathbf{z}\in \bigcup\nolimits_{\mathbf{x}\in\Phi_{\rm b}} {\mathcal{V}}_\mathbf{x}\right],\\
&=q_{\rm d} F({\mathcal{J}})+ q_{\rm d}(1-\zeta_{\rm b})(1-F({\mathcal{J}})),\numberthis\label{eq:D2D_Link_scheduling_Probability}
\end{align*}
where $\zeta_{\rm b}=\mathbb{E}[\zeta_{\rm b}(\mathbf{z}|\Phi))|\mathbf{z}\in \bigcup\nolimits_{\mathbf{x}\in\Phi_{\rm b}}]$. { The scheduling probability $\zeta_{\rm b}$ can be obtained using the probability mass function (${\rm pmf}$) of $N_{{\mathcal{V}}_o}$ which will be derived in Lemma \ref{lemma:NoDevice_pmf}.}
{ As discussed above, we approximate the locations of devices transmitting regular messages and status updates using independent point processes and denote them by $\Omega_{\rm d}$ and $\Omega_{\rm b}$, respectively. }
Thus, the conditional success probability can be written as
\begin{align*}
{\rm P_b}(\mathbf{y},\Phi)&=\prod_{{\bf x}\in\tilde{\Omega}_{\rm b}}\bigg(\frac{\zeta_{\rm b}}{1+\beta_{\rm b} R_{\rm b}^{\alpha(1-\epsilon)} D_\mathbf{x}^{\alpha\epsilon} \|{\bf x}\|^{-\alpha}} +1-\zeta_{\rm b}\bigg)\\
&~~~\times\prod_{{\bf x}\in\Omega_{\rm d}}\bigg(\frac{\zeta_{\rm d}}{1+\beta_{\rm b} R_{\rm b}^{\alpha(1-\epsilon)}\|{\bf x}\|^{-\alpha}\frac{p_{\rm d}}{p_{\rm b}}} + 1-\zeta_{\rm d}\bigg)
\end{align*}
where $\tilde{\Omega}_{\rm b}=\Omega_{\rm b}\setminus\{\Omega_{\rm b}\cap{\mathcal{V}}_o\}$.
The $b$-th moment of conditional success probability is given by
{\begin{align*}
M_b&=\mathbb{E}_{\mathbf{y},\Phi}[{\rm P_b}(\mathbf{y},\Phi)^b]\\
&=\mathbb{E}_{R_{\rm b}}\bigg[\underbrace{\mathbb{E}\prod_{{\bf x}\in\tilde{\Omega}_{\rm b}}\bigg(1-\frac{\zeta_{\rm b}}{1+\beta_{\rm b}^{-1} R_{\rm b}^{\alpha(\epsilon-1)} D_\mathbf{x}^{-\alpha\epsilon}\|{\bf x}\|^{\alpha}}\bigg)^b}_{{\cal A}}\\
&\underbrace{\mathbb{E}\prod_{{\bf x}\in\Omega_{\rm d}}\left(1-\frac{\zeta_{\rm d}}{1+\beta_{\rm b}^{-1} R_{\rm b}^{\alpha(\epsilon-1)} \|{\bf x}\|^\alpha\frac{p_{\rm b}}{p_{\rm d}}}\right)^b}_{{\cal B}}\bigg].\numberthis\label{eq:Mb_1}
\end{align*} }
Based on the arguments presented in Section \ref{subsec:SucceProb_d}, it is reasonable to assume that the devices with regular messages follow a homogeneous PPP with density $\lambda_{\rm d}$ and model their medium access probability using $\zeta_{\rm d}$ given in \eqref{eq:D2D_Link_scheduling_Probability}. Therefore, using \cite[Theorem 1]{Haenggi_Meta}, we obtain
\begin{align}
{\cal B}=\exp\bigg(-\pi\lambda_{\rm d}R_{\rm b}^{2(1-\epsilon)}C(b)\bigg),
\end{align}
where
\begin{align}
C(b)=\frac{(\beta_{\rm b}p_{\rm d}/p_{\rm b})^{\delta}}{{\rm sinc}(\delta)}\sum_{k=1}^\infty {b\choose k}{\delta-1\choose k-1} \zeta_{\rm d}^k.
\label{eq:Cb}
\end{align}
On the other hand, to determine the expectation involved in the term ${\cal A}$ of \eqref{eq:Mb_1}, we require the distribution of $\tilde{\Omega}_{\rm b}$ as seen from the typical BS at $o$. For this, we first charaterize the point process $\tilde{\Psi}_{\rm b}$ which contains the devices from $\tilde{\Omega}_{\rm b}$ transmitting status updates in a given time slot. The pair correlation function ($\mathtt{pcf}$) of this point process of interferers $\tilde{\Psi}_{\rm b}$ with respect to the BS at $o$ for given ${\mathcal{J}}$ is derived in \cite{Priyo_2019_FPR} as
\begin{align}
g(r;{\mathcal{J}})=1-\exp\left(-2\pi \bar{{\mathcal{V}}}_{o}^{-1}r^2\right), \text{~for~} r\geq 0,
\end{align}
where $\bar{{\mathcal{V}}}_{o}^{-1}=\mathbb{E}[|{\mathcal{V}}_o|^{-1}]$ and $|A|$ represents the area of set $A$. The $\mathtt{pdf}$ of $|{\mathcal{V}}_o|$ will be derived in Section \ref{sec:schedulin_probability_AoI} which can be used here to determine $\bar{{\mathcal{V}}}_{o}^{-1}$.
Further, the authors of \cite{Priyo_2019_FPR} used this $\mathtt{pcf}$ to approximate $\tilde{\Psi}_{\rm d}$ using a non-homogeneous PPP with density $\lambda_{\rm b}g(r)$.
However, in our case, the active set of interferers are actually scheduled from $\tilde{\Omega}_{\rm b}$ by their associated BSs such that there is exactly one interfering device in each cell ${\mathcal{V}}_\mathbf{x}$ at a given time slot.
Therefore, we can approximate $\tilde{\Omega}_{\rm b}$ using a non-homogeneous PPP with density $\lambda_{\rm d}D(r;{\mathcal{J}})$ where
\begin{align}
D(r;{\mathcal{J}})=F({\mathcal{J}})g(r;{\mathcal{J}}),\label{eq:Dg}
\end{align}
such that the term $F({\mathcal{J}})$ represents the probability that a device is located in one of the cells ${\mathcal{V}}_\mathbf{x}$ for $\mathbf{x}\in\Phi_{\rm b}$.
Thus, we can interpret that $\tilde{\Psi}_{\rm b}$ is a result of thinning $\tilde{\Omega}_{\rm b}$ with scheduling probability $\zeta_{\rm b}$.
Assuming $D_\mathbf{x}$s to be independent of each other, we can write $ {\mathcal{A}}=$
\begin{align*}
\mathbb{E}_{\tilde{\Phi}_{\rm d}}\prod_{\mathbf{x}\in \tilde{\Omega}_{\rm b}} \int \bigg[1-\frac{\zeta_{\rm b}}{(1+\beta_{\rm b}^{-1} R_{\rm b}^{\alpha(\epsilon-1)} u^{-\alpha\epsilon}\|\mathbf{x}\|^\alpha)^k}\bigg]^bf_{D_\mathbf{x}}(u){\rm d}u.
\end{align*}
The distribution of distance from the nucleus to a uniformly random point in the typical PV cell follows $1-\exp(-\pi\lambda_{\rm b}{\rm c_1}r^2)$, where ${\rm c_1}=\frac{9}{7}$ \cite[Theorem 3]{mankar2019distance}. Thus, the $\mathtt{pdf}$ of link distance $D_\mathbf{x}$ of device associated with a randomly selected BS can be approximated using \eqref{eq:Distance_Distribution} with corrected density ${\rm c_1}\lambda_{\rm b}$. However, it may be noted that the link distance $D_\mathbf{x}$ of interfering user $\mathbf{x}$ must be smaller than $\|\mathbf{x}\|$ as it is closer to its serving BS than the typical BS at $o$.
Thus, using the $\mathtt{pdf}$ of $D_\mathbf{x}$ and the $\mathtt{PGFL}$ of the non-homogeneous PPP approximation of $\tilde{\Omega}_{\rm b}$, we obtain $ {\mathcal{A}} =$
\begin{align}
\exp\left(-4\pi^2{\rm c_1}\lambda_{\rm d}\lambda_{\rm b}\int\nolimits_0^\infty \hspace{-4mm}D(v;{\mathcal{J}}) \int\nolimits_0^{\min(v,{\mathcal{J}})}\hspace{-6mm} f(u,v;R_b,b) {\rm d}uv{\rm d}v \right)
\end{align}
where $f(u,v;R_b,b)=$
\begin{align}
\left(1-\left[1-\frac{\zeta_{\rm b}\beta_{\rm b} R_{\rm b}^{\alpha(1-\epsilon)} u^{\alpha\epsilon}}{\beta_{\rm b} R_{\rm b}^{\alpha(1-\epsilon)} u^{\alpha\epsilon}+v^\alpha}\right]^b\right)\frac{u\exp(-\pi{\rm c_1}\lambda_{\rm b}u^2)}{F(\sqrt{{\rm c_1}}\min(v,{\mathcal{J}}))}.\label{eq:fd}
\end{align}
Finally, by substituting ${\cal A}$ and ${\cal B}$ in \eqref{eq:Mb_1} and then averaging using the $\mathtt{pdf}$ of serving link distance $R_{\rm b}$ given in \eqref{eq:Distance_Distribution}, we obtain the $b$-th moment of ${\rm P_b}(\mathbf{y},\Phi)$ in the following theorem.
\begin{thm}
\label{thm:Moment_Cond_SuccessProb}
For given $\epsilon$, the $b$-th moment of the conditional success probability of status update at the typical BS is
\begin{align*}
M_b=&\frac{2\pi {\rm c_1}\lambda_{\rm b}}{F(\sqrt{{\rm c_1}}{\mathcal{J}})}\int_0^{\mathcal{J}} r\exp\bigg(-\pi {\rm c_1}\lambda_{\rm b}r^2 -\pi\lambda_{\rm d}\\
&~~~~\left({\cal G}(r,b) + r^{2(1-\epsilon)}C(b)\right)\bigg){\rm d}r,\numberthis\label{eq:SuccessProba_pa}
\end{align*}
\text{where}~
\begin{align*}
{\cal G}(r,b)&=4\pi\lambda_{\rm b}{\rm c_1}\int_0^\infty D(v;{\mathcal{J}})\int_0^{\min(v,{\mathcal{J}})}f(u,v;r,b)v{\rm d}u{\rm d}v,\\
\end{align*}
and $C(b)$, $D(v;{\mathcal{J}})$ and $f(u,v;r,b)$ are given by \eqref{eq:Cb}, \eqref{eq:Dg}, and \eqref{eq:fd}, respectively.
\end{thm}
The following lemma presents simplified expressions for $M_b$ given in Theorem \ref{thm:Moment_Cond_SuccessProb} for the special cases of no power control and full power control.
\begin{cor}
\label{lemma:SuccessProba_pa}
The $b$-th moment of the conditional success probability of status update at the typical BS under full power control (i.e., $\epsilon=1$) is
\begin{align*}
M_b=&\exp\left(-\pi\lambda_{\rm d}\left(\tilde{\cal G}(b)+C(b)\right) \right), \numberthis\label{eq:SuccessProba_pa_epi1}
\end{align*}
where
\begin{align*}
\tilde{\cal G}(b)=&4\pi\lambda_{\rm b}{\rm c_1}\int_0^\infty D(v;{\mathcal{J}})\int_0^{\min(v,{\mathcal{J}})}f(u,v;1,b){\rm d}uv{\rm d}v,
\end{align*}
and under no power control (i.e., $\epsilon=0$) is
\begin{align*}
M_b=&\frac{2\pi {\rm c_1}\lambda_{\rm b}}{F({\mathcal{J}})}\int_0^{\mathcal{J}} \exp\bigg(-\pi {\rm c_1}\lambda_{\rm b}r^2 \\
&~~~~~~~~-\pi\lambda_{\rm d}\left(\hat{\cal G}(r,b)+r^2C(b)\right) \bigg)r{\rm d}r,\numberthis\label{eq:SuccessProba_pa_epi0}
\end{align*}
where
\begin{align*}
\hat{\cal G}(r,b)=2\int_0^\infty D(v;{\mathcal{J}})\bigg(1-\bigg[1-\frac{\zeta_{\rm b}\beta_{\rm b}r^{\alpha}}{\beta_{\rm b}r^{\alpha}+v^\alpha}\bigg]^{b}\bigg)v{\rm d}v.
\end{align*}
\end{cor}
\begin{cor}
\label{lemma:SuccessProba_pa_ortho}
Under orthogonal access, the $b$-th moment of the conditional success probability of status update at the typical BS is
\begin{align}
\tilde{M}_b=&\frac{2\pi {\rm c_1}\lambda_{\rm b}}{F({\mathcal{J}})}\int_0^{\mathcal{J}} r\exp\left(-\pi {\rm c_1}\lambda_{\rm b}r^2 -\pi\lambda_{\rm d}{\cal G}(r,b) \right){\rm d}r,\numberthis\label{eq:SuccessProba_pa_ortho}
\end{align}
which under full power control and no power control becomes
\begin{align}
\tilde{M}_b=&\exp\left(-\pi\lambda_{\rm d}\tilde{\cal G}(b) \right)
\end{align}
and $\tilde{M}_b=$
\begin{align}
&\frac{2\pi {\rm c_1}\lambda_{\rm b}}{F({\mathcal{J}})}\int_0^{\mathcal{J}} \exp\bigg(-\pi {\rm c_1}\lambda_{\rm b}r^2 -\pi\lambda_{\rm d}\hat{\cal G}(r,b) \bigg)r{\rm d}r,\numberthis\label{eq:SuccessProba_pa_epi10_ortho}
\end{align}
respectively, where ${\cal G}(r,b)$ is given in Theorem \ref{thm:Moment_Cond_SuccessProb}, and $\tilde{\cal G}(b)$ and $\hat{\cal G}(r,b)$ are given in Corollary \ref{lemma:SuccessProba_pa}.
\end{cor}
\begin{proof}
The proof follows by setting $\zeta_{\rm d}=0$ in \eqref{eq:SuccessProba_pa}-\eqref{eq:SuccessProba_pa_epi0}.
\end{proof}
\section{Analysis of Cell Load}
\label{sec:schedulin_probability_AoI}
As discussed in Section \ref{subsec:Performance_Metrics}, the temporal mean AoI seen by a status update link depends jointly on its ability of successful transmission and probability of getting scheduled.
Therefore, in this section, we derive the scheduling probability of the typical IoT device and then use it along with Assumption \ref{assumption} to derive the moments of the conditional mean AoI in Section \ref{sec:AoI_Througput}.
Recall that each BS is assumed to schedule the status update transmission uniformly at random from one of its associated devices in a given time slot. Thus, the scheduling probability of a device associated with the typical BS placed at $o$ depends on the load of cell ${\mathcal{V}}_o$ (i.e., number of devices $N_{{\mathcal{V}}_o}$ located in ${\mathcal{V}}_o$). As a result, the scheduling probability of a device at $\mathbf{y}\in\Phi_{\rm d}\cap{\mathcal{V}}_o$ for given $\Phi$ is
$\zeta_{\rm b}(\mathbf{y},\Phi)=N_{{\mathcal{V}}_o}^{-1}$.
By the PPP definition, the distribution of number devices located in a region is parameterized by its area. Thus, the knowledge for the area distribution of ${\mathcal{V}}_o$ is essential to determine the scheduling probability of a device associated with the typical BS placed at $o$. However, it is difficult to directly derive the area distribution of a random set. Thus, we first determine the moments of area of ${\mathcal{V}}_o$ which will then be used to accurately characterize its distribution. While these moments are derived in \cite{Priyo_2019_FPR}, we derive a simplified expression for the second moment of area of ${\mathcal{V}}_o$ in Lemma \ref{lemma:Area_Moments} using the approach presented in \cite{Foss1993OnAC}.
\begin{lemma}
\label{lemma:Area_Moments}
For a given ${\mathcal{J}}$, the mean of area of the typical cell ${\mathcal{V}}_o$ is
\begin{align}
\bar{{\mathcal{V}}}_o^1=\frac{1}{\lambda_{\rm b}}\left(1-\exp\left(-\pi\lambda_{\rm b}{\mathcal{J}}^2\right)\right),
\label{eq:mean_Vo}
\end{align}
and the second moment of area of the typical cell ${\mathcal{V}}_o$ is
\begin{align}
\bar{{\mathcal{V}}}_o^2&=2\pi\lambda_{\rm b}^{-2}\int_0^\pi\int_{0}^{\pi-u} \frac{G(u,v)}{S(u,v)^2}\bigg[1-\left(1+\lambda_{\rm b}{\mathcal{J}}^2S^\prime(u,v)\right)\nonumber\\
&~~~~\exp\left(-\lambda_{\rm b}{\mathcal{J}}^2{S}^\prime(u,v)\right)\bigg]{\rm d}v {\rm d}u,
\label{eq:2nd_moment_Vo}
\end{align}
\text{where}~
\begin{align*}
G(u,v)&=\sin(u)\sin(v)\sin(u+v),\\ ~S^\prime(u,v)&=S(u,v)\max(\sin(u),\sin(v))^{-2},\\
\text{and}~
S(u,v)&=G(u,v) +\left(\pi-v\right) \sin(u)+\left(\pi-u\right)\sin(v).
\end{align*}
\end{lemma}
\begin{proof}
Please refer to Appendix \ref{appendix:Area_Moments} for the proof.
\end{proof}
Let $R_m$ be the half of the distance from the typical BS to its nearest BS. We have ${\mathcal{V}}_o={\mathcal{B}}_o({\mathcal{J}})$ whenever the event ${\mathcal{E}}=\{R_m>{\mathcal{J}}\}$ occurs. Thus, the $\mathtt{pdf}$ of the area of ${\mathcal{V}}_o$ becomes
\begin{align*}
f_{{\mathcal{V}}_o}(v)=\delta(\pi{\mathcal{J}}^2)\mathbb{P}[{\mathcal{E}}] + f_{{\mathcal{V}}_o}(v|{\mathcal{E}}^C)\mathbb{P}[{\mathcal{E}}^C],
\end{align*}
where $\delta(\cdot)$ is the Dirac-delta function and $\mathbb{P}[{\mathcal{E}}^C]=1-\mathbb{P}[{\mathcal{E}}]$. From the {\em void probability} of PPP, we get $\mathbb{P}[{\mathcal{E}}]=\exp(-4\pi\lambda_{\rm b}{\mathcal{J}}^2)$. Similar to \cite{Priyo_2019_FPR}, we approximate the distribution $f_{{\mathcal{V}}_o}(v|{\mathcal{E}}^C)$ using the truncated beta distribution as
\begin{align}
f_{{\mathcal{V}}_o}(v|{\mathcal{E}}^C)=\frac{v^{\kappa_1-1}(2 \pi{\mathcal{J}}^2-v)^{\kappa_2-1}}{(2\pi{\mathcal{J}}^2)^{\kappa_1+\kappa_2-1}{\rm B}(\kappa_1,\kappa_2)},
\end{align}
~\text{for}~$0\leq v\leq \pi{\mathcal{J}}^2$, \text{where} ${\rm B}(\kappa_1,\kappa_2)=\int_0^{1/2} v^{\kappa_1-1}(1-v)^{\kappa_2-1}{\rm d}v$.
Note that the support of the truncated distribution is $[0,\pi{\mathcal{J}}^2]$ whereas the support of untruncated distribution is considered to be $[0,2\pi{\mathcal{J}}^2]$.
We determine the parameters $\kappa_1$ and $\kappa_2$ through moment matching method. For this, we obtained the first and second moments of the area of ${\mathcal{V}}_o$ conditioned on ${\mathcal{E}}^C$ using Lemma \ref{lemma:Area_Moments} as
\begin{align}
\tilde{{\mathcal{V}}}_o^1&=\mathbb{E}[|{\mathcal{V}}_o||{\mathcal{E}}^C],\nonumber\\
&=\left(\mathbb{E}[{\mathcal{V}}_o]-\mathbb{E}[{\mathcal{V}}_o|{\mathcal{E}}]\mathbb{P}[{\mathcal{E}}]\right)\mathbb{P}[{\mathcal{E}}^C]^{-1},\nonumber\\
&=\frac{\bar{{\mathcal{V}}}_o^1-\pi{\mathcal{J}}^2\exp(-4\pi\lambda_{\rm b}{\mathcal{J}}^2)}{1-\exp(-4\pi\lambda_{\rm b}{\mathcal{J}}^2)},
\end{align}
and
\begin{align}
\tilde{{\mathcal{V}}}_o^2&=\mathbb{E}[|{\mathcal{V}}_o|^2|{\mathcal{E}}^C],\nonumber\\
&=\left(\mathbb{E}[|{\mathcal{V}}_o|^2]-\mathbb{E}[|{\mathcal{V}}_o|^2|{\mathcal{E}}]\mathbb{P}[{\mathcal{E}}]\right)\mathbb{P}[{\mathcal{E}}^C]^{-1},\nonumber\\
&=\frac{\bar{{\mathcal{V}}}_o^2-\pi^2{\mathcal{J}}^4\exp(-4\pi\lambda_{\rm b}{\mathcal{J}}^2)}{1-\exp(-4\pi\lambda_{\rm b}{\mathcal{J}}^2)}.
\end{align}
Therefore, the parameters of approximate truncated beta distribution can be determined by solving the following simultaneous equations
\begin{align}
\tilde{{\mathcal{V}}}_o^1&=2 \pi{\mathcal{J}}^2\frac{{\rm B}(\kappa_1+1,\kappa_2)}{{\rm B}(\kappa_1,\kappa_2)},\\
\text{~and~}\tilde{{\mathcal{V}}}_o^2&=(2 \pi{\mathcal{J}}^2)^2\frac{{\rm B}(\kappa_1+2,\kappa_2)}{{\rm B}(\kappa_1,\kappa_2)}.
\end{align}
Finally, by substituting the truncated beta approximation of $f_{{\mathcal{V}}_o}(v|{\mathcal{E}})$ in $f_{{\mathcal{V}}_o}(v)$, we obtain
\begin{align}
&f_{{\mathcal{V}}_o}(v)=\delta(\pi{\mathcal{J}}^2)\exp(-4\pi\lambda_{\rm b}{\mathcal{J}}^2)\nonumber\\
&+\frac{1-\exp(-4\pi\lambda_{\rm b}{\mathcal{J}}^2)}{(2 \pi{\mathcal{J}}^2)^{\kappa_1+\kappa_2-1}{\rm B}(\kappa_1,\kappa_2)}v^{\kappa_1-1}(2\pi{\mathcal{J}}^2-v)^{\kappa_2-1},
\label{eq:Area_pdf}
\end{align}
for $0\leq v\leq \pi{\mathcal{J}}^2$. The accuracy of the above approximation of area distribution of ${\mathcal{V}}_o$ has been discussed extensively in \cite{Priyo_2019_FPR}.
Using \eqref{eq:Area_pdf}, we now present the ${\rm pmf}$ of number of IoT devices located in ${\mathcal{V}}_o$ in the following lemma, which will be used to analyze AoI in Section \ref{subsec:AoI}.
\begin{lemma}
\label{lemma:NoDevice_pmf}
The ${\rm pmf}$ of the number of devices residing in $\Phi_{\rm d}\cap{\mathcal{V}}_o$ is
\begin{align}
\mathbb{P}[N_{{\mathcal{V}}_o}=n] = \frac{1}{n!}\int_0^{\pi{\mathcal{J}}^2}(\lambda_{\rm d}v)^n\exp(-\lambda_{\rm d}v)f_{{\mathcal{V}}_o}(v){\rm d}v,
\end{align}
\text{~for~} $n\geq 0$, where $f_{{\mathcal{V}}_o}(v)$ is given by \eqref{eq:Area_pdf}.
\end{lemma}
\section{ D2D Throughput and Average AoI }
\label{sec:AoI_Througput}
In this section, we first determine the D2D network throughput using the success probability of regular message transmissions derived in Theorem \ref{thm:SuccessProba_pd}. Next, we will characterize the spatial distribution of the temporal mean AoI using the moments of conditional success probability of update transmissions derived in Theorem \ref{thm:Moment_Cond_SuccessProb} and the cell load distribution derived in Lemma \ref{lemma:NoDevice_pmf}.
\subsection{Throughput of D2D Network}
\label{subsec:Throughput}
The network throughput is measured by the average number of successfully delivered information bits per unit area per second per Hertz (bit/s/Hz/m$^2$).
Note that the effective probability of an IoT device transmitting the regular messages is $\zeta_{\rm d}$ (refer to \eqref{eq:D2D_Link_scheduling_Probability}). Therefore, for a given density $\lambda_{\rm d}$ of the IoT devices, the throughputs of the typical D2D link and the D2D network can be determined as
\begin{align}
{\rm T_d}=\zeta_{\rm d}{\rm B}\log_2(1+\beta_{\rm d}){\rm P_d} \text{~and~} {\rm T_{N}}=\lambda_{\rm d}{\rm T_d},
\end{align}
respectively, where $\zeta_{\rm d}$ is given in \eqref{eq:D2D_Link_scheduling_Probability} and ${\rm P_d}$ is given in Theorem \ref{thm:SuccessProba_pd}.
\subsection{Spatial Distribution of Temporal Mean AoI }
\label{subsec:AoI}
In this section, our goal is to derive the spatial distribution of the temporal mean AoI observed by the IoT device-BS links.
\begin{figure}[h]
\centering
\includegraphics[clip, trim=1.3cm 14cm 0.5cm 5cm, width=0.5\textwidth]{AoI_Curve_a.pdf}
\caption{{ Sample path of AoI $A_{\bf y}(k)$ for the IoT device at ${\bf y}$.} The red upward and blue downward arrows show the transmission attempts and successful transmissions, respectively.}
\label{fig:aoi}
\end{figure}
Fig. \ref{fig:aoi} depicts a representative sample path of the AoI for the system model discussed in Section \ref{subsec:Performance_Metrics}. { Let $Y_{{\bf y},k}$ and $X_{{\bf y},k}$ denote the sum of AoI $A_{\bf y}(k)$ (i.e., area of shaded region) and the time difference between the successful reception of the $k$-th and the ($k+1$)-th status updates from device at ${\bf y}$, respectively. Thus, we can write
\begin{equation}
Y_{{\bf y},k}=\sum_{k=t_k}^{t_{k+1}} A_{\bf y}(k) \text{~and~} X_{{\bf y},k}=\sum\limits_{i=1}^{L_{\bf y}}T_{{\bf y},i},
\label{eq:X_k}
\end{equation}
where $T_{{\bf y},i}$ denotes the time elapsed between two consecutive scheduling instances of device ${\bf y}$ and $L_{\bf y}$ denotes the number of attempted transmissions between two successfully received status updates from device ${\bf y}$.} The temporal mean AoI (for a device-BS link conditioned on $\Phi$) is charaterized here similarly to \cite{infocom19} wherein the authors determine temporal mean AoI for the case of a single point-to-point link. { For a period of $N$ time slots, where $K_{\bf y}$ successful updates occur, the temporal mean AoI for device at ${\bf y}$ conditioned on $\Phi$ is
\begin{align*}
\Delta({\bf y},\Phi;N)&=\frac{1}{N}\sum\limits_{k=1}^{N}A_{\bf y}(k),\\
&=\frac{1}{N}\sum\limits_{k=1}^{K_{\bf y}}Y_{{\bf y},k},\\
&=\frac{K_{\bf y}}{N}\frac{1}{K_{\bf y}}\sum\limits_{k=1}^{K}Y_{{\bf y},k}.\numberthis
\end{align*}
Using $\lim\limits_{N\rightarrow\infty}\frac{K_{\bf y}}{N}=\frac{1}{\mathbb{E}[X_{\bf y}]} \text{~and~} \lim\limits_{K_{\bf y}\to\infty}\frac{1}{K_{\bf y}}\sum\limits_{k=1}^{K_{\bf y}}Y_{\bf y}=\mathbb{E}[Y_{\bf y}],$
we can obtain the mean AoI for the device ${\bf y}$ for given $\Phi$ as
\begin{equation}
\Delta({\bf y},\Phi)=\lim\limits_{N\rightarrow\infty}\Delta({\bf y},\Phi;N)=\frac{\mathbb{E}[Y_{\bf y}]}{\mathbb{E}[X_{\bf y}]}.
\end{equation}
Further, we can establish the relation between $Y_{{\bf y},k}$ and $X_{{\bf y},k}$ as
\begin{equation}
Y_{{\bf y},k}=\sum\limits_{m=1}^{X_{{\bf y},k}}m=\frac{1}{2}X_{{\bf y},k}(X_{{\bf y},k}+1).
\end{equation}
Thus, we can obtain
\begin{equation}
\Delta({\bf y},\Phi)=\frac{1}{2}\frac{\mathbb{E}\left[X_{{\bf y},k}(X_{{\bf y},k}+1)\right]}{\mathbb{E}[X_{\bf y}]}=\frac{\mathbb{E}[X_{{\bf y}}^2]}{2\mathbb{E}[X_{{\bf y}}]}+\frac{1}{2}.
\label{eq:aoi}
\end{equation}
From \eqref{eq:aoi}, it is evident that the knowledge of the first two moments of $X_{{\bf y},k}$ is sufficient to evaluate the temporal mean of AoI. However, the distribution of $X_{{\bf y},k}$ is not identical for the IoT devices spread across the network for the following reasons. The distribution of $X_{{\bf y},k}$ of an IoT device-BS link jointly depends on its scheduling and successful transmission probabilities.
In particular, for a given $\Phi$ and the IoT device at $\mathbf{y}\in V_o$, the scheduling probability $\zeta_{\rm b}(\mathbf{y},\Phi)$ and conditional success probability ${\rm P_b}(\mathbf{y},\Phi)$ charaterize the distributions of $T_{{\bf y},i}$ and $L_{\bf y}$, respectively, which essentially determine the temporal mean AoI through $X_{{\bf y},k}$. This implies that the temporal mean AoI observed at an IoT device-BS link is conditioned on the locations of the IoT devices and the BSs. Hence, we refer to this mean AoI as the {\em conditional temporal mean AoI}. Our goal is to derive the spatial distribution of the temporal mean AoI.
\subsubsection{Conditional temporal mean AoI}
For the IoT device at $\mathbf{y}\in{\mathcal{V}}_o$ given $\Phi$, the probability of successful transmission of status update is ${\rm P_b}(\mathbf{y},\Phi)$ and the probability that it is scheduled for the status update is $\zeta_{\rm b}(\mathbf{y},\Phi)$. Therefore, the $\mathtt{pmf}$s of $T_{{\bf y},i}$ and $L_{\bf y}$ become
\begin{align}
\mathbb{P}[T_{{\bf y},i}=t|\Phi]&=\zeta_{\rm b}(\mathbf{y},\Phi)[1-\zeta_{\rm b}(\mathbf{y},\Phi)]^{t-1},\label{eq:Tyi}\\
\text{~and~}\mathbb{P}[L_{\bf y}=m|\mathbf{y},\Phi]&={\rm P_b}(\mathbf{y},\Phi)[1-{\rm P_b}(\mathbf{y},\Phi)]^{m-1},\label{eq:Ly}
\end{align}
for $1\leq m,t$, respectively. Since $T_{{\bf y},i}$s are independent and identically distributed (because of the random scheduling), we can apply the Wald's identity and obtain the mean of $X_{{\bf y},k}$ as
\begin{equation} \label{EX-gen}
\mathbb{E}[X_{{\bf y}}]=\mathbb{E}[T_{{\bf y}}]\mathbb{E}[L_{\bf y}]= \frac{1}{\zeta_{\rm b}(\mathbf{y},\Phi){\rm P_b}(\mathbf{y},\Phi)}.
\end{equation}
Now, we determine the second moment of $X_{{\bf y},k}$. From its definition, we can write
\begin{equation*}
X_{{\bf y},k}^2=\left(\sum\limits_{i=1}^{L_{\bf y}}T_{{\bf y},i}\right)^2=\sum\limits_{i=1}^{L_{\bf y}}T_{{\bf y},i}^2+\sum\limits_{i=1}^{L_{\bf y}}\sum\limits_{j=1,j\neq i}^{L_{\bf y}}T_{{\bf y},i} T_{{\bf y}j}.
\end{equation*}
Note that $T_{{\bf y},i}$ and $T_{{\bf y}j}$, for $i\neq j$, are independent because each BS schedules its associated IoT devices uniformly at random in a given slot. Thus, for $L_{\bf y}=m$, we get
\begin{align*}
\mathbb{E}[X_{{\bf y}}^2 \vert L_{\bf y}=m]&=m\mathbb{E}[T_{{\bf y}}^2]+m(m-1)\mathbb{E}[T_{{\bf y}}]^2,\nonumber\\
&=m {\rm Var}[T] + m^2\mathbb{E}[T]^2,\nonumber\\
&=m\frac{1-\zeta_{\rm b}(\mathbf{y},\Phi)}{\zeta_{\rm b}(\mathbf{y},\Phi)^2}+m^2\frac{1}{\zeta_{\rm b}(\mathbf{y},\Phi)^2}
\end{align*}
Now, by averaging over the $\mathtt{pmf}$ of $L_{\bf y}$ given in \eqref{eq:Ly}, we obtain
\begin{align*}
\mathbb{E}[X_{{\bf y}}^2 ]&=\frac{1-\zeta_{\rm b}(\mathbf{y},\Phi)}{\zeta_{\rm b}(\mathbf{y},\Phi)^2}\mathbb{E}[L_{\bf y}]+\frac{1}{\zeta_{\rm b}(\mathbf{y},\Phi)^2}\mathbb{E}[L_{\bf y}^2]\\
&=\frac{1-\zeta_{\rm b}(\mathbf{y},\Phi)}{\zeta_{\rm b}(\mathbf{y},\Phi)^2}\frac{1}{{\rm P_b}(\mathbf{y},\Phi)}+\frac{1}{\zeta_{\rm b}(\mathbf{y},\Phi)^2}\frac{2-{\rm P_b}(\mathbf{y},\Phi)}{{\rm P_b}(\mathbf{y},\Phi)^2}.\numberthis\label{EX2-gen}
\end{align*}}
Finally, by substituting \eqref{EX-gen} and \eqref{EX2-gen} into \eqref{eq:aoi}, we obtain the conditional temporal mean AoI as given in the following lemma.
\begin{lemma}
\label{lemma:Cond_Mean_AoI}
For a given $\Phi$, the conditional temporal mean AoI measured by the typical BS of the status updates from the IoT device located at $\mathbf{y}\in {\mathcal{V}}_o$ is
\begin{equation}
\Delta(\mathbf{y},\Phi) = \frac{1}{\zeta_{\rm b}(\mathbf{y},\Phi){\rm P_b}(\mathbf{y},\Phi)}.
\label{eq:Cond_Mean_AoI}
\end{equation}
\end{lemma}
\subsubsection{Spatial Moments of $\Delta(\mathbf{y},\Phi)$}
In this subsection, we analyze the spatial distribution of temporal mean AoI under Assumption \ref{assumption}.
Thus, it is apparent from Lemma \ref{lemma:Cond_Mean_AoI} that the $n$-th moment of $\Delta(\mathbf{y},\Phi)$ is equal to the product of $n$-th moments of ${\rm P_b}(\mathbf{y},\Phi)^{-1}$ and $\zeta_{\rm b}(\mathbf{y},\Phi)^{-1}$ which can be directly obtained from Theorem \ref{thm:Moment_Cond_SuccessProb} and Lemma \ref{lemma:NoDevice_pmf}, respectively.
\setcounter{theorem}{2}
\begin{theorem}
\label{theorem:Moments_conditional_AoI}
The $n$-th moment of the temporal mean AoI of the status updates generated from the IoT devices is
\begin{align}
\Delta_{n}=\mathbb{E}[N_{{\mathcal{V}}_o}^n|N_{{\mathcal{V}}_o}\geq 1]M_{-n},\label{eq:Moment_AoI_n}
\end{align}
where $M_{-n}$ is given in Theorem \ref{thm:Moment_Cond_SuccessProb} and ${\rm pmf}$ of $N_{{\mathcal{V}}_o}$ is given in Lemma \ref{lemma:NoDevice_pmf}.
\end{theorem}
\begin{proof}
Using the assumption of independence of $\zeta_{\rm b}(\mathbf{y},\Phi)$ and ${\rm P_b}(\mathbf{y},\Phi)$ and Lemma \ref{lemma:Cond_Mean_AoI}, the $n$-th moment of the conditional temporal mean AoI can be obtained as
\begin{align*}
\Delta_n&=\mathbb{E}_{\mathbf{y},\Phi}[\Delta(\mathbf{y},\Phi)^n]=\mathbb{E}_{\mathbf{y},\Phi}[{\zeta_{\rm b}(\mathbf{y},\Phi)}^{-n}]\mathbb{E}_{\mathbf{y},\Phi}[{\rm P_b}(\mathbf{y},\Phi)^{-n}].
\end{align*}
Thus, we arrive at \eqref{eq:Moment_AoI_n} by plugging the $(-n)$-th moment of ${\rm P_b}(\mathbf{y},\Phi)$ from Theorem \ref{thm:Moment_Cond_SuccessProb} and using the $\mathtt{pmf}$ of $N_{{\mathcal{V}}_o}$ given in Lemma \ref{lemma:NoDevice_pmf}.
\end{proof}
\begin{figure*}[h]
\centering
\hspace{-5mm}\includegraphics[ width=.33\textwidth]{Success_Prob_D2D_New.pdf}
\includegraphics[ width=.33\textwidth]{M1_Cond_Success_Prob_New.pdf}
\includegraphics[ width=.33\textwidth]{M2_Cond_Success_Prob_New.pdf}
\caption{Left: success probability of regular message transmissions on D2D links. Middle and Right: first and second moments of conditional success probability of status update transmissions.}
\label{fig:SuccessProb_Pd}
\end{figure*}
{\begin{cor}
The spatiotemporal mean of the AoI is
\begin{equation}
\Delta_{1}=\frac{\lambda_{\rm d}}{\lambda_{\rm b}}\left(1-\exp(-\pi{\rm c_1}\lambda_{\rm b}{\mathcal{J}}^2)\right)M_{-1}
\end{equation}
where $M_{-1}$ is given in Theorem \ref{thm:Moment_Cond_SuccessProb}.
\end{cor}}
Simplified expressions for the moments of the temporal mean AoI can be obtained for the special cases of no power control and full power control using the moments of conditional success probability $M_b$ presented in Corollary \ref{lemma:SuccessProba_pa}.
In addition, the moments of the temporal mean AoI for the orthogonal access can also be obtained using the moments of conditional success probability $\tilde{M}_{b}$ presented in Corollary \ref{lemma:SuccessProba_pa_ortho}. They not repeated here due to lack of space.
{\begin{remark}
Note that Theorem \ref{theorem:Moments_conditional_AoI} presents the spatial moments of the mean AoI for a general case as it allows to control the status update support for the devices experiencing link quality (which is expected to decrease with the increase of serving link distance) above a certain percentile by appropriately setting ${\mathcal{J}}$ (or, $P_{\rm max}$ and $\epsilon$). The status update support for all devices is a special case to which our analysis can be easily extended by simply setting ${\mathcal{J}}=\infty$ (for which, we need $P_{\rm max}=\infty$ or $\epsilon=0$). However, it may be noted that $M_{-n}$ (thus the spatial moments $\Delta_n$) becomes unbounded as ${\mathcal{J}}\to\infty$ which can be verified using \eqref{eq:SuccessProba_pa}. Therefore, it is important to appropriately select ${\mathcal{J}}$ such that it covers the devices of interest. From this perspective, the JM cell based analysis of AoI is meaningful.
\end{remark}}
\section{Numerical Analysis and Discussion}
\label{sec:Results}
In this section, we first verify the success probabilities of transmissions of regular messages and status updates derived in Section \ref{sec:SuccessProb} using simulation results. Next, we will discuss the impact of various system design parameters on our key performance metrics (i.e., D2D network throughput and AoI associated with status updates) presented in Section \ref{sec:AoI_Througput} using numerical results. For the numerical analysis, the system parameters are considered as $\lambda_{\rm b}=10^{-4}$ BSs/m$^2$, $\lambda_{\rm d}=20\lambda_{\rm b}$ devices/m$^2$, ${\rm B}=200$ KHz, ${\mathcal{J}}=40$ m, $p_{\rm b}=p_{\rm d}=100$ dBm, $\alpha=4$, $q_{\rm d}=0.3$, $R_{\rm d}=2$ m, and $\beta_{\rm b}=3$ dB, unless mentioned otherwise. Note that the JM cell radius ${\cal J}=40$ m provides coverage to around $40$\% of the IoT devices for the status update transmissions. {In our simulations, we perform the spatial averaging of temporal mean AoI and conditional success probability over 10000 network realizations and for each realization the temporal averaging (on small scale fading) is performed over 1000 transmission slots. }
Fig. \ref{fig:SuccessProb_Pd} (left) verifies the accuracy of the success probability of the regular message transmissions, and Fig. \ref{fig:SuccessProb_Pd} (middle and right) verifies the accuracy of the first two moments of the conditional success probability of the status update transmissions. The curves correspond to the analytical results whereas the markers correspond to the simulation results.
Fig. \ref{fig:SuccessProb_Pd} (middle and right) shows that the power control provides improvement in the success probability of the status update transmissions. However, it can be observed from the figure that increasing power control fraction $\epsilon$ beyond $0.3$ will not contribute much in the improvement of success probability of status update because it becomes limited by the interference from the regular message transmissions over D2D links. In addition, it is also necessary to select a small value of $\epsilon$ to ensure better success probability of D2D links. { A smaller $\epsilon$ provides better success probability in the high $\mathtt{SIR}$ regime. This is because the devices with higher $\mathtt{SIR}$ lie closer to their serving BSs, thus for these devices, the desired signal power received at their BSs does not improve faster with increasing $\epsilon$ compared to the increase of the inter-cell interference.}
Let $\mathcal{D}_{\rm \lambda}=\frac{\lambda_{\rm d}}{\lambda_{\rm b}}$ represents the ratio of densities of devices and BSs. Fig. \ref{fig:Througput_AoI} (left) shows the impact of $\mathcal{D}_{\rm \lambda}$ and $\epsilon$ on the achievable throughput of D2D network for $R_{\rm d}=$ 2 m and 5 m. The achievable throughputs of D2D link and D2D network are determined as ${\rm T}^*_{\rm d}=\max_{\beta_{\rm d}} {\rm T}_{\rm d}$ and ${\rm T}_{\rm N}^*=\lambda_{\rm d}{\rm T}_{\rm d}^*$, respectively.
The initial rise in the achievable D2D link throughput is because of better chances of medium access for regular message transmission (since the update scheduling probability drops with increasing $\mathcal{D}_{\rm \lambda}$). However, the D2D link throughput drops eventually with increasing $\mathcal{D}_{\rm \lambda}$ because of the increased interference. Nevertheless, the achievable D2D network throughput monotonically increases with $\mathcal{D}_{\rm \lambda}$. The figure also shows that the achievable throughput is higher when D2D communication range is shorter. { The BS density $\lambda_{\rm b}$ has two interrelated impacts on the D2D network throughput performance: 1) increasing $\lambda_{\rm b}$ reduces the transmission powers of the status updating devices (because of the smaller serving link distances) which positively affects the D2D throughput, and 2) increasing $\lambda_{\rm b}$ leads to higher density of status updating devices which negatively affects the D2D throughput. Fig. 5 (right) shows the D2D throughput as a function of $\lambda_{\rm b}$ for a fixed $\lambda_{\rm d}=10^{-2}$ and sufficiently large ${\mathcal{J}}$ (such that ${\mathcal{V}}_o\approx V_o$). The larger value of ${\mathcal{J}}$ is selected to see the maximum benefit of increasing $\lambda_{\rm b}$ through the reduced transmission power as stated above. However, the figure reveals that the D2D throughput degrades as $\lambda_{\rm b}$ increases which in turn implies that the negative impact is dominant. }
\begin{figure*}[h]
\centering
\includegraphics[ width=.45\textwidth]{Througput_new.pdf}
\includegraphics[width=.45\textwidth]{D2D_NetThr_lamb.pdf}
\caption{ Left: achievable D2D network and D2D link throughputs. { Right: achievable D2D network throughput vs $\lambda_{\rm b}$ for $\lambda_{\rm d}=10^{-2}$.}}
\label{fig:Througput_AoI}
\end{figure*}
\begin{figure*}[h]
\centering
\hspace{-4mm} \includegraphics[ width=.33\textwidth]{AoI_Thr_vs_Beta_new.pdf}
\hspace{-2mm}\includegraphics[ width=.33\textwidth]{AoI_JMCell_Radius_new_new.pdf}
\includegraphics[width=.33\textwidth]{Interplay_vs_pow.pdf}
\caption{Left: mean AoI and D2D network throughput versus the $\mathtt{SIR}$ threshold. Interplay of AoI and D2D transmission rate with respect to JM cell radius ${\mathcal{J}}$ (middle) and power ratio $\frac{p_{\rm b}}{p_{\rm d}}$ (right). }
\label{fig:Interplay_fig}
\end{figure*}
Fig. \ref{fig:Interplay_fig} (left) shows the impact of $\mathtt{SIR}$ thresholds on the spatio-temporal mean AoI of status update transmissions and the throughput of D2D network.
The mean AoI increases with the $\mathtt{SIR}$ threshold $\beta_{\rm b}$, which is expected as the success probability of status updates drops with the increase of $\beta_{\rm b}$.
The figure shows that the mean AoI $\Delta_{1}$ is almost equal to $\mathbb{E}[N_{{\mathcal{V}}_o}]=\mathcal{D}_{\rm \lambda}(1-\exp(-\pi\lambda_{b}{\mathcal{J}}^2))$ for a small value of $\beta_{\rm b}$.
{ That is the mean AoI is equal to the mean number of slots required for scheduling the status updates from the typical device when $\beta$ is very small.}
This happens because the success probability of status updates is almost equal to one for small values of $\beta_{\rm b}$ and the mean number of slots required for a device to attempt the transmission is equal to the number of devices in the associated with the serving BS. On the other hand, $\Delta_{1}$ rises rapidly as $\beta_{\rm b}$ increases ultimately approaching to a value where the success probability of the status updates is close to zero (the corresponding points can be confirmed from Fig. \ref{fig:SuccessProb_Pd}), which is expected. However, a finite mean AoI can be supported for large values of $\beta_{\rm b}$ by increasing the power control fraction $\epsilon$. The figure shows the mean AoI curves for the extreme cases of power control (i.e., $\epsilon=0$ and $\epsilon=1$).
\begin{figure*}[h]
\centering
\hspace{-5mm}\includegraphics[ width=.33\textwidth]{AoI_JMCell_Radius_new.pdf}
\includegraphics[ width=.33\textwidth]{AoI_OrthogonalCompare.pdf}
\includegraphics[ width=.33\textwidth]{NetworkThr_OrthogonalCompare.pdf}
\caption{{ Left: mean AoI versus status update coverage for $\beta_{\rm b}=0$ dB. Middle and right: Co-channel and orthogonal access comparisons for the mean AoI and the D2D network throughput. }}
\label{fig:orthogonal_comparision}
\end{figure*}
The interplay between mean AoI and achievable D2D network throughput with respect to the JM cell radius ${\mathcal{J}}$ and the ratio of powers of update and regular transmissions are presented in Fig. \ref{fig:Interplay_fig} (middle) and Fig. \ref{fig:Interplay_fig} (right), respectively. Fig. \ref{fig:Interplay_fig} (middle) shows that both the mean AoI and D2D throughput degrade with increasing cell radius ${\mathcal{J}}$.
With the increase in ${\mathcal{J}}$, both the scheduling probability and the success probability drop, which in turn causes poor AoI performance. In particular, with increasing ${\mathcal{J}}$, the scheduling probability decreases because of the need to support status updates for a large number of devices while the success probability drops because of the increase in both the serving link distance and interference. On the other hand, the
degradation in the D2D throughput is due to the fact that status updates will need to be transmitted at a higher power because of the increased link distances (with increasing ${\mathcal{J}}$), which increases the aggregate interference power.
Further, the figure shows that higher $\epsilon$ results in a better AoI performance at the cost of degraded D2D throughput. Therefore, for a given $\lambda_{\rm d}$, we can maximize the D2D network throughput by selecting minimum $\epsilon$ that keeps the mean AoI below a predefined performance threshold.
Fig. \ref{fig:Interplay_fig} (right) shows that the mean AoI improves and the D2D network throughput degrades with the increase in the ratio $\frac{p_{\rm b}}{p_{\rm d}}$, which is quite expected. However, in this regime, the impact of the increasing power ratio becomes insignificant on the mean AoI since the interference from the D2D transmission becomes insignificant (thus the success probability of status update becomes invariant to $p_{\rm b}$).
It may be noted that both the D2D throughput and the mean AoI depend on $p_{\rm b}$ and $p_{\rm d}$ through their ratio.
{ For a given ${\mathcal{J}}$, the fraction of devices with status update support (i.e., status update coverage) is equal to $1-\exp(-\pi\lambda_{\rm b}{\mathcal{J}}^2)$.
Fig. \ref{fig:orthogonal_comparision} (left) shows the interplay between the mean AoI and status update coverage. It particular, it shows that one can tune $\epsilon$ in the power control model to achieve a higher status update coverage for a given mean AoI target. For instance, the figure shows that the full power control provides coverage of approximately 80\%, whereas $\epsilon=0.3$ supports the coverage of approximately 55\% when the mean AoI threshold is 30 and $\mathcal{D}_{\rm \lambda}=20$. It is worth noting that allowing full status update coverage (i.e., ${\mathcal{J}}=\infty$) will result in unbounded mean AoI as the AoI grows rapidly when the conditional success probability approaches to zero. Therefore, the knowledge of feasible status update coverage is important from the perspective of network design to ensure bounded mean AoI.}
{ Fig. \ref{fig:orthogonal_comparision} (middle and right) shows that the mean AoI degrades and the achievable D2D network throughput improves with the increase in ${\mathcal{D}}_\lambda$, which is expected.
From the middle figure, it can be observed that the power control fraction $\epsilon$ does not affect the mean AoI much under the orthogonal access. Moreover, the co-channel mode with full power control results in almost equal mean AoI as the orthogonal access case. Thus, the orthogonal access is preferable when the transmission power is limited, while the co-channel access is preferable when the spectrum is limited. The right figure shows that the orthogonal access provides higher D2D throughput compared to the co-channel access and the gain increases with $\epsilon$. }
\section{Conclusion}
This paper presented a stochastic geometry-based analysis of throughput and AoI performance metrics in a cellular-based IoT network while accounting for the spatial disparity in the AoI performance experienced by various wireless links spread across the network. In particular, the throughput was used to characterize the QoS of D2D communications between IoT devices, whereas the AoI was employed to quantify the freshness of status updates (regarding some time-sensitive applications) transmitted by the IoT devices to cellular BSs. The locations of IoT devices and BSs were modeled as a bipolar PPP and an independent PPP, respectively.
Further, we considered that each BS schedules the transmission of status updates from the IoT devices located in its JM cell. In addition, the IoT devices were assumed to employ a distance-proportional fractional power control scheme for uplink transmissions to improve the success delivery rate of status updates. For this setup, the mean success probability for the D2D links was derived to characterize the average network throughput. On the other hand, we captured the spatial disparity in the AoI performance by characterizing spatial moments of the temporal mean AoI. Specifically, we obtained the spatial moments of the temporal mean AoI by deriving the moments of both the conditional success probability and the conditional scheduling probability for status update links.
We validated the analytical results using extensive simulations. Our numerical results demonstrated the impact of power control, medium access probability and density of IoT devices on the achievable D2D network throughput and the spatio-temporal mean AoI. In particular, the results showed that the power control can facilitate the transmission of status updates from a large number of IoT devices such that the mean AoI remains below some predefined threshold.
{ The analysis of the interplay between AoI and throughput for the case where the IoT devices can employ superposition coding for the non-orthogonal transmission of the regular packets (to other devices) and status updates (to the BSs) could be considered as the direction of this work.}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 1,441
|
\section{Introduction}
Minimizers of a submodular function form a distributive lattice, and are compactly represented by a poset (partially ordered set) via Birkhoff representation theorem.
This fact reveals a useful hierarchical structure of the minimizers, and is applied to the DM-decomposition of matrices and further refined block-triangular decompositions~\cite{Murota2000}.
In this paper, we address such a Birkhoff-type representation for minimizers of a \emph{$k$-submodular function}.
Here $k$-submodular functions, introduced by Huber--Kolmogorov~\cite{Huber2012}, are functions on $\setprn{0, 1, 2, \ldots, k}^n$ defined by submodular-type inequalities.
This generalization of (bi)submodular functions has recently gained attention for algorithm design and modeling~\cite{Gridchyn2013, Hirai2015, Hirai2016, IwataS2016, IwataY2016}.
Our main result is to establish a compact representation for minimizers of a $k$-submodular function.
This can be viewed as a generalization of the above poset representation for submodular functions and Ando--Fujishige's signed poset representation for bisubmodular functions~\cite{Ando1994}.
A feature of our representation is to utilize a \emph{poset with inconsistent pairs (PIP)}~\cite{Ardila2011, Barthelemy1993, Nielsen1981}, which is a discrete structure having a stronger power of expression than that of a signed poset.
Actually a PIP is a poset endowed with an additional binary relation (\emph{inconsistency relation}), and is viewed as a poset reformulation of 2-CNF.
This concept, also known as an \emph{event structure}, was first introduced by Nielsen--Plotkin--Winskel~\cite{Nielsen1981} as a model of concurrency in theoretical computer science, and was independently considered by Barthelemy--Constantin~\cite{Barthelemy1993} to establish a Birkhoff-type representation theorem for a \emph{median semilattice}---a semilattice generalization of a distributive lattice.
A PIP was recently rediscovered by Ardila--Owen--Sullivant~\cite{Ardila2011} to represent nonpositively-curved cube complexes; the term ``PIP'' is due to them.
Our results consist of structural and algorithmic ones, summarized as follows:
\paragraph{Structural results.}
We show that minimizers of a $k$-submodular function form a median semilattice (Lemma~3).
By a Birkhoff-type representation theorem~\cite{Barthelemy1993} for median semilattices, the minimizer set is represented by a PIP, where minimizers are encoded into special ideals in the PIP, called \emph{consistent ideals}.
PIPs arising from $k$-submodular functions are rather special.
We completely characterize such PIPs (Theorem~\ref{thm:closed_set_and_elementary_pip}), which we call \emph{elementary}.
This representation is actually compact.
We show that the size of the elementary PIP for a $k$-submodular function of $n$ variables is $\Order{kn}$ (Proposition~\ref{prop:number_of_irreducibles}).
\paragraph{Algorithmic results.}
We present algorithms to construct the elementary PIP of the minimizers of a $k$-submodular function $f$ under the following three situations:
\begin{itemize}
\item[(i)] A minimizing oracle of $f$ is given.
\item[(ii)] $f$ is network-representable.
\item[(iii)] $f$ arises from a Potts energy function.
\end{itemize}
For (i), we show that the PIP is obtained by calling the minimizing oracle $\Order{kn^2}$ time (Theorem~\ref{thm:alg_oracle}).
Notice that a polynomial time algorithm to minimize $k$-submodular functions is not known for the value-oracle model but is known for the valued-CSP model~\cite{Kolmogorov2015}.
Our result for (i) is applicable to such a case.
For (ii) (and (iii)), we consider a class of efficiently minimizable $k$-submodular functions considered in~\cite{IwataY2016}, where a $k$-submodular function in this class is represented by the cut function in a network of $\Order{kn}$ vertices and can be minimized by a minimum-cut computation.
We show that the PIP is naturally obtained from the residual graph of a maximum flow in the network (Theorems~\ref{thm:network_algo} and~\ref{thm:network_time}).
For (iii), we deal with a $k$-submodular function $\funcdoms{\tilde{g}}{\setprn{0, 1, 2, \ldots, k}^n}{\setR}$ obtained from a $k$-label Potts energy function $\funcdoms{g}{\setprn{1, 2, \ldots, k}^n}{\setR}$ by adding the $0$-label (meaning ``non-labeled'').
Such a $k$-submodular function, called \emph{Potts $k$-submodular}, is particularly useful in vision applications.
Indeed, via the \emph{persistency property}~\cite{Gridchyn2013, IwataY2016}, a minimizer of $g$ (an optimal labeling) is partly recovered from a minimizer of the relaxation $\tilde{g}$.
Gridchyn--Kolmogorov~\cite{Gridchyn2013} showed that a minimizer of a Potts $k$-submodular function can be obtained by $\Order{\log k}$ calls of a max-flow algorithm performed on a network of $\Order{n}$ vertices.
We show that the PIP is also obtained in the same time complexity (Theorem~\ref{thm:Potts}).
In showing this result, we reveal an intriguing structure of the PIP for a Potts $k$-submodular function (Theorem~\ref{thm:PIP_Potts}), and utilize results~\cite{Hirai2010, Ibaraki1998} from undirected multiflow theory.
We also discuss enumeration aspects for minimizers.
Maximal minimizers, which are minimizers with a maximum number of nonzero components, are of particular interest from the view of partial optimal labeling.
For a Potts $k$-submodular function, we show that the problem of enumerating all maximal minimizers reduces to the problem of enumerating all ideals of a single poset (Theorem~\ref{thm:enumeration_potts}).
This enables us to use an existing fast enumeration algorithm, and leads to a practical algorithm enumerating all maximal partial optimal labeling in actual computer vision problems.
We present experimental results for real instances of stereo matching problems.
\paragraph{Organization.}
The rest of this paper is organized as follows.
In Section~\ref{sec:preliminaries}, we give preliminaries including a Birkhoff-type representation theorem between PIPs and median semilattices.
In Section~\ref{sec:structure}, we prove the above-mentioned structural results.
In Section~\ref{sec:algorithms}, we prove algorithmic results.
Finally, in Section~\ref{sec:application}, we describe applications and present experimental results.
\section{Preliminaries}
\label{sec:preliminaries}
For a nonnegative integer $n$, we denote $\setprn{1, 2, \ldots, n}$ by $\intset{n}$ (with $\intset{0} \defeq \varnothing$).
For a subset $X$ of an ordered set, let $\min X$ denote the minimum element in $X$ (if it exists).
Let $\setR$ be the set of real numbers and $\overline{\setR} \defeq \setR \cup \setprn{+\infty}$.
For a function $f$ from a set $D$ to $\overline{\setR}$, a \emph{minimizer} of $f$ is an element $x \in D$ that satisfies $\app{f}{x} \leq \app{f}{y}$ for all $y \in D$.
The set of minimizers of $f$ is simply called the \emph{minimizer set} of $f$.
We assume that posets are always finite, and assume the standard notions of lattice theory, such as join $\join$ and meet $\meet$.
\subsection{$k$-submodular function}
Let $k$ be a positive integer.
Let $S_k$ denote $\setprn{0, 1, 2, \ldots, k}$.
The partial order $\preceq$ on $S_k$ is defined by $a \preceq b$ if and only if $a \in \setprn{0, b}$ for each $a, b \in S_k$.
Consider the $n$-product ${S_k}^n$ of $S_k$, where the partial order on ${S_k}^n$ is defined as the direct product of $\preceq$ and is also denoted by $\preceq$.
In this way, ${S_k}^n$ and its subsets are regarded as posets.
For $x = \paren{x_1, x_2, \ldots, x_n} \in {S_k}^n$, the \emph{support} of $x$ is the set of indices $i \in \intset{n}$ with nonzero $x_i$, and is denoted by $\mathop{\mathrm{supp}} x$:
\begin{align*}
\mathop{\mathrm{supp}} x \defeq \setprnsep{i \in \intset{n}}{x_i \neq 0}.
\end{align*}
A \emph{$k$-submodular function}~\cite{Huber2012} is a function $\funcdoms{f}{{S_k}^n}{\overline{\setR}}$ satisfying the following inequalities
\begin{align} \label{neq:k-submodularity}
\app{f}{x} + \app{f}{y} \geq \app{f}{x \mathbin\sqcap y} + \app{f}{x \mathbin\sqcup y}
\end{align}
for all $x, y \in {S_k}^n$.
Here the binary operation $\mathbin\sqcap$ on ${S_k}^n$ is given by
\begin{align} \label{def:sqmeet}
\paren{x \mathbin\sqcap y}_i \defeq \begin{cases}
\min \setprn{x_i, y_i} & \text{($x_i$ and $y_i$ are comparable with respect to $\preceq$)}, \\
0 & \text{($x_i$ and $y_i$ are incomparable with respect to $\preceq$)},
\end{cases}
\end{align}
for every $x, y \in {S_k}^n$ and $i \in \intset{n}$.
The operation $\mathbin\sqcup$ in \eqref{neq:k-submodularity} is defined by changing $\min$ to $\max$ in \eqref{def:sqmeet}.
Besides its recent introduction, a $k$-submodular function seems to be recognized when Bouchet~\cite{Bouchet1997} introduced \emph{multimatroids}.
Indeed, a $k$-submodular function is a direct generalization of the rank function of a multimatroid, and was suggested by Fujishige~\cite{Fujishige1995} in 1995 as a \emph{multisubmodular function}.
It is not known whether $k$-submodular functions for $k \geq 3$ can be minimized in polynomial time on the standard oracle model.
However, some special classes of $k$-submodular functions are efficiently minimizable.
For example, Kolmogorov--Thapper--\v{Z}ivn\'{y}~\cite{Kolmogorov2015} showed that a sum of low-arity $k$-submodular functions can be minimized in polynomial time, where the \emph{arity} of a function is the number of variables.
A nonnegative combination of binary \emph{basic $k$-submodular functions}, introduced by Iwata--Wahlstr\"{o}m--Yoshida~\cite{IwataY2016}, can be minimized by computing a minimum $\paren{s,t}$-cut on a directed network; see Section~\ref{sec:network}.
A nonempty subset of ${S_k}^n$ is said to be \emph{$\paren{\mathbin\sqcap, \mathbin\sqcup}$-closed} if it is closed under the operations $\mathbin\sqcap$ and $\mathbin\sqcup$.
From~\eqref{neq:k-submodularity}, the following obviously holds.
\begin{lemma}
The minimizer set of a $k$-submodular function is $\paren{\mathbin\sqcap, \mathbin\sqcup}$-closed.
\end{lemma}
\subsection{Median semilattice and PIP}
A key tool for providing a compact representation for $\paren{\mathbin\sqcap, \mathbin\sqcup}$-closed sets is a correspondence between median semilattices and PIPs, which was established by Barth\'{e}lemy--Constantin~\cite{Barthelemy1993}.
A recent paper~\cite{Chepoi2012} also contains an exposition of this correspondence.
A \emph{median semilattice}~\cite{Sholander1954} is a meet-semilattice $L = \paren{L, \leq}$ satisfying the following conditions:
\begin{namedenum}{MS}
\item Every principal ideal is a distributive lattice.
\item For all $x, y, z \in L$, if $x \join y ,\; y \join z$ and $z \join x$ exist, then $x \join y \join z$ exists in $L$.
\end{namedenum}
Note that every distributive lattice is a median semilattice.
An element of $L$ is said to be \emph{join-irreducible} if it is not minimum and is not represented as a join of other elements.
Let $\irreducibles{L}$ denote the set of join-irreducible elements of $L$.
Next we introduce a \emph{poset with inconsistent pairs (PIP)}.
A PIP~\cite{Ardila2011, Barthelemy1993, Nielsen1981} is a poset $P = \paren{P, \leq}$ endowed with an additional symmetric relation $\mathrel\smile$ satisfying the following conditions:
\begin{namedenum}{IC}
\item For all $p, q \in P$ with $p \mathrel\smile q$, there is no $r \in P$ with $p \leq r$ and $q \leq r$.
\item For all $p, q, p', q' \in P$, if $p' \leq p, q' \leq q$ and $p' \mathrel\smile q'$, then $p \mathrel\smile q$.
\end{namedenum}
A PIP is also denoted by a triple $\paren{P, \leq, \mathrel\smile}$.
The relation $\mathrel\smile$ is called an \emph{inconsistency relation}.
Each unordered pair $\setprn{p, q}$ of $P$ is called \emph{inconsistent} if $p \mathrel\smile q$.
Note that every inconsistent pair of $P$ is incomparable.
An inconsistent pair $\setprn{p, q}$ of $P$ is said to be \emph{minimally inconsistent} if $p' \leq p$, $q' \leq q$ and $p' \mathrel\smile q'$ imply $p = p'$ and $q = q'$ for all $p', q' \in P$.
If $\setprn{p, q}$ is minimally inconsistent, the $p \mathrel\smile q$ is particularly denoted by $p \mathrel{\overset{{}_{\scriptscriptstyle{\bullet}}}{\smile}} q$.
We can easily check the following properties of the minimal inconsistency relation:
\begin{namedenum}{MIC}
\item For all $p, q \in P$ with $p \mathrel{\overset{{}_{\scriptscriptstyle{\bullet}}}{\smile}} q$, there is no $r \in P$ with $p \leq r$ and $q \leq r$.
\item For all $p, q, p', q' \in P$ with $p' \leq p$ and $q' \leq q$, if $p' \mathrel{\overset{{}_{\scriptscriptstyle{\bullet}}}{\smile}} q'$ and $p \mathrel{\overset{{}_{\scriptscriptstyle{\bullet}}}{\smile}} q$, then $p' = p$ and $q' = q$.
\end{namedenum}
Actually, PIPs can also be defined as a triple $\paren{P, \leq, \mathrel{\overset{{}_{\scriptscriptstyle{\bullet}}}{\smile}}}$, where $\mathrel{\overset{{}_{\scriptscriptstyle{\bullet}}}{\smile}}$ is a binary symmetric relation on a poset $P = \paren{P, \leq}$ satisfying the conditions (MIC1) and (MIC2).
In this definition, the inconsistency relation $\mathrel\smile$ on $P$ is obtained by
\begin{align*}
\text{$p \mathrel\smile q$ if and only if there exist $p', q' \in P$ with $p' \leq p$, $q' \leq q$ and $p' \mathrel{\overset{{}_{\scriptscriptstyle{\bullet}}}{\smile}} q'$}
\end{align*}
for every $p, q \in P$.
Since both definitions of PIP are equivalent, we will use a convenient one.
For a PIP $P$, an ideal of $P$ is said to be \emph{consistent} if it contains no (minimally) inconsistent pair.
Let $\consideals{P}$ denote the family of consistent ideals of $P$.
Regard $\consideals{P}$ as a poset with respect to the inclusion order $\subseteq$.
\begin{figure}[tb]
\begin{minipage}[t][2.7cm][t]{0.33\linewidth}
\centering
\begin{tikzpicture}[every node/.style={circle, draw, scale=0.8}, x=15pt, y=20pt]
\node (a) at (0, 0) {};
\node (b) at (2, 0) {};
\node (c) at (1, 1) {};
\node[draw=none, scale=1.0] (p) at (0.4, 1) {$p$};
\node (d) at (4, 0) {};
\node (e) at (4, 1) {};
\node[draw=none, scale=1.0] (q) at (4.6, 1) {$q$};
\node (f) at (0, 2) {};
\node (g) at (2.5, 2) {};
\node[draw=none, scale=1.0] (r) at (2.5, 2.4) {$r$};
\foreach \u / \v in {a/c, b/c, d/e, c/f, c/g, e/g}
\draw[->, >=latex'] (\v) -- (\u);
\draw[line width=0.3mm, dash pattern=on .03mm off .8mm, line cap=round] (c) to (e);
\draw[line width=0.3mm, dash pattern=on .03mm off .8mm, line cap=round] (e) to (f);
\end{tikzpicture}
\subcaption{violating (IC1)}
\end{minipage}%
\begin{minipage}[t][2.7cm][t]{0.33\linewidth}
\centering
\begin{tikzpicture}[every node/.style={circle, draw, scale=0.8}, x=15pt, y=20pt]
\node (a) at (0, 0) {};
\node (b) at (2, 0) {};
\node (c) at (1, 1) {};
\node (d) at (4, 0) {};
\node[draw=none, scale=1.0] (p) at (4.6, 0) {$p$};
\node (e) at (4, 1) {};
\node[draw=none, scale=1.0] (qr) at (5.1, 1) {$q=r$};
\node (f) at (0, 2) {};
\foreach \u / \v in {a/c, b/c, d/e, c/f}
\draw[->, >=latex'] (\v) -- (\u);
\draw[line width=0.3mm, dash pattern=on .03mm off .8mm, line cap=round] (c) to (e);
\draw[line width=0.3mm, dash pattern=on .03mm off .8mm, line cap=round] (d) to [bend right=40] (e);
\draw[line width=0.3mm, dash pattern=on .03mm off .8mm, line cap=round] (e) to (f);
\end{tikzpicture}
\subcaption{violating (IC1)}
\end{minipage}%
\begin{minipage}[t][2.7cm][t]{0.33\linewidth}
\centering
\begin{tikzpicture}[every node/.style={circle, draw, scale=0.8}, x=15pt, y=20pt]
\node (a) at (0, 0) {};
\node (b) at (2, 0) {};
\node (c) at (1, 1) {};
\node (d) at (4, 0) {};
\node (e) at (4, 1) {};
\node (f) at (0, 2) {};
\foreach \u / \v in {a/c, b/c, d/e, c/f}
\draw[->, >=latex'] (\v) -- (\u);
\draw[densely dashed] (c) to (e);
\draw[line width=0.3mm, dash pattern=on .03mm off .8mm, line cap=round] (e) to (f);
\end{tikzpicture}
\subcaption{PIP}
\end{minipage}
%
\begin{minipage}[t][2.5cm][t]{0.5\linewidth}
\centering
\begin{tikzpicture}[every node/.style={circle, draw, scale=0.8}, x=15pt, y=20pt]
\node (a) at (0, 0) {};
\node (b) at (2, 0) {};
\node[draw=none, scale=1.0] (p') at (1.4, 0) {$p'$};
\node (c) at (1, 1) {};
\node[draw=none, scale=1.0] (p') at (0.4, 1) {$p$};
\node (d) at (4, 0) {};
\node[draw=none, scale=1.0] (p') at (4.65, 0) {$q'$};
\node (e) at (4, 1) {};
\node[draw=none, scale=1.0] (p') at (4.65, 1) {$q$};
\node (f) at (0, 2) {};
\foreach \u / \v in {a/c, b/c, d/e, c/f}
\draw[->, >=latex'] (\v) -- (\u);
\draw[line width=0.3mm, dash pattern=on .03mm off .8mm, line cap=round] (b) to (d);
\end{tikzpicture}
\subcaption{violating (IC2)}
\end{minipage}%
\begin{minipage}[t][2.5cm][t]{0.5\linewidth}
\centering
\begin{tikzpicture}[every node/.style={circle, draw, scale=0.8}, x=15pt, y=20pt]
\node (a) at (0, 0) {};
\node (b) at (2, 0) {};
\node (c) at (1, 1) {};
\node (d) at (4, 0) {};
\node (e) at (4, 1) {};
\node (f) at (0, 2) {};
\foreach \u / \v in {a/c, b/c, d/e, c/f}
\draw[->, >=latex'] (\v) -- (\u);
\foreach \u / \v in {b/e, d/c, d/f, c/e, e/f}
\draw[line width=0.3mm, dash pattern=on .03mm off .8mm, line cap=round] (\v) -- (\u);
\draw[densely dashed] (b) to (d);
\end{tikzpicture}
\subcaption{PIP}
\end{minipage}
%
\caption{
Examples of PIPs and non-PIP structures.
Solid arrows indicate the orders between elements (drawn from higher elements to lowers).
Dotted lines and dashed lines indicate the inconsistency relations.
In (a), (b) and (d), labeled elements indicate where the violations of (IC1) and (IC2) are.
In (c) and (e), the minimal inconsistency relations are drawn by dashed lines.
}
\label{fig:pip}
\end{figure}
Figure~\ref{fig:pip} shows examples of PIPs and non-PIP structures.
The following theorem establishes a one-to-one correspondence between median semilattices and PIPs.
\begin{theorem}[{\cite[Theorem 2.16]{Barthelemy1993}}] \label{thm:median_semilattice_and_pip}
\begin{enumerate}
\item Let $L = \paren{L, \leq}$ be a median semilattice and $\mathrel\smile$ a symmetric binary relation on $L$ defined by
%
\begin{align*}
\text{$x \mathrel\smile y$ if and only if $x \join y$ does not exist in $L$}
\end{align*}
%
for every $x, y \in L$.
Then $\paren{\irreducibles{L}, \leq, \mathrel\smile}$ forms a PIP with inconsistency relation $\mathrel\smile$.
The consistent ideal family $\consideals{\irreducibles{L}}$ is isomorphic to $L$, and an isomorphism is given by $I \mapsto \bigjoin_{x \in I} x$ for $I \neq \varnothing$ and $\varnothing \mapsto \min L$.
\item Let $P$ be a PIP.
The consistent ideal family $\consideals{P}$ forms a median semilattice.
The PIP $\paren{\irreducibles{\consideals{P}}, \subseteq, \mathrel\smile}$ obtained in the same way as (1) is isomorphic to $P$.
\end{enumerate}
\end{theorem}
The latter part of Theorem~\ref{thm:median_semilattice_and_pip}~(2) is implicit in~\cite{Barthelemy1993}, and follows from Theorem~\ref{thm:median_semilattice_and_pip}~(1) and the fact that for PIPs $P$ and $P'$, if $\consideals{P}$ and $\consideals{P'}$ are isomorphic, then $P$ and $P'$ are also isomorphic~\cite[p.57]{Barthelemy1993}.
\begin{remark} \label{lem:pip_and_cnf}
A PIP is an alternative expression of a satisfiable Boolean 2-CNF, where consistent ideals correspond to true assignments.
Indeed, for a PIP $\paren{P, \leq, \mathrel\smile}$ with $P = \intset{n}$, consider the following 2-CNF of Boolean variables $x_1, x_2, \dots, x_n \in \setprn{0, 1}$:
%
\begin{align*}
\paren{\bigland_\condition{i,j \in P}{i < j} x_i \lor \bar{x}_j}
\land
\paren{\bigland_\condition{i,j \in P}{i \mathrel\smile j} \bar{x}_i \lor \bar{x}_j}.
\end{align*}
%
Then an assignment $\paren{x_1, x_2, \ldots, x_n} \in \setprn{0, 1}^n$ is true if and only if the set of elements $i \in P$ with $x_i = 1$ is a consistent ideal.
The reverse construction of a PIP from a 2-CNF satisfiable at $\paren{0, 0, \ldots, 0}$ is also easily verified.
\end{remark}
\section{$\paren{\mathbin\sqcap, \mathbin\sqcup}$-closed set and elementary PIP}
\label{sec:structure}
The starting point for a compact representation for $\paren{\mathbin\sqcap, \mathbin\sqcup}$-closed sets is the following.
\begin{lemma} \label{lem:closed_set_is_median_semilattice}
Every $\paren{\mathbin\sqcap, \mathbin\sqcup}$-closed set is a median semilattice.
\end{lemma}
\begin{proof}
Let $M \subseteq {S_k}^n$ be a $\paren{\mathbin\sqcap, \mathbin\sqcup}$-closed set.
Then $M$ is a semilattice since ${S_k}^n$ is a semilattice with minimum element $\bm{0} \defeq \paren{0, 0, \ldots, 0} \in {S_k}^n$, and the operator $\mathbin\sqcap$ coincides with $\meet$ on ${S_k}^n$.
We show that $M$ satisfies the conditions (MS1) and (MS2).
(MS1).
Let $I$ be the principal ideal of $x \in M$.
For all $y \in I$ and $i \in \intset{n}$, $y_i$ is equal to either 0 or $x_i$.
Therefore, for all $y, z \in I$, the join $y \join z$ exists and it holds $y \join z = y \mathbin\sqcup z \in I$.
Next let $\funcdoms{\phi}{I}{\Power{\intset{n}}}$ be an injection defined by $\app{\phi}{y} \defeq \mathop{\mathrm{supp}} y$ for every $y \in I$.
One can easily see that $\app{\phi}{y \meet z} = \app{\phi}{y} \cap \app{\phi}{z}$ and $\app{\phi}{y \join z} = \app{\phi}{y} \cup \app{\phi}{z}$ for every $y, z \in I$.
In other words, $\phi$ is an isomorphism from $\paren{I, \preceq}$ to $\paren{\app{\phi}{I}, \subseteq}$.
Since any nonempty subset of $\Power{\intset{n}}$ closed under $\cap$ and $\cup$ is a distributive lattice ordered by inclusion, $I$ is also distributive.
(MS2).
Let $x, y, z \in M$ be such that the join of any two of them exists in $M$.
Since $x_i, y_i$ and $z_i$ are comparable for any $i \in \intset{n}$, the join $x \join y \join z$ exists in ${S_k}^n$, and coincides with $x \mathbin\sqcup y \mathbin\sqcup z$.
Finally since $M$ is closed under $\mathbin\sqcup$, the join $x \join y \join z$ belongs to $M$.
\end{proof}
Let $\mathrel\smile$ be a symmetric binary relation on ${S_k}^n$ defined by
\begin{align*}
\text{$x \mathrel\smile y$ if and only if $x \join y$ does not exist in ${S_k}^n$}
\end{align*}
for every $x, y \in {S_k}^n$.
Note that for every $x, y \in M$, if $x \not\mathrel\smile y$ then $x \join y$ is equal to $x \mathbin\sqcup y$.
From Theorem~\ref{thm:median_semilattice_and_pip}~(1) and Lemma~\ref{lem:closed_set_is_median_semilattice}, we obtain the following.
\begin{theorem} \label{thm:closed_set_and_pip}
Let $M$ be a $\paren{\mathbin\sqcap, \mathbin\sqcup}$-closed set.
Then $\paren{\irreducibles{M}, \preceq, \mathrel\smile}$ forms a PIP with inconsistency relation $\mathrel\smile$.
The consistent ideal family $\consideals{\irreducibles{M}}$ is isomorphic to $M$, and the isomorphism is given by $I \mapsto \bigjoin_{x \in I} x$ for $I \neq \varnothing$ and $\varnothing \mapsto \min M$.
\end{theorem}
\begin{figure}[t]
\begin{minipage}[t][3cm][t]{0.5\linewidth}
\centering
\begin{tikzpicture}[every node/.style={rectangle, draw, scale=0.8}, x=40pt, y=20pt]
\node [] (000) at ( 0, 0) {00002};
\node [double] (100) at (-1, 1) {13002};
\node [double] (001) at ( 1, 1) {00012};
\node [double] (110) at (-1.5, 2) {13102};
\node [] (101) at (-0.5, 2) {13012};
\node [double] (120) at ( 0.5, 2) {13202};
\node [double] (031) at ( 1.5, 2) {00312};
\node [] (111) at (-1.5, 3) {13112};
\node [] (121) at (-0.5, 3) {13212};
\node [] (131) at ( 0.5, 3) {13312};
\node [double] (231) at ( 1.5, 3) {22312};
\foreach \u / \v in {
000/100, 000/001, 100/110, 100/101, 100/120, 001/101, 001/031,
110/111, 101/111, 101/121, 101/131, 120/121, 031/131, 031/231}
\draw[->, >=latex'] (\v) -- (\u);
\end{tikzpicture}
\subcaption{a $(\mathbin\sqcap, \mathbin\sqcup)$-closed set on ${S_3}^5$}
\end{minipage}%
\begin{minipage}[t][3cm][t]{0.5\linewidth}
\centering
\begin{tikzpicture}[every node/.style={rectangle, draw, double, scale=0.8}, x=35pt, y=25pt]
\node (100) at (-1, 0.5) {13002};
\node (110) at (-1.5, 1.5) {13102};
\node (120) at (-0.5, 1.5) {13202};
\node (001) at ( 1, 0) {00012};
\node (031) at ( 1, 1) {00312};
\node (231) at ( 1, 2) {22312};
\foreach \u / \v in {100/110, 100/120, 001/031, 031/231}
\draw[->, >=latex'] (\v) -- (\u);
\foreach \u / \v in {110/120, 120/031, 100/231}
\draw[densely dashed] (\v) -- (\u);
\draw[densely dashed] (110) to [bend right=17] (031);
\end{tikzpicture}
\subcaption{the PIP corresponding to (a)}
\end{minipage}
%
\caption{
Example of a $(\mathbin\sqcap, \mathbin\sqcup)$-closed set and the corresponding PIP.
In (a), elements surrounded by double-lined frames are join-irreducible.
In (b), non-minimal inconsistency relations are not drawn.
}
\label{fig:example_of_closed_set_and_pip}
\end{figure}
Figure~\ref{fig:example_of_closed_set_and_pip} shows an example of a $(\mathbin\sqcap, \mathbin\sqcup)$-closed set and the corresponding PIP.
From Theorem~\ref{thm:closed_set_and_pip}, it will turn out that the set $\irreducibles{M}$ of join-irreducible elements of every $\paren{\mathbin\sqcap, \mathbin\sqcup}$-closed set $M$ does not lose any information about the structure of $M$.
That is, non-minimum elements in $M$ can be obtained as the join of one or more join-irreducible elements of $M$ (notice that we cannot obtain the minimum element of $M$ in this way).
Therefore we call $\irreducibles{M}$ a \emph{PIP-representation} of $M$.
Furthermore, the following proposition, which will be proved in Section~\ref{sec:proof_of_theorem_1}, says that this representation is actually compact.
\begin{proposition} \label{prop:number_of_irreducibles}
Let $M$ be a $\paren{\mathbin\sqcap, \mathbin\sqcup}$-closed set on ${S_k}^n$.
The number of join-irreducible elements of $M$ is at most $kn$.
\end{proposition}
Theorem~\ref{thm:closed_set_and_pip} states that any $\paren{\mathbin\sqcap, \mathbin\sqcup}$-closed set can be represented by a PIP.
However, not all PIPs correspond to some $\paren{\mathbin\sqcap, \mathbin\sqcup}$-closed sets.
A natural question then arises: \textit{What class of PIPs represents $\paren{\mathbin\sqcap, \mathbin\sqcup}$-closed sets?}
The main result (Theorem~\ref{thm:closed_set_and_elementary_pip}) of this section answers this question.
\begin{definition} \label{def:elementary}
A PIP $P = \paren{P, \leq}$ is called \emph{elementary} if it satisfies the following conditions:
%
\begin{namedenum}{EP}
\item[(EP0)] $P$ is the disjoint union of $P_1, P_2, \ldots, P_n$ such that every pair $\setprn{x, y} \subseteq P$ of distinct elements is minimally inconsistent if and only if $\setprn{x, y} \subseteq P_i$ for some $i \in \intset{n}$.
\item[(EP1)] For any distinct $i, j \in \intset{n}$, if $\absprn{P_i} \geq 2$ and $P_j = \setprn{y}$, there is no element $x \in P_i$ with $x < y$.
\item[(EP2)] For any distinct $i, j \in \intset{n}$, if $\absprn{P_i} \geq 2$ and $\absprn{P_j} \geq 2$, either of the following two holds:
%
\begin{namedenum}{EP}
\item[(EP2-1)] Every pair of $x \in P_i$ and $y \in P_j$ is not comparable.
\item[(EP2-2)] There exist $x^\circ \in P_i$ and $y^\circ \in P_j$ such that $x^\circ < y$ and $y^\circ < x$ for all $x \in P_i \setminus \setprn{x^\circ}$ and $y \in P_j \setminus \setprn{y^\circ}$.
\end{namedenum}
\end{namedenum}
\end{definition}
\begin{figure}[t]
\begin{minipage}[t][1.9cm][t]{0.25\linewidth}
\centering
\begin{tikzpicture}[every node/.style={circle, draw, scale=0.8}, x=20pt, y=20pt]
\node (01) at (0, 0) {};
\node (02) at (1, 0) {};
\node (03) at (2, 0) {};
\node[fill] (10) at (0, 1) {};
\draw[->, >=latex'] (10) -- (01);
\draw[densely dashed] (01) -- (02);
\draw[densely dashed] (02) -- (03);
\draw[densely dashed] (01.south east) to [bend right=25] (03.south west);
\end{tikzpicture}
\subcaption{violating (EP1)}
\end{minipage}%
\begin{minipage}[t][1.9cm][t]{0.25\linewidth}
\centering
\begin{tikzpicture}[every node/.style={circle, draw, scale=0.8}, x=20pt, y=20pt]
\node (01) at (0, 1) {};
\node (02) at (1, 1) {};
\node (03) at (2, 1) {};
\node[fill] (10) at (0, 0) {};
\draw[->, >=latex'] (01) -- (10);
\draw[densely dashed] (01) -- (02);
\draw[densely dashed] (02) -- (03);
\draw[densely dashed] (01.north east) to [bend left=25] (03.north west);
\end{tikzpicture}
\subcaption{elementary}
\end{minipage}%
\begin{minipage}[t][1.9cm][t]{0.25\linewidth}
\centering
\begin{tikzpicture}[every node/.style={circle, draw, scale=0.8}, x=20pt, y=20pt]
\node (10) at (0, 0) {};
\node (20) at (1, 0) {};
\node (30) at (2, 0) {};
\node[fill] (01) at (0, 1) {};
\node[fill] (02) at (1, 1) {};
\node[fill] (03) at (2, 1) {};
\draw[->, >=latex'] (01) -- (10);
\draw[->, >=latex'] (02) -- (20);
\draw[->, >=latex'] (03) -- (30);
\draw[densely dashed] (01) -- (02);
\draw[densely dashed] (02) -- (03);
\draw[densely dashed] (01.north east) to [bend left=25] (03.north west);
\draw[densely dashed] (10) -- (20);
\draw[densely dashed] (20) -- (30);
\draw[densely dashed] (10.south east) to [bend right=25] (30.south west);
\end{tikzpicture}
\subcaption{violating (EP2)}
\end{minipage}%
\begin{minipage}[t][1.9cm][t]{0.25\linewidth}
\centering
\begin{tikzpicture}[every node/.style={circle, draw, scale=0.8}, x=20pt, y=20pt]
\node (10) at ( 0, 0) {};
\node[draw=none, scale=1.0] (x) at (-0.5, 0.05) {$x^\circ$};
\node[fill] (02) at (-0.5, 1) {};
\node[fill] (03) at ( 0.5, 1) {};
\node[fill] (01) at ( 2, 0) {};
\node[draw=none, scale=1.0] (x) at (2.5, 0.05) {$y^\circ$};
\node (20) at ( 1.5, 1) {};
\node (30) at ( 2.5, 1) {};
\draw[->, >=latex'] (02) -- (10);
\draw[->, >=latex'] (03) -- (10);
\draw[->, >=latex'] (20) -- (01);
\draw[->, >=latex'] (30) -- (01);
\draw[densely dashed] (01) -- (03);
\draw[densely dashed] (02) -- (03);
\draw[densely dashed] (02) to [bend right=10] (01);
\draw[densely dashed] (10) -- (20);
\draw[densely dashed] (20) -- (30);
\draw[densely dashed] (10) to [bend right=10] (30);
\end{tikzpicture}
\subcaption{elementary}
\end{minipage}
\caption{
Examples of elementary PIPs and non-elementary PIPs.
In all diagrams, the drawn PIPs satisfy the condition (EP0) with $n = 2$.
Each element is filled or not filled according to the corresponding part $P_i$.
Non-minimal inconsistency relations are not drawn in each diagram.
}
\label{fig:example_of_elementary_pip}
\end{figure}
Figure~\ref{fig:example_of_elementary_pip} shows examples of elementary PIPs and non-elementary PIPs.
\begin{theorem} \label{thm:closed_set_and_elementary_pip}
\begin{enumerate}
\item For every $\paren{\mathbin\sqcap, \mathbin\sqcup}$-closed set $M$, the PIP $\paren{\irreducibles{M}, \preceq, \mathrel\smile}$ is elementary.
\item For every elementary PIP $P$, there is a $\paren{\mathbin\sqcap, \mathbin\sqcup}$-closed set $M$ isomorphic to $\consideals{P}$.
\end{enumerate}
\end{theorem}
An elementary PIP corresponds to a $\paren{\mathbin\sqcap, \mathbin\sqcup}$-closed set on the product of the most ``elementary'' median semilattice $S_k$, whereas general PIP can represent an arbitrary median semilattice (by Theorem~\ref{thm:median_semilattice_and_pip}).
This is why we use the term ``elementary.''
\begin{remark}
Consider an elementary PIP $P$ with the property that each $P_i$ has the cardinality at most 2.
Such a PIP arises from $\paren{\mathbin\sqcap, \mathbin\sqcup}$-closed sets on ${S_2}^n$.
If we assign a sign $+,-$ to each element so that two nodes in $P_i$ have a different sign, then the PIP is equivalently transformed into a \emph{signed poset}~\cite{Reiner1993}, which is a certain ``acyclic and transitive'' bidirected graph and is used by Ando--Fujishige~\cite{Ando1994} for representing $\paren{\mathbin\sqcap, \mathbin\sqcup}$-closed sets in ${S_2}^n$.
Then \emph{ideals} in the signed poset correspond to consistent ideals in the original PIP.
In the transformation, elements in the signed poset are nonempty members in $P_1, P_2, \ldots, P_n$.
Bidirected edges are given according to an appropriate rule; one can guess the rule from the example in Figure~\ref{fig:example_of_signed_poset}. (In this figure, we omit redundant edges derived from the transitive closure.)
In this way, one can see that the PIP-representation for $\paren{\mathbin\sqcap, \mathbin\sqcup}$-closed sets on ${S_2}^n$ is equivalent to the one by Ando--Fujishige~\cite{Ando1994}.
\begin{figure}[t]
\begin{minipage}[t][3.4cm][t]{0.5\linewidth}
\centering
\begin{tikzpicture}[every node/.style={circle, draw, scale=0.8}, x=10pt, y=10pt]
\node[label={[label distance=-15pt]\tiny $+$}] (1p) at (-1, 0) {};
\node[label={[label distance=-15pt]\tiny $-$}] (1n) at ( 1, 0) {};
\node[draw, rectangle, rounded corners=5pt, minimum width=50pt, minimum height=20pt, densely dotted, label=right:{\small $P_1$}] at (0, 0) {};
\draw[densely dashed] (1p) -- (1n);
\node[label={[label distance=-15pt]\tiny $+$}] (2p) at (-2, -2) {};
\node[label={[label distance=-15pt]\tiny $-$}] (2n) at (-4, -2) {};
\node[draw, rectangle, rounded corners=5pt, minimum width=50pt, minimum height=20pt, densely dotted, label=left:{\small $P_2$}] at (-3, -2) {};
\draw[densely dashed] (2p) -- (2n);
\node[label={[label distance=-15pt]\tiny $+$}] (3p) at ( 2, -2) {};
\node[label={[label distance=-15pt]\tiny $-$}] (3n) at ( 4, -2) {};
\node[draw, rectangle, rounded corners=5pt, minimum width=50pt, minimum height=20pt, densely dotted, label=right:{\small $P_3$}] at (3, -2) {};
\node[label={[label distance=-15pt]\tiny $+$}] (4) at ( 0, -4) {};
\node[draw, rectangle, rounded corners=5pt, minimum width=20pt, minimum height=20pt, densely dotted, label=right:{\small $P_4$}] at (0, -4) {};
\draw[densely dashed] (3p) -- (3n);
\node[label={[label distance=-15pt]\tiny $-$}] (5) at (-3, -6) {};
\node[draw, rectangle, rounded corners=5pt, minimum width=20pt, minimum height=20pt, densely dotted, label=left:{\small $P_5$}] at (-3, -6) {};
\node[label={[label distance=-15pt]\tiny $+$}] (6) at ( 3, -6) {};
\node[draw, rectangle, rounded corners=5pt, minimum width=20pt, minimum height=20pt, densely dotted, label=right:{\small $P_6$}] at (3, -6) {};
%
\draw[->, >=latex'] (1p) -- (2n);
\draw[->, >=latex'] (1p) -- (3p);
\draw[->, >=latex'] (2p) -- (1n);
\draw[->, >=latex'] (3n) -- (1n);
\draw[->, >=latex'] (2p) -- (4);
\draw[->, >=latex'] (2n) -- (4);
\draw[->, >=latex'] (3p) -- (4);
\draw[->, >=latex'] (4) -- (5);
\draw[->, >=latex'] (4) -- (6);
\end{tikzpicture}
\subcaption{an elementary PIP with assigned signs}
\end{minipage}%
\begin{minipage}[t][3.4cm][t]{0.5\linewidth}
\centering
\begin{tikzpicture}[every node/.style={circle, draw, scale=0.8}, x=10pt, y=10pt]
\node[draw, rectangle, rounded corners=5pt, minimum width=20pt, minimum height=20pt, densely dotted] (1) at (0, 0) {\small $P_1$};
\node[draw, rectangle, rounded corners=5pt, minimum width=20pt, minimum height=20pt, densely dotted] (2) at (-3, -2) {\small $P_2$};
\node[draw, rectangle, rounded corners=5pt, minimum width=20pt, minimum height=20pt, densely dotted] (3) at ( 3, -2) {\small $P_3$};
\node[draw, rectangle, rounded corners=5pt, minimum width=20pt, minimum height=20pt, densely dotted] (4) at ( 0, -4) {\small $P_4$};
\node[draw, rectangle, rounded corners=5pt, minimum width=20pt, minimum height=20pt, densely dotted] (5) at (-3, -6) {\small $P_5$};
\node[draw, rectangle, rounded corners=5pt, minimum width=20pt, minimum height=20pt, densely dotted] (6) at ( 3, -6) {\small $P_6$};
%
\draw[font=\tiny] (1) to node [draw=none, very near start, xshift=-2pt, yshift=4pt] {$+$} node [draw=none, very near end, xshift=-2pt, yshift=4pt] {$+$} (2);
\draw[font=\tiny] (1) to node [draw=none, very near start, xshift=2pt, yshift=4pt] {$+$} node [draw=none, very near end, xshift=2pt, yshift=4pt] {$-$} (3);
\draw[shorten >= -2pt, font=\tiny, bend left=10] (2) to node [draw=none, very near start, xshift=2pt, yshift=4pt] {$+$} node [draw=none, very near end, xshift=4pt, yshift=2pt] {$-$} (4);
\draw[shorten <= -2pt, font=\tiny, bend right=10] (2) to node [draw=none, very near start, xshift=-5pt, yshift=-2pt] {$-$} node [draw=none, very near end, xshift=-1.5pt, yshift=-4pt] {$-$} (4);
\draw[font=\tiny] (3) to node [draw=none, very near start, xshift=-2pt, yshift=4pt] {$+$} node [draw=none, very near end, xshift=-2pt, yshift=4pt] {$-$} (4);
\draw[font=\tiny] (4) to node [draw=none, very near start, xshift=-2pt, yshift=4pt] {$+$} node [draw=none, very near end, xshift=-2pt, yshift=4pt] {$+$} (5);
\draw[font=\tiny] (4) to node [draw=none, very near start, xshift=2pt, yshift=4pt] {$+$} node [draw=none, very near end, xshift=2pt, yshift=4pt] {$-$} (6);
\draw[font=\tiny] (4) to [loop, in=240, out=300, looseness=5] node [draw=none, very near start, xshift=-5pt, yshift=3pt] {$-$} node [draw=none, very near end, xshift=5pt, yshift=3pt] {$-$} (4);
\draw[font=\tiny] (5) to [loop, in=150, out=210, looseness=4] node [draw=none, very near start, xshift=4pt, yshift=-4pt] {$+$} node [draw=none, very near end, xshift=4pt, yshift=4pt] {$+$} (5);
\draw[font=\tiny] (6) to [loop, in=-30, out=30, looseness=4] node [draw=none, very near start, xshift=-4pt, yshift=4pt] {$-$} node [draw=none, very near end, xshift=-4pt, yshift=-4pt] {$-$} (6);
\end{tikzpicture}
\subcaption{the singed poset corresponding to (a)}
\end{minipage}
\caption{Example of an elementary PIP on ${S_2}^n$ and the corresponding signed poset.}
\label{fig:example_of_signed_poset}
\end{figure}
\end{remark}
The following corollary of Theorem~\ref{thm:median_semilattice_and_pip}~(2) and Theorem~\ref{thm:closed_set_and_elementary_pip}~(1) will be used in Section~\ref{sec:algorithms}.
\begin{corollary} \label{cor:elementary_pip}
Let $P$ be a PIP.
If $\consideals{P}$ is isomorphic to some $\paren{\mathbin\sqcap, \mathbin\sqcup}$-closed set, then $P$ is elementary.
\end{corollary}
The remaining part of this section is devoted to proving Theorem~\ref{thm:closed_set_and_elementary_pip}.
To get a motivation behind the properties of elementary PIPs which we prove below, readers may choose to read Algorithm~\ref{alg:get_irreducibles_minimizers} in Section~\ref{sec:minimizing_oracle} first.
\subsection{Proof of Theorem~\ref{thm:closed_set_and_elementary_pip}~(1)}
\label{sec:proof_of_theorem_1}
The proof of Theorem~\ref{thm:closed_set_and_elementary_pip}~(1) is outlined as follows:
\begin{enumerate}
\item[1.] First we define the \emph{differential} of a join-irreducible element $x$ as the difference between $x$ and the unique lower cover $x'$ of $x$.
\item[2.] Next we introduce a \emph{normalized} $\paren{\mathbin\sqcap, \mathbin\sqcup}$-closed set, which is a $\paren{\mathbin\sqcap, \mathbin\sqcup}$-closed set such that every differential has exactly one nonzero component.
We show that every $\paren{\mathbin\sqcap, \mathbin\sqcup}$-closed set is isomorphic to some normalized $\paren{\mathbin\sqcap, \mathbin\sqcup}$-closed set.
This set gives us a natural partition of join-irreducible elements.
\item[3.] Finally we construct an elementary PIP from the partition.
\end{enumerate}
A $\paren{\mathbin\sqcap, \mathbin\sqcup}$-closed set $M$ is said to be \emph{simple} if $\min M = \bm{0}$.
Any $\paren{\mathbin\sqcap, \mathbin\sqcup}$-closed set can be converted to a simple $\paren{\mathbin\sqcap, \mathbin\sqcup}$-closed set without any structural change.
\begin{definition} \label{def:differential}
Let $M \subseteq {S_k}^n$ be a simple $\paren{\mathbin\sqcap, \mathbin\sqcup}$-closed set.
For $x, y \in M$, we say that $y$ is a \emph{lower cover} of $x$, or \emph{$x$ covers $y$}, if $y \prec x$ and there is no $z \in M$ such that $y \prec z \prec x$.
For a join-irreducible element $x \in \irreducibles{M}$, there uniquely exists $y \in M$ covered by $x$.
The \emph{differential} $\bar{x} \in {S_k}^n$ of $x$ is defined by $\bar{x}_i \defeq x_i$ if $x_i \succ y_i = 0$ and $\bar{x}_i \defeq 0$ if $x_i = y_i$, for each $i \in \intset{n}$.
\end{definition}
The uniqueness of a lower cover of a join-irreducible element $x \in \irreducibles{M}$ can be seen from the fact that if $x$ has two or more lower covers, then $x$ is obtained as the join of these lower covers.
\begin{figure}[t]
\begin{minipage}[t][3.7cm][t]{0.5\linewidth}
\centering
\begin{tikzpicture}[every node/.style={rectangle, draw, scale=0.8}, x=40pt, y=20pt]
\node [] (000) at ( 0, 0) {0000};
\node [double] (100) at (-1, 1) {1300};
\node [double] (001) at ( 1, 1) {0001};
\node [double] (110) at (-1.5, 2) {1310};
\node [] (101) at (-0.5, 2) {1301};
\node [double] (120) at ( 0.5, 2) {1320};
\node [double] (031) at ( 1.5, 2) {0031};
\node [] (111) at (-1.5, 3) {1311};
\node [] (121) at (-0.5, 3) {1321};
\node [] (131) at ( 0.5, 3) {1331};
\node [double] (231) at ( 1.5, 3) {2231};
\foreach \u / \v in {
000/100, 000/001, 100/110, 100/101, 100/120, 001/101, 001/031,
110/111, 101/111, 101/121, 101/131, 120/121, 031/131, 031/231}
\draw[->, >=latex'] (\v) -- (\u);
\end{tikzpicture}
\subcaption{a simple $(\mathbin\sqcap, \mathbin\sqcup)$-closed set on ${S_3}^4$}
\end{minipage}%
\begin{minipage}[t][3.7cm][t]{0.5\linewidth}
\centering
\begin{tikzpicture}[every node/.style={rectangle, draw, double, scale=0.7, text width=width("1300")}, x=35pt, y=30pt]
\node (100) at (-1, 0.5) {1300\\\textit{1300}};
\node (110) at (-1.5, 1.5) {1310\\\textit{0010}};
\node (120) at (-0.5, 1.5) {1320\\\textit{0020}};
\node (001) at ( 1, 0) {0001\\\textit{0001}};
\node (031) at ( 1, 1) {0031\\\textit{0030}};
\node (231) at ( 1, 2) {2231\\\textit{2200}};
\foreach \u / \v in {100/110, 100/120, 001/031, 031/231}
\draw[->, >=latex'] (\v) -- (\u);
\foreach \u / \v in {110/120, 120/031, 100/231}
\draw[densely dashed] (\v) -- (\u);
\draw[densely dashed] (110) to [bend right=20] (031);
\end{tikzpicture}
\subcaption{the PIP corresponding to (a)}
\end{minipage}
%
\begin{minipage}[t][3.3cm][t]{0.5\linewidth}
\centering
\begin{tikzpicture}[every node/.style={rectangle, draw, scale=0.8}, x=40pt, y=20pt]
\node [] (000) at ( 0, 0) {000};
\node [double] (100) at (-1, 1) {100};
\node [double] (001) at ( 1, 1) {001};
\node [double] (110) at (-1.5, 2) {110};
\node [] (101) at (-0.5, 2) {101};
\node [double] (120) at ( 0.5, 2) {120};
\node [double] (031) at ( 1.5, 2) {031};
\node [] (111) at (-1.5, 3) {111};
\node [] (121) at (-0.5, 3) {121};
\node [] (131) at ( 0.5, 3) {131};
\node [double] (231) at ( 1.5, 3) {231};
\foreach \u / \v in {
000/100, 000/001, 100/110, 100/101, 100/120, 001/101, 001/031,
110/111, 101/111, 101/121, 101/131, 120/121, 031/131, 031/231}
\draw[->, >=latex'] (\v) -- (\u);
\end{tikzpicture}
\subcaption{a normalized $(\mathbin\sqcap, \mathbin\sqcup)$-closed set on ${S_3}^3$}
\end{minipage}%
\begin{minipage}[t][3.3cm][t]{0.5\linewidth}
\centering
\begin{tikzpicture}[every node/.style={rectangle, draw, scale=0.7, double, text width=width("100")}, x=35pt, y=30pt]
\node (100) at (-1, 0.5) {100\\\textit{100}};
\node (110) at (-1.5, 1.5) {110\\\textit{010}};
\node (120) at (-0.5, 1.5) {120\\\textit{020}};
\node (001) at ( 1, 0) {001\\\textit{001}};
\node (031) at ( 1, 1) {031\\\textit{030}};
\node (231) at ( 1, 2) {231\\\textit{200}};
\foreach \u / \v in {100/110, 100/120, 001/031, 031/231}
\draw[->, >=latex'] (\v) -- (\u);
\foreach \u / \v in {110/120, 120/031, 100/231}
\draw[densely dashed] (\v) -- (\u);
\draw[densely dashed] (110) to [bend right=20] (031);
\end{tikzpicture}
\subcaption{the PIP corresponding to (c)}
\end{minipage}
%
\caption{
Examples of a simple $(\mathbin\sqcap, \mathbin\sqcup)$-closed set, a normalized set and the corresponding PIPs.
In (b) and (d), the differential of each join-irreducible element is written in italics.
}
\label{fig:example_of_differential_and_normalizing}
\end{figure}
Figure~\ref{fig:example_of_differential_and_normalizing}~(a) and (b) show examples of a simple $\paren{\mathbin\sqcap, \mathbin\sqcup}$-closed set and the corresponding PIP, respectively.
We show some properties about differentials.
In what follows, we denote the subset $\setprnsep{x \in M}{x_i = \alpha}$ by $\partfix{M}{i}{\alpha}$ for $i \in \intset{n}$ and $\alpha \in \intset{k}$.
Note that $\partfix{M}{i}{\alpha}$ also forms a $\paren{\mathbin\sqcap, \mathbin\sqcup}$-closed set if $\partfix{M}{i}{\alpha} \neq \varnothing$.
\begin{lemma} \label{lem:differential}
Let $M \subseteq {S_k}^n$ be a simple $\paren{\mathbin\sqcap, \mathbin\sqcup}$-closed set.
The following hold:
%
\begin{enumerate}
\item For every $i \in \intset{n}$ and $\alpha \in \intset{k}$ with $\partfix{M}{i}{\alpha} \neq \varnothing$, $x \defeq \min \partfix{M}{i}{\alpha}$ is join-irreducible in $M$ and $\bar{x}_i = \alpha$ holds.
\item For every $x \in \irreducibles{M}$ and $i \in \intset{n}$ with $\alpha \defeq \bar{x}_i \neq 0$, it holds $x = \min \partfix{M}{i}{\alpha}$.
\item For every $i \in \intset{n}$ and $\alpha \in \intset{k}$, there is at most one join-irreducible element $x \in \irreducibles{M}$ such that $\bar{x}_i = \alpha$.
\item For every $x \in \irreducibles{M}$, the differential $\bar{x}$ of $x$ has at least one nonzero component.
\item The map $x \mapsto \bar{x}$ is an injection from $\irreducibles{M}$ to ${S_k}^n$.
\end{enumerate}
\end{lemma}
\begin{proof}
(1).
Let $i \in \intset{n} ,\; \alpha \in \intset{k}$ and $x \defeq \min \partfix{M}{i}{\alpha}$.
Suppose to the contrary that $x \notin \irreducibles{M}$.
Then there exist $y, z \in M$ such that $x \succ y, z$ and $x = y \join z$.
Since $\alpha = x_i = y_i \join z_i$, either $y_i$ or $z_i$ is equal to $\alpha$.
This contradicts the assumption that $x = \min \partfix{M}{i}{\alpha}$ and $x \succ y, z$.
Hence $x$ is join-irreducible.
Moreover, from Definition~\ref{def:differential}, it holds $\bar{x}_i = \alpha$.
(2).
Let $x \in \irreducibles{M}$ and $i \in \intset{n}$ such that $\alpha \defeq \bar{x}_i \neq 0$.
Then $x \in \partfix{M}{i}{\alpha}$.
Let $y \in M$ be the lower cover of $x$ and let $z \in \partfix{M}{i}{\alpha}$ be the minimum element of $\partfix{M}{i}{\alpha}$.
Suppose that $x \neq z$.
Then it holds $z \preceq y \prec x$ since $z \prec x$.
Hence we obtain $z_i = y_i = x_i = \alpha$, which claims that $\bar{x}_i = 0$ by Definition~\ref{def:differential}.
This contradicts the assumption.
Thus $x = z = \min \partfix{M}{i}{\alpha}$ holds.
(3).
Suppose that $M$ has a join-irreducible element $x \in \irreducibles{M}$ such that $\bar{x}_i = \alpha$.
From (2), it holds $x = \min \partfix{M}{i}{\alpha}$.
This lemma follows from the uniqueness of the minimum element of $\partfix{M}{i}{\alpha}$.
(4).
Assume that $M$ has a join-irreducible element $x$ such that $\bar{x} = \bm{0}$.
Let $y \in M$ be the lower cover of $x$.
Then $x_i = y_i$ must hold for each $i \in \intset{n}$, which contradicts that $y \prec x$.
(5).
Let $x, y \in \irreducibles{M}$ such that $\bar{x} = \bar{y}$.
Since $\bar{x} = \bar{y} \neq \bm{0}$ from (4), there exists $i \in \intset{n}$ such that $\bar{x}_i = \bar{y}_i \neq 0$.
Then $x = y$ follows from (3).
\end{proof}
Now Proposition~\ref{prop:number_of_irreducibles} is a consequence of Lemma~\ref{lem:differential}.
\begin{proof}[Proof of Proposition~\ref{prop:number_of_irreducibles}]
It suffices to consider the case where $M$ is simple.
From Lemmas~\ref{lem:differential}~(3) and (4), it holds $\absprn{\setprnsep{\bar{x}}{x \in \irreducibles{M}}} \leq kn$.
Furthermore, since the map $x \to \bar{x}$ is injective, we have $\absprn{\irreducibles{M}} = \absprn{\setprnsep{\bar{x}}{x \in \irreducibles{M}}}$.
Hence $\absprn{\irreducibles{M}}$ is at most $kn$.
\end{proof}
A simple $\paren{\mathbin\sqcap, \mathbin\sqcup}$-closed set $M$ is said to be \emph{normalized} if it satisfies $\absprn{\mathop{\mathrm{supp}} \bar{x}} = 1$ for all $x \in \irreducibles{M}$.
Examples of a normalized $\paren{\mathbin\sqcap, \mathbin\sqcup}$-closed set and the corresponding PIP are shown in Figure~\ref{fig:example_of_differential_and_normalizing}~(c) and (d), respectively.
\begin{lemma} \label{lem:normalized_is_general}
For any $\paren{\mathbin\sqcap, \mathbin\sqcup}$-closed set $M$, there exists a normalized $\paren{\mathbin\sqcap, \mathbin\sqcup}$-closed set that is isomorphic to $M$ with respect to the relations $\preceq$ and $\smile$.
\end{lemma}
\begin{proof}
We can suppose that $M$ is simple.
We first show:
%
\begin{enumerate}
\item[(1)] For $x, y \in \irreducibles{M}$, it holds that $\mathop{\mathrm{supp}} \bar{x} = \mathop{\mathrm{supp}} \bar{y}$ or $\mathop{\mathrm{supp}} \bar{x} \cap \mathop{\mathrm{supp}} \bar{y} = \varnothing$.
\end{enumerate}
%
Suppose to the contrary that there exist $x,y \in \irreducibles{M}$ such that $\bar{x}_i \neq 0 \neq \bar{y}_i$ and $\bar{x}_j \neq 0 = \bar{y}_j$ for distinct $i, j \in \intset{n}$.
Then it holds $\bar{x}_i \neq \bar{y}_i$ from Lemma~\ref{lem:differential}~(3).
Hence we have $x \not\preceq x \mathbin\sqcup y$ since $\paren{x \mathbin\sqcup y}_i = 0$.
However, both $x$ and $x \mathbin\sqcup y$ belong to $\partfix{M}{j}{x_j}$ since $\paren{x \mathbin\sqcup y}_j = x_j \neq 0$, thus it holds $x \preceq x \mathbin\sqcup y$ from Lemma~\ref{lem:differential}~(2).
This is a contradiction.
By (1), we can define an equivalence relation $\sim$ over the index set
%
\begin{align*}
\setprnsep{i \in \intset{n}}{\text{there exists $x \in \irreducibles{M}$ such that $\bar{x}_i \neq 0$}}
\end{align*}
%
as follows:
%
\begin{align*}
\text{$i \sim j$ if and only if there exists $x \in \irreducibles{M}$ such that $\bar{x}_i \neq 0$ and $\bar{x}_j \neq 0$}.
\end{align*}
%
Then each equivalence class can be ``contracted'' into a single index without any structural change of $M$ as follows.
Let $\setprn{I_1, I_2, \ldots, I_{\tilde{n}}}$ be the set of equivalence classes.
For $j \in \intset{\tilde n}$, let $\setprn{x^{j,1}, x^{j,2}, \ldots, x^{j,k_{j}}} \subseteq \irreducibles{M}$ be the set of join-irreducible elements having the differentials of support $I_j$.
Then, by Lemma~\ref{lem:differential},
%
\begin{enumerate}
\item[(2)] For every $x \in M$ and $j \in \intset{\tilde{n}}$, either $x_i = 0$ for all $i \in I_j$ or there uniquely exists $\alpha \in \intset{k_j}$ such that $x_i = \paren{x^{j, \alpha}}_i$ for all $i \in I_j$.
\end{enumerate}
%
Let $\tilde{k} \defeq \max_{j \in [\tilde n]} k_j$.
Define $\funcdoms{\phi}{M}{{S_{\tilde{k}}}^{\tilde{n}}}$ by $\app{\phi}{x}_j = 0$ if $x_i = 0$ for $i \in I_j$, and $\app{\phi}{x}_j = \alpha$ if $x_i = \paren{x^{j,\alpha}}_i$ for $i \in I_j$.
It is easily verified (from Lemma~\ref{lem:differential}) that the map $\phi$ is injective and preserves $\preceq$ and $\mathrel\smile$.
An irreducible element of $\app{\phi}{M}$ is the image of an irreducible element of $M$, and, by construction, has the differential of a singleton support.
Thus $\app{\phi}{M}$ is a normalized $\paren{\mathbin\sqcap, \mathbin\sqcup}$-closed set.
\end{proof}
Now we are ready to prove Theorem~\ref{thm:closed_set_and_elementary_pip}~(1).
\begin{proof}[Proof of Theorem~\ref{thm:closed_set_and_elementary_pip}~(1)]
By Lemma~\ref{lem:normalized_is_general}, it suffices to consider the case where $M$ is normalized.
For every $i \in \intset{n}$, let $J_i \defeq \setprnsep{x \in \irreducibles{M}}{\mathop{\mathrm{supp}} \bar{x} = \setprn{i}}$.
From the definition of normalized $\paren{\mathbin\sqcap, \mathbin\sqcup}$-closed sets, $\setprn{J_1, J_2, \ldots, J_n}$ forms a partition of $\irreducibles{M}$ (note that $J_i$ may be empty).
We show that the PIP $\paren{\irreducibles{M}, \preceq, \smile}$ satisfies the axiom of elementary PIPs with $P_i = J_i$ for every $i \in \intset{n}$.
(EP0, ``only if'' part).
Let $\setprn{x, y} \subseteq \irreducibles{M}$ be a minimally inconsistent pair.
Then there exists $i \in \intset{n}$ such that $0 \neq x_i \neq y_i \neq 0$.
We show $0 \neq \bar{x}_i \neq \bar{y}_i \neq 0$.
Suppose that $\bar{x}_i = 0$.
From Definition~\ref{def:differential}, there exists $x' \in \irreducibles{M}$ such that $x' \prec x$ and $x'_i = x_i$.
Now we have $x' \prec x$ and $x' \smile y$, which contradict the assumption that $x$ and $y$ are minimally inconsistent.
Therefore $\bar{x}_i \neq 0$ holds, and we can show $\bar{y}_i \neq 0$ in the same way.
Thus $\setprn{x, y} \subseteq J_i$ holds.
(EP1) is an immediate consequence of the following property:
%
\begin{itemize}
\item[($*$)] Let $i, j \in \intset{n}$ be distinct.
If there exist $x' \in J_i$ and $y \in J_j$ such that $x' \prec y$, then for all $x \in J_i \setminus \setprn{x'}$, there exists $y' \in J_j \setminus \setprn{y}$ such that $y'
\prec x$; in particular $|J_j| \geq 2$ if $|J_i| \geq 2$.
\end{itemize}
We show ($*$).
Let $x' \in J_i$ and $y \in J_j$ such that $x' \prec y$.
Now it holds $x'_i = y_i \neq 0$ and $y_j \neq 0$.
Let $x \in J_i \setminus \setprn{x'}$.
We have $y_i \neq \paren{x \mathbin\sqcup y}_i = 0$ since $0 \neq x_i \neq x'_i = y_i \neq 0$.
Thus $y \preceq x \mathbin\sqcup y$ does not hold.
We show that $0 \neq x_j \neq y_j$.
If not, $\paren{x \mathbin\sqcup y}_j$ is equal to $y_j$, hence $x \mathbin\sqcup y$ belongs to $\partfix{M}{j}{y_j}$.
Therefore it holds $y \preceq x \mathbin\sqcup y$ since $y$ is the minimum element of $\partfix{M}{j}{y_j}$ from Lemma~\ref{lem:differential}~(2).
We have a contradiction here.
Let $y' \defeq \min \partfix{M}{j}{x_j}$.
This $y'$ belongs to $J_j$ from Lemma~\ref{lem:differential}~(1), and it holds $y \neq y' \prec x$.
(EP2).
Let $i, j \in \intset{n}$ be distinct indices such that $\absprn{J_i} \geq 2$ and $\absprn{J_j} \geq 2$.
We can assume that (EP2-1) does not hold, i.e., there exist $x' \in J_i$ and $y \in J_j$ such that $x' \prec y$.
Consider $x, z \in J_i \setminus \setprn{x'}$.
By ($*$), there exist $y', y'' \in J_j \setminus \setprn{y}$ such that $y' \prec x$ and $y'' \prec z$.
We show $y' = y''$. Suppose not.
Since $y' \prec x$ and $y'' \in J_j \setminus \setprn{y'}$, we can take $x'' \in J_i \setminus \setprn{x}$ such that $x'' \prec y''$ by ($*$) with changing the role of $i$ and $j$.
Now we have $x'' \prec y'' \prec z$, which contradicts $x'' \smile z$.
Therefore $y'$ and $y''$ are same elements.
Consequently, the required element $y^\circ$ in (EP2-2) is given by $y'$.
By changing the role of $i$ and $j$, we see that $x^\circ$ is given by $x'$.
(EP0, ``if'' part).
Let $x, y \in J_i$ be distinct with $i \in \intset{n}$.
Now since $x \smile y$, there exists a minimally inconsistent pair $\setprn{x', y'} \subseteq \irreducibles{M}$ such that $x' \preceq x$ and $y' \preceq y$.
From the ``only if'' part of (EP0), $x'$ and $y'$ belong to $J_j$ for some $j \in \intset{n}$.
If $i \neq j$, then we have $x, y \in J_i$, $x',y' \in J_j$, $x' \prec x$ and $y' \prec y$, which contradict (EP2).
Hence $i = j$ and it must hold $\setprn{x', y'} = \setprn{x, y}$.
\end{proof}
\subsection{Proof of Theorem~\ref{thm:closed_set_and_elementary_pip}~(2)}
Let $\paren{P, \leq, \mathrel\smile}$ be an elementary PIP with partition $\setprn{P_1, P_2, \ldots, P_n}$ of condition (EP0).
For every $i \in \intset{n}$, let $P_i = \setprn{e^{i,1}, e^{i,2}, \ldots, e^{i,k_i}}$, where $k_i \defeq \absprn{P_i}$.
Let $k \defeq \max_{i \in \intset{n}} k_i$.
For a consistent ideal $I$, let $\app{x}{I} = \paren{\app{x_1}{I}, \app{x_2}{I}, \ldots, \app{x_n}{I}} \in {S_k}^n$ be defined by
\begin{align*}
\app{x_i}{I} \defeq \begin{cases}
\alpha & \text{($I \cap P_i = \setprn{e^{i,\alpha}}$),} \\
0 & \text{($I \cap P_i = \varnothing$)}
\end{cases}
\quad
\paren{i \in \intset{n}}.
\end{align*}
Now $\app{x}{I}$ is well-defined since every consistent ideal $I$ of $P$ has at most one element in each $P_i$ by (EP0).
Let $M \defeq \setprnsep{\app{x}{I}}{I \in \consideals{P}}$.
Then $\consideals{P}$ and $M$ are clearly isomorphic.
Therefore the rest of the proof of Theorem~\ref{thm:closed_set_and_elementary_pip}~(2) is to show that $M$ forms a $\paren{\mathbin\sqcap, \mathbin\sqcup}$-closed set.
We define binary operations $\mathbin\sqcap$ and $\mathbin\sqcup$ on $\consideals{P}$ as $I \mathbin\sqcap J \defeq I \cap J$ and
\begin{align*}
I \mathbin\sqcup J \defeq \bigcup_{i=1}^n \setprnsep{p \in P_i}{\paren{I \cup J} \cap P_i = \setprn{p}}
\end{align*}
for every $I, J \in \consideals{P}$.
Theorem~\ref{thm:closed_set_and_elementary_pip}~(2) follows immediately from:
\begin{lemma} \label{lem:consistent_ideal_family_of_P_is_closed}
For every $I, J \in \consideals{P}$, it hold $I \mathbin\sqcap J \in \consideals{P}, I \mathbin\sqcup J \in \consideals{P}$, $\app{x}{I \mathbin\sqcap J} = \app{x}{I} \mathbin\sqcap \app{x}{J}$ and $\app{x}{I \mathbin\sqcup J} = \app{x}{I} \mathbin\sqcup \app{x}{J}$.
\end{lemma}
\begin{proof}
Let $I, J \in \consideals{P}$.
Since the consistent ideal family of a PIP is closed under the intersection, $I \mathbin\sqcap J$ also forms a consistent ideal of $P$.
In addition, we can easily check that $\app{x}{I \mathbin\sqcap J} = \app{x}{I} \mathbin\sqcap \app{x}{J}$ holds.
Next we consider $I \mathbin\sqcup J$.
We show that $I \mathbin\sqcup J$ is a consistent ideal.
Suppose that $I \mathbin\sqcup J$ is not an ideal of $P$.
There exist $q \in I \mathbin\sqcup J$ and $p \in P \setminus \paren{I \mathbin\sqcup J}$ such that $p < q$.
Without loss of generality, we assume $q \in I$.
Now $I$ also contains $p$ since $I$ is an ideal.
Let $i, j \in \intset{n}$ such that $p \in P_i$ and $q \in P_j$.
We can take $r \in \paren{J \cap P_i} \setminus \setprn{p}$ since $p \notin I \mathbin\sqcup J$.
Thus $\absprn{P_i}$ is greater than 1, and $\absprn{P_j}$ is also greater than 1 since $p < q$ contradicts the condition (EP1) if $\absprn{P_j} = 1$.
From (EP2-2), there exists $s \in P_j \setminus \setprn{q}$ such that $s < r$.
It holds $s \in J$ since $r \in J$.
Now we have $q \neq s$, $q \in I$, $s \in J$ and $q, s \in P_j$.
This contradicts $q \in I \mathbin\sqcup J$.
Therefore $I \mathbin\sqcup J$ is an ideal.
Finally suppose that $I \mathbin\sqcup J$ includes an inconsistent pair $\setprn{p, q}$.
Since $I \mathbin\sqcup J$ is an ideal, it also includes the minimally inconsistent pair $\setprn{p', q'}$ with $p' \leq p$ and $q' \leq q$.
From (EP0), $p'$ and $q'$ belong to the same part $P_i$ of the partition.
This contradicts the fact that $\absprn{\paren{I \mathbin\sqcup J} \cap P_i} \leq 1$, and thus $I \mathbin\sqcup J$ is a consistent ideal.
$\app{x}{I \mathbin\sqcup J} = \app{x}{I} \mathbin\sqcup \app{x}{J}$ follows from the definitions of $\mathbin\sqcup$ on ${S_k}^n$ and on $\consideals{P}$.
\end{proof}
\section{Algorithms}
\label{sec:algorithms}
In this section, we study algorithmic aspects of constructing PIP-representations for the minimizer sets of $k$-submodular functions.
Let $\minimizers{f}$ denote the minimizer set of a function $f$.
Let $\maxflow{n}{m}$ denote the time complexity of an algorithm of a maximum flow (and a minimum cut) in a network of $n$ vertices and $m$ edges.
We assume a standard max-flow algorithm, such as preflow-push algorithm, and hence assume that $\maxflow{n}{m}$ is not less than $\Order{nm}$; notice that the current fastest one is
an $\Order{nm}$ algorithm by Orlin~\cite{Orlin2013}.
\subsection{By a minimizing oracle}
\label{sec:minimizing_oracle}
We can obtain the PIP-representation for the minimizer set of a $k$-submodular function $\funcdoms{f}{{S_k}^n}{\overline{\setR}}$ by using a minimizing oracle $k$-SFM, which returns a minimizer of $f$ and its restrictions.
Let $\min f$ be the minimum value of $f$.
For $i \in \intset{n}$ and $a \in S_k$, we define a new $k$-submodular function $\funcdoms{\fixarg{f}{i}{a}}{{S_k}^n}{\overline{\setR}}$ from $f$ by
\begin{align*}
\app{\fixarg{f}{i}{a}}{x_1, \ldots, x_i, \ldots, x_n} \defeq f(x_1, \ldots, \vectorpos{a}{i}, \ldots, x_n)
\quad
\paren{x \in {S_k}^n}.
\end{align*}
Namely, $\fixarg{f}{i}{a}$ is a function obtained by fixing the $i$-th variable of $f$ to $a$.
Before describing the main part of our algorithm, we present a subroutine \textproc{GetMinimumMinimizer} in Algorithm~\ref{alg:get_minimum_minimizer}.
This subroutine returns the minimum minimizer of a $k$-submodular function.
The validity of this subroutine can be checked by the fact that $\min \fixarg{f}{i}{0}$ is equal to $\min f$ if $\paren{\min \minimizers{f}}_i = 0$ and otherwise it holds $\min \fixarg{f}{i}{0} > \min f$.
This subroutine calls $k$-SFM at most $n+1$ times.
\begin{algorithm}[tp]
\caption{Obtain the minimum minimizer of a $k$-submodular function}
\label{alg:get_minimum_minimizer}
\begin{algorithmic}[1]
\Input A $k$-submodular function $\funcdoms{f}{{S_k}^n}{\overline{\setR}}$
\Output The minimum minimizer $\min \minimizers{f}$ of $f$
\Function{GetMinimumMinimizer}{$f$}
\State{$x \gets \Call{$k$-SFM}{f}$}
\For{$i \in \mathop{\mathrm{supp}} x$}
\If{$\min \fixarg{f}{i}{0} = \min f$}
\State{$x_i \gets 0$}
\EndIf
\EndFor
\State{\Return $x$}
\EndFunction
\end{algorithmic}
\end{algorithm}
Algorithm~\ref{alg:get_irreducibles_minimizers} shows a procedure to collect all join-irreducible minimizers of a $k$-submodular function.
Let $x$ be the minimum minimizer of $f$.
The function $\funcdoms{\tilde{f}}{{S_k}^n}{\overline{\setR}}$ in Algorithm~\ref{alg:get_irreducibles_minimizers} is defined as $\app{\tilde{f}}{y} \defeq \app{f}{\paren{y \mathbin\sqcup x} \mathbin\sqcup x}$ for every $y \in {S_k}^n$.
Since $\paren{\paren{y \mathbin\sqcup x} \mathbin\sqcup x}_i$ is equal to $y_i$ if $x_i = 0$ and to $x_i$ if $x_i \neq 0$, we can regard $\tilde{f}$ as a $k$-submodular function obtained by fixing each $i$-th variable of $f$ to $x_i$ if $x_i \neq 0$.
Note that the minimum values of $f$ and $\tilde{f}$ are the same.
The correctness of this algorithm is based on Lemma~\ref{lem:differential}~(1) and (2).
Namely, the set of join-irreducible minimizers of $f$ coincides with the set
\begin{align} \label{set:min}
\setprnsep{\min \minimizers{\fixarg{\tilde{f}}{i}{\alpha}}}{i \in \intset{n} \setminus \mathop{\mathrm{supp}}{x} ,\; \alpha \in \intset{k} ,\; \min \fixarg{\tilde{f}}{i}{\alpha} = \min f}.
\end{align}
The algorithm collects each join-irreducible minimizer according to \eqref{set:min} by calling \textproc{GetMinimumMinimizer} at most $nk+1$ times.
Consequently, if a minimizing oracle is available, the minimizer set can also be obtained in polynomial time.
\begin{theorem} \label{thm:alg_oracle}
The PIP-representation for the minimizer set of a $k$-submodular function $\funcdoms{f}{{S_k}^n}{\overline{\setR}}$ is obtained by $\Order{kn^2}$ calls of $k$-SFM.
\end{theorem}
\begin{algorithm}[tp]
\caption{Collect all join-irreducible minimizers of a $k$-submodular function}
\label{alg:get_irreducibles_minimizers}
\begin{algorithmic}[1]
\Input A $k$-submodular function $\funcdoms{f}{{S_k}^n}{\overline{\setR}}$
\Output The set $\irreducibles{\minimizers{f}}$ of all join-irreducible minimizers of $f$
\Function{GetJoinIrreducibleMinimizers}{$f$}
\State{$x \defeq \Call{GetMinimumMinimizer}{f}$}
\State{$\tilde{f} \defeq $ the function obtained by fixing the $i$-th variable of $f$ to $x_i$ for all $i \in \mathop{\mathrm{supp}} x$}
\State{$J \gets \varnothing$}
\For{$i \in \intset{n} \setminus \mathop{\mathrm{supp}} x$}
\ForTo{$\alpha \gets 1$}{$k$}
\If{$\min \fixarg{\tilde{f}}{i}{\alpha} = \min f$}
\State{$J \gets J \cup \setprn{\Call{GetMinimumMinimizer}{\fixarg{\tilde{f}}{i}{\alpha}}}$}
\EndIf
\EndFor
\EndFor
\State{\Return $J$}
\EndFunction
\end{algorithmic}
\end{algorithm}
\subsection{Network-representable $k$-submodular functions}
\label{sec:network}
Iwata--Wahlstr\"{o}m--Yoshida~\cite{IwataY2016} introduced \emph{basic $k$-submodular functions}, which form a special class of $k$-submodular functions.
They showed a reduction of the minimization problem of a nonnegative combination of binary basic $k$-submodular functions to the minimum cut problem on a directed network.
We describe their method and present an algorithm to obtain the PIP-representation for the minimizer set.
Let $n$ and $k$ be positive integers.
We consider a directed network $N = \paren{V, A, c}$ with vertex set $V$, edge set $A$ and nonnegative edge capacity $c$.
Suppose that $V$ consists of source $s$, sink $t$ and other vertices $v_i^\alpha$, where $i \in \intset{n}$ and $\alpha \in \intset{k}$.
Let $U_i \defeq \setprn{v_i^1, v_i^2, \ldots, v_i^k}$ for $i \in \intset{n}$.
An $\paren{s,t}$-cut of $N$ is a subset $X$ of $V$ such that $s \in X$ and $t \notin X$.
We call an $\paren{s,t}$-cut $X$ \emph{legal} if $\absprn{X \cap U_i} \leq 1$ for every $i \in \intset{n}$.
There is a natural bijection $\psi$ from ${S_k}^n$ to the set of legal $\paren{s,t}$-cuts of $N$ defined by
\begin{align*}
\app{\psi}{x} \defeq \setprn{s} \cup \setprnsep{v_i^{x_i}}{i \in \mathop{\mathrm{supp}} x}
\quad
\paren{x \in {S_k}^n}.
\end{align*}
See Figure~\ref{fig:example_of_legal_cut}.
\begin{figure}[t]
\centering
\begin{tikzpicture}[every node/.style={scale=0.8}, x=8pt, y=8pt]
\tikzstyle{vertex}=[circle, draw, scale=0.6];
\tikzstyle{group}=[circle, draw, rectangle, rounded corners=10pt, minimum width=70pt, minimum height=30pt, densely dotted, label=above:{#1}];
%
\node[vertex] (11) at (0, 0) {};
\node[vertex] (12) at (2, 0) {};
\node[vertex] (13) at (4, 0) {};
\node[group=$U_1$] at (2, 0) {};
%
\node[vertex] (21) at (8, 0) {};
\node[vertex] (22) at (10, 0) {};
\node[vertex] (23) at (12, 0) {};
\node[group=$U_2$] at (10, 0) {};
%
\node[vertex] (31) at (16, 0) {};
\node[vertex] (32) at (18, 0) {};
\node[vertex] (33) at (20, 0) {};
\node[group=$U_3$] at (18, 0) {};
%
\node[vertex] (41) at (24, 0) {};
\node[vertex] (42) at (26, 0) {};
\node[vertex] (43) at (28, 0) {};
\node[group=$U_4$] at (26, 0) {};
%
\node[vertex] (51) at (32, 0) {};
\node[vertex] (52) at (34, 0) {};
\node[vertex] (53) at (36, 0) {};
\node[group=$U_5$] at (34, 0) {};
%
\node[vertex, fill, above=35pt of 32, label=above right:{$t$}] (t) {};
\node[vertex, fill, below=25pt of 32, label=above right:{$s$}] (s) {};
%
\draw[thick] (-1, -1)
.. controls +(0, 0) and +(0, 0) .. (-1, 0)
.. controls +(0, 1.5) and +(0, 1.5) .. (1, 0)
.. controls +(0, 0) and +(0, 0) .. (1, -1)
.. controls +(0, -1) and +(-1, 0) .. (3, -2.4)
.. controls +(0, 0) and +(0, 0) .. (17, -2.4)
.. controls +(1, 0) and +(0, -1) .. (19, -1)
.. controls +(0, 0) and +(0, 0) .. (19, 0)
.. controls +(0, 1.5) and +(0, 1.5) .. (21, 0)
.. controls +(0, 0) and +(0, 0) .. (21, -1)
.. controls +(0, -2) and +(0, -2) .. (25, -1)
.. controls +(0, 0) and +(0, 0) .. (25, 0)
.. controls +(0, 1.5) and +(0, 1.5) .. (27, 0)
.. controls +(0, 0) and +(0, 0) .. (27, -1)
.. controls +(0, -2) and +(0, -2) .. (31, -1)
.. controls +(0, 0) and +(0, 0) .. (31, 0)
.. controls +(0, 1.5) and +(0, 1.5) .. (33, 0)
.. controls +(0, 0) and +(0, 0) .. (33, -1)
.. controls +(0, -3) and +(3, 0) .. (29, -5)
.. controls +(0, 0) and +(0, 0) .. (3, -5)
.. controls +(-3, 0) and +(0, -3) .. (-1, -1)
;
\node[right=115pt of s] {$X$};
\end{tikzpicture}
%
\caption{%
Legal cut $X \subseteq V$ corresponding to $\paren{1,0,3,2,1} \in {S_3}^5$.
Vertices in each $U_i$ are $v_i^1, v_i^2, v_i^3$ from left to right.
}
\label{fig:example_of_legal_cut}
\end{figure}
For an $\paren{s,t}$-cut $X$ of $N$, let $\legalize{X}$ denote the legal $\paren{s,t}$-cut obtained by removing vertices in $X \cap U_i$ from $X$ for every $i \in \intset{n}$ with $\absprn{U_i \cap X} \geq 2$.
The \emph{capacity} $\app{c}{X}$ of $X$ is defined as sum of capacities $\app{c}{e}$ of all edges $e$ from $X$ to $V \setminus X$.
We say that a network $N$ \emph{represents} a function $\funcdoms{f}{{S_k}^n}{\overline{\setR}}$ if it satisfies the following conditions:
\begin{namedenum}{NR}
\item There exists a constant $K \in \setR$ such that $\app{f}{x} = \app{c}{\app{\psi}{x}} + K$ for all $x \in {S_k}^n$.
\item It holds $\app{c}{\legalize{X}} \leq \app{c}{X}$ for all $\paren{s,t}$-cuts $X$ of $N$.
\end{namedenum}
From (NR1), the minimum value of $f - K$ is equal to the capacity of a minimum $\paren{s,t}$-cut of $N$.
For every minimum $\paren{s,t}$-cut $X$ of $N$, $\legalize{X}$ is also a minimum $\paren{s,t}$-cut since $N$ satisfies the condition (NR2).
Therefore $\app{\psi^{-1}}{\legalize{X}}$ is a minimizer of $f$, and a minimum $\paren{s,t}$-cut can be computed by maximum flow algorithms.
Indeed, Iwata--Wahlstr\"{o}m--Yoshida~\cite{IwataY2016} showed that nonnegative combinations of basic $k$-submodular functions are representable by such networks; see Iwamasa~\cite{Iwamasa2017} for further study on this network construction.
Now we shall consider obtaining the PIP-representation for the minimizer set of a $k$-submodular function $\funcdoms{f}{{S_k}^n}{\overline{\setR}}$ represented by a network $N$.
The minimizer set of $f$ is isomorphic to the family of legal minimum $\paren{s,t}$-cuts of $N$ ordered by inclusion, where the isomorphism is $\psi$.
It is well-known that the family of (not necessarily legal) minimum $\paren{s,t}$-cuts forms a distributive lattice.
Thus, by Birkhoff representation theorem, the family is efficiently representable by a poset.
Picard--Queyranne~\cite{Picard1980} showed an algorithm to obtain the poset from the residual graph corresponding to a maximum $\paren{s,t}$-flow of $N$.
We describe their theorem briefly.
For an $\paren{s,t}$-flow $\phi$ of $N$, the \emph{residual graph} corresponding to $\phi$ is a directed graph $\paren{V, A_\phi}$, where
\begin{align*}
A_\phi \defeq \setprnsep{a \in A}{\app{\phi}{a} < \app{c}{a}} \cup \setprnsep{\paren{u, v} \in V \times V}{\text{$\paren{v, u} \in A$ and $0 < \app{\phi}{v, u}$}}.
\end{align*}
\begin{theorem}[{\cite[Theorem~1]{Picard1980}}] \label{thm:picard}
Let $N = \paren{V, A, c}$ be a directed network with $s, t \in V$ and $G$ the residual graph corresponding to a maximum $\paren{s, t}$-flow of $N$.
Let $\Sigma$ be the set of strongly connected components (sccs) of $G$ other than the following:
%
\begin{namedenum}{}
\item Sccs reachable from $s$.
\item Sccs reachable to $t$.
\end{namedenum}
%
Let $\leq$ be a partial order on $\Sigma$ defined by
%
\begin{align*}
\text{$X \leq Y$ if and only if $X$ is reachable from $Y$ on $G$}
\end{align*}
%
for every $X, Y \in \Sigma$.
The ideal family of the poset $\paren{\Sigma, \leq}$ is isomorphic to the family of minimum $\paren{s,t}$-cuts of $N$ ordered by inclusion.
The isomorphism $\tau$ is given by $\app{\tau}{I} \defeq X_0 \cup \paren{\bigcup_{X \in I} X}$, where $X_0$ is the set of vertices reachable from $s$.
\end{theorem}
Our result is the following.
\begin{theorem} \label{thm:network_algo}
Let $N$ be a network representing a $k$-submodular function $\funcdoms{f}{{S_k}^n}{\overline{\setR}}$ and $G$ the residual graph corresponding to a maximum $\paren{s, t}$-flow of $N$.
Let $\Sigma$ be the set of sccs of $G$ other than the following:
%
\begin{namedenum}{}
\item Sccs reachable from $s$.
\item Sccs reachable to $t$.
\item Sccs reachable to an scc containing two or more elements in $U_i$ for some $i \in \intset{n}$.
\item Sccs reachable to sccs $X$ and $Y$ such that $X \neq Y$ and $\absprn{X \cap U_i} = \absprn{Y \cap U_i} = 1$ for some $i \in \intset{n}$.
\end{namedenum}
%
A partial order $\leq$ on $\Sigma$ is defined in the same way as Theorem~\ref{thm:picard}.
Let $\mathrel\smile$ be a symmetric binary relation on $\Sigma$ defined as
%
\begin{align*}
& \text{$X \mathrel\smile Y$ if and only if there are distinct $X', Y' \in \Sigma$ such that} \\
& \text{$X' \leq X, Y' \leq Y$ and $\absprn{X' \cap U_i} = \absprn{Y' \cap U_i} = 1$ for some $i \in \intset{n}$}.
\end{align*}
%
Then $\Sigma$ forms an elementary PIP with inconsistency relation $\mathrel\smile$.
The consistent ideal family of $\Sigma$ is isomorphic to the minimizer set of $f$, where the isomorphism is $\psi^{-1} \circ \tau$.
\end{theorem}
\begin{proof}
First we prove that $\Sigma$ is a PIP.
We can see that $\mathrel\smile$ satisfies the condition (IC1) since for every $X, Y \in \Sigma$ with $X \mathrel\smile Y$, an scc $Z$ reachable to $X$ and $Y$ does not belong to $\Sigma$ according to the above exclusion rule (4).
The condition (IC2) is also satisfied from the definition of the relation $\mathrel\smile$.
Thus $\Sigma$ forms a PIP.
Next we show $\app{\psi^{-1}}{\app{\tau}{I}} \in \minimizers{f}$ for every consistent ideal $I$ of $\Sigma$.
Let $\Sigma'$ be the poset given in Theorem~\ref{thm:picard}.
Note that $\Sigma$ is a subposet of $\Sigma'$.
We show that $I$ is an ideal of $\Sigma'$.
Suppose not.
Then there exist $X \in I$ and $Y \in \Sigma' \setminus \Sigma$ such that $Y$ is reachable from $X$ and meets the above exclusion rules (3) or (4).
Now since $X$ also satisfies the same exclusion rule, $X$ does not belong to $\Sigma$.
This is a contradiction.
Hence $I$ is an ideal of $\Sigma'$, and $\app{\tau}{I}$ is a minimum $\paren{s,t}$-cut (Theorem~\ref{thm:picard}).
Moreover, from the exclusion rule (3) and the definition of $\mathrel\smile$, we can see that $\app{\tau}{I}$ is legal.
Therefore $\app{\psi^{-1}}{\app{\tau}{I}}$ is a minimizer of $f$.
Conversely, let $x \in {S_k}^n$ be a minimizer of $f$.
Since $\app{\psi}{x}$ is a minimum $\paren{s,t}$-cut, $I \defeq \app{{\tau}^{-1}}{\app{\psi}{x}}$ is an ideal of $\Sigma'$ (Theorem~\ref{thm:picard}).
Suppose that $I \nsubseteq \Sigma$.
Then there exists $X \in I \setminus \Sigma$ which meets the exclusion rule (3) or (4).
Suppose that $X$ meets the rule (3).
Then $X$ is reachable to an scc $Y$ such that $\absprn{Y \cap U_i} \geq 2$ for some $i \in \intset{n}$.
Now $Y$ is not reachable to $t$ since $X$ is not reachable to $t$.
Thus $Y$ meets the rule (1) or belongs to $I$ otherwise.
In either case it holds $Y \subseteq \app{\psi}{x}$.
This contradicts the fact that $\app{\psi}{x}$ is legal.
A similar argument can also be applied in the case where $X$ meets the rule (4).
Therefore $I \subseteq \Sigma$ holds, and $I$ is an ideal of $\Sigma$ since $\Sigma$ is a subposet of $\Sigma'$.
The consistency of $I$ is an immediate consequence of the fact that $\app{\psi}{x}$ is legal.
Now we have shown that $\psi^{-1} \circ \tau$ is a bijection from $\consideals{\Sigma}$ to $\minimizers{f}$.
In addition, $\psi^{-1} \circ \tau$ clearly preserves the orders, hence it is an isomorphism.
Finally from Corollary~\ref{cor:elementary_pip}, $\Sigma$ is elementary.
\end{proof}
Algorithm~\ref{alg:remove_sccs} shows a procedure to obtain $\Sigma$ from the residual graph $G$.
First we can obtain the sccs of $G$ in $\Order{kn + \tilde{m}}$ time, where $\tilde{m} \defeq \absprn{A}$.
Additionally, the exclusion rules (1), (2) and (3) can be applied to the sccs in the same time complexity.
Hence it is only the exclusion rule (4) that we should carefully take account of.
An efficient way is described in Line 4 to 10 in Algorithm~\ref{alg:remove_sccs}.
For each scc $X$, the algorithm memorizes the set $U_X$ of vertices reachable to $X$.
Now since the size of each $U_X$ is $\Order{n}$ at any moment, Algorithm~\ref{alg:remove_sccs} runs in $\Order{\absprn{V} + n\absprn{A}} = \Order{kn + n\tilde{m}}$ time.
Therefore the time complexity for obtaining $\Sigma$ from $G$ is much less than the one for computing $G$ from the network $N$.
Consequently, we obtain the following theorem:
\begin{algorithm}[tp]
\caption{Obtain sccs which do not meet the exclusion rules}
\label{alg:remove_sccs}
\begin{algorithmic}[1]
\Input The residual graph $G = \paren{V, A_\phi}$ corresponding to a maximum $\paren{s,t}$-flow $\phi$
\Output The set $\Sigma$ of sccs of $G$ defined in Theorem~\ref{thm:network_algo}
\Function{ApplyExclusionRules}{$G$}
\State{$\Sigma \gets \text{the set of sccs of $G$}$}
\State{Remove all sccs from $\Sigma$ which meet the exclusion rules (1), (2) or (3)}
\For{$X \in \Sigma$ in the reverse topological order of $G$}
\State{$U_X \gets X$}
\State{$\mathcal{Y} \defeq \setprnsep{Y \in \Sigma}{\text{there is an edge $\paren{x, y} \in A_\phi$ for some $x \in X$ and $y \in Y$}}$}
\For{$Y \in \mathcal{Y}$}
\State{$U_X \gets U_X \cup U_Y$}
\If{$\absprn{U_X \cap U_i} \geq 2$ for some $i \in \intset{n}$}
\State{Remove all sccs from $\Sigma$ which are reachable to $X$, and go to Line 4}
\EndIf
\EndFor
\EndFor
\State{\Return $\Sigma$}
\EndFunction
\end{algorithmic}
\end{algorithm}
\begin{theorem} \label{thm:network_time}
Let $\funcdoms{f}{{S_k}^n}{\overline{\setR}}$ be a $k$-submodular function represented by a network $N$ with $\tilde{m}$ edges.
The PIP-representation for the minimizer set of $f$ is obtained in $\Order{\maxflow{kn}{\tilde{m}}}$ time.
\end{theorem}
\subsection{Potts $k$-submodular functions}
\label{sec:potts}
Here we consider a practically important subclass of network representable $k$-submodular functions, called \emph{Potts $k$-submodular functions}.
Let $\paren{V, E}$ be a connected undirected graph on vertex set $V = \intset{n}$ with $m = \absprn{E}$, where each edge $\setprn{i, j} \in E$ has a positive edge weight $\lambda_{i, j}$.
Let $\intset{k}$ be the set of labels.
A Potts $k$-submodular function is a $k$-submodular function $\funcdoms{\tilde{g}}{{S_k}^n}{\setR}$ of the following form:
\begin{align} \label{eqn:tilde_g}
\app{\tilde{g}}{x} = \sum_{i=1}^n \app{\tilde{g_i}}{x_i} + \sum_{\setprn{i, j} \in E} \lambda_{i, j} \app{d}{x_i, x_j}
\quad
\paren{x \in {S_k}^n},
\end{align}
where $g_i$ is any $k$-submodular function on $S_k$ for each $i \in \intset{n}$ and $d$ is a $k$-submodular function on ${S_k}^2$ defined by
\begin{align*}
\app{d}{a, b} \defeq \begin{cases}
1 & \paren{0 \neq a \neq b \neq 0}, \\
0 & \paren{a = b}, \\
1/2 & \mathrm{otherwise}
\end{cases}
\end{align*}
for each $a,b \in S_k$.
A Potts $k$-submodular function is naturally associated with a \emph{Potts energy function} $\funcdoms{g}{\intset{k}^n}{\setR}$:
\begin{align} \label{eq:potts}
\app{g}{x} = \sum_{i=1}^n \app{g_i}{x_i} + \sum_{\setprn{i, j} \in E} \lambda_{i, j} \app{1_{\neq}}{x_i, x_j}
\quad \paren{x \in \intset{k}^n},
\end{align}
where $g_i$ is any function on $\intset{k}$ for each $i \in \intset{n}$ and $\funcdoms{1_{\neq}}{\intset{k}^2}{\setR}$ is defined by $\app{1_{\neq}}{\alpha, \beta} \defeq 1$ if $\alpha \neq \beta$ and $\app{1_{\neq}}{\alpha, \beta} \defeq 0$ if $\alpha = \beta$.
Finding a labeling $x \in \intset{k}^n$ of the minimum Potts energy is NP-hard for $k \geq 3$ but particularly important in computer vision applications.
Useful information of optimal labelings of the Potts energy can be extracted from a minimizer of a Potts $k$-submodular function with appropriate $k$-submodular functions $\tilde{g}_i$.
Define each $\tilde{g}_i$ by $\app{\tilde{g}_i}{\alpha} \defeq \app{g_i}{\alpha}$ for $\alpha \in \intset{k}$ and $\app{\tilde{g}_i}{0} \defeq \min_\condition{\beta, \gamma \in \intset{k}}{\beta \neq \gamma} \paren{\app{g_i}{\beta} + \app{g_i}{\gamma}}/2$.
In this case, $\tilde{g}$ is a \emph{$k$-submodular relaxation} of $g$,
and an optimal labeling of $g$ is a partially recovered from a minimizer of $g$; see the next section.
Another choice of $\tilde{g_i}$ is: $\app{\tilde{g_i}}{\alpha} \defeq \paren{\app{g_i}{\alpha} - \min_{\beta \in \intset{k} \setminus \setprn{\alpha}} \app{g_i}{\beta}}/2$ for $\alpha \in \intset{k}$ and $\app{\tilde{g}}{0} \defeq 0$.
Also in this case, a part of an optimal labeling is obtained from a minimizer of $\tilde{g}$, and coincides with Kovtun's partial labeling~\cite{Gridchyn2013, Kovtun2003}.
The goal of this section is to develop a fast algorithm to construct the PIP of a Potts $k$-submodular function $\tilde{g}$.
Notice that $\tilde{g}$ is network-representable with $km$ edges~\cite{IwataY2016}.
Therefore we can obtain a minimizer as well as the PIP-representation for $\tilde{g}$ in $\Order{\maxflow{kn}{km}}$ time by the network construction in the previous section.
However it is hard to apply this algorithm to the vision application with large $k \paren{\sim 60}$ in~\cite{Gridchyn2013}.
Gridchyn--Kolmogorov~\cite{Gridchyn2013} developed an $\Order{\log k \cdot \maxflow{n}{m}}$-time algorithm to find a minimizer of $\tilde{g}$.
The main theorem in this section is a stronger result that the PIP-representation is also obtained in the same time complexity.
\begin{theorem} \label{thm:Potts}
The PIP-representation for the minimizer set of $\tilde{g}$ is obtained in\\
$\Order{\log k \cdot \maxflow{n}{m}}$ time.
\end{theorem}
The rest of this subsection is devoted to proving this theorem.
First we construct a network $N$, different from the one in the previous section.
For each $i \in \intset{n}$, decompose $\tilde{g}_i$ as follows.
Let $\funcdoms{1_{=}}{{S_k}^2}{\setR}$ be defined by $\app{1_{=}}{a, b} \defeq 1$ if $a = b$ and $\app{1_{=}}{a, b} \defeq 0$ otherwise.
Choose a minimizer $\gamma_i \in S_k$ of $\tilde{g}_i$.
Then $\tilde{g}_i$ is represented as
\begin{align*}
\app{\tilde{g}_i}{x_i}
= \app{\tilde{g}_i}{\gamma_i}
+ \mu_i \app{d}{\gamma_i, x_i}
+ \sum_{\alpha \in \intset{k} \setminus \setprn{\gamma_i}} \sigma_{i, \alpha} \app{1_{=}}{\alpha, x_i},
\end{align*}
where $\mu_i \defeq 2\paren{\app{\tilde{g}_i}{0} - \app{\tilde{g}_i}{\gamma_i}} \, \paren{\geq 0}$ and
$\sigma_{i, \alpha} \defeq \app{\tilde{g}_i}{\alpha} - 2 \app{\tilde{g}_i}{0} + \app{\tilde{g}_i}{\gamma_i}$ for $\alpha \in \intset{k}$.
We remark that $\sigma_{i, \alpha}$ is nonnegative by $k$-submodularity, and that $\mu_i > 0$ implies $\gamma_i \neq 0$.
Let us construct $N$.
Starting from $\paren{V, E}$, define the edge-capacity $\app{c}{\setprn{i, j}}$ of each edge $\setprn{i, j} \in E$ by $\lambda_{i, j}$.
Next add new vertices $s_1, s_2, \ldots, s_k$, called \emph{terminals}.
For each $i \in \intset{n}$, if $\mu_i > 0$ with $\alpha = \gamma_i \in \intset{k}$, add a new edge $\setprn{i, s_\alpha}$ of capacity $\app{c}{\setprn{i, s_\alpha}} \defeq \mu_i$.
An edge $\setprn{i, s_\alpha}$ is called a \emph{terminal edge}.
For each $\alpha \in \intset{k}$ with $\sigma_{i, \alpha} > 0$, add a new vertex $i^\alpha$ and a new edge $\setprn{i, i^\alpha}$ of capacity $\app{c}{\setprn{i, i^\alpha}} \defeq 2 \sigma_{i, \alpha}$.
A vertex $i^\alpha$ is called the \emph{$\alpha$-fringe} of $i$.
Let $S \defeq \setprn{s_1, s_2, \ldots, s_k}$.
Let $V_0$ be the set of all fringes, $E_0$ the set of all edges incident to fringes, and $E_S$ the set of all terminal edges.
Let $\tilde{V} \defeq V \cup V_0 \cup S$ and $\tilde{E} \defeq E \cup E_0 \cup E_S$.
Let $N = \paren{\tilde{V}, \tilde{E}, c}$ be the resulting network.
Second we show that $\tilde{g}$ is represented as a certain multicut function in $N$.
For a vertex subset $X$, the cut capacity $\app{c}{X}$ of $X$ is the sum of $\app{c}{e}$ of all edges $e$ between $X$ and $V \setminus X$.
For $\alpha \in \intset{k}$, a vertex subset $X$ is called an \emph{$s_\alpha$-isolating cut} or \emph{$\alpha$-cut} if $s_\alpha \in X$, $s_\beta \not \in X$ for $\beta \in \intset{k} \setminus \setprn{\alpha}$, and $X$ contains no $\alpha$-fringe.
A \emph{semi-multicut} is an ordered partition $\paren{X_0, X_1, \ldots, X_k}$ of $\tilde{V}$ such that $X_\alpha$ is an $\alpha$-cut for each $\alpha \in \intset{k}$.
The \emph{capacity} $\app{c}{\mathcal{X}}$ of a semi-multicut $\mathcal{X} = \paren{X_0, X_1, \ldots, X_k}$ is defined by
\begin{align*}
\app{c}{\mathcal{X}} \defeq \frac{1}{2} \sum_{\alpha \in \intset{k}} \app{c}{X_\alpha}.
\end{align*}
An \emph{admissible} semi-multicut is a semi-multicut $\paren{X_0, X_1, X_2, \ldots, X_k}$ such that for each $\alpha \in \intset{k}$, each $\alpha$-fringe $i^\alpha$ belongs to $X_0$ if $i \in X_0 \cup X_\alpha$ and belongs to $X_\beta$ if $i \in X_\beta$ for $\beta \in \intset{k} \setminus \setprn{\alpha}$.
Observe that the part to which a fringe of $i \in \intset{n}$ belongs is uniquely determined from the part which $i$ belongs.
For an admissible semi-multicut $\mathcal{X} = \paren{X_0, X_1, \ldots, X_k}$, define $\app{x}{\mathcal{X}} = \paren{\app{x_1}{\mathcal{X}}, \app{x_2}{\mathcal{X}}, \ldots, \app{x_n}{\mathcal{X}}} \in {S_k}^n$ by $\app{x_i}{\mathcal{X}} \defeq a \in S_k$ if and only if $i \in X_a$.
This map $\mathcal{X} \mapsto \app{x}{\mathcal{X}}$ is a bijection from the family of all admissible semi-multicuts to ${S_k}^n$; see Figure~\ref{fig:example_of_admissible_semimultiway_cut}.
\begin{figure}[t]
\centering
\begin{tikzpicture}[every node/.style={scale=0.8}, x=5pt, y=5pt]
\node at (0, 70pt) {$X_1$};
\node at (-90pt, -35pt) {$X_2$};
\node at ( 90pt, -35pt) {$X_3$};
%
\begin{scope}
\tikzstyle{vertex}=[circle, draw, scale=0.6];
%
\draw[name path=oval] ellipse (90pt and 60pt);
\clip (0,0) ellipse (90pt and 60pt);
\draw[name path=x1, thick] ( 0pt, 40pt) circle (45pt);
\draw[name path=x2, thick] (-90pt, -25pt) circle (50pt);
\draw[name path=x3, thick] ( 90pt, -25pt) circle (50pt);
%
\node[vertex, label=right:1] (1) at (-30pt, 25pt) {};
\node[vertex, left=20pt of 1, label=above:$1^1$] (11) {};
\node[vertex, below right=10pt of 1, label=right:$1^2$] (12) {};
\node[vertex, above=10pt of 1, label=right:$1^3$] (13) {};
\draw (1) -- (11);
\draw (1) -- (12);
\draw (1) -- (13);
%
\node[vertex, label=above:2] (2) at (0pt, -25pt) {};
\node[vertex, below left=10pt of 2, label=below:$2^1$] (21) {};
\node[vertex, below=10pt of 2, label=below:$2^2$] (22) {};
\node[vertex, below right=10pt of 2, label=below:$2^3$] (23) {};
\draw (2) -- (21);
\draw (2) -- (22);
\draw (2) -- (23);
%
\node[vertex, label=right:3] (3) at (50pt, -20pt) {};
\node[vertex, above right=10pt of 3, label=right:$3^1$] (31) {};
\node[vertex, below=10pt of 3, label=right:$3^2$] (32) {};
\node[vertex, left=20pt of 3, label=above:$3^3$] (33) {};
\draw (3) -- (31);
\draw (3) -- (32);
\draw (3) -- (33);
%
\node[vertex, label=left:4] (4) at (-50pt, -20pt) {};
\node[vertex, above left=10pt of 4, label=left:$4^1$] (41) {};
\node[vertex, right=20pt of 4, label=above:$4^2$] (42) {};
\node[vertex, below=10pt of 4, label=left:$4^3$] (43) {};
\draw (4) -- (41);
\draw (4) -- (42);
\draw (4) -- (43);
%
\node[vertex, label=left:5] (5) at (30pt, 25pt) {};
\node[vertex, right=20pt of 5, label=above:$5^1$] (51) {};
\node[vertex, below left=10pt of 5, label=left:$5^2$] (52) {};
\node[vertex, above=10pt of 5, label=left:$5^3$] (53) {};
\draw (5) -- (51);
\draw (5) -- (52);
\draw (5) -- (53);
%
\node[vertex, fill, label=above right:$s_1$] (s1) at ( 0pt, 45pt) {};
\node[vertex, fill, label=above left:$s_2$] (s3) at (-70pt, 5pt) {};
\node[vertex, fill, label=above right:$s_3$] (s3) at ( 70pt, 5pt) {};
\end{scope}
\end{tikzpicture}
%
\caption{Admissible semi-multiway cut $\mathcal{X} = \paren{X_0, X_1, X_2, X_3}$ corresponding to $\paren{1,0,3,2,1} \in {S_3}^5$.}
\label{fig:example_of_admissible_semimultiway_cut}
\end{figure}
The next lemma says that a $k$-submodular function $\tilde{g}$ is actually represented by capacities of admissible semi-multicuts.
\begin{lemma}
For any admissible semi-multicut $\mathcal{X}$, it holds
%
\begin{align*}
\app{\tilde{g}}{\app{x}{\mathcal{X}}}
= \app{c}{\mathcal{X}}
+ \sum_{i \in \intset{n}} \app{\tilde{g}_i}{\gamma_i}.
\end{align*}
\end{lemma}
\begin{proof}
Let $x \defeq \app{x}{\mathcal{X}}$.
The capacity $2 \sigma_{i, \alpha}$ of a fringe edge $\setprn{i, i^\alpha}$ contributes to $\app{c}{\mathcal{X}}$ by $\sigma_{i, \alpha}$ if $i \in X_\alpha$ and by $0$ otherwise.
Thus the contribution is equal to $\sigma_{i, \alpha} \app{1_{=}}{\alpha, x_i}$.
The capacity $\mu_i$ of a terminal edge $\setprn{i, s_\alpha}$ contributes to $\app{c}{\mathcal{X}}$ by $0$ if $i \in X_\alpha$ and by $\mu_i / 2$ if $i \in X_0$, and by $\mu_i$ if $i \in X_\beta$ with $\beta \neq \alpha$.
Thus the contribution is equal to $\mu_i \app{d}{x_i, \alpha}$.
Similarly, we verify that the contribution of the capacity $\lambda_{i, j}$ of $\setprn{i, j} \in E$ is equal to $\lambda_{i, j} \app{d}{x_i, x_j}$.
Thus the claimed equality holds.
\end{proof}
Third we show that a minimum admissible semi-multicut is easily obtained by $k$ max-flow computations, where ``minimum'' is with regard to the cut capacity.
An \emph{admissible} $\alpha$-cut is an $\alpha$-cut $X$ such that for each $\beta \in \intset{k} \setminus \setprn{\alpha}$, each $\beta$-fringe $i^\beta$ belongs to $X$ if $i \in X$ and $\tilde{V} \setminus X$ otherwise.
Then an admissible semi-multicut $\paren{X_0, X_1, X_2, \ldots, X_k}$ is exactly a partition of $\tilde{V}$ such that $X_\alpha$ is an admissible $\alpha$-cut for each $\alpha \in \intset{k}$.
\begin{lemma} \label{lem:minimum_semimultiway_cut}
\begin{enumerate}
\item Any minimum $\alpha$-cut is admissible.
\item For $\alpha \in \intset{k}$, let $Y_\alpha$ be the inclusion-minimal minimum $\alpha$-cut.
Then $\paren{Y_0, Y_1, \ldots, Y_k}$ is a minimum admissible semi-multicut.
\end{enumerate}
%
In particular, a minimum admissible semi-multicut is exactly a partition $(X_0, X_1, \ldots, X_k)$ of $\tilde{V}$ such that $X_\alpha$ is a minimum $\alpha$-cut for each $\alpha \in \intset{k}$.
\end{lemma}
\begin{proof}
(1).
Let $X$ be an $\alpha$-cut.
For $\beta \in \intset{k} \setminus \setprn{\alpha}$, if the $\beta$-fringe $i^\beta$ of $i \in X$ is outside of $X$, then include $i^\beta$ into $X$ to decrease the cut capacity.
Similarly, for $\beta \in \intset{k} \setminus \setprn{\alpha}$, if the $\beta$-fringe $i^\beta$ of $i \in V \setminus X$ belongs to $X$, then remove $i^\beta$ from $X$ to decrease the cut capacity.
(2) is immediate from the standard uncrossing argument; see the proof of Lemma~\ref{lem:uncrossing}.
\end{proof}
In particular, a minimum admissible multicut is obtained by computing a minimal minimum $\alpha$-cut for each $\alpha \in \intset{k}$.
The network $N$ has at most $k + n + nk$ vertices and $m + n+ nk$ edges.
When computing a minimum $\alpha$-cut, all $\beta$-fringes with $\beta \neq \alpha$ can be removed, and a max-flow algorithm is performed on a network of $n+2$ vertices and $m + 2n$ edges
(after combining $s_\beta$ for $\beta \neq \alpha$ and all $\alpha$-fringes into a single vertex).
Thus we obtain the following, which was essentially shown in~\cite{Gridchyn2013, Kovtun2003}.
\begin{lemma}[\cite{Gridchyn2013, Kovtun2003}]
A minimizer of $\tilde{g}$ can be obtained in $\Order{k \maxflow{n}{m}}$ time.
\end{lemma}
Fourth we explain how to obtain the PIP representation from maximum $\alpha$-flows for $\alpha \in \intset{k}$, where by an \emph{$\alpha$-flow} we mean a flow from $s_\alpha$ to the union of
$S \setminus \setprn{s_\alpha}$ and $\alpha$-fringes.
To construct the PIP, we use the following intersecting properties of minimum isolating cuts.
Here a minimum $\alpha$-cut is simply called an {\em $\alpha$-mincut}.
\begin{lemma} \label{lem:uncrossing}
\begin{enumerate}
\item For distinct $\alpha, \beta \in \intset{k}$, if $X$ is an $\alpha$-mincut and $Y$ is a $\beta$-mincut, then $X \setminus Y$ is an $\alpha$-mincut and $Y \setminus X$ is a $\beta$-mincut.
\item For distinct $\alpha, \beta, \gamma \in \intset{k}$, if $X$ is an $\alpha$-mincut, $Y$ is a $\beta$-mincut and $Z$ is a $\gamma$-mincut, then $X \cap Y \cap Z = \varnothing$.
\end{enumerate}
\end{lemma}
\begin{proof}
In the theory of minimum cuts on undirected networks, the following inequalities are well-known:
%
\begin{align*}
\app{c}{X} + \app{c}{Y} & \geq \app{c}{X \setminus Y} + \app{c}{Y \setminus X}, \\
\app{c}{X} + \app{c}{Y} + \app{c}{Z} & \geq \app{c}{X \setminus \paren{Y \cup Z}} + \app{c}{Y \setminus \paren{Z \cup X}} + \app{c}{Z \setminus \paren{X \cup Y}} + \app{c}{X \cap Y \cap Z}
\end{align*}
%
for every $X, Y, Z \subseteq \tilde{V}$.
Then (1) is an immediate consequence of the first inequality and the fact that any subset of an $\alpha$-cut containing $s_\alpha$ is again an $\alpha$-cut.
(2) is also immediate from the second inequality and the condition that
$\paren{V, E}$ is connected and each edge of $N$ has a positive capacity.
\end{proof}
By Lemma~\ref{lem:uncrossing}~(2), each vertex belongs to at most two minimum isolating cuts.
Let $\overrightarrow{N}$ denote the directed network obtained from $N$ by replacing each undirected edge $\setprn{u, v} \in \tilde E$ by two directed edge $\paren{u, v}$ and $\paren{v, u}$ of capacity $\app{c}{u, v} = \app{c}{v, u} \defeq \app{c}{\setprn{u, v}}$.
For each $\alpha \in \intset{k}$, consider the network obtained from $\overrightarrow{N}$
by removing all $\beta$-fringes with $\beta \neq \alpha$ and contracting terminals $s_\beta$ with $\beta \neq \alpha$ and $\alpha$-fringes into a single terminal $s'$, and consider
the residual graph $G_\alpha$ corresponding to a maximum $\paren{s_\alpha, s'}$-flow in this network.
Let $\Sigma_\alpha = \paren{\Sigma_\alpha, \leq_\alpha}$ be the poset obtained from $G_\alpha$ in the same way as defined in Theorem~\ref{thm:picard}.
Here each element in $\Sigma_\alpha$ is a subset of $V$ (not including terminals and fringes).
The ideal family of each $\Sigma_\alpha$ is isomorphic to
the family of minimum $\alpha$-cuts.
The intersecting part in $\Sigma_\alpha$ and $\Sigma_\beta$ is described as follows.
\begin{lemma} \label{lem:intersection_of_isolating_cuts}
Let $\alpha, \beta \in \intset{k}$ with $\alpha \neq \beta$.
The following hold:
%
\begin{enumerate}
\item For every $A \in \Sigma_\alpha$ and $B \in \Sigma_\beta$, it holds either $A \cap B = \varnothing$ or $A = B$.
\item For every $A, B \in \Sigma_\alpha \cap \Sigma_\beta$, if $A \leq_\alpha B$, then it holds $B \leq_\beta A$.
\end{enumerate}
\end{lemma}
\begin{proof}
(1).
Assume that $A \cap B \neq \varnothing$ and $A \neq B$.
We can assume $A \setminus B \neq \varnothing$.
Consider an $\alpha$-mincut $X$ with $A \subseteq X$ and consider a $\beta$-mincut $Y$ with $B \subseteq Y$.
Take $Y$ minimal.
Then every scc of $G_\beta$ included in $Y$ is less than or equal to $B$ with respect to $\leq_\beta$.
Suppose that $Y$ contains $A$.
There is a $\beta$-mincut $Z$ containing $A \setminus B$ and disjoint from $B$.
By Lemma~\ref{lem:uncrossing}~(1), $X \setminus Z$ is an $\alpha$-mincut and properly intersects $A$.
However this is impossible since the set of non-fringe vertices in each $\alpha$-mincut is a disjoint union of sccs of $G_\alpha$.
Suppose that $Y$ does not contain $A$.
Then $X \setminus Y$ is an $\alpha$-mincut and properly intersects $A$ again.
This is a contradiction.
(2).
Assume that $A \leq_\alpha B$ and $B \not\leq_\beta A$.
There is a $\beta$-mincut $Y$ containing $A$ and disjoint with $B$.
Consider an $\alpha$-mincut $X$ containing $B$.
Then $X \setminus Y$ is an $\alpha$-mincut, contains $B$, and does not contain $A$.
However this contradicts the assumption that $A \leq_\alpha B$.
\end{proof}
By Lemma~\ref{lem:intersection_of_isolating_cuts}, we obtain the elementary PIP representing minimum admissible cuts just by ``gluing'' $\Sigma_1, \Sigma_2, \ldots, \Sigma_k$ along the intersections.
Let $P \defeq \bigcup_{\alpha \in \intset{k}} \Sigma_\alpha \times \setprn{\alpha}$ and $\leq$ a partial order on $P$ defined by
\begin{align*}
\text{$\paren{X, \alpha} \leq \paren{Y, \beta}$ if and only if $\alpha = \beta$ and $X \leq_\alpha Y$}
\end{align*}
for every $\paren{X, \alpha}, \paren{Y, \beta} \in P$.
In addition, let $\mathrel{\overset{{}_{\scriptscriptstyle{\bullet}}}{\smile}}$ be a symmetric binary relation on $P$ defined by
\begin{align*}
\text{$\paren{X, \alpha} \mathrel{\overset{{}_{\scriptscriptstyle{\bullet}}}{\smile}} \paren{Y, \beta} $ if and only if $\alpha \neq \beta$ and $X = Y$}
\end{align*}
for every $\paren{X, \alpha}, \paren{Y, \beta} \in \Sigma$.
\begin{theorem} \label{thm:PIP_Potts}
The triplet $P = \paren{P, \leq, \mathrel{\overset{{}_{\scriptscriptstyle{\bullet}}}{\smile}}}$
is an elementary PIP with minimal inconsistency relation $\mathrel{\overset{{}_{\scriptscriptstyle{\bullet}}}{\smile}}$.
The consistent ideal family $\consideals{P}$ and the family of minimum admissible semi-multicuts of $N$ are in one-to-one correspondence by the map
%
\begin{align*}
I \mapsto \paren{X_0^I, X^I_1, X^I_2, \ldots, X^I_k},
\end{align*}
%
where, for each $\alpha \in \intset{k}$, $X_\alpha^I$ is the admissible $\alpha$-cut containing all vertices $i \in V$ such that $i$ is reachable from $s_\alpha$ in $G_\alpha$ or belongs to $X$ for some $\paren{X, \alpha} \in I$.
\end{theorem}
\begin{proof}
It is easy to see from Lemma~\ref{lem:intersection_of_isolating_cuts}~(2) that $P$ is a PIP with minimal inconsistency relation $\mathrel{\overset{{}_{\scriptscriptstyle{\bullet}}}{\smile}}$.
We next show that $\consideals{P}$ represents the family of minimum semi-multiway cuts.
Let $I \in \consideals{P}$.
Then $X_\alpha^I$ is a minimum $s_\alpha$-isolating cut (by Theorem~\ref{thm:picard}).
By consistency, it necessarily holds $X_\alpha^I \cap X_\beta^I = \emptyset$
for $\alpha \neq \beta$.
Thus $\paren{X^I_0, X^I_1, X^I_2, \ldots, X^I_k}$ is a minimum semi-multiway cut.
Conversely, let $\paren{X_0, X_1, X_2, \ldots, X_k}$ be a minimum semi-multiway cut.
Each $X_\alpha$ is a minimum $s_\alpha$-isolating cut, and is represented by an ideal $I_\alpha$ of $\Sigma_\alpha$.
Now $I \defeq \bigcup_{\alpha \in \intset{k}} I_\alpha \times \setprn{\alpha}$ is a consistent ideal of $P$ since $X_1, X_2, \ldots, X_k$ are pairwise disjoint.
Then it holds $X_\alpha = X_\alpha^I$ for $\alpha \in \intset{k}$.
Now $P$ represents a $\paren{\sqcap, \sqcup}$-closed set in ${S_k}^n$, and is necessarily elementary by Corollary~\ref{cor:elementary_pip}.
\end{proof}
Therefore the PIP-representation is obtained by computing a maximum $\alpha$-flow for each $\alpha \in \intset{k}$.
\begin{lemma}
The PIP-representation for the minimizer set of $\tilde{g}$ is obtained in $\mathrm{O}(k \maxflow{n}{m})$ time.
\end{lemma}
Finally we present an improved algorithm of time complexity $\Order{\log k \cdot \maxflow{n}{m}}$.
The key is the existence of a single ``multiflow'' that includes all maximum $\alpha$-flows.
Let $\mathcal{Q}$ denote the set of $\alpha$-paths over all $\alpha \in \intset{k}$, where an \emph{$\alpha$-path} is a path connecting $s_\alpha$ and an $\alpha$-fringe or a terminal $s_\beta$ with $\beta \neq \alpha$.
A \emph{multiflow} is a nonnegative-valued function $f$ on $\mathcal{Q}$ satisfying the capacity constraint:
\begin{align*}
\app{f}{e} \defeq \sum \setprnsep{\app{f}{Q}}{Q \in \mathcal{Q}: \text{$Q$ contains $e$}} \leq \app{c}{e} \quad \paren{e \in \tilde{E}}.
\end{align*}
Let $\absprn{f}$ denote the total-flow value of $f$:
\begin{align*}
\absprn{f} \defeq \sum \setprnsep{\app{f}{Q}}{Q \in \mathcal{Q}}.
\end{align*}
For $\alpha \in \intset{k}$, let $f_\alpha$ be the submultiflow of $f$ defined by $\app{f_\alpha}{Q} \defeq \app{f}{Q}$ if $Q$ is an $\alpha$-path and $\app{f_\alpha}{Q} \defeq 0$ otherwise.
Although the set $\mathcal{Q}$ is exponential, we can efficiently handle multiflow $f$ by keeping $f$ as $k$ flows of node-arc form in $\overrightarrow{N}$, as in \cite[p. 65--66]{Ibaraki1998}.
The following is a special case of~\cite[Theorem 1.2]{Hirai2010} (a version of \emph{multiflow locking theorem}).
\begin{lemma}[\cite{Hirai2010}]
There exists a multiflow $f$ such that $\absprn{f_\alpha}$ is equal to the minimum capacity of an $\alpha$-cut for each $\alpha \in \intset{k}$.
\end{lemma}
Thus the submultiflow $f_\alpha$ of $f$ turns into a maximum $\alpha$-flow in $\overrightarrow{N}$.
We call such a multiflow \emph{locking}.
Our goal is to show that a locking multiflow $f$ is obtained in $\Order{\log k \cdot \maxflow{n}{m}}$ time.
This, consequently, yields $\Order{\log k \cdot \maxflow{n}{m}}$-time algorithm
to obtain posets $\Sigma_1, \Sigma_2, \ldots, \Sigma_k$ and the desired PIP $P = \bigcup_{\alpha \in \intset{k}} \Sigma_\alpha \times \setprn{\alpha}$.
In the case where there are no fringes, the problem of finding a locking multiflow is nothing but the \emph{maximum free multiflow problem}, which is a well-studied problem in multiflow theory.
Ibaraki--Karzanov--Nagamochi~\cite{Ibaraki1998} developed an $\Order{\log k \cdot \maxflow{n}{m}}$-time algorithm (\emph{IKN-algorithm}) to obtain a locking multiflow.
Babenko--Karzanov~\cite{Babenko2012} extended the IKN-algorithm to a more general case, and can be applied to our case.
For completeness, we present a direct adaptation of IKN-algorithm to the case where fringes exist, though our algorithm may be regarded as a specialization of~\cite{Babenko2012}.
The pseudo code is shown in Algorithm~\ref{alg:locking}.
\begin{algorithm}[tp]
\caption{Compute a locking multiflow}
\label{alg:locking}
%
\begin{algorithmic}[1]
\Input A network $N$ with terminal set $S$
\Output A locking multiflow in $N$
\Function{Locking}{$N$}
\If{$\absprn{S} \geq 4$}
\State{Divide $S$ into $S'$ and $S''$ with $\absprn{S'} = \floor{\absprn{S}/2}$ and $\absprn{S''} = \ceil{\absprn{S}/2}$}
\State{Compute a minimum cut $X$ with $S' \subseteq X$ and $X \cap S'' = \varnothing$}
\State{Construct two networks $N'$ and $N''$}
\State{$f' \defeq \Call{Locking}{N'}$ and $f'' \defeq \Call{Locking}{N''}$}
\State{Aggregate $f'$ and $f''$ into a locking multiflow $f$ in $N$}
\Else
\If{there is an $\alpha$-fringe}
\State{Compute a minimum $\alpha$-cut $X$}
\State{Construct two network $N'$ and $N''$}
\State{$f' \defeq \text{a maximum $\paren{s_\alpha, s'}$-flow}$ and $f'' \defeq \Call{Locking}{N''}$}
\State{Aggregate $f'$ and $f''$ to obtain a locking multiflow $f$ in $N$}
\Else
\State{Compute a locking multiflow $f$ by IKN-algorithm}
\EndIf
\EndIf
\State{\Return $f$}
\EndFunction
\end{algorithmic}
\end{algorithm}
Let us explain the detail of the algorithm.
Consider the case $\absprn{S} \geq 4$.
As in IKN-algorithm, our algorithm divides terminal set $S$ into two sets $S'$ and $S''$ such that $\absprn{S'} = \floor{\absprn{S}/2}$ and $\absprn{S''} = \ceil{\absprn{S}/2}$, and find a minimum cut $X$ with $S' \subseteq X$ and $S'' \cap X = \varnothing$.
Here fringes may be removed in computation since $i \in X$ implies that all fringes of $i$ belong to $X$.
Two networks $N'$ and $N''$ are constructed as follows.
The network $N'$ is obtained from $N$ by contracting $\tilde{V} \setminus X$ into a single terminal $s'$ and by removing all $\alpha$-fringes for $\alpha \in S''$.
Similarly, the network $N''$ is obtained from $N$ by contracting $X$ into a single terminal $s''$ and by removing all $\alpha$-fringes for $\alpha \in S'$.
Suppose that we have a locking multiflow $f'$ in $N'$ and locking multiflow $f''$ in $N''$.
Then a locking multiflow $f$ in $N$ is obtained by ``aggregating'' $f'$ and $f''$ as follows.
An $\alpha$-path $Q$ in $N'$ not connecting $s'$ is regarded as an $\alpha$-path in $N$.
Set $\app{f}{Q} \defeq \app{f'}{Q}$ for such a path $Q$.
Similarly, set $\app{f}{Q} \defeq \app{f''}{Q}$ for each $\alpha$-path $Q$ in $N''$ not connecting $s''$.
Next consider paths connecting $s'$ in $N'$ and $s''$ in $N''$.
Observe that $\setprn{s'}$ is a minimum $s'$-cut in $N'$ and $\setprn{s''}$ is a minimum $s''$-cut in $N''$.
An edge $e$ in $N$ joining $X$ and $\tilde{V} \setminus X$ becomes an edge connecting $s'$ in $N'$ and an edge connecting $s''$ in $N''$.
Then $\app{f'}{e} = \app{f''}{e} = \app{c}{e}$ necessarily holds.
Consider an $s'$-path $Q'$ in $N'$ and $s''$-path $Q''$ in $N''$ containing $e$.
The two paths $Q'$ and $Q''$ are concatenated along $e$ into an $\paren{s_\beta, s_\gamma}$-path $Q$ in $N$ for $s_\beta \in S', s_\gamma \in S''$, and set $\app{f}{Q} \defeq \min \setprn{ \app{f'}{Q'}, \app{f''}{Q''}}$.
Decrease $f'$ by $\app{f}{Q}$ on $Q'$ (no $s''$-flows in $N''$), and decrease $f''$ by $\app{f}{Q}$ on $Q''$.
Repeating this process until there are no $s'$-flows in $N'$, we obtain a multiflow $f$ in $N$.
Here $f$ is a locking in $N$.
This follows from the fact (obtained from uncrossing) that for $\alpha \in \intset{k}$ with $s_\alpha \in S'$ (resp. $S''$), a minimum $\alpha$-cut in $N'$ (resp. $N''$) is a minimum $\alpha$-cut in $N$.
Multiflows are kept as node-arc forms.
This procedure, called the \emph{aggregation},
can be done in $\Order{nm}$ time as in~\cite[Section 2.2]{Ibaraki1998}.
Suppose that $\absprn{S} \leq 3$.
Suppose that there is an $\alpha$-fringe.
Compute a minimum $\alpha$-cut $X$.
Construct $N'$ and $N''$ as above, find locking multiflows $f'$ in $N'$ and $f''$ in $N''$, and aggregate $f'$ and $f''$ into a locking multiflow $f$ in $N$.
In $N'$, there are two terminals, and a locking multiflow is obtained by a maximum flow.
In $N''$, there are (at most) three terminals but no $\alpha$-fringes.
After recursing at most three times, we arrive at the situation that there are no fringes.
This situation is precisely the same as \cite[Section 2.1]{Ibaraki1998}.
Then a locking multiflow is obtained in at most three max-flow computations.
The time complexity of this algorithm is analyzed in precisely the same way as \cite[Section 2.3]{Ibaraki1998}, sketched as follows.
For simplicity of analysis, we use Orlin's $\Order{nm}$-time algorithm~\cite{Orlin2013} to find a maximum flow and minimum cut.
Let $\app{T}{k, n, m}$ denote the time complexity of the algorithm applied to Potts $k$-submodular functions on graph $\paren{V, E}$ with $\absprn{V} = n$, and $\absprn{E} = m$.
Suppose that the time complexity of the max-flow algorithm and the aggregation procedure are bounded by $D nm$ and by $D'nm$ for constants $D$ and $D'$, respectively.
We show by induction that $\app{T}{k, n, m} \leq C nm \log k$ for a constant $C$ (to be determined later).
For $k \leq 3$, it holds $\app{T}{3, n, m} \leq \paren{4D + 3D'} nm$.
Suppose that $k \geq 4$.
Then $\app{T}{k, n, m} \leq \app{T}{k/2, n', m'} + \app{T}{k/2, n'', m''} + D nm + D' nm$ with $n' + n'' = n + 2$.
By induction, we have
\begin{align*}
\app{T}{k, n, m} & \leq C n'm' \log k/2 + C n''m'' \log k/2 + \paren{D+D'} nm \\
& \leq C nm \log k - C nm \paren{1 - 2 \paren{\log k/2}/n} + \paren{D+D'}nm \\
& \leq C nm \log k - C nm/2 + \paren{D+D'} nm,
\end{align*}
where we use $k \leq n$ and $2 \paren{\log n/2}/n \leq 1/2$.
For $C \geq 4 \paren{D+D'}$, it holds $\app{T}{k, n, m} \leq C nm \log k$ as required.
This completes the proof of Theorem~\ref{thm:Potts}.
\subsection{Enumeration aspect}
\label{sec:enumeration}
The compact representation for $\paren{\mathbin\sqcap, \mathbin\sqcup}$-closed sets by an elementary PIP is kind of a data compression.
Hence it is natural to consider an efficient way to extract elements of the original $\paren{\mathbin\sqcap, \mathbin\sqcup}$-closed set.
This corresponds to the enumeration of consistent ideals of an elementary PIP.
As seen in Remark~\ref{lem:pip_and_cnf}, consistent ideals correspond to true assignments of a Boolean 2-CNF.
Thus we can enumerate all consistent ideals in output-polynomial time~\cite{Feder1994} (i.e., the algorithm stops in time polynomial in the length of the input and output).
Maximal consistent ideals are of special interest, as described in Section~\ref{sec:relaxation}.
For a PIP $P$, let $\maxconsideals{P}$ denote the family of maximal consistent ideals.
Now we consider the enumeration of $\maxconsideals{P}$.
This can also be done in output-polynomial time by using the algorithm of~\cite{Kavvadias2000} in $\Order{k^3 n^3}$ time per output.
We here develop a considerably faster algorithm for the elementary PIP of a Potts $k$-submodular function $\tilde{g}$.
Our algorithm utilizes its amalgamated structure by posets (Theorem~\ref{thm:PIP_Potts}).
In fact, the structure of $\maxconsideals{P}$ is quite simple, which we now explain.
Let $\Sigma_1, \Sigma_2, \ldots, \Sigma_k$ be the posets, and $P \defeq \bigcup_{\alpha \in \intset{k}} \Sigma_\alpha \times \setprn{\alpha}$ the PIP defined in the previous section.
For distinct $\alpha, \beta \in \intset{k}$, let $\Sigma_{\alpha, \beta} \defeq \Sigma_\alpha \cap \Sigma_\beta$ be the subposet of $\Sigma_\alpha$.
In particular, $\Sigma_{\alpha, \beta}$ is equal to $\Sigma_{\beta, \alpha}$ as a set, and the partial order of $\Sigma_{\alpha, \beta}$ is the reverse of that of $\Sigma_{\beta, \alpha}$ by Lemma~\ref{lem:intersection_of_isolating_cuts}.
Let $\Sigma_{\alpha, 0} \defeq \Sigma_\alpha \setminus \bigcup_{\beta \in \intset{k} \setminus \setprn{\alpha}} \Sigma_{\alpha, \beta}$.
Now $\Sigma_1 \cup \Sigma_2 \cup \cdots \cup \Sigma_k$ is the disjoint union of $\Sigma_{\alpha, \beta}$ and $\Sigma_{\alpha', 0}$ for $\alpha, \alpha', \beta \in \intset{k}$ with $\alpha < \beta$ (recall Lemma~\ref{lem:uncrossing} that the intersection of three distinct $\Sigma_\alpha, \Sigma_\beta, \Sigma_\gamma$ is empty).
Define the poset $R$ by
\begin{align*}
R \defeq \bigcup_{1 \leq \alpha < \beta \leq k} \Sigma_{\alpha, \beta},
\end{align*}
where partial order $\leq$ on $R$ is defined as: the relation on $\Sigma_{\alpha, \beta}$ is the same as the partial order of $\Sigma_{\alpha, \beta}$ and there is no relation between $\Sigma_{\alpha, \beta}$ and $\Sigma_{\alpha', \beta'}$ for $\paren{\alpha, \beta} \neq \paren{\alpha', \beta'}$.
For an ideal $J$ of $R$, let $\overline{J}$ be defined by
\begin{align*}
\overline{J} \defeq
\paren{
\bigcup_{1 \leq \alpha \leq k} \Sigma_{\alpha, 0} \times \setprn{\alpha}
}
\cup
\paren{
\bigcup_{1 \leq \alpha < \beta \leq k}
\paren{J \cap \Sigma_{\alpha, \beta}} \times \setprn{\alpha}
\cup
\paren{\Sigma_{\beta, \alpha} \setminus J} \times \setprn{\beta}
}.
\end{align*}
\begin{theorem} \label{thm:enumeration_potts}
The map $J \mapsto \overline{J}$ is a bijection from the ideal family of $R$ to $\maxconsideals{P}$.
\end{theorem}
\begin{proof}
Let $J$ be an ideal of $R$.
We first show that $\overline{J}$ is a consistent ideal.
Consider $\paren{X', \alpha} \leq \paren{X, \alpha} \in \overline{J}$.
If $\paren{X, \alpha} \in \Sigma_{\alpha, 0} \times \setprn{\alpha}$, then $\paren{X', \alpha} \in \Sigma_{\alpha, 0} \times \setprn{\alpha} \subseteq \overline{J}$ since $\Sigma_{\alpha, 0} \times \setprn{\alpha}$ is an ideal by (EP1).
Suppose that $\paren{X, \alpha} \in \paren{J \cap \Sigma_{\alpha', \beta'}} \times \setprn{\alpha'}$.
Then $\alpha = \alpha'$.
Since $J$ is an ideal in $\Sigma_{\alpha, \beta}$, $J \cup \Sigma_{\alpha, 0}$ is an ideal in $\Sigma_\alpha$.
Consequently $X' \in J \cup \Sigma_{\alpha, 0}$, and $\paren{X', \alpha} \in \overline{J}$.
Suppose that $\paren{X, \alpha} \in \paren{\Sigma_{\beta', \alpha'} \setminus J} \times \setprn{\beta}$. Then $\alpha = \beta'$.
Observe that $\Sigma_{\beta', 0} \cup \Sigma_{\beta', \alpha'} \setminus J$ is an ideal in $\Sigma_{\beta'}$.
From this, we obtain $\paren{X', \alpha} \in \overline{J}$, as above.
Since $\overline{J}$ contains exactly one of $\paren{X, \alpha}, \paren{X, \beta} \in \Sigma$ with $\alpha \neq \beta$, the image $\overline{J}$ is consistent and maximal.
Let $I$ be a maximal consistent ideal of $\Sigma$.
Necessarily $I$ contains $\Sigma_{\alpha, 0} \times \setprn{\alpha}$ for all $\alpha \in \intset{k}$.
Consider $\paren{X, \alpha}, \paren{X, \beta} \in \Sigma$ with $\alpha \neq \beta$.
Then $I$ contains exactly one of $\paren{X, \alpha}, \paren{X, \beta}$.
Otherwise, consider the principal ideal $I'$ of $\paren{X, \alpha}$, and the ideal $I \cup I'$.
By maximality, $I \cup I'$ is inconsistent.
Then there are $\paren{Y, \alpha} \in I'$ and $\paren{Y, \beta'} \in I$ with $\alpha \neq \beta'$.
By (EP1), (EP2) and Lemma~\ref{lem:intersection_of_isolating_cuts}, there is $\paren{X, \beta'} \in \Sigma$ with $\paren{X, \beta'} \leq \paren{Y, \beta'}$.
Since $I$ is an ideal, it holds $\paren{X, \beta'} \in I$.
Necessarily $\beta = \beta'$ and $\paren{X, \beta} \in I$; this is a contradiction.
For distinct $\alpha, \beta \in \intset{k}$ let $J_{\alpha, \beta} \defeq \setprnsep{X}{\paren{X, \alpha} \in (I \cap \Sigma_{\alpha, \beta}) \times \setprn{\alpha}}$. Then $\Sigma_{\alpha, \beta}$ is the disjoint union of $J_{\alpha, \beta}$ and $J_{\beta, \alpha}$ (as a set).
Thus, letting $J \defeq \bigcup_{1 \leq \alpha < \beta \leq k} J_{\alpha, \beta}$,
\end{proof}
Therefore our problem of enumerating all maximal minimizers of $\tilde g$ is reduced to the enumeration of all ideals of poset $R$.
This is a well-studied enumeration problem.
One of the current best algorithms is Squire's algorithm~\cite{Squire1995} that enumerates all ideals of an $n$-element poset in amortized $\Order{\log n}$ time per output.
\begin{theorem}
From the elementary PIP for the minimizer set of Potts $k$-submodular function $\funcdoms{\tilde{g}}{{S_k}^n}{\setR}$, all maximal minimizers of $\tilde{g}$ can be enumerated in amortized $\Order{\log n}$ time per output.
\end{theorem}
\begin{remark}
The above poset $R$ may be viewed as a ``compact representation'' of maximal minimizers of Potts $k$-submodular function $\tilde{g}$.
In a general elementary PIP $P$ (for the minimizer set of a general $k$-submodular function), such a compact representation is still possible if $P$ has a maximal consistent ideal $C$
satisfying the following property:
%
\begin{itemize}
\item[(P)] $C$ contains exactly one of $x^\circ$ and $y^\circ$ for each $i, j$ of the case (EP2-1).
\end{itemize}
%
In this case, as in $J \mapsto \overline{J}$, there is a bijection between $\consideals{P \setminus C}$ and $\maxconsideals{P}$.
One can see that the PIP $P \setminus C$ has a simple structure similar to the above poset $R$ (though it is not elementary).
We developed an algorithm to enumerate consistent ideals of
$P \setminus C$ in $\Order{n}$ time per output, and announced in the conference version of this paper~\cite{isco2016} that such a fast enumeration is possible for maximal consistent ideals
of PIP $P$.
However we found an elementary PIP that having no maximal consistent ideal with the property (P); consider PIP $P = \setprn{x, x', y, y', z, z'}$ with $x \mathrel{\overset{{}_{\scriptscriptstyle{\bullet}}}{\smile}} x'$, $y \mathrel{\overset{{}_{\scriptscriptstyle{\bullet}}}{\smile}} y'$, $z \mathrel{\overset{{}_{\scriptscriptstyle{\bullet}}}{\smile}} z'$, $x \succ y' \prec z$, $y \succ z' \prec x$, and
$z \succ x' \prec y$.
Therefore \cite[Theorem 14]{isco2016} is not true for such a PIP.
\end{remark}
\section{Application}
\label{sec:application}
\subsection{$k$-submodular relaxation}
\label{sec:relaxation}
A \emph{$k$-submodular relaxation} $\tilde{f}$ of a function $\funcdoms{f}{\intset{k}^n}{\overline{\setR}}$ is a $k$-submodular function on ${S_k}^n$ such that $\app{f}{x} = \app{\tilde{f}}{x}$ for all $x \in \intset{k}^n \paren{\subseteq {S_k}^n}$.
Iwata--Wahlstr\"{o}m--Yoshida~\cite{IwataY2016} investigated $k$-submodular relaxations as a key tool for designing efficient FPT algorithms.
Gridchyn--Kolmogorov~\cite{Gridchyn2013} applied $k$-submodular relaxations to labeling problems on computer vision, which we describe below.
A label assignment is a process of assigning a label to each pixel of a given image.
For example, in the object extraction, each pixel is labeled as ``foreground'' or ``background''.
In stereo matching, the disparity of each pixel is computed from the given two photos taken from slightly different positions, and the pixel is labeled according to the estimated depth.
We consider the labels to be numbered from 1 to $k$.
Such a labeling problem is formulated as the problem of minimizing an \emph{energy function}.
A Potts energy function is simple but widely used energy function.
However the exact minimization of a Potts energy function is computationally intractable.
Gridchyn--Kolmogorov~\cite{Gridchyn2013} applied the $k$-submodular relaxation, that is, the energy function is relaxed to a $k$-submodular function by allowing some pixels to have 0 (meaning ``non-labeled'').
The following property, called \emph{persistency}~\cite{Gridchyn2013, IwataY2016}, is the reason why they introduced the relaxation.
\begin{theorem}[{\cite[Proposition~10]{Gridchyn2013} and~\cite[Lemma~2]{IwataY2016}}] \label{thm:persistency}
Let $\funcdoms{f}{\intset{k}^n}{\overline{\setR}}$ be a function and $\funcdoms{\tilde{f}}{{S_k}^n}{\overline{\setR}}$ a $k$-submodular relaxation of $f$.
For every minimizer $x \in {S_k}^n$ of $\tilde{f}$, there exists a minimizer $y \in \intset{k}^n$ of $f$ such that $x_i \neq 0$ implies $x_i = y_i$ for each $i \in \intset{n}$.
\end{theorem}
Namely, each minimizer of $\tilde{f}$ gives us partial information about a minimizer of $f$.
An efficient algorithm for minimizing $k$-submodular relaxations of Potts functions was also proposed in~\cite{Gridchyn2013}.
Hence we can obtain a partial labeling extensible to an optimal labeling, which we call a \emph{persistent labeling}.
In Section~\ref{sec:potts} we gave an efficient algorithm to construct the elementary PIP representing all the minimizers of a Potts $k$-submodular function.
Since minimizers that contain more nonzero elements have more information, we want to find a minimizer whose support is largest.
In fact, such minimizers are precisely maximal minimizers.
\begin{proposition}
Let $M$ be a $\paren{\mathbin\sqcap, \mathbin\sqcup}$-closed set on ${S_k}^n$.
The supports of maximal elements in $M$ are the same.
\end{proposition}
\begin{proof}
Let $x, y \in M$ be maximal and $z \defeq \paren{x \mathbin\sqcup y} \mathbin\sqcup y$.
For each $i \in \intset{n}$, it holds $z_i = x_i$ if $y_i = 0$ and $z_i = y_i$ if $y_i \neq 0$.
In particular, $y \preceq z$ and $\mathop{\mathrm{supp}} z = \mathop{\mathrm{supp}} x \cup \mathop{\mathrm{supp}} y$ hold.
Since $y$ is maximal, we obtain $y = z$ and $\mathop{\mathrm{supp}} x \subseteq \mathop{\mathrm{supp}} y$.
By changing the role of $x$ and $y$, we also have $\mathop{\mathrm{supp}} x \supseteq \mathop{\mathrm{supp}} y$.
Thus $\mathop{\mathrm{supp}} x = \mathop{\mathrm{supp}} y$.
\end{proof}
From this lemma, it turns out that all maximal minimizers of $\tilde{f}$ have the same and largest amount of information about minimizers of $f$.
In labeling problem with Potts energy, all maximal persistent labelings (with respect to a $k$-submodular relaxation) can be efficiently generated by the algorithm in Section~\ref{sec:enumeration}.
\subsection{Experiments}
We implemented our algorithm on the stereo matching problem with Potts energy function~\eqref{eq:potts}.
This has an aspect of the replication of the experiment in~\cite{Gridchyn2013}, but we computed not only one of the persistent labelings but also its PIP-representation.
We used ``tsukuba'' and ``cones'' in the Middlebury data~\cite{Scharstein2003, Scharstein2001} as input images.
\paragraph{Problem setting and formulation.}
We are given photo images $L$ and $R$ taken from left and right positions, respectively.
The images $L$ and $R$ are $N \times M$ arrays such that entries $\sqapp{L}{x, y}$ and $\sqapp{R}{x, y}$ are RGB vectors $\in \setprn{0, 1, 2, \ldots, 255}^3$ of the intensity at pixel $\paren{x, y}$, where each pixel is represented by a pair $\paren{x, y}$ of its horizontal coordinate $x = 1, 2, \ldots, N$ and vertical coordinate $y = 1, 2, \ldots, M$.
The goal of the stereo matching problem is to assign to each pixel the ``disparity label'' $\in \intset{k}$ that represents the depth of the object on the pixel.
We model this problem as a minimization of a Potts energy function~\eqref{eq:potts} on diagonal grid graph $\paren{V, E}$, where $V$ is the set of pixels, and two pixels $\paren{x, y}$ and $\paren{x', y'}$ have an edge in $E$ if and only if $\absprn{x - x'} \leq 1$ and $\absprn{y - y'} \leq 1$.
The first and the second term of~\eqref{eq:potts} are called ``data term'' and ``smoothness term''~\cite{Scharstein2001}, respectively.
For each pixel $i \in V$, the data term $g_i$ measures how well the estimated disparity of pixel $i$ agrees with the pair of given images.
We employed the traditional averaged SSD (sum of squared difference) costs as in~\cite{Gridchyn2013}:
\begin{align}
\app{g_i}{\alpha} \defeq \text{the nearest integer of $\frac{1}{\absprn{W_i}} \sum_{\paren{x, y} \in W_i} \norm{\sqapp{L}{x, y} - \sqapp{R}{x - d_\alpha, y}}^2$}
\quad
\paren{\alpha \in \intset{k}},
\end{align}
where $W_i$ is the $9 \times 9$ window centered at $i = \paren{x, y}$ (i.e., the set of pixels $\paren{x', y'}$ with $\absprn{x' - x} \leq 4$ and $\absprn{y' - y} \leq 4$), $\norm{\cdot}$ is the 2-norm, $d_\alpha \geq 0$ is the disparity corresponding to the label $\alpha$.
We set $d_\alpha \defeq 2 \paren{\alpha - 1}$ for each $\alpha \in \intset{k}$.
For each pair of adjacent pixels $\setprn{i, j} \in E$, the smoothness term increases the energy by $\lambda_{i, j}$ if $i$ and $j$ have different labels.
We set every $\lambda_{i, j}$ to be the same value $\lambda$ as in~\cite{Gridchyn2013}, and conducted experiments with $\lambda = 1$ and 20 to see the effect of $\lambda$.
\paragraph{Experimental results.}
\begin{figure}[tbp]
\begin{minipage}[t][4.5cm][t]{0.33\linewidth}
\centering
\includegraphics[scale=0.35]{image/tsukuba_1.png}
\subcaption{$\lambda = 1$}
\end{minipage}%
\begin{minipage}[t][4.5cm][t]{0.33\linewidth}
\centering
\includegraphics[scale=0.35]{image/tsukuba_20.png}
\subcaption{$\lambda = 20$}
\end{minipage}%
\begin{minipage}[t][4.5cm][t]{0.33\linewidth}
\centering
\includegraphics[scale=0.35]{image/tsukuba_true.png}
\subcaption{ground truth}
\end{minipage}
%
\begin{minipage}[b]{0.33\linewidth}
\centering
\includegraphics[scale=0.3]{image/cones_1.png}
\subcaption{$\lambda = 1$}
\end{minipage}%
\begin{minipage}[b]{0.33\linewidth}
\centering
\includegraphics[scale=0.3]{image/cones_20.png}
\subcaption{$\lambda = 20$}
\end{minipage}%
\begin{minipage}[b]{0.33\linewidth}
\centering
\includegraphics[scale=0.3]{image/cones_true.png}
\subcaption{ground truth}
\end{minipage}
%
\caption{Results for ``tsukuba'' (top row) with $k = 16$ and ``cones'' (bottom row) with $k = 26$.}
\label{fig:result_image}
\end{figure}
Figure~\ref{fig:result_image} and Table~\ref{tbl:result} show the results of our experiment.
The pixels labeled in the minimum persistent labeling are colored in gray of the brightness corresponding to each label.
The blue pixels are unlabeled even in maximal persistent labelings.
The red pixels are the difference between the minimum persistent labeling and maximal ones, i.e., the pixel was labeled in (any of) maximal persistent labelings but not in the minimum one.
We can observe that there are few red pixels as mentioned in~\cite{Gridchyn2013}, and they are mainly located on the boundary of two regions with different labels.
A possible reason is the following: consider a simple 1-dimensional case where a pixel $i$ is adjacent only to pixels $j$ and $j'$.
Let $x \in {S_k}^n$ be the minimum persistent labeling and assume $x_{j'} \neq x_j \neq 0$.
Then the increment of the energy is the same ($= \lambda$) even if $x_i$ is set to any of $\setprn{0, x_j, x_{j'}}$.
Therefore the pixel $i$ will be red if $\app{\tilde{g}_i}{0} = \app{\tilde{g}_i}{x_j}$, and thus we think that this will occur in boundaries more frequently than inside of regions.
With regard to the effect of $\lambda$, the larger $\lambda$ decreases the percentages of gray and red pixels on both tsukuba and cones, and increases the blue pixels to the contrary.
This result agrees with the experiments in~\cite{Gridchyn2013}.
We consider that this is due to the fact that the value of each $\app{\tilde{g}_i}{0}$ is moderately lower in $\tilde{g}_i$ since $\app{\tilde{g}_i}{0}$ is the average of the minimum and the second minimum values of $g_i$ as described in Section~\ref{sec:potts}.
Hence if $\lambda$ is large, the energy will be lower just by letting all $x_i \defeq 0$ than by tuning each $x_i$ finely according to the values of the corresponding data term $\tilde{g}_i$.
\begin{table}[tbp]
\centering
\caption{Experimental result}
%
\begin{tabular}{l|r|ccc|c}\hline
image & \multicolumn{1}{|c|}{$\lambda$} & \% of gray & \% of red & \% of blue & \# of max. pers. labelings \\ \hline \hline
tsukuba & $1$ & 93.84 & 0.53 & 5.63 & $2^{66} \times 3^{5} \times 4 \times 5^2 \times 18$\\
tsukuba & $20$ & 90.64 & 0.07 & 9.29 & $2^{11}$ \\
cones & $1$ & 99.00 & 0.30 & 0.70 & $2^{114} \times 3^{9} \times 5$ \\
cones & $20$ & 93.37 & 0.04 & 6.59 & $2^{17} \times 3$ \\
\hline
\end{tabular}
%
\label{tbl:result}
\end{table}
\begin{table}[tbp]
\centering
\caption{Experimental result without rounding in $g_i$}
%
\begin{tabular}{l|r|ccc|p{50pt}c}\hline
\multirow{2}{*}{image} & \multicolumn{1}{c|}{\multirow{2}{*}{$\lambda$}} & \multirow{2}{*}{\% of gray} & \multirow{2}{*}{\% of red} & \multirow{2}{*}{\% of blue} & \multicolumn{2}{c}{\# of pers. labelings} \\ \cline{6-7}
&&&&& \hfil all \hfil & \hfil max \hfil \\ \hline \hline
tsukuba & $1$ & 94.18 & 0.007 & 5.81 & \hfil $2^4 \times 3^3$ \hfil & \hfil $2^3$ \hfil \\
tsukuba & $20$ & 90.71 & 0.002 & 9.29 & \hfil $2^2$ \hfil & \hfil 1 \hfil \\
cones & $1$ & 99.20 & 0.007 & 0.80 & \hfil $2^7 \times 3^2$ \hfil & \hfil $2^2$ \hfil \\
cones & $20$ & 93.40 & 0.000 & 6.60 & \hfil 1 \hfil & \hfil 1 \hfil \\
\hline
\end{tabular}
%
\label{tbl:result_without_rounding}
\end{table}
\paragraph{The structure of the PIP.}
\begin{figure}[tbp]
\centering
\includegraphics[scale=0.16]{image/tred.pdf}
\caption{The elementary PIP for persistent labelings of tsukuba with $\lambda = 1$.}
\label{fig:result_pip}
\end{figure}
Figure~\ref{fig:result_pip} shows the PIP-representation for the partial labelings on tsukuba with $\lambda = 1$.
The PIP consists of many small connected PIPs, which correspond to each of connected red regions in Figure~\ref{fig:result_image}.
Thus we can easily calculate the number of maximal persistent labelings by multiplying the number of maximal consistent ideals of each connected PIP (notice that an ideal of the PIP is maximal and consistent if and only if it contains all elements having no inconsistent pair and one element of each minimally inconsistent pairs).
The right most column of Table~\ref{tbl:result} shows the number of maximal persistent labelings in each experiment.
We discovered the fact that there are plenty of maximal persistent labelings even though the percentages of red pixels are small.
\paragraph{Effect of rounding.}
In our experiment, the data term $g_i$ is defined to be integer-valued by rounding a rational to the nearest integer.
One of the referees conjectured that if $g_i$ is defined without the rounding, then there is a unique persistent labeling.
We did an experiment to verify this conjecture.
Table~\ref{tbl:result_without_rounding} shows the result.
Without the rounding, the percentage of the red pixels and the number of persistent labelings dramatically decrease, though there are some cases where a persistent labeling is not unique.
\section*{Acknowledgments}
We thank Kazuo Murota, Satoru Fujishige, and the referees for helpful comments.
This work was partially supported by JSPS KAKENHI Grant Numbers 25280004, 26330023, 26280004, and by JST, ERATO, Kawarabayashi Large Graph Project.
\input{reference.bbl}
\end{document}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 8,682
|
Q: Can an assignment result in a potentially expensive deep-copy of a tuple? The Rust Programming Language states:
So what types are Copy?
[...]
*
*Tuples, if they only contain types that are also Copy. For example, (i32, i32) is Copy, but (i32, String) is not.
Does this mean that an assignment of a tuple with a considerable number of elements that are also Copy can result in a potentially expensive deep-copy of a tuple?
In this example, would Rust make a deep copy of the tuple and all of its contents?
let tpl = (0, 1, 2, 3, 4, 5, 6, 7, 8, 9); // and many more entries
let tpl2 = tpl;
println!("{:?} {:?}", tpl, tpl2);
This seems counter-intuitive for a language that is fast in almost everything it does. Are tuples (of items that are Copy) just meant to be short enough that this will not have an impact on performance?
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 5,635
|
Жак де Серізе́ (; 1594, Париж — листопад 1653, Ла-Рошфуко, департамент Шаранта) — французький поет, літератор. Член Французької академії, а також один із її засновників.
З біографії
Жак де Серізе працював в управлінні володіннями герцогів Ла Рошфуко. 1634 року він відіграв важливу роль у заснуванні Французької академії та став її першим президентом. Він також був першим власником крісла № 3. Серізе, член Товариства друзів Конрата, був одним з двох противників заснування Французької академії під протекторатом кардинала де Рішельє.
В кінці 1653 року Жак Де Серізе помер, а навесні наступного року його наступником в академії був обраний єпископ Поль-Філіпп де Шомон.
Творчість
Щодо друкованих збірок поета відомостей немає, однак є інформація, що деякі вірші та твори було надруковано в збірках іншого французького митця Charles de Sercy.
Література
Paul Mesnard: Historie de l'Académie française depuis sa fondation jusqu'en 1830. Charpentier, Paris 1857.
Посилання
Померли 1653
Народились 1594
Члени Французької академії
Французькі поети
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 6,388
|
Q: XPATH Query in JRXML I have the following xml file :
<?xml version="1.0" encoding="UTF-8"?>
<pages>
<page>
<firstname>X</firstname>
<lastname>Y</lastname>
</page>
<page>
<firstname>Z</firstname>
<lastname>V</lastname>
</page>
<page>
<firstname>B</firstname>
<lastname>S</lastname>
</page>
</pages>
I want to calculate the number of times page tag is appearing in my XML.
This information I want to pass it to the subreport which is included in my main report.
The main report has access to the XML file.
How can I do this ?
Something like
<queryString language="xPath">
<![CDATA[pages/page]]>
</queryString>
I am not sure.
A: The XPath expression that counts page elements is count(//page). Have you tried it ?
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 2,523
|
Q: How do the new Missions work in CS GO?
With the latest Patch and Operation Breakthrough Valve has introduced Missions to the game. As far as I can see you get 2 objectives with 1 Mission.
My question is, do the missions cycle over time? Or do you first have to complete all Missions before you get 2 new ones? How often will you be able to get a new Mission and do you need the operation badge to complete them?
A: As missions are quite new, I can only tell from my experience:
How missions work in general
Every mission explains itself in its short description. Most of them are "win a complete match on this specific map" or "get a number of kills in this specific game mode". After you completed this mission, you get rewarded with a weapon drop.
A little bit more in detail
You do have 2 missions at start. Every mission is explained quite simple and in order to achieve it / get your reward you need to finish the map you would complete the mission - so don't leave to early.
For example: "Get 6 kills in game mode Destroy." This means you have to look for a game in this game mode. You will join a server and you likely will kill 6 people. After you have killed those guys, be sure you stay until this map is finished.
In the end screen score board, you will receive your mission reward as a weapon drop. (Since now I only got trash drops, I don't know if they cover up uncommon or rare items, too. All items seem to be out of the new added items, no old ones.)
How to get new/more missions
For this you only have to play one supported game in the finding a game screen. This covers up match making, Gungame, Destroy and so on. In the end of the game, where weapons drop, you will now have an additional chance of a mission drop.
So if you need some missions, you may play a few Gungames, as they're finished quite fast and you get the chance for a mission drop after each game.
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 5,505
|
- Reserve Today! -
Family Resort Camping on Lake George in Portage, WI!
Our Campground
Maps & Rules
On-Site Fun
Themed Weekends
Free Golf
Camp With Us
Group Getaways
Pride of America Camping Resort strives to ensure that its services are accessible to people with disabilities. We have invested a significant amount of resources to help ensure that this website is made easier to use and more accessible for people with disabilities, with the strong belief that every person has the right to live with dignity, equality, comfort and independence.
Accessibility on camppoa.com
camppoa.com.com makes available ADA-friendly software that is powered by a dedicated accessibility server. The software allows camppoa.com.com to improve its compliance with the Web Content Accessibility Guidelines (WCAG 2.1).
The camppoa.com accessibility menu can be enabled by clicking the accessibility menu icon that appears on the right hand side of each page. After triggering the accessibility menu, please wait a moment for the accessibility menu to load in its entirety.
Pride of America Camping Resort continues its efforts to constantly improve the accessibility of its site and services in the belief that it is our collective moral obligation to allow seamless, accessible and unhindered use also for those of us with disabilities.
Despite our efforts to make all pages and content on camppoa.com.com fully accessible, some content may not have yet been fully adapted to the strictest accessibility standards. This may be a result of not having found or identified the most appropriate technological solution.
If you are experiencing difficulty with any content on camppoa.com.com or require assistance with any part of our site, please contact us during normal business hours as detailed below and we will be happy to assist.
If you wish to report an accessibility issue, have any questions or need assistance, please contact camppoa.com Customer Support by clicking the link below:
W7520 West Bush Road, Pardeeville, WI 53954
800-236-6395 | Send us an email | Accessibility Statement
© 2023 Pride of America Camping Resort. All rights reserved.
#TheOneForFun
Website Design by Campground Studios
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 6,516
|
{"url":"https:\/\/answers.opencv.org\/question\/49991\/pose-estimation-and-feature-detection\/","text":"# Pose Estimation and Feature Detection\n\nHi all,\n\nI am trying to make a fiducial (QR marker) based pose estimation program which would be able to track multiple markers. I have started by building upon the OpenCV documentation example.\n\nTo do so I started by finding key points and descriptors using the SIFT algorithm. Then a used Brute Force matching to find good matches (used ratio test as well).\n\nNow I need to use solvePnpRansac to find the pose estimation. However, as per my understanding the pose estimation algorithm requires coordinates between the real world object and 2D scene. How can I get the coordinates of the keypoints which have been matched by the SIFT algorithm?\n\nThanks.\n\nedit retag close merge delete\n\nSort by \u00bb oldest newest most voted\n\nDepends on your application. Do you have a set of fixed markers or a several markers which can move around the scene ?\n\nAs you said, solvePNP will give the RT matrix of a camera given the 3D coordinates of some points on the image, and these coordinates have to be known by another method.\n\nFor augmented reality with markers, the concept is that you have an idea about the real-world size of the markers a priori, so, for instance, for a 10cm square marker you can say that the coordinates of its corners are (0,0,0), (0.1,0,0), (0,0.1,0), (0.1,0.1,0). Once you have detected it, solvePNP will give you the relative pose of the camera towards this marker.\n\nNote that the RT matrix is the transform that converts absolute world coordinates to relative coordinates towards the camera. So, if the centre of the marker is the position P = (0.05,0.05,0,1.0) (homogeneous coordinates) will be the centre of the marker, and its relative position in relation to the camera will be RT*P. This can be also be used to determine the marker orientation.\n\nLikewise, if you want draw something as overlay over the marker (augmented reality), you can use the coordinates of the marker as the \"world coordinates\", and render the overlay based in the computed camera pose.\n\nThat said, if you have several mobile markers, you have to compute for each marker the relative pose of the camera from it with separated calls of solvePNP.\n\nNote that if the appearance of the markers is known, and you don't have their real-world size, you will have to assign a defined size in an arbitrary unit, since there is a infinite number of possible sizes + 3D positions which will have the same appearance in the camera.\n\nImportant: RT is a 4x4 Matrix and P is a 4x1 matrix (x,y,z,w) where w is 1.0 (homogeneous coordinates). Solve PNP will give you the the euler angles R', and a translation matrix T'. You should compute the rotation matrix R (3x3) using cv::Rodrigues. I use the following procedure to compute RT from rvec and tvec from solvePNP :\n\nvoid RvecTvecToRT(cv::Mat& Rvec, cv::Mat& Tvec, cv::Mat& RT)\n{\n\nRT = cv::Mat::eye(4,4,CV_64F); \/\/identity matrix\ncv::Mat R;\ncv::Rodrigues(Rvec, R);\n\/\/We store the R and T that transforms from World to Camera coordinates\nfor(int i = 0; i < 3; i++) {\nRT.at<double>(i,3) = Tvec.at<double>(i,0);\nfor(int j = 0; j < 3; j++) {\nRT.at<double>(i,j) = R.at<double>(i,j);\n}\n}\n\n}\n\n\nBased in your comment, it is very similar with what I had implemented such thing long time ago, using pictures as AR markers.\n\nBasically, as pre-processing step, you have first to compute the keypoints and associated descriptors for each AR marker. That is, for a marker, you will have a set of ...\n\nmore\n\nDear Saracchini,\n\nThank you for your reply. I want to find the global pose of an object which has multiple uniquely identifiable markers attached to it at different angles\/view points.\n\nAs you stated, my idea is to pass the solvePnp algorithm the real world (3D) co-ordinates of the identifiable key points. As for the 2D points it would be the co-ordinates of the keypoints which have been positively matched by brute force. I want to know how can I extract the marker identity and 2D co-ordinates of the matched key points for further use in PnP algorithm.\n\nIn actual I want to get an extremely stable sort of ARToolKit type functionality.\n\nThanks for your patience and help.\n\n( 2014-11-11 01:29:04 -0500 )edit\n\nOfficial site\n\nGitHub\n\nWiki\n\nDocumentation\n\n## Stats\n\nSeen: 1,333 times\n\nLast updated: Nov 12 '14","date":"2021-04-15 08:58:16","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 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\": 0.26255255937576294, \"perplexity\": 1112.7932385681731}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 5, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-17\/segments\/1618038084601.32\/warc\/CC-MAIN-20210415065312-20210415095312-00342.warc.gz\"}"}
| null | null |
\section{Introduction}
\label{sec:introduction}
Recently, the parameter twin-width was introduced by Bonnet et al.~\cite{Bonnet0TW20} over a series of papers.
The $\emph{twin-width}$ of a graph $G$, denoted by $\tww(G)$, roughly measures the distance of a graph from being a cograph, and has demonstrated to have various advantages that make it stand out as an important graph parameter.
One of the main motivations to study twin-width comes from the fact that the class of bounded twin-width contains several interesting and diverse graphs as bounded boolean-width, bounded rank-width, bounded clique-width, unit interval, proper-minor closed or also $K_t$-minor free graphs~\cite{BonnetG0TW21}.
On the algorithmic side, FO model checking is \ensuremath{\textsf{FPT}}\xspace on classes with bounded twin-width~\cite{Bonnet0TW20}.
Moreover, various intractable problems like \prob{Independent Set}, \prob{Dominating Set}, and \prob{Clique} can be solved in time $2^{\Oh(k)}n$-time \cite{BonnetG0TW21}.
It is also shown there that graphs of twin-width $d$ admit an interval biclique partition of size $\Oh(dn)$. Using such an edge-partition, they show how to solve \prob{All-Pairs Shortest Paths} in time $\Oh(n^2\log{n})$.
In this report, we show how to solve the \prob{Triangle Counting} problem on graphs with $n$ vertices and $m$ edges in time $\Oh(d^2n+m)$, with $d$ denoting the twin-width of the graph.
A graph $G$ has twin-width at most $d$ if there is a so-called $d$-contraction sequence of $G$, which is defined in Section~\ref{sec:preliminaries}.
Deciding if the twin-width of a graph is at most $4$ is \ensuremath{\textsf{NP}}\xspace-hard~\cite{BergBD21}. Thus, we assume that a $d$-contraction sequence is given together with the graph $G$.
The currently fastest (unparameterized) algorithm for \prob{Triangle Counting} is due to
Alon, Yuster, and Zwick~\cite{AlonYZ97}, that have showed that \prob{Triangle Counting} can be solved in time $\Oh(n^\omega)$ using fast matrix multiplication where $2 \leq \omega < 2.372863$. For sparse graphs one can solve \prob{Triangle Counting} in time $\Oh(m^{\frac{2\omega}{\omega+1}}) = \Oh(m^{1.41})$.
It is conjectured that there is no $\Oh(n^{3-\varepsilon})$ time combinatorial algorithm.
Within a parameterized framework, Coudert, Ducoffe, and Popa gave an algorithm that runs in time $\Oh(\cw^2(n+m))$ where $\cw$ denotes the $\emph{clique-width}$ of the input graph \cite{CoudertDP19} whereas Kratsch and Nelles obtained an $\Oh(\mw^{\omega-1}n+m)$ where $\mw$ is the $\emph{modular-width}$ of the input graph~\cite{KratschN18}.
\section{Preliminaries}
\label{sec:preliminaries}
All graphs considered are finite, undirected, and simple. We refer to \cite{0030488} for the basic concepts and notions of graph theory.
In particular, given a graph $G = (V,E)$, we denote by $V(G)$ its vertex set and by $E(G)$ its edge set.
For a graph $G=(V,E)$ and a subset $X \subseteq V$, we define the induced subgraph over the vertex set $X$ as $G[X] = (X , E')$ where $E' = \{\{u,v\} \in V \mid u, v \in X\}$.
We refer by $N(v)$ to the set of neighbors of a vertex $v \in V(G)$, i.e., $N(v) = \{ u \in V(G) \mid \{u,v\} \in E(G) \} $.
Given a vertex $v \in V(G)$, the \emph{degree} $d(v)$ of $v$ is the number of neighbors of $v$, i.e., $d(v) = |N(v)|$.
Furthermore, we say that two vertices $u,v \in V(G)$ are \emph{twins} if $N(v) \setminus \{u, v \} = N(u) \setminus \{u, v\}$.
For any integers $j, k \in \mathbb{N}$, we denote $[j,k] = \{j,j+1,\ldots,k \}$ and in particular $[k]=[1,k]=\{1,2,\ldots,k\}$.
\subparagraph{Twin-width.}
A \emph{trigraph} $G$ is a triple $G = (V, E, R)$ where $E$ and $R$ are two disjoint sets of edges. We refer to an edge in $E$ as a black edge and to an edge in $R$ as a red edge.
By setting $R = \emptyset$, one can interprete any graph $(V,E)$ as a trigraph $(V,E,\emptyset)$.
A trigraph $G = (V, E, R)$ with maximum red degree $d$, i.e., maximum degree in the graph $(V, R)$, is called a $d$-trigraph.
Furthermore, for any trigraph $G=(V,E,R)$ and any vertex $v \in V$, we denote by $N_R(v)$ the set of red neighbors of $v$, i.e., $N_R(v) = \{ u \in V \mid \{u,v\} \in R \} $.
For a trigraph $G = (V,E,R)$ and two vertices $u, v \in V$, we define $G/u,v = (V', E', R')$ as the trigraph obtained from $G$ by contracting $u$ and $v$ into a new vertex $w$ and after updating the edge sets in the following way: A vertex $x$ is linked to the new vertex $w$ in $G/u,v$ by a black edge if and only if $x$ is linked to $u$ \emph{and} to $v$ in $G$ by a black edge. Moreover, $x$ is not adjacent to $w$, if $x$ is neither adjacent to $u$ nor to $v$ in $G$. In all other cases $x$ is linked to $w$ by a red edge. Formally, $V' = (V \setminus \{u,v\} \cup \{w\})$ with $\{w, x \} \in E'$ if and only if $ \{u,x\} \in E$ and $ \{v,x\} \in E$; $\{w,x\} \notin E' \cup R'$ if and only if $ \{u,x\} \notin E \cup R$ and $\{v,x\} \notin E \cup R$; and $\{w,x\} \in R'$ otherwise. All edges that are not incident to $u$ nor to $v$ remain unchanged in $G/u,v$. Notice that $u$ and $v$ do not need to be adjacent.
For any integer $d \geq 0$, if both $G$ and $G/u,v$ are $d$-trigraphs, $G/u,v$ is called a \emph{$d$-contraction}.
A trigraph $G$ is \emph{$d$-collapsible} if there exists a sequence of $d$-contractions which contracts $G$ to a single vertex.
The minimum integer $d \geq 0$ such that $G$ is $d$-collapsible is called the twin-width of $G$, denoted by $\tww(G)$.
In other words, for any graph $G$ with $\tww(G) = d$, there exists a sequence of trigraphs $G_n, G_{n-1}, \ldots, G_2, G_1$ with $G_n = G$, $G_1 = K_1$ (the clique of size $1$) and $G_k$ is a $d$-contraction of $G_{k+1}$ for $k \in [n-1]$.
To represent such a contraction sequence efficiently, it is sufficient to only specify the vertices that get contracted:
\begin{definition}[Compact representation of a $d$-sequence]\label{def:compactRepresentation}
Let $G = G_n, G_{n-1}, \ldots, G_1 = K_1$ be a $d$-contraction sequence of an $n$-vertex graph $G = (V,E)$ with $V = \{v_1, v_2, \ldots, v_n\}$. Then, we call $(v_{i_k},v_{j_k})_{n \geq k \geq 2}$ with
$G_{k-1} = G_{k}/v_{i_k},v_{j_k}$ a \emph{compact representation} of a $d$-contraction sequence. The graph $G_{k-1}$ results from $G_{k}$ by contracting the two vertices $v_{i_{k}}$ and $v_{j_{k}}$ into a new vertex $v_{{2n-k+1}}$ for $k \in [2,n]$.
\end{definition}
Finally, for a vertex $v \in V(G_k)$, we denote by $\SetOfVertex{v}$ the subset of vertices in $G$ eventually contracted into $v$ in $G_k$ and we denote $\GraphOfVertex{v} = G[\SetOfVertex{v}]$.
\section{Algorithm}\label{sec:algorithm}
In the \prob{Triangle Counting} problem, we are given a graph $G = (V,E)$ and we are asked to count the number of triangles in $G$, that is, the number of elements in the set $\TriInGraph{G} = \{\{x,y,z\} \subseteq \binom{V}{3} \mid \{x,y\},\{y,z\},\{z,x\} \in E \}$. We will prove the following theorem:
\begin{theorem}\label{thm:TriangleCounting}
Let $G = (V,E)$ be a graph with $\tww(G) = d$, and let a compact representation of a $d$-contraction sequence as defined in Definition~\ref{def:compactRepresentation} be given. Then, one can solve \prob{Triangle Counting} in time $\Oh(d^2n+m)$.
\end{theorem}
Using the compact representation of the $d$-contraction sequence, we gradually construct the graphs $G = G_n, G_{n-1}, \ldots, G_1 = K_1$.
Consider a trigraph $G_k = (V_k, E_k, R_k)$ of the contraction sequence of $G$ for $k \in [n]$ and a fixed triangle $\{a,b,c\}$ in $G$ with $a,b,c \in V(G)$. The vertices of the triangle can be in subgraphs corresponding to one, two, or three vertices of $V_k$. More formally, we observe the following:
\begin{observation}\label{obs:CasesOfTrianglesInGi}
Let $G=G_n ,\ldots, G_1 = K_1$ be a contraction sequence of a graph $G$, let $G_k = (V_k, E_k, R_k)$ a trigraph of the contraction sequence, and let $\{a,b,c\}$ be a triangle in $G$. Then, exactly one of the following statements is true (after possibly reordering $a$, $b$, and $c$):
\begin{enumerate}[$(i)$]
\item $a \in \SetOfVertex{x}$, $b \in \SetOfVertex{y}$, $c \in \SetOfVertex{z}$ with $\{x,y\},\{y,z\},\{z,x\} \in E_k$ \label{obs:item:TriangleThreeBlack}
\item $a \in \SetOfVertex{x}$, $b \in \SetOfVertex{y}$, $c \in \SetOfVertex{z}$ with $\{x,y\},\{y,z\} \in E_k$, $\{z,x\} \in R_k$ \label{obs:item:TriangleTwoBlack}
\item $a \in \SetOfVertex{x}$, $b \in \SetOfVertex{y}$, $c \in \SetOfVertex{z}$ with $\{x,y\} \in E_k$, $\{y,z\},\{z,x\} \in R_k$ \hfill $(\star)$
\label{obs:item:TriangleOneBlack}
\item $a \in \SetOfVertex{x}$, $b \in \SetOfVertex{y}$, $c \in \SetOfVertex{z}$ with $\{x,y\},\{y,z\},\{z,x\} \in R_k$ \hfill $(\star)$
\label{obs:item:TriangleZeroBlack}
\item $a \in \SetOfVertex{x}$ and $b,c \in \SetOfVertex{y}$ with $\{x,y\} \in E_k$
\label{obs:item:EdgeBlack}
\item $a \in \SetOfVertex{x}$ and $b,c \in \SetOfVertex{y}$ with $\{x,y\} \in R_k$ \hfill $(\star)$
\label{obs:item:EdgeRed}
\item $a,b,c \in \SetOfVertex{x}$ for $x \in V(G_k)$ \hfill $(\star)$
\label{obs:item:Vertex}
\end{enumerate}
\end{observation}
Let $G_{k-1} = G_k/u,v$.
A triangle $T$ of $G$ might transition from a case in $G_{k-1}$ to a different case in $G_k$ if $T$ consists of vertices in $\SetOfVertex{u}$ or $\SetOfVertex{v}$. If $T$ consists of vertices in both $\SetOfVertex{u}$ and $\SetOfVertex{v}$, one vertex less is needed in $G_{k-1}$ to specify $T$. If $T$ does only admit a non-empty cut with one of the two sets $\SetOfVertex{u}$ or $\SetOfVertex{v}$, the incident edges of $u$ (resp.\ $v$) in $G_{k-1}$ might turned red.
See Figure~\ref{fig:ChangeOfCases} for a full diagram of all possible case transitions for a triangle in $G$ from $G_k$ to $G_{k-1}$.
\begin{figure}[t]
\centering
\begin{tabular}{c|c}
\begin{subfigure}[b]{0.5\textwidth}
\begin{tikzpicture}
\node [gray] (1) at (0, 4) {\ObsCase{\ref*{obs:item:TriangleThreeBlack}}};
\node [gray] (2) at (0, 3) {\ObsCase{\ref*{obs:item:TriangleTwoBlack}}};
\node [black,very thick] (3) at (0, 2) {\ObsCase{\ref*{obs:item:TriangleOneBlack}}$^*$};
\node [black,very thick] (4) at (0, 1) {\ObsCase{\ref*{obs:item:TriangleZeroBlack}}$^*$};
\node [gray] (5) at (3, 2) {\ObsCase{\ref*{obs:item:EdgeBlack}}};
\node [black,very thick] (6) at (3, 1) {\ObsCase{\ref*{obs:item:EdgeRed}}$^*$};
\node [black,very thick] (7) at (6, 1) {\ObsCase{\ref*{obs:item:Vertex}}$^*$};
\draw [->,gray] (1) to (5);
\draw [->,gray] (2) to (5);
\draw [->,gray] (3) to (6);
\draw [->,gray] (4) to (6);
\draw [->, very thick] (5) to (7);
\draw [->,gray] (6) to (7);
\draw [->,gray] (1) to (2);
\draw [->, very thick] (2) to (3);
\draw [->,gray] (3) to (4);
\draw [->, very thick] (5) to (6);
\draw [->, very thick] (2) to (6);
\draw [->, bend right= 50, very thick] (1) to (3);
\draw [->, bend right = 50, very thick] (2) to (4);
\end{tikzpicture}
\caption{Diagram of case transitions.}
\label{fig:red_square}
\end{subfigure}
&
\begin{subfigure}[b]{0.5\textwidth}
\resizebox{0.9\columnwidth}{!}{
\begin{tikzpicture}[]
\node[shape=circle,draw=black,fill, inner sep=2pt] (11) at (0,5) {};
\node[shape=circle,draw=black,fill, inner sep=2pt] (12) at (1,5) {};
\node[shape=circle,draw=black,fill, inner sep=2pt] (13) at (0.5,5.85) {};
\draw (11) -- (12);
\draw (11) -- (13);
\draw (12) -- (13);
\node [black] (0) at (0.5, 4.5) {\ObsCase{\ref*{obs:item:TriangleThreeBlack}}};
\node[shape=circle,draw=black,fill, inner sep=2pt] (21) at (2,5) {};
\node[shape=circle,draw=black,fill, inner sep=2pt] (22) at (3,5) {};
\node[shape=circle,draw=black,fill, inner sep=2pt] (23) at (2.5,5.85) {};
\draw[red] (21) -- (22);
\draw (21) -- (23);
\draw (22) -- (23);
\node [black] (1) at (2.5, 4.5) {\ObsCase{\ref*{obs:item:TriangleTwoBlack}}}
\node[shape=circle,draw=black,fill, inner sep=2pt] (31) at (4,5) {};
\node[shape=circle,draw=black,fill, inner sep=2pt] (32) at (5,5) {};
\node[shape=circle,draw=black,fill, inner sep=2pt] (33) at (4.5,5.85) {};
\draw (31) -- (32);
\draw[red,] (31) -- (33);
\draw[red] (32) -- (33);
\node[] (2) at (4.5, 4.5) {\ObsCase{\ref*{obs:item:TriangleOneBlack}}$^*$}
\node[shape=circle,draw=black,fill, inner sep=2pt] (41) at (6,5) {};
\node[shape=circle,draw=black,fill, inner sep=2pt] (42) at (7,5) {};
\node[shape=circle,draw=black,fill, inner sep=2pt] (43) at (6.5,5.85) {};
\draw[red] (41) -- (42);
\draw[red] (41) -- (43);
\draw[red] (42) -- (43);
\node[] (3) at (6.5, 4.5) {\ObsCase{\ref*{obs:item:TriangleZeroBlack}}$^*$}
\node[shape=circle,draw=black,fill, inner sep=2pt] (51) at (1,3) {};
\node[shape=circle,draw=black,fill, inner sep=2pt] (52) at (2,3) {};
\draw (51) -- (52);
\node (4) at (1.5, 2.5) {\ObsCase{\ref*{obs:item:EdgeBlack}}};
\node[shape=circle,draw=black,fill, inner sep=2pt] (61) at (3.5,3) {};
\node[shape=circle,draw=black,fill, inner sep=2pt] (62) at (4.5,3) {};
\draw[red] (61) -- (62);
\node (5) at (4, 2.5) {\ObsCase{\ref*{obs:item:EdgeRed}}$^*$};
\node[shape=circle,draw=black,fill, inner sep=2pt] (71) at (6,3) {};
\node (6) at (6, 2.5) {\ObsCase{\ref*{obs:item:Vertex}}$^*$};
\end{tikzpicture}
}
\caption{Illustration of the different cases.}
\label{fig:blue_square}
\end{subfigure}
\end{tabular}
\caption{Possible case transitions of a triangle in $G$ from $G_k$ to $G_{k-1}$ as described in Observation~\ref{obs:CasesOfTrianglesInGi}. Cases that are stored in the variable $t$ in the invariant are marked by a star. Selfloops are omitted. Transitions from an unmarked case to a marked case are represented by thick arrows.}
\label{fig:ChangeOfCases}
\end{figure}
Over the course of the algorithm, we store the number of triangles of $G$ that appear in $G_k$ as a case marked by a star $(\star)$ in Observation~\ref{obs:CasesOfTrianglesInGi} in a variable $t_k$. To do so, we keep track of the number of vertices and the number of edges of the subgraphs of $G$ that get contracted into a vertex $x$ in $G_k$, i.e., the values $\n{x} = \vert V(\GraphOfVertex{x}) \vert $ and $\m{x} = \vert E(\GraphOfVertex{x}) \vert$ for each vertex $x \in V_k$. Also, we store for each red edge $\{x,y\} \in R_k$, the number of edges between $\GraphOfVertex{x}$ and $\GraphOfVertex{y}$, i.e., $\NumRedE{x}{y} = \vert \{ \{a, b\} \in E \mid a \in \SetOfVertex{x}, b \in \SetOfVertex{y} \} \vert$.
In each iteration $k$ of the algorithm, the two vertices $v_{i_k}$ and $v_{j_k}$, given in the compact representation of the contraction sequence, are contracted to form the trigraph $G_{k-1}$. The algorithm updates the auxiliary values $\n{x}$, $\m{x}$, and $\NumRedE{x}{y}$ that have changed, for all $x,y \in V_k$.
Informally, the algorithm then counts a triangle of $G$ whenever it becomes a case marked by a star in Observation~\ref{obs:CasesOfTrianglesInGi} for the first time. Whenever a triangle is of a marked case, it cannot transition back to an unmarked case and, eventually, all triangles will be of Case~\ObsCase{\ref{obs:item:Vertex}}. Note, that for $G = G_n$, every triangle is of Case~\ObsCase{\ref{obs:item:TriangleThreeBlack}}.
More precisely, the transition from Case~\ObsCase{\ref{obs:item:EdgeBlack}} to Case~\ObsCase{\ref{obs:item:Vertex}} is dealt by the main Algorithm \ref{alg:BaseAlgorithm}. In addition, the procedure \textsc{TriCountOneNeighbor} focuses on the transitions from Case~\ObsCase{\ref{obs:item:TriangleTwoBlack}} and Case~\ObsCase{\ref{obs:item:EdgeBlack}} to Case~\ObsCase{\ref{obs:item:EdgeRed}} whereas the procedure \textsc{TriCountTwoNeighbors} handles the transitions from Case~\ObsCase{\ref{obs:item:TriangleThreeBlack}} and Case~\ObsCase{\ref{obs:item:TriangleTwoBlack}} to Case~\ObsCase{\ref{obs:item:TriangleOneBlack}} and from Case~\ObsCase{\ref{obs:item:TriangleTwoBlack}} to Case~\ObsCase{\ref{obs:item:TriangleZeroBlack}}.
Consider a trigraph $G_k$ that will be contracted into $G_{k-1} = G_k/{v_{i_k},v_{j_k}}$ according to the contraction sequence. For simplicity, we define $u := v_{i_k}$ and $v := v_{j_k}$ as the two vertices in $V(G_k)$ that get contracted into the new vertex $w := v_{2n-k+1}$ of $G_{k-1}$.
For the vertex $w \in V(G_{k-1})$, the number of vertices in $\GraphOfVertex{w}$ is the sum of these numbers in $\GraphOfVertex{u}$ and $\GraphOfVertex{v}$. For the number of edges, we also need to add the number of edges between $\GraphOfVertex{u}$ and $\GraphOfVertex{v}$. Therefore, $\n{w} = \n{u} + \n{v}$ and
\begin{align*}
\m{w} = \begin{cases}
\m{u} + \m{v} + \n{u} \cdot \n{v} & \mbox{if $\{u,v\} \in E_k$,} \\
\m{u} + \m{v} + \NumRedE{u}{v} & \mbox{if $\{u,v\} \in R_k$,} \\
\m{u} + \m{v} & \mbox{otherwise.}
\end{cases}
\end{align*}
For every other vertex $x \in V(G_{k-1})$, $x \neq w$, these values remain unchanged.
Finally, for any vertex $x \in V(G_{k-1})$, such that $\{w,x\} \in R(G_{k-1})$ the number of edges between $G^w$ and $G^x$ can be computed as follows:
\begin{align*}
\NumRedE{w}{x} =
\begin{cases}
\n{u} \cdot \n{x} & \mbox{if $\{u,x\} \in E_k$ and $\{v,x\} \notin (E_k \cup R_k)$,} \\
\n{v} \cdot \n{x} & \mbox{if $\{u,x\} \notin (E_k \cup R_k)$ and $\{v,x\} \in E_k$,} \\
\NumRedE{u}{x} & \mbox{if $\{u,x\} \in R_k$ and $\{v,x\} \notin (E_k \cup R_k)$,} \\
\NumRedE{v}{x} & \mbox{if $\{u,x\} \notin (E_k \cup R_k)$ and $\{v,x\} \in R_k$,} \\
\NumRedE{u}{x} + \n{v} \cdot \n{x} & \mbox{if $\{u,x\} \in R_k$ and $\{v,x\} \in E_k$,} \\
\NumRedE{v}{x} + \n{u} \cdot \n{x} & \mbox{if $\{u,x\} \in E_k$ and $\{v,x\} \in R_k$,} \\
\NumRedE{u}{x} + \NumRedE{v}{x} & \mbox{if $\{u,v\} \in R_k$ and $\{v,x\} \in R_k$.}
\end{cases}
\end{align*}
For every other vertex $y \in V(G_{k-1})$, $y \neq w$, such that $ \{x,y\} \in R(G_{k-1})$, the value $\NumRedE{x}{y}$ remains unchanged.
We give a pseudocode of the algorithm below. For algorithmic purposes, we assume that we are given a graph $G=(V,E)$ that will, over the course of the algorithm, be updated into the successive trigraphs defined by the contraction sequence. Similarly, the variable $t$ in the algorithm represents the number of triangles in $G$ computed so far. The procedure \textsc{UpdateAuxiliaryValues} is not given but is explained previously whereas the procedures \textsc{TriCountOneNeighbor} and \textsc{TriCountTwoNeighbors} will be described in the next paragraphs. Finally, \textsc{UpdateGraph} performs the actual contraction of the graph $G$. The pseudocode of this procedure is omitted.
\begin{algorithm}
\hspace*{\algorithmicindent} \textbf{Input:} A graph $G=(V,E)$ and a compact representation of a contraction sequence $(v_{i_k},v_{j_k})_{n \geq k \geq 2}$\\
\hspace*{\algorithmicindent} \textbf{Output: } The number of triangles $t$ in the graph $G$
\begin{algorithmic}[1]
\State $t := 0$ \Comment{number of triangles in $G$ of Case~\ObsCase{\ref{obs:item:TriangleOneBlack}}, \ObsCase{\ref{obs:item:TriangleZeroBlack}}, \ObsCase{\ref{obs:item:EdgeRed}}, and \ObsCase{\ref{obs:item:Vertex}}}
\State $R = \emptyset$
\For{every vertex $x \in V$}
\State $\n{x} := 1$ \Comment{number of vertices in $\GraphOfVertex{x}$}
\State $\m{x} := 0$ \Comment{number of edges in $\GraphOfVertex{x}$}
\EndFor
\For{$n \geq k \geq 2$}
\State $u := v_{i_k}$
\State $v := v_{j_k}$
\State $w := v_{2n-k+1}$
\State \textsc{UpdateAuxiliaryValues}$(G,u,v,w)$ \;
\If{$\{u,v\} \in E$}
\State $t = t + \n{u} \cdot \m{v} + \n{v} \cdot \m{u}$
\Comment{Case~\ObsCase{\ref{obs:item:EdgeBlack}} $\rightarrow$ Case~\ObsCase{\ref{obs:item:Vertex}}}\label{alg:BlackEdge:Vertex}
\EndIf
\For{each $x \in N_R(w)$}
\State \textsc{TriCountOneNeighbor}$(G,u,v,w,x)$
\State \textsc{TriCountTwoNeighbors}$(G,u,v,w,x)$
\EndFor
\State \textsc{UpdateGraph}$(G,u,v,w)$
\EndFor
\State \textbf{return} $t$
\end{algorithmic}
\caption{}
\label{alg:BaseAlgorithm}
\end{algorithm}
In the procedure \textsc{TriCountOneNeighbor}, we focus on the red edge between the newly introduced vertex $w$ and one of its red neighbors $x \in N_R(w)$. We then consider the different edges between $u$, $v$, and $x$ to detect triangles in $G$ that transition from Case~\ObsCase{\ref{obs:item:TriangleTwoBlack}} and Case~\ObsCase{\ref{obs:item:EdgeBlack}} to Case~\ObsCase{\ref{obs:item:EdgeRed}}.
\begin{algorithm}[H]
\begin{algorithmic}[1]
\Procedure{TriCountOneNeighbor}{$G,u,v,w,x$}
\If{$\{u,x\} \in E$}
\State $t = t + \n{u} \cdot \m{x} + \n{x} \cdot \m{u}$
\Comment{Case~\ObsCase{\ref{obs:item:EdgeBlack}} $\rightarrow$ Case~\ObsCase{\ref{obs:item:EdgeRed}}}\label{alg:EdgeBlack:EdgeRed:u}
\If{$\{u,v\}\in E$ and $\{v,x\} \in R$}
\State $t = t + \NumRedE{v}{x} \cdot \n{u}$
\Comment{Case~\ObsCase{\ref{obs:item:TriangleTwoBlack}} $\rightarrow$ Case~\ObsCase{\ref{obs:item:EdgeRed}}}\label{alg:TriangleTwoBlack:EdgeRed:2}
\EndIf
\ElsIf{$\{v,x\} \in E$}
\State $t = t + \n{v} \cdot \m{x} + \n{x} \cdot \m{v}$
\Comment{Case~\ObsCase{\ref{obs:item:EdgeBlack}} $\rightarrow$ Case~\ObsCase{\ref{obs:item:EdgeRed}}}\label{alg:EdgeBlack:EdgeRed:v}
\If{$\{u,v\}\in E$ and $\{u,x\} \in R$}
\State $t = t + \NumRedE{u}{x} \cdot \n{v}$
\Comment{Case~\ObsCase{\ref{obs:item:TriangleTwoBlack}} $\rightarrow$ Case~\ObsCase{\ref{obs:item:EdgeRed}}}\label{alg:TriangleTwoBlack:EdgeRed:1}
\EndIf
\EndIf
\EndProcedure
\end{algorithmic}
\label{alg:TriCountOverRedEdge}
\end{algorithm}
Finally, in the procedure \textsc{TriCountTwoNeighbors} we focus on the edges between the newly introduced vertex $w$ and two of its neighbors $x,y \in N_R(w)$. We then consider the different edges between $u$, $v$, $x$, and $y$ to detect triangles in $G$ that transitions from Case~\ObsCase{\ref{obs:item:TriangleThreeBlack}} and Case~\ObsCase{\ref{obs:item:TriangleTwoBlack}} to Case~\ObsCase{\ref{obs:item:TriangleOneBlack}} and from Case~\ObsCase{\ref{obs:item:TriangleTwoBlack}} to Case~\ObsCase{\ref{obs:item:TriangleZeroBlack}}.
\begin{algorithm}[H]
\begin{algorithmic}[1]
\Procedure{TriCountTwoNeighbors}{$G,u,v,w,x$}
\For{each $y \in V$ such that $\{x,y\} \in R$ and $\{w,y\} \in E$}
\If{$\{u,x\} \in E$}
\State $t = t + \NumRedE{x}{y} \cdot \n{u}$\Comment{Case~\ObsCase{\ref{obs:item:TriangleTwoBlack}} $\rightarrow$ Case~\ObsCase{\ref{obs:item:TriangleOneBlack}}} \label{alg:TwoBlack:OneBlack:xyRed:u}
\ElsIf{$\{v,x\} \in E$}
\State $t = t + \NumRedE{x}{y} \cdot \n{v}$
\Comment{Case~\ObsCase{\ref{obs:item:TriangleTwoBlack}} $\rightarrow$ Case~\ObsCase{\ref{obs:item:TriangleOneBlack}}}\label{alg:TwoBlack:OneBlack:xyRed:v}
\EndIf
\EndFor
\For{each $y \in V$ such that $\{w,y\} \in R$}
\If{$\{x,y\} \in E$}
\If{$\{u,x\} \in E$ and $\{u,y\} \in E$}
\State $t = t + \n{u} \cdot \n{x} \cdot \n{y}$
\Comment{Case~\ObsCase{\ref{obs:item:TriangleThreeBlack}} $\rightarrow$ Case~\ObsCase{\ref{obs:item:TriangleOneBlack}}}\label{alg:ThreeBlack:OneBlack1}
\ElsIf{$\{v,x\} \in E$ and $\{v,y\} \in E$}
\State $t = t + \n{v} \cdot \n{x} \cdot \n{y}$
\Comment{Case~\ObsCase{\ref{obs:item:TriangleThreeBlack}} $\rightarrow$ Case~\ObsCase{\ref{obs:item:TriangleOneBlack}}}\label{alg:ThreeBlack:OneBlack2}
\EndIf
\If{$\{u,x\} \in R$ and $\{u,y\} \in E$}
\State $t = t + \NumRedE{u}{x} \cdot \n{y}$
\Comment{Case~\ObsCase{\ref{obs:item:TriangleTwoBlack}} $\rightarrow$ Case~\ObsCase{\ref{obs:item:TriangleOneBlack}}}\label{alg:TriangleTwoBlack:TriangleOneBlack:xyBlack:1}
\ElsIf{$\{v,x\} \in R$ and $\{v,y\} \in E$}
\State $t = t + \NumRedE{v}{x} \cdot \n{y}$
\Comment{Case~\ObsCase{\ref{obs:item:TriangleTwoBlack}} $\rightarrow$ Case~\ObsCase{\ref{obs:item:TriangleOneBlack}}}\label{alg:TriangleTwoBlack:TriangleOneBlack:xyBlack:2}
\EndIf
\If{$\{u,x\} \in E$ and $\{u,x\} \in R$}
\State $t = t + \NumRedE{u}{x} \cdot \n{x}$
\Comment{Case~\ObsCase{\ref{obs:item:TriangleTwoBlack}} $\rightarrow$ Case~\ObsCase{\ref{obs:item:TriangleOneBlack}}}
\ElsIf{$\{v,x\} \in E$ and $\{v,y\} \in R$}\label{alg:TriangleTwoBlack:TriangleOneBlack:xyBlack:3}
\State $t = t + \NumRedE{v}{x} \cdot \n{x}$
\Comment{Case~\ObsCase{\ref{obs:item:TriangleTwoBlack}} $\rightarrow$ Case~\ObsCase{\ref{obs:item:TriangleOneBlack}}}\label{alg:TriangleTwoBlack:TriangleOneBlack:xyBlack:4}
\EndIf
\ElsIf{$\{x,y\} \in R$}
\If{$\{u,x\} \in E$ and $\{u,y\} \in E$}
\State $t = t + \NumRedE{x}{y} \cdot \n{u}$
\Comment{Case~\ObsCase{\ref{obs:item:TriangleTwoBlack}} $\rightarrow$ Case~\ObsCase{\ref{obs:item:TriangleZeroBlack}}}\label{alg:TriangleTwoBlack:TriangleZeroBlack:1}
\ElsIf{$\{v,x\} \in E$ and $\{v,y\} \in E$}
\State $t = t + \NumRedE{x}{y} \cdot \n{v}$
\Comment{Case~\ObsCase{\ref{obs:item:TriangleTwoBlack}} $\rightarrow$ Case~\ObsCase{\ref{obs:item:TriangleZeroBlack}}}\label{alg:TriangleTwoBlack:TriangleZeroBlack:2}
\EndIf
\EndIf
\EndFor
\EndProcedure
\end{algorithmic}
\label{alg:TriCountOverRedWedge}
\end{algorithm}
\noindent
We have now described the algorithm and can prove Theorem~\ref{thm:TriangleCounting}.
\begin{proof}[Proof of Theorem~\ref{thm:TriangleCounting}]
Given the compact representation of the $d$-sequence $(v_{i_k},v_{j_k})_{n \geq k \geq 2}$, the algorithm generates iteratively the contraction sequence $G = G_n, G_{n-1}, \ldots, G_1 = K_1$ with $G_{k-1} = G_k/{v_{i_k},v_{j_k}}$ using the procedure \textsc{UpdateGraph} at the end of each iteration.
The values $\n{x}$, $\m{x}$, and $\NumRedE{x}{y}$ are updated by the procedure \textsc{UpdateAuxiliaryValues} in each iteration as described in the previous paragraph.
To prove that the final value of $t$ is equal to the number of triangles in $G$, we will prove that the following invariant is true at the beginning of each iteration, i.e., for each graph $G_k = (V_k,E_k,R_k)$ in the contraction sequence for $k \in [n]$:
\begin{align*}
\vert \TriInGraph{G} \vert = t_k + \underbrace{\sum_{\substack{\{x,y\},\\ \{y,z\},\{x,z\} \in E_k}} \n{x} \n{y} \n{z}}_{\text{Case~\ObsCase{\ref*{obs:item:TriangleThreeBlack}}}} + \underbrace{\sum_{\substack{ \{x,z\} \in R_k \\\{x,y\},\{y,z\}\in E_k }} \NumRedE{x}{z} \n{y}}_{\text{Case~\ObsCase{\ref*{obs:item:TriangleTwoBlack}}}} +\underbrace{\sum_{\{x,y\} \in E_k} (\n{x} \m{y} + \m{x} \n{y})}_{\text{Case~\ObsCase{\ref*{obs:item:EdgeBlack}}}}
\end{align*}
We denote by $t_k$ the current value of $t$ at the start of iteration $k$ (and $t_1$ the final value after iteration $k = 2$).
Recall that $\vert T(G) \vert$ denotes the number of triangles in $G$.
For $k = n$, the value of $t_n$ is initialized to zero
since $R_n = \emptyset$, $\m{x} = 0$, and $\n{x}=1$ for all $x \in V_n$. Therefore, the invariant simplifies to the second summand only, which is indeed the desired number of all triangles in $G$.
We will show that the value of the invariant will never change. Thus, for $i = 1$, it then holds that $\vert \TriInGraph{G} \vert = t_1 + 0 + 0+0$ and the correctness of Algorithm~\ref{alg:BaseAlgorithm} follows.
As described in Observation~\ref{obs:CasesOfTrianglesInGi}, we distinguish seven cases of a possible occurrence of a triangle of $G$ in $G_k$. In the beginning, all triangles in $G$ are of Case~\ObsCase{\ref{obs:item:TriangleThreeBlack}} but some may change from a case to another one whenever $G_k$ gets contracted to $G_{k-1}$. For a fixed triangle, all possible case transitions are depicted in Figure~\ref{fig:ChangeOfCases}.
Notice that the triangles of $G$ of Case~\ObsCase{\ref{obs:item:TriangleThreeBlack}}, \ObsCase{\ref{obs:item:TriangleTwoBlack}}, or \ObsCase{\ref{obs:item:EdgeBlack}}, are counted directly by the corresponding sums in the invariant.
We are left to show that the (current) value of $t_k$ is indeed the count of all triangles of $G$ that appear in $G_k$ of Case~\ObsCase{\ref{obs:item:TriangleOneBlack}},\ObsCase{\ref{obs:item:TriangleZeroBlack}}, \ObsCase{\ref{obs:item:EdgeRed}}, or \ObsCase{\ref{obs:item:Vertex}}.
Notice that once a fixed triangle is of one of the latter cases, this triangle can never transition back to an unmarked case.
By induction, we can assume that the invariant is true for $G_k$. To prove the invariant for $k-1$, we keep track of all triangles whose case changes from $G_k$ to $G_{k-1}$ regarding Observation~\ref{obs:CasesOfTrianglesInGi}. Note that we only need to consider the triangles that are of a case that is not marked by a star in $G_k$, but in a case that is marked in $G_{k-1}$.
Let $G_{k-1} = G_k /u,v$ and let $w$ be the new vertex of $G_{k-1}$.
Case~\ObsCase{\ref{obs:item:TriangleThreeBlack}} to Case~\ObsCase{\ref{obs:item:TriangleOneBlack}}:
Let $\{a,b,c\}$ be a triangle in $G$ that is of Case~\ObsCase{\ref{obs:item:TriangleThreeBlack}} in $G_k$ but of Case~\ObsCase{\ref{obs:item:TriangleOneBlack}} in $G_{k-1}$.
This implies that there exist $x,y \in V_{k-1}$ with $a \in \SetOfVertex{w}$, $b \in \SetOfVertex{x}$, and $c \in \SetOfVertex{y}$
and $\{w,x\}, \{w,y\} \in R_k$. Since $w$ is the contraction of $u$ and $v$, it holds that either $a \in \SetOfVertex{u}$ with $\{u,x\}, \{u,y\} \in R_k$ or $a \in \SetOfVertex{v}$ with $\{v,x\}, \{v,y\} \in R_k$. In the former case, it is counted in the procedure \textsc{TriCountTwoNeighbors}, Line~\ref{alg:ThreeBlack:OneBlack1}. In the latter case it is counted in Line~\ref{alg:ThreeBlack:OneBlack2}.
Case~\ObsCase{\ref{obs:item:TriangleTwoBlack}} to Case~\ObsCase{\ref{obs:item:TriangleOneBlack}}:
This implies that there exist $x,y \in V_{k-1}$ with $a \in \SetOfVertex{w}$, $b \in \SetOfVertex{x}$, and $c \in \SetOfVertex{y}$.
Let us first assume that $\{x,y\} \in R_{k-1}$. Since $\{a,b,c\}$ is a triangle of Case~\ObsCase{\ref{obs:item:TriangleTwoBlack}} in $G_k$, it holds that either $\{u,x\},\{u,y\} \in E_k$ or $\{v,x\},\{x,y\} \in E_k$. In the former case, it is counted in the procedure \textsc{TriCountTwoNeighbors}, Line~\ref{alg:TwoBlack:OneBlack:xyRed:u}, and in the latter case, in Line~\ref{alg:TwoBlack:OneBlack:xyRed:v}.
Now assume that $\{x,y\} \in E_{k-1}$, i.e., $\{w,x\},\{w,y\} \in R_{k-1}$. Since $\{a,b,c\}$ is a triangle of Case~\ObsCase{\ref{obs:item:TriangleTwoBlack}} in $G_k$, it now holds that either $\{u,x\} \in R_k$ and $\{u,y\} \in E_k$ (counted in the procedure \textsc{TriCountTwoNeighbors}, Line~\ref{alg:TriangleTwoBlack:TriangleOneBlack:xyBlack:1}); $\{v,x\} \in R_k$ and $\{v,y\} \in E_k$ (Line~\ref{alg:TriangleTwoBlack:TriangleOneBlack:xyBlack:2}); $\{u,x\} \in E_k$ and $\{u,y\} \in R_k$ (Line~\ref{alg:TriangleTwoBlack:TriangleOneBlack:xyBlack:3}); or $\{v,x\} \in E_k$ and $\{v,y\} \in R_k$ (Line~\ref{alg:TriangleTwoBlack:TriangleOneBlack:xyBlack:4}).
Note that since $\{w,x\}$, $\{w,y\} \in R_{k-1}$, it cannot be that the first two or the last two cases occur simultaneously.
Case~\ObsCase{\ref{obs:item:TriangleTwoBlack}} to Case~\ObsCase{\ref{obs:item:TriangleZeroBlack}}:
Suppose there are $x,y \in V_{k-1}$ with $a \in \SetOfVertex{w}$, $b \in \SetOfVertex{x}$, $c \in \SetOfVertex{y}$ and $\{w,x\}, \{w,y\}, \{x,y\}\in R_{k-1}$. Since $\{a,b,c\}$ is of Case~\ObsCase{\ref{obs:item:TriangleTwoBlack}} in $G_k$, it either holds that $\{u,x\}, \{u,y\} \in E_k$ or $\{v,x\}, \{v,y\} \in E_k$. The former is counted in the procedure \textsc{TriCountTwoNeighbors}, Line~\ref{alg:TriangleTwoBlack:TriangleZeroBlack:1} and the latter in Line~\ref{alg:TriangleTwoBlack:TriangleZeroBlack:2}.
Case~\ObsCase{\ref{obs:item:TriangleTwoBlack}} to Case~\ObsCase{\ref{obs:item:EdgeRed}} and Case~\ObsCase{\ref{obs:item:EdgeBlack}} to Case~\ObsCase{\ref{obs:item:EdgeRed}}:
Let $\{a,b,c\}$ be a triangle of Case~\ObsCase{\ref{obs:item:EdgeRed}} in $G_{k-1}$, i.e., there exists $x \in V_{k-1}$ with $\{w,x\} \in R_{k-1}$ and either $a \in \SetOfVertex{w}$ and $b,c \in \SetOfVertex{x}$ or $a,b \in \SetOfVertex{w}$ and $c \in \SetOfVertex{x}$. If $\{a,b,c\}$ is of Case~\ObsCase{\ref{obs:item:TriangleTwoBlack}} in $G_{k-1}$, it holds that $\{u,v\} \in E_k$ (otherwise the edge $\{w,x\}$ would not be in $R_{k-1}$) and that either $\{u,x\} \in R_k$ and $\{v,x\} \in E_k$ (counted in the procedure \textsc{TriCountOneNeighbor}, Line~\ref{alg:TriangleTwoBlack:EdgeRed:1}), or $\{v,x\} \in R_k$ and $\{u,x\} \in E_k$ (Line~\ref{alg:TriangleTwoBlack:EdgeRed:2}).
If $\{a,b,c\}$ is of Case~\ObsCase{\ref{obs:item:EdgeBlack}} in $G_k$, the black edge is either incident to $u$ (counted in the procedure \textsc{TriCountOneNeighbor}, Line~\ref{alg:EdgeBlack:EdgeRed:u}) or to $v$ (Line~\ref{alg:EdgeBlack:EdgeRed:v}).
Case~\ObsCase{\ref{obs:item:EdgeBlack}} to Case~\ObsCase{\ref{obs:item:Vertex}}:
Finally, if a triangle $\{a,b,c\}$ is of Case~\ObsCase{\ref{obs:item:EdgeBlack}} in $G_k$ and of Case~\ObsCase{\ref{obs:item:Vertex}} in $G_{k-1}$ it now holds that $a,b,c \in \SetOfVertex{w}$ and such a triangle is counted in Algorithm~\ref{alg:BaseAlgorithm}, Line~\ref{alg:BlackEdge:Vertex}.
Thus, the number of all the triangles of $G$ that are of Case~\ObsCase{\ref{obs:item:TriangleOneBlack}}, \ObsCase{\ref{obs:item:TriangleZeroBlack}}, \ObsCase{\ref{obs:item:EdgeRed}}, and \ObsCase{\ref{obs:item:Vertex}} in $G_{k-1}$ is indeed computed and stored in the variable $t$ after the iteration $k$.
Since the algorithm only increases $t$ whenever a triangle transitions from an unmarked case to a marked case after contraction, the value $t$ is exactly the desired value.
We store the graph in sorted adjacency lists, which can be initially realized in time $\Oh(n+m)$ using a linear-time sorting algorithm to sort the vertices $v_1, \ldots, v_n$. To contract the two vertices $u$ and $v$ in each iteration, we can scan the sorted adjacency lists of $u$ and $v$ to identify the red neighborhood and black neighborhood of $w$. Since $w$ has at most $d$ incident red edges and, for each black neighbor, we decrease the number of total edges by one, the total running time, for every call of the procedure $\textsc{UpdateGraph}$, sums up to $\Oh(dn+m)$. Since the auxiliary values only change for $w$ and for the incident red edges of $w$, they can be updated in time $\Oh(d)$ per iteration. Eventually, it takes $\Oh(dn)$ for every call of the procedure \textsc{UpdateAuxiliaryValues}. Finally, the procedures $\textsc{TriCountOneNeighbor}$ and $\textsc{TriCountTwoNeighbors}$ are called at most $d$ times per iteration, taking respectively $\Oh(1)$ and\ $\Oh(d)$ time. Thus, the overall running time of Algorithm~\ref{alg:BaseAlgorithm} is $\Oh(d^2n + m)$.
\end{proof}
\section{Conclusion}
We have obtained an efficient parameterized algorithm for \prob{Triangle Counting} parameterized by the twin-width $\tww$ of the input graph. As a matter of fact, the algorithm is adaptive as it runs in time $\Oh(\tww^2n+m)$ whereas the best unparameterized combinatorial algorithms run in time $\mathcal{O}(n^3)$. Our algorithm is based on dynamic programming and stores a few values that need to be updated at each contraction step.
Some future directions would be to extend this approach and design efficient algorithms to solve other tractable problems when parameterized by the twinwidth of the input graph. It would, furthermore, be highly interesting to find the most general parameter for which an adaptive algorithm for \prob{Triangle Counting} exists. Finally, our algorithm is adaptive when compared to the best combinatorial algorithms, however, there exists a non-combinatorial algorithm that runs in time $\Oh(n^{\omega})$ where $\omega < 2.372863$ \cite{AlonYZ97}. An improvement would then be to obtain an $\Oh(\tww^{\omega-1}n + m)$-time algorithm.
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 9,598
|
{"url":"http:\/\/ilovephilosophy.com\/viewtopic.php?f=2&t=195506&p=2761843","text":"## the 10,000 club\n\nThis is the place to shave off that long white beard and stop being philosophical; a forum for members to just talk like normal human beings.\n\n### the 10,000 club\n\nDan 10,099\nMoreno 10,305\nXunzian 10,462\nGobbo 11,111\nphyllo 11,563\ntentative 12,419\nImpenitent 12706\nIerrellus 12,739\nUccisore 13,279\nArcturus Descending 15,658\nFaust 16,897\nMagsJ 19,195\nKriswest 20,553\nMr Reasonable 25,948\nJames S Saint 25,976\niambiguous 33,998\n\nMost are still around.\n\nAlso, though I have the most, that number also includes my music thread posts. Of the 14,000 posts there, I'm guessing at least 13,800 are mine. Then the 7,900 posts from my mundane ironist thread, at least 7,600 of which are mine.\n\nSo, the actual number of \"normal\" posts from me is closer to around 14,000.\n\nFinally, some members are here with 2 or more \"accounts\". Jacob and Joker for example.\n\nCarry on....\nHe was like a man who wanted to change all; and could not; so burned with his impotence; and had only me, an infinitely small microcosm to convert or detest. John Fowles\n\nStart here: viewtopic.php?f=1&t=176529\nThen here: viewtopic.php?f=15&t=185296\nAnd here: viewtopic.php?f=1&t=194382\n\niambiguous\nILP Legend\n\nPosts: 35063\nJoined: Tue Nov 16, 2010 8:03 pm\nLocation: baltimore maryland\n\n### Re: the 10,000 club\n\nIn fact, if Jacob and Fixed Cross are the same dude [and I don't follow these things too closely] he is in the club too with 16,764 posts.\n\nYou know, if this is something to be proud of.\nHe was like a man who wanted to change all; and could not; so burned with his impotence; and had only me, an infinitely small microcosm to convert or detest. John Fowles\n\nStart here: viewtopic.php?f=1&t=176529\nThen here: viewtopic.php?f=15&t=185296\nAnd here: viewtopic.php?f=1&t=194382\n\niambiguous\nILP Legend\n\nPosts: 35063\nJoined: Tue Nov 16, 2010 8:03 pm\nLocation: baltimore maryland\n\n### Re: the 10,000 club\n\nEvery one of your collective thoughts are masterpieces. If only I had the time to read it all. I am certain it would make me a better person.\nMowk\nPhilosopher\n\nPosts: 1857\nJoined: Thu Feb 02, 2012 8:17 pm\nLocation: In a state of excessive consumption\n\n### Re: the 10,000 club\n\nMowk wrote:Every one of your collective thoughts are masterpieces. If only I had the time to read it all. I am certain it would make me a better person.\n\nNot really. After all, look what happened to me.\nHe was like a man who wanted to change all; and could not; so burned with his impotence; and had only me, an infinitely small microcosm to convert or detest. John Fowles\n\nStart here: viewtopic.php?f=1&t=176529\nThen here: viewtopic.php?f=15&t=185296\nAnd here: viewtopic.php?f=1&t=194382\n\niambiguous\nILP Legend\n\nPosts: 35063\nJoined: Tue Nov 16, 2010 8:03 pm\nLocation: baltimore maryland\n\n### Re: the 10,000 club\n\nI didn\u2019t mean to.. how the hell did that happen?\nThe possibility of anything we can imagine existing is endless and infinite.. - MagsJ\n\nI haven't got the time to spend the time reading something that is telling me nothing, as I will never be able to get back that time, and I may need it for something at some point in time.. Wait, What! - MagsJ\n\nThe Lions Anger is Noble\n\nMagsJ\nThe Londonist: a chic geek\n\nPosts: 19468\nJoined: Wed Nov 01, 2006 2:59 pm\nLocation: London, NC1 \u2026 \u2026 \u2026 \u2026 \u2026 \u2026 \u2026 \u2026 \u2026 \u2026 \u2026 \u2026 \u2026 \u2026 \u2026 \u2026 \u2026 \u2026 Nobilis Est Ira Leonis\n\n### Re: the 10,000 club\n\nTime to publish the minimum number as well. For religious reasons.\n'those that are first shall be last' and visa versa. ( also in praise of minimalism)\n\n&everything in-between, for it would be odd to leave them out.\n\nSo it's better to publish a grand list from most to least, or least to most published of every single member ever on ILP!\n\nInquiry: how long would that list be, and how long would it take, perhaps better fit job for AI.?\nMeno_\nILP Legend\n\nPosts: 6230\nJoined: Tue Dec 08, 2015 2:39 am\nLocation: Mysterium Tremendum\n\n### Re: the 10,000 club\n\nMeno_ wrote:Time to publish the minimum number as well. For religious reasons.\n'those that are first shall be last' and visa versa. ( also in praise of minimalism)\n\n&everything in-between, for it would be odd to leave them out.\n\nSo it's better to publish a grand list from most to least, or least to most published of every single member ever on ILP!\n\nInquiry: how long would that list be, and how long would it take, perhaps better fit job for AI.?\n\nClick on members. Click on posts. 142 pages of names. Least to most start page 1. Most to least start page 142.\n\nUnless, of course, ILP is using the same APP here as the Democratic Party in Iowa.\n\nFortunately, this is all being done very, very much tongue in cheek.\nHe was like a man who wanted to change all; and could not; so burned with his impotence; and had only me, an infinitely small microcosm to convert or detest. John Fowles\n\nStart here: viewtopic.php?f=1&t=176529\nThen here: viewtopic.php?f=15&t=185296\nAnd here: viewtopic.php?f=1&t=194382\n\niambiguous\nILP Legend\n\nPosts: 35063\nJoined: Tue Nov 16, 2010 8:03 pm\nLocation: baltimore maryland\n\n### Re: the 10,000 club\n\nto other posters....top 30... ummm, no wonder my wife complains\nI am always posting...\u2026\n\nSecond, I notice how many in the top 30 is no longer posting anymore.\n\nJames, for instance... many posters have left over the years....\nI wonder why?\n\nCould it have been they found something better then posting here?\n\nHeaven forbid, you might find something more interesting then here?\n\nKropotkin\n\"Those who sacrifice liberty for security\nwind up with neither.\"\n\"Ben Franklin\"\nPeter Kropotkin\nILP Legend\n\nPosts: 7724\nJoined: Thu Apr 07, 2005 1:47 am\nLocation: blue state\n\n### Re: the 10,000 club\n\nPeter Kropotkin wrote:many posters have left over the years....\nI wonder why?\n\nIt is possible to say things until you run out of things to say.\nhttps:\/\/dannerz.itch.io\/ -- a new and minimal webside now hosting two of my free game projects.\n\nDan~\nILP Legend\n\nPosts: 10129\nJoined: Thu Nov 24, 2005 8:14 am\nLocation: May the loving spirit of papa hitler watch over and bless you all.\n\n### Re: the 10,000 club\n\nDan~ wrote:\nPeter Kropotkin wrote:many posters have left over the years....\nI wonder why?\n\nIt is possible to say things until you run out of things to say.\n\nMaybe. But then you just keep repeating the same things over and over and over again.\nHe was like a man who wanted to change all; and could not; so burned with his impotence; and had only me, an infinitely small microcosm to convert or detest. John Fowles\n\nStart here: viewtopic.php?f=1&t=176529\nThen here: viewtopic.php?f=15&t=185296\nAnd here: viewtopic.php?f=1&t=194382\n\niambiguous\nILP Legend\n\nPosts: 35063\nJoined: Tue Nov 16, 2010 8:03 pm\nLocation: baltimore maryland\n\n### Re: the 10,000 club\n\nI was about to say that yours don't count because you just say the same thing over and over again then I noticed someone else already said that then I just said it anyway.\nYou see...a pimp's love is very different from that of a square.\nDating a stripper is like eating a noisy bag of chips in church. Everyone looks at you in disgust, but deep down they want some too.\n\nWhat exactly is logic? -Magnus Anderson\n\nSupport the innocence project on AmazonSmile instead of Turd's African savior biker dude.\nhttp:\/\/www.innocenceproject.org\/\n\nMr Reasonable\nresident contrarian\n\nPosts: 25953\nJoined: Sat Mar 17, 2007 8:54 am\nLocation: pimping a hole straight through the stratosphere itself\n\n### Re: the 10,000 club\n\nMr Reasonable wrote:I was about to say that yours don't count because you just say the same thing over and over again then I noticed someone else already said that then I just said it anyway.\n\nWelcome back, Mr. Capitalist!\n\nSpeaking of which, any stock market tips to get us through the crisis?\n\nAlso, are you still the dude every lady wants and every man wants to be?\n\nNever said that before, right?\nHe was like a man who wanted to change all; and could not; so burned with his impotence; and had only me, an infinitely small microcosm to convert or detest. John Fowles\n\nStart here: viewtopic.php?f=1&t=176529\nThen here: viewtopic.php?f=15&t=185296\nAnd here: viewtopic.php?f=1&t=194382\n\niambiguous\nILP Legend\n\nPosts: 35063\nJoined: Tue Nov 16, 2010 8:03 pm\nLocation: baltimore maryland\n\n### Re: the 10,000 club\n\nIs the Scooby gang back again? Where's Blurry? Where's Natalie?\n\"I'm sorry, but the lifestyle you've ordered that you've grown accustomed to is completely out of stock. Have a nice day! \"-$$\u201cAssuming one can never leave permanent social exile and alienation keep on living only to observe the total collapse of entire societies, nations, or civilizations where afterwards in the inevitable chaos revel in its total destruction taking satisfaction within it as a casual witness. Let it all burn and come crashing down in a festival or spectacle orgy of violence.\u201d-Myself Zero_Sum Evil Neo-Nazi Extraordinaire. Posts: 3302 Joined: Thu Nov 30, 2017 7:05 pm Location: U.S.S.A- Newly lead Bolshevik Soviet block. Also known as Weimar America. ### Re: the 10,000 club iambiguous wrote: Mr Reasonable wrote:I was about to say that yours don't count because you just say the same thing over and over again then I noticed someone else already said that then I just said it anyway. Welcome back, Mr. Capitalist! Speaking of which, any stock market tips to get us through the crisis? Also, are you still the dude every lady wants and every man wants to be? Never said that before, right? Now's a good time to buy the dip! If I had money I would go all in buying as much stocks as possible! Tomorrow morning is going to be a real good record for stawks to be sure, I would invest my entire life savings if I had any! Now's a great time to buy! \"I'm sorry, but the lifestyle you've ordered that you've grown accustomed to is completely out of stock. Have a nice day! \"-$$$\u201cAssuming one can never leave permanent social exile and alienation keep on living only to observe the total collapse of entire societies, nations, or civilizations where afterwards in the inevitable chaos revel in its total destruction taking satisfaction within it as a casual witness. Let it all burn and come crashing down in a festival or spectacle orgy of violence.\u201d-Myself Zero_Sum Evil Neo-Nazi Extraordinaire. Posts: 3302 Joined: Thu Nov 30, 2017 7:05 pm Location: U.S.S.A- Newly lead Bolshevik Soviet block. Also known as Weimar America. ### Re: the 10,000 club iambiguous wrote: Mr Reasonable wrote:I was about to say that yours don't count because you just say the same thing over and over again then I noticed someone else already said that then I just said it anyway. Welcome back, Mr. Capitalist! Speaking of which, any stock market tips to get us through the crisis? Also, are you still the dude every lady wants and every man wants to be? Never said that before, right? You are not by chance referring to me reversely? Excluding the premise : ..\".... ...every lady wants.......\" {that should sqwash any whispers of self indulgence on my part...... } Meno_ ILP Legend Posts: 6230 Joined: Tue Dec 08, 2015 2:39 am Location: Mysterium Tremendum ### Re: the 10,000 club Zero_Sum wrote: iambiguous wrote: Mr Reasonable wrote:I was about to say that yours don't count because you just say the same thing over and over again then I noticed someone else already said that then I just said it anyway. Welcome back, Mr. Capitalist! Speaking of which, any stock market tips to get us through the crisis? Also, are you still the dude every lady wants and every man wants to be? Never said that before, right? Now's a good time to buy the dip! If I had money I would go all in buying as much stocks as possible! Tomorrow morning is going to be a real good record for stawks to be sure, I would invest my entire life savings if I had any! Now's a great time to buy! Too rique & tongue in cheek, ...... besides I'm in gamblers anynomous, and that would add another thing I would need to hide. But if You may prove right, buying say on 10000 calls of a penny stock would have been another irresitible bet to regret as hindsight. Oh if only I would have been ever able to read tomorrows paper yesterday, I could have invested the little mad money neaster egg I put away for a rainy day. Last edited by Meno_ on Sun Mar 15, 2020 7:58 pm, edited 1 time in total. Meno_ ILP Legend Posts: 6230 Joined: Tue Dec 08, 2015 2:39 am Location: Mysterium Tremendum ### Re: the 10,000 club Meno_ wrote:Too rique & tongue in cheek, ...... besides I'm in gamblers anynomous, and that would add another thing I would need to hide. What are you talking about? This is the greatest economy ever especially with a viral pandemic everywhere! You're not against MAGA, are you? Do your patriotic duty and invest your life savings in this awesome economy or stock market! If you don't that just makes you a big commie... \"I'm sorry, but the lifestyle you've ordered that you've grown accustomed to is completely out of stock. Have a nice day! \"-$$\u201cAssuming one can never leave permanent social exile and alienation keep on living only to observe the total collapse of entire societies, nations, or civilizations where afterwards in the inevitable chaos revel in its total destruction taking satisfaction within it as a casual witness. Let it all burn and come crashing down in a festival or spectacle orgy of violence.\u201d-Myself Zero_Sum Evil Neo-Nazi Extraordinaire. Posts: 3302 Joined: Thu Nov 30, 2017 7:05 pm Location: U.S.S.A- Newly lead Bolshevik Soviet block. Also known as Weimar America. ### Re: the 10,000 club Meno_ wrote: But if You may prove right, buying say on 10000 calls of a penny stock would have been another irresitible bet to regret as hindsight. Oh if only I would have been ever able to read tomorrows paper yesterday, I could have invested the little mad money neaster egg I put away for a rainy day. My prediction is that the DOW will be somewhere between 5000-10000 here really soon and just maybe even less than that. \"I'm sorry, but the lifestyle you've ordered that you've grown accustomed to is completely out of stock. Have a nice day! \"-$$$\n\n\u201cAssuming one can never leave permanent social exile and alienation keep on living only to observe the total collapse of entire societies, nations, or civilizations where afterwards in the inevitable chaos revel in its total destruction taking satisfaction within it as a casual witness. Let it all burn and come crashing down in a festival or spectacle orgy of violence.\u201d-Myself\n\nZero_Sum\nEvil Neo-Nazi Extraordinaire.\n\nPosts: 3302\nJoined: Thu Nov 30, 2017 7:05 pm\nLocation: U.S.S.A- Newly lead Bolshevik Soviet block. Also known as Weimar America.","date":"2020-04-09 07:27:25","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.3433072865009308, \"perplexity\": 7141.0991420946075}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2020-16\/segments\/1585371830894.88\/warc\/CC-MAIN-20200409055849-20200409090349-00530.warc.gz\"}"}
| null | null |
package org.perfcake.ide.core.components;
import org.perfcake.message.Message;
import org.perfcake.message.correlator.Correlator;
import org.perfcake.message.generator.MessageGenerator;
import org.perfcake.message.receiver.Receiver;
import org.perfcake.message.sender.MessageSender;
import org.perfcake.message.sequence.Sequence;
import org.perfcake.reporting.destination.Destination;
import org.perfcake.reporting.reporter.Reporter;
import org.perfcake.scenario.Scenario;
import org.perfcake.scenario.ScenarioFactory;
import org.perfcake.validation.MessageValidator;
/**
* Represents a PerfCake component. Only the components which are has own model class in pc4ide are
* listed in this enum. Other components are considered too simple, so they are represented just as
* a property of some other component.
*
* @author jknetl
*/
public enum PerfCakeComponent {
GENERATOR(MessageGenerator.class, ScenarioFactory.DEFAULT_GENERATOR_PACKAGE),
SENDER(MessageSender.class, ScenarioFactory.DEFAULT_SENDER_PACKAGE),
RECEIVER(Receiver.class, ScenarioFactory.DEFAULT_RECEIVER_PACKAGE),
CORRELATOR(Correlator.class, ScenarioFactory.DEFAULT_CORRELATOR_PACKAGE),
SEQUENCE(Sequence.class, ScenarioFactory.DEFAULT_SEQUENCE_PACKAGE),
REPORTER(Reporter.class, ScenarioFactory.DEFAULT_REPORTER_PACKAGE),
DESTINATION(Destination.class, ScenarioFactory.DEFAULT_DESTINATION_PACKAGE),
VALIDATOR(MessageValidator.class, ScenarioFactory.DEFAULT_VALIDATION_PACKAGE),
MESSAGE(Message.class, null), //message has no implementation classes
SCENARIO(Scenario.class, null); //scenario has no implementation classes
/**
* Class of the inspector interface.
*/
private Class<?> api;
/**
* Default package for implementation classes.
*/
private String defaultPackage;
PerfCakeComponent(Class<?> api, String defaultPackage) {
this.api = api;
this.defaultPackage = defaultPackage;
}
/**
* Gets an interface which represent supertype of inspector..
*
* @return Class which represents the inspector type in the PerfCake
*/
public Class<?> getApi() {
return api;
}
/**
* Gets default package for implementation classes.
*
* @return the default package for implementation classes of this component.
*/
public String getDefaultPackage() {
return defaultPackage;
}
/**
* Detects PerfCake component by implementation class.
*
* @param clazz implementation of some component.
* @return PerfCake component which is implemented by the clazz or null if clazz is not a perfcake component implementation.
*/
public static PerfCakeComponent detectComponentType(Class<?> clazz) {
PerfCakeComponent result = null;
for (PerfCakeComponent c : values()) {
if (c.getApi().isAssignableFrom(clazz)) {
result = c;
}
}
return result;
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 4,480
|
namespace gl
{
class HandleAllocator final : angle::NonCopyable
{
public:
// Maximum handle = MAX_UINT-1
HandleAllocator();
// Specify maximum handle value
HandleAllocator(GLuint maximumHandleValue);
~HandleAllocator();
void setBaseHandle(GLuint value);
GLuint allocate();
void release(GLuint handle);
void reserve(GLuint handle);
private:
GLuint mBaseValue;
GLuint mNextValue;
typedef std::vector<GLuint> HandleList;
HandleList mFreeValues;
// Represents an inclusive range [begin, end]
struct HandleRange
{
HandleRange(GLuint beginIn, GLuint endIn) : begin(beginIn), end(endIn) {}
GLuint begin;
GLuint end;
};
struct HandleRangeComparator;
// The freelist consists of never-allocated handles, stored
// as ranges, and handles that were previously allocated and
// released, stored in a stack.
std::vector<HandleRange> mUnallocatedList;
std::vector<GLuint> mReleasedList;
};
} // namespace gl
#endif // LIBANGLE_HANDLEALLOCATOR_H_
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 6,978
|
package com.zyl.melife.view;
import android.content.Context;
import android.view.LayoutInflater;
import android.view.ViewGroup;
import android.widget.LinearLayout;
import com.zyl.melife.R;
import com.zyl.melife.utils.ViewUtil;
import butterknife.ButterKnife;
import butterknife.OnClick;
/**
* Created by froger_mcs on 15.12.14.
*/
public class EveryFaceContextMenu extends LinearLayout {
private static final int CONTEXT_MENU_WIDTH = ViewUtil.dpToPx(240);
private int everyfaceItem = -1;
private OnEveryFaceContextMenuItemClickListener onItemClickListener;
public EveryFaceContextMenu(Context context) {
super(context);
init();
}
private void init() {
LayoutInflater.from(getContext()).inflate(R.layout.view_context_menu, this, true);
setBackgroundResource(R.drawable.bg_container_shadow);
setOrientation(VERTICAL);
setLayoutParams(new LayoutParams(CONTEXT_MENU_WIDTH, ViewGroup.LayoutParams.WRAP_CONTENT));
}
public void bindToItem(int feedItem) {
this.everyfaceItem = feedItem;
}
@Override
protected void onAttachedToWindow() {
super.onAttachedToWindow();
ButterKnife.inject(this);
}
public void dismiss() {
((ViewGroup) getParent()).removeView(EveryFaceContextMenu.this);
}
@OnClick(R.id.btnSharePhoto)
public void onSharePhotoClick() {
if (onItemClickListener != null) {
onItemClickListener.onSharePhotoClick(everyfaceItem);
}
}
@OnClick(R.id.btnDelete)
public void onDeleteClick() {
if (onItemClickListener != null) {
onItemClickListener.onDeleteEveryFaceClick(everyfaceItem);
}
}
@OnClick(R.id.btnCancel)
public void onCancelClick() {
if (onItemClickListener != null) {
onItemClickListener.onCancelClick(everyfaceItem);
}
}
public void setOnEveryFaceMenuItemClickListener(OnEveryFaceContextMenuItemClickListener onItemClickListener) {
this.onItemClickListener = onItemClickListener;
}
public interface OnEveryFaceContextMenuItemClickListener {
public void onSharePhotoClick(int everyfaceItem);
public void onDeleteEveryFaceClick(int everyfaceItem);
public void onCancelClick(int everyfaceItem);
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 2,406
|
{"url":"https:\/\/lifelines.readthedocs.io\/en\/stable\/fitters\/regression\/CoxTimeVaryingFitter.html","text":"CoxTimeVaryingFitter\u00b6\n\nclass lifelines.fitters.cox_time_varying_fitter.CoxTimeVaryingFitter(alpha=0.05, penalizer=0.0, l1_ratio: float = 0.0, strata=None)\n\nBases: lifelines.fitters.SemiParametricRegressionFitter, lifelines.fitters.mixins.ProportionalHazardMixin\n\nThis class implements fitting Cox\u2019s time-varying proportional hazard model:\n\n$h(t|x(t)) = h_0(t)\\exp((x(t)-\\overline{x})'\\beta)$\nParameters: alpha (float, optional (default=0.05)) \u2013 the level in the confidence intervals. penalizer (float, optional) \u2013 the coefficient of an L2 penalizer in the regression\nparams_\n\nThe estimated coefficients. Changed in version 0.22.0: use to be .hazards_\n\nType: Series\nhazard_ratios_\n\nThe exp(coefficients)\n\nType: Series\nconfidence_intervals_\n\nThe lower and upper confidence intervals for the hazard coefficients\n\nType: DataFrame\nevent_observed\n\nThe event_observed variable provided\n\nType: Series\nweights\n\nThe event_observed variable provided\n\nType: Series\nvariance_matrix_\n\nThe variance matrix of the coefficients\n\nType: DataFrame\nstrata\n\nthe strata provided\n\nType: list\nstandard_errors_\n\nthe standard errors of the estimates\n\nType: Series\nbaseline_cumulative_hazard_\nType: DataFrame\nbaseline_survival_\nType: DataFrame\nAIC_partial_\n\n\u201cpartial\u201d because the log-likelihood is partial\n\ncheck_assumptions(training_df: pandas.core.frame.DataFrame, advice: bool = True, show_plots: bool = False, p_value_threshold: float = 0.01, plot_n_bootstraps: int = 10, columns: Optional[List[str]] = None) \u2192 None\n\nUse this function to test the proportional hazards assumption. See usage example at https:\/\/lifelines.readthedocs.io\/en\/latest\/jupyter_notebooks\/Proportional%20hazard%20assumption.html\n\nParameters: training_df (DataFrame) \u2013 the original DataFrame used in the call to fit(...) or a sub-sampled version. advice (bool, optional) \u2013 display advice as output to the user\u2019s screen show_plots (bool, optional) \u2013 display plots of the scaled schoenfeld residuals and loess curves. This is an eyeball test for violations. This will slow down the function significantly. p_value_threshold (float, optional) \u2013 the threshold to use to alert the user of violations. See note below. plot_n_bootstraps \u2013 in the plots displayed, also display plot_n_bootstraps bootstrapped loess curves. This will slow down the function significantly. columns (list, optional) \u2013 specify a subset of columns to test.\n\nExamples\n\nfrom lifelines.datasets import load_rossi\nfrom lifelines import CoxPHFitter\n\ncph = CoxPHFitter().fit(rossi, 'week', 'arrest')\n\ncph.check_assumptions(rossi)\n\n\nNotes\n\nThe p_value_threshold is arbitrarily set at 0.01. Under the null, some covariates will be below the threshold (i.e. by chance). This is compounded when there are many covariates.\n\nSimilarly, when there are lots of observations, even minor deviances from the proportional hazard assumption will be flagged.\n\nWith that in mind, it\u2019s best to use a combination of statistical tests and eyeball tests to determine the most serious violations.\n\nReferences\n\ncompute_followup_hazard_ratios(training_df: pandas.core.frame.DataFrame, followup_times: Iterable[T_co]) \u2192 pandas.core.frame.DataFrame\n\nRecompute the hazard ratio at different follow-up times (lifelines handles accounting for updated censoring and updated durations). This is useful because we need to remember that the hazard ratio is actually a weighted-average of period-specific hazard ratios.\n\nParameters: training_df (pd.DataFrame) \u2013 The same dataframe used to train the model followup_times (Iterable) \u2013 a list\/array of follow-up times to recompute the hazard ratio at.\ncompute_residuals(training_dataframe: pandas.core.frame.DataFrame, kind: str) \u2192 pandas.core.frame.DataFrame\n\nCompute the residuals the model.\n\nParameters: training_dataframe (DataFrame) \u2013 the same training DataFrame given in fit kind (string) \u2013 One of {\u2018schoenfeld\u2019, \u2018score\u2019, \u2018delta_beta\u2019, \u2018deviance\u2019, \u2018martingale\u2019, \u2018scaled_schoenfeld\u2019}\n\nNotes\n\n\u2022 'scaled_schoenfeld': lifelines does not add the coefficients to the final results, but R does when you call residuals(c, \"scaledsch\")\nfit(df, event_col, start_col='start', stop_col='stop', weights_col=None, id_col=None, show_progress=False, step_size=None, robust=False, strata=None, initial_point=None, formula: str = None)\n\nFit the Cox Proportional Hazard model to a time varying dataset. Tied survival times are handled using Efron\u2019s tie-method.\n\nParameters: df (DataFrame) \u2013 a Pandas DataFrame with necessary columns duration_col and event_col, plus other covariates. duration_col refers to the lifetimes of the subjects. event_col refers to whether the \u2018death\u2019 events was observed: 1 if observed, 0 else (censored). event_col (string) \u2013 the column in DataFrame that contains the subjects\u2019 death observation. If left as None, assume all individuals are non-censored. start_col (string) \u2013 the column that contains the start of a subject\u2019s time period. stop_col (string) \u2013 the column that contains the end of a subject\u2019s time period. weights_col (string, optional) \u2013 the column that contains (possibly time-varying) weight of each subject-period row. id_col (string, optional) \u2013 A subject could have multiple rows in the DataFrame. This column contains the unique identifier per subject. If not provided, it\u2019s up to the user to make sure that there are no violations. show_progress (since the fitter is iterative, show convergence) \u2013 diagnostics. robust (bool, optional (default: True)) \u2013 Compute the robust errors using the Huber sandwich estimator, aka Wei-Lin estimate. This does not handle ties, so if there are high number of ties, results may significantly differ. See \u201cThe Robust Inference for the Cox Proportional Hazards Model\u201d, Journal of the American Statistical Association, Vol. 84, No. 408 (Dec., 1989), pp. 1074- 1078 step_size (float, optional) \u2013 set an initial step size for the fitting algorithm. strata (list or string, optional) \u2013 specify a column or list of columns n to use in stratification. This is useful if a categorical covariate does not obey the proportional hazard assumption. This is used similar to the strata expression in R. See http:\/\/courses.washington.edu\/b515\/l17.pdf. initial_point ((d,) numpy array, optional) \u2013 initialize the starting point of the iterative algorithm. Default is the zero vector. formula (str, optional) \u2013 A R-like formula for transforming the covariates self \u2013 self, with additional properties like hazards_ and print_summary CoxTimeVaryingFitter\nfit_right_censoring(*args, **kwargs)\n\nAlias for fit\n\nhazard_ratios_\nlog_likelihood_ratio_test()\n\nThis function computes the likelihood ratio test for the Cox model. We compare the existing model (with all the covariates) to the trivial model of no covariates.\n\nConveniently, we can actually use CoxPHFitter class to do most of the work.\n\nplot(columns=None, ax=None, **errorbar_kwargs)\n\nProduces a visual representation of the coefficients, including their standard errors and magnitudes.\n\nParameters: columns (list, optional) \u2013 specify a subset of the columns to plot errorbar_kwargs \u2013 pass in additional plotting commands to matplotlib errorbar command ax \u2013 the matplotlib axis that be edited. matplotlib axis\nplot_covariate_groups(**kwargs)\n\nDeprecated as of v0.25.0. Use plot_partial_effects_on_outcome instead.\n\npredict_log_partial_hazard(X) \u2192 pandas.core.series.Series\n\nThis is equivalent to R\u2019s linear.predictors. Returns the log of the partial hazard for the individuals, partial since the baseline hazard is not included. Equal to $$(x - \\bar{x})'\\beta$$\n\nParameters: X (numpy array or DataFrame) \u2013 a (n,d) covariate numpy array or DataFrame. If a DataFrame, columns can be in any order. If a numpy array, columns must be in the same order as the training data. DataFrame\n\nNote\n\nIf X is a DataFrame, the order of the columns do not matter. But if X is an array, then the column ordering is assumed to be the same as the training dataset.\n\npredict_partial_hazard(X) \u2192 pandas.core.series.Series\n\nReturns the partial hazard for the individuals, partial since the baseline hazard is not included. Equal to $$\\exp{(x - \\bar{x})'\\beta }$$\n\nParameters: X (numpy array or DataFrame) \u2013 a (n,d) covariate numpy array or DataFrame. If a DataFrame, columns can be in any order. If a numpy array, columns must be in the same order as the training data. DataFrame\n\nNote\n\nIf X is a DataFrame, the order of the columns do not matter. But if X is an array, then the column ordering is assumed to be the same as the training dataset.\n\nprint_summary(decimals=2, style=None, columns=None, **kwargs)\n\nPrint summary statistics describing the fit, the coefficients, and the error bounds.\n\nParameters: decimals (int, optional (default=2)) \u2013 specify the number of decimal places to show style (string) \u2013 {html, ascii, latex} columns \u2013 only display a subset of summary columns. Default all. kwargs \u2013 print additional meta data in the output (useful to provide model names, dataset names, etc.) when comparing multiple outputs.\nsummary\n\nSummary statistics describing the fit.\n\nReturns: df \u2013 Contains columns coef, np.exp(coef), se(coef), z, p, lower, upper DataFrame","date":"2020-08-11 03:27:38","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 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\": 0.31254857778549194, \"perplexity\": 6553.162164828328}, \"config\": {\"markdown_headings\": false, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2020-34\/segments\/1596439738727.76\/warc\/CC-MAIN-20200811025355-20200811055355-00332.warc.gz\"}"}
| null | null |
Q: PySpark structured Streaming + Kafka Error (Caused by: java.lang.ClassNotFoundException: org.apache.spark.sql.sources.v2.StreamWriteSupport ) I am trying to run Python Spark Structured Streaming + Kafka, when I run the command
Master@MacBook-Pro spark-3.0.0-preview2-bin-hadoop2.7 % bin/spark-submit --packages org.apache.spark:spark-sql-kafka-0-10_2.12:2.4.5 \
examples/src/main/python/sql/streaming/structured_kafka_wordcount.py \
/Users/Master/Projects/bank_kafka_spark/spark_job1.py localhost:9092 transaction
receiving next
20/04/22 13:06:04 WARN Utils: Your hostname, MacBook-Pro.local resolves to a loopback address: 127.0.0.1; using 192.168.0.103 instead (on interface en0)
20/04/22 13:06:04 WARN Utils: Set SPARK_LOCAL_IP if you need to bind to another address
WARNING: An illegal reflective access operation has occurred
WARNING: Illegal reflective access by org.apache.spark.unsafe.Platform (file:/Users/Master/Projects/spark-3.0.0-preview2-bin-hadoop2.7/jars/spark-unsafe_2.12-3.0.0-preview2.jar) to constructor java.nio.DirectByteBuffer(long,int)
WARNING: Please consider reporting this to the maintainers of org.apache.spark.unsafe.Platform
WARNING: Use --illegal-access=warn to enable warnings of further illegal reflective access operations
WARNING: All illegal access operations will be denied in a future release
Ivy Default Cache set to: /Users/Master/.ivy2/cache
The jars for the packages stored in: /Users/Master/.ivy2/jars
:: loading settings :: url = jar:file:/Users/Master/Projects/spark-3.0.0-preview2-bin-hadoop2.7/jars/ivy-2.4.0.jar!/org/apache/ivy/core/settings/ivysettings.xml
org.apache.spark#spark-sql-kafka-0-10_2.12 added as a dependency
:: resolving dependencies :: org.apache.spark#spark-submit-parent-cd5905ea-5f80-4b14-995d-6ba03a353bb0;1.0
confs: [default]
found org.apache.spark#spark-sql-kafka-0-10_2.12;2.4.5 in central
found org.apache.kafka#kafka-clients;2.0.0 in central
found org.lz4#lz4-java;1.4.0 in central
found org.xerial.snappy#snappy-java;1.1.7.3 in central
found org.slf4j#slf4j-api;1.7.16 in central
found org.spark-project.spark#unused;1.0.0 in local-m2-cache
:: resolution report :: resolve 315ms :: artifacts dl 6ms
:: modules in use:
org.apache.kafka#kafka-clients;2.0.0 from central in [default]
org.apache.spark#spark-sql-kafka-0-10_2.12;2.4.5 from central in [default]
org.lz4#lz4-java;1.4.0 from central in [default]
org.slf4j#slf4j-api;1.7.16 from central in [default]
org.spark-project.spark#unused;1.0.0 from local-m2-cache in [default]
org.xerial.snappy#snappy-java;1.1.7.3 from central in [default]
---------------------------------------------------------------------
| | modules || artifacts |
| conf | number| search|dwnlded|evicted|| number|dwnlded|
---------------------------------------------------------------------
| default | 6 | 0 | 0 | 0 || 6 | 0 |
---------------------------------------------------------------------
:: retrieving :: org.apache.spark#spark-submit-parent-cd5905ea-5f80-4b14-995d-6ba03a353bb0
confs: [default]
0 artifacts copied, 6 already retrieved (0kB/6ms)
20/04/22 13:06:04 DEBUG NativeCodeLoader: Trying to load the custom-built native-hadoop library...
20/04/22 13:06:04 DEBUG NativeCodeLoader: Failed to load native-hadoop with error: java.lang.UnsatisfiedLinkError: no hadoop in java.library.path: [/Users/Master/Library/Java/Extensions, /Library/Java/Extensions, /Network/Library/Java/Extensions, /System/Library/Java/Extensions, /usr/lib/java, .]
20/04/22 13:06:04 DEBUG NativeCodeLoader: java.library.path=/Users/Master/Library/Java/Extensions:/Library/Java/Extensions:/Network/Library/Java/Extensions:/System/Library/Java/Extensions:/usr/lib/java:.
20/04/22 13:06:04 WARN NativeCodeLoader: Unable to load native-hadoop library for your platform... using builtin-java classes where applicable
Traceback (most recent call last):
File "/Users/Master/Projects/spark-3.0.0-preview2-bin-hadoop2.7/examples/src/main/python/sql/streaming/structured_kafka_wordcount.py", line 68, in <module>
.option(subscribeType, topics)\
File "/Users/Master/Projects/spark-3.0.0-preview2-bin-hadoop2.7/python/lib/pyspark.zip/pyspark/sql/streaming.py", line 406, in load
File "/Users/Master/Projects/spark-3.0.0-preview2-bin-hadoop2.7/python/lib/py4j-0.10.8.1-src.zip/py4j/java_gateway.py", line 1286, in __call__
File "/Users/Master/Projects/spark-3.0.0-preview2-bin-hadoop2.7/python/lib/pyspark.zip/pyspark/sql/utils.py", line 98, in deco
File "/Users/Master/Projects/spark-3.0.0-preview2-bin-hadoop2.7/python/lib/py4j-0.10.8.1-src.zip/py4j/protocol.py", line 328, in get_return_value
py4j.protocol.Py4JJavaError: An error occurred while calling o31.load.
: java.lang.NoClassDefFoundError: org/apache/spark/sql/sources/v2/StreamWriteSupport
at java.base/java.lang.ClassLoader.defineClass1(Native Method)
at java.base/java.lang.ClassLoader.defineClass(ClassLoader.java:1016)
at java.base/java.security.SecureClassLoader.defineClass(SecureClassLoader.java:151)
at java.base/jdk.internal.loader.BuiltinClassLoader.defineClass(BuiltinClassLoader.java:821)
at java.base/jdk.internal.loader.BuiltinClassLoader.findClassOnClassPathOrNull(BuiltinClassLoader.java:719)
at java.base/jdk.internal.loader.BuiltinClassLoader.loadClassOrNull(BuiltinClassLoader.java:642)
at java.base/jdk.internal.loader.BuiltinClassLoader.loadClass(BuiltinClassLoader.java:600)
at java.base/jdk.internal.loader.ClassLoaders$AppClassLoader.loadClass(ClassLoaders.java:178)
at java.base/java.lang.ClassLoader.loadClass(ClassLoader.java:575)
at java.base/java.lang.ClassLoader.loadClass(ClassLoader.java:521)
at java.base/java.lang.Class.forName0(Native Method)
at java.base/java.lang.Class.forName(Class.java:416)
at java.base/java.util.ServiceLoader$LazyClassPathLookupIterator.nextProviderClass(ServiceLoader.java:1210)
at java.base/java.util.ServiceLoader$LazyClassPathLookupIterator.hasNextService(ServiceLoader.java:1221)
at java.base/java.util.ServiceLoader$LazyClassPathLookupIterator.hasNext(ServiceLoader.java:1265)
at java.base/java.util.ServiceLoader$2.hasNext(ServiceLoader.java:1300)
at java.base/java.util.ServiceLoader$3.hasNext(ServiceLoader.java:1385)
at scala.collection.convert.Wrappers$JIteratorWrapper.hasNext(Wrappers.scala:43)
at scala.collection.Iterator.foreach(Iterator.scala:941)
at scala.collection.Iterator.foreach$(Iterator.scala:941)
at scala.collection.AbstractIterator.foreach(Iterator.scala:1429)
at scala.collection.IterableLike.foreach(IterableLike.scala:74)
at scala.collection.IterableLike.foreach$(IterableLike.scala:73)
at scala.collection.AbstractIterable.foreach(Iterable.scala:56)
at scala.collection.TraversableLike.filterImpl(TraversableLike.scala:255)
at scala.collection.TraversableLike.filterImpl$(TraversableLike.scala:249)
at scala.collection.AbstractTraversable.filterImpl(Traversable.scala:108)
at scala.collection.TraversableLike.filter(TraversableLike.scala:347)
at scala.collection.TraversableLike.filter$(TraversableLike.scala:347)
at scala.collection.AbstractTraversable.filter(Traversable.scala:108)
at org.apache.spark.sql.execution.datasources.DataSource$.lookupDataSource(DataSource.scala:644)
at org.apache.spark.sql.streaming.DataStreamReader.load(DataStreamReader.scala:170)
at java.base/jdk.internal.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
at java.base/jdk.internal.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62)
at java.base/jdk.internal.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)
at java.base/java.lang.reflect.Method.invoke(Method.java:567)
at py4j.reflection.MethodInvoker.invoke(MethodInvoker.java:244)
at py4j.reflection.ReflectionEngine.invoke(ReflectionEngine.java:357)
at py4j.Gateway.invoke(Gateway.java:282)
at py4j.commands.AbstractCommand.invokeMethod(AbstractCommand.java:132)
at py4j.commands.CallCommand.execute(CallCommand.java:79)
at py4j.GatewayConnection.run(GatewayConnection.java:238)
at java.base/java.lang.Thread.run(Thread.java:830)
Caused by: java.lang.ClassNotFoundException: org.apache.spark.sql.sources.v2.StreamWriteSupport
at java.base/jdk.internal.loader.BuiltinClassLoader.loadClass(BuiltinClassLoader.java:602)
at java.base/jdk.internal.loader.ClassLoaders$AppClassLoader.loadClass(ClassLoaders.java:178)
at java.base/java.lang.ClassLoader.loadClass(ClassLoader.java:521)
... 43 more
I use example from PySpark examples/src/main/python/sql/streaming/structured_kafka_wordcount.py.
structured_kafka_wordcount.py.
#
# Licensed to the Apache Software Foundation (ASF) under one or more
# contributor license agreements. See the NOTICE file distributed with
# this work for additional information regarding copyright ownership.
# The ASF licenses this file to You under the Apache License, Version 2.0
# (the "License"); you may not use this file except in compliance with
# the License. You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
#
"""
Consumes messages from one or more topics in Kafka and does wordcount.
Usage: structured_kafka_wordcount.py <bootstrap-servers> <subscribe-type> <topics>
<bootstrap-servers> The Kafka "bootstrap.servers" configuration. A
comma-separated list of host:port.
<subscribe-type> There are three kinds of type, i.e. 'assign', 'subscribe',
'subscribePattern'.
|- <assign> Specific TopicPartitions to consume. Json string
| {"topicA":[0,1],"topicB":[2,4]}.
|- <subscribe> The topic list to subscribe. A comma-separated list of
| topics.
|- <subscribePattern> The pattern used to subscribe to topic(s).
| Java regex string.
|- Only one of "assign, "subscribe" or "subscribePattern" options can be
| specified for Kafka source.
<topics> Different value format depends on the value of 'subscribe-type'.
Run the example
`$ bin/spark-submit examples/src/main/python/sql/streaming/structured_kafka_wordcount.py \
host1:port1,host2:port2 subscribe topic1,topic2`
"""
from __future__ import print_function
import sys
from pyspark.sql import SparkSession
from pyspark.sql.functions import explode
from pyspark.sql.functions import split
if __name__ == "__main__":
if len(sys.argv) != 4:
print("""
Usage: structured_kafka_wordcount.py <bootstrap-servers> <subscribe-type> <topics>
""", file=sys.stderr)
sys.exit(-1)
bootstrapServers = sys.argv[1]
subscribeType = sys.argv[2]
topics = sys.argv[3]
spark = SparkSession\
.builder\
.appName("StructuredKafkaWordCount")\
.getOrCreate()
# Create DataSet representing the stream of input lines from kafka
lines = spark\
.readStream\
.format("kafka")\
.option("kafka.bootstrap.servers", bootstrapServers)\
.option(subscribeType, topics)\ # HERE IT STOPS AND RETURNS ERROR
.load()\
.selectExpr("CAST(value AS STRING)")
# Split the lines into words
words = lines.select(
# explode turns each item in an array into a separate row
explode(
split(lines.value, ' ')
).alias('word')
)
# Generate running word count
wordCounts = words.groupBy('word').count()
# Start running the query that prints the running counts to the console
query = wordCounts\
.writeStream\
.outputMode('complete')\
.format('console')\
.start()
query.awaitTermination()
Kafka server is runing, topic was created.
Java version 13.0.2
Scala 2.13.1
Kafka 2.12-2.4.1
Spark spark-3.0.0-preview2-bin-hadoop2.7
What is the problem?
A: I was having the exact same issue too until I realized I was adding the wrong dependency!
Instead of:
--packages org.apache.spark:spark-sql-kafka-0-10_2.12:2.4.5
Use:
--packages org.apache.spark:spark-sql-kafka-0-10_2.12:3.0.0-preview2
A: org.apache.spark.sql.sources.v2.StreamWriteSupport class is no longer part for Spark-Sql version 3.
But some pyspark libraries are still trying to load the class which causes above exception.
Should be a Spark:3.0.0 bug
A: THere https://spark.apache.org/docs/latest/structured-streaming-kafka-integration.html#deploying states that :
spark-sql-kafka-0-10_2.12 and its dependencies can be directly added
to spark-submit using --packages
A: You gotta make sure that your PySpark version is compatible with the Kafka version you're setting as a dependency. For me it was: Spark 3.3.0 -> org.apache.spark:spark-sql-kafka-0-10_2.12:3.3.1.
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 1,472
|
Shin Bong-sun (; born October 6, 1980) is a South Korean comedienne and entertainer. She took a five-year hiatus from comedy from 2010 to 2015, which ended when she joined Comedy Big League. She is currently a member of the South Korean girl group Celeb Five.
Television series
MasterChef Korea Celebrity
Happy Together Season 3
Heroes
Family Outing 2
Infinite Girls
Secret
Exploration of Genders
BIGsTORY
Gold Miss is Coming
Change
Gag Concert
Answer Me 1997
Kim Jung-eun's Chocolate
The Thousandth Man (cameo)
King of Mask Singer (fixed panelist, contestant ep 87)
Idol Maid
Sweet Revenge 2 (cameo)
Blindly Commerce (2021,Host)
Song-eun's Manga Comeback tvN D Studio (STUDIO) with Song Eun-i
Goal Girls ( Cast Member , 2021)
Goal Girls 2 ( Cast Member, 2021)
Marriage Is Crazy (2021) - Host
Curling Queens (2022) - Host / MBC Lunar New Year special pilot
Chart Sisters (2022) ; Host with Celeb Five Member
Groom's Class (2022); Cast
Web shows
Radio shows
Awards and nominations
References
1980 births
Living people
South Korean women comedians
South Korean television presenters
South Korean women television presenters
South Korean radio presenters
People from Busan
Gag Concert
South Korean women radio presenters
Best Variety Performer Female Paeksang Arts Award (television) winners
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 80
|
Q: How to enable https in ngcordova android I am using ngcordova and application is working fine on http mode if i shift to https ios is working fine but android application is not connecting and showing error net::ERR_INSECURE_RESPONSE in console.Is there anything else i need to add.
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 14
|
Judge Stark Grants Plaintiff's Motion for Partial Summary Judgment as to Defendants' Affirmative Defenses of Laches, Acquiescence and Statute of Limitations in Trademark Infringement Action
Gregory Williams
Fox Rothschild LLP
By Memorandum Order entered by the Honorable Leonard P. Stark in Emerson Radio Corp. v. Emerson Quiet Kool Co. Ltd., Civil Action No. 20-1652-LPS (D.Del. November 5, 2021), the Court granted the motion for partial summary judgment of Plaintiff Emerson Radio Corp. as to the affirmative defenses of laches, acquiescence, and statute of limitations of Defendants as to Defendants' allegedly infringing use of the EMERSON QUIET KOOL trademark.
In so ruling, the Court found that Defendants' affirmative defenses of laches and acquiescence failed as a matter of law because (1) they were based on an alleged 2017 assignment of the EMERSON QUIET KOOL trademark from American Ductless AC Corp. ("American Ductless") to Defendant Emerson Quiet Kool Co. Ltd., and (2) there was no genuine dispute of material fact that the alleged assignment of the trademark was invalid because there was no consideration paid to American Ductless. Id. at *3-4. The Court also found that there was no genuine dispute of material fact that the instances of Defendants' alleged infringing activities occurred within the six-year limitations period preceding the filing of the lawsuit by Plaintiff. Id. at *6.
A copy of the Memorandum Order is attached.
[View source.]
Judge Noreika Grants Defendant's Post-Trial Renewed Motion for Judgment as a Matter of Law Reversing the Jury's Finding of Liability for False Advertising under the Lanham Act and Award of Punitive Damages Against Defendant
Judge Stark Denies Defendant's Motion to Dismiss Under 35 U.S.C. § 101 After Finding Patent-in-Suit Is Not Directed to an Abstract Idea
Judge Andrews Construes Two Remaining Disputed Terms of Patent Relating to Improved Process to Convert Benzindene Triol to Trespostinil
Judge Andrews Grants Amazon's Motion for Summary Judgment of Non-Infringement in Patent Infringement Action Claiming Infringement by Amazon's Alexa Technology
Judge Noreika Denies Plaintiff's Motion for Preliminary Injunction in Patent Infringement Action
Judge Noreika Denies Plaintiffs and Defendants' Respective Motions For Summary Judgment On Infringement/Non-Infringement In Trademark Infringement Action And Grants-In-Part Defendants' Motion With Respect To Actual Damages
© Fox Rothschild LLP | Attorney Advertising
Fox Rothschild LLP on:
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 1,310
|
<?xml version="1.0" encoding="UTF-8"?>
<configuration>
<property name="LOG_HOME" value="/usr/local/dir_samba/HC_logs/tcm"/>
<appender name="STDOUT" class="ch.qos.logback.core.ConsoleAppender">
<Encoding>UTF-8</Encoding>
<layout class="ch.qos.logback.classic.PatternLayout">
<pattern>%d{yyyy-MM-dd HH:mm:ss.SSS} [%thread] %-5level %logger{50} - %msg%n
</pattern>
</layout>
</appender>
<appender name="SRTEINFO" class="ch.qos.logback.core.rolling.RollingFileAppender">
<Encoding>UTF-8</Encoding>
<rollingPolicy class="ch.qos.logback.core.rolling.TimeBasedRollingPolicy">
<!--用户行为操作的日志打印到以log-user开头的文件中 -->
<FileNamePattern>${LOG_HOME}/srte/srte-info.%d{yyyy-MM-dd}.%i.log</FileNamePattern>
<timeBasedFileNamingAndTriggeringPolicy class="ch.qos.logback.core.rolling.SizeAndTimeBasedFNATP">
<maxFileSize>100MB</maxFileSize>
</timeBasedFileNamingAndTriggeringPolicy>
</rollingPolicy>
<layout class="ch.qos.logback.classic.PatternLayout">
<pattern>%d{yyyy-MM-dd HH:mm:ss.SSS} [%thread] %-5level %logger{50} - %msg%n%ex
</pattern>
</layout>
</appender>
<logger name="org.apache.ibatis" level="INFO" />
<logger name="org.mybatis" level="INFO"/>
<logger name="com.ah.manager.mapper" level="INFO"/>
<logger name="SRTE" level="DEBUG" additivity="false">
<appender-ref ref="SRTEINFO"/>
<appender-ref ref="STDOUT"/>
</logger>
<!-- 日志输出级别 -->
<root level="DEBUG">
<appender-ref ref="STDOUT"/>
</root>
</configuration>
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 6,623
|
Q: return statements in recursive calls From what I understand about recursive calls, is that when you are recursing into by calling the function ,the statement needs to be a return statement ,because basically when it pops out of the function stack it expects some value from the earlier call .
I have some code like for inserting in a BST
insertCorrectLocation(root, newNode) {
if (newNode.data < root.data) {
if (root.left == null) {
root.left = newNode
} else {
return this.insertCorrectLocation(root.left, newNode)
}
}
else {
if (root.right == null) {
root.right = newNode
} else {
return this.insertCorrectLocation(root.right, newNode)
}
}
}
This works even if I remove the return statements for the calls ,such as
else {
if (root.right == null) {
root.right = newNode
} else {
this.insertCorrectLocation(root.right, newNode)
}
}
How does that happen ?
A: In a recursive function, you only need to (explicitly) return if the outer consumer of the recursive function needs to receive a value, for example:
const foundNode = tree.findNode(5);
In this case, since you're only inserting a value, but not retrieving one, there's no need for recursive returns.
(functions will automatically return once they reach the end of their block if there's no return statement, passing control back to the caller)
A: There is no requirement to return any values from a function that is mainly for side effects. Recursive functions have no special treatments so it goes for those as well. eg. console.log is mainly for effect and it returns the default value undefined. Thus in your example where a recursive function alters an existing object will be able to use the root node as the whole tree after the process has finished.
The most common error is when the contract is supposed to return a value and you forget to return in some places. Eg.
function factorial(n) {
if (n === 1) return 1;
factorial(n - 1) * n;
}
factorial(1) ; //==> 1
factorial(2) ; //==> undefined
A function that does not explicitly return a value always return undefined. Thus for a factorial returning undefined is clearly a bug, but it did rewind the stack and did all the calculations, only that it didn't use the result.
A: I agree with everything said about not needing an explicit return in recursive function.
But I'm currently looking at a huge recursive function, about 600 lines, with many if-else statements. I think it can be dangerous for long recursive functions to not explicitly return. And while I know there are other problems with a long recursive function, it really doesn't hurt to just return;, especially that is the intention.
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 7,750
|
# THE PHENOMENAL WORLDWIDE BESTSELLER
IACOCCA: AN AUTOBIOGRAPHY
"His flamboyance as the chairman who saved Chrysler Corp. from bankruptcy has made him the business world's leading celebrity.... Many people admire Iacocca for his marketing savvy and management expertise. But it is probably his knack for plain talk that strikes the most responsive note among his fans.... The book, written in collaboration with journalist-lecturer William Novak, surges from personal history to management tips to lectures on such pet Iacocca topics as auto safety, labor costs, and industrial policy.... It is vintage Iacocca."
— _Business Week_
"The story of the resurrection of the Chrysler Corporation is exciting and well handled by Mr. Iacocca... There are plenty of clues to Mr. Iacocca's management methods. He's a good listener, but when the times come to stop listening and act, he becomes a decisive commander. People both like him and respect his talents so he can attract other talented people like a magnet. And he has the all-important leadership quality of humility: the reason your employees follow you, he writes, 'is not because you're providing some mysterious leadership. It's because you're following them.'... Every mother who has sons or daughters headed for a business career will want to give them _Iacocca_ for Christmas."
— _The New York Times Book Review_
_"Iacocca_ reads like Iacocca talks... the voice is unmistakable.... He is a big guy (6 ft. 1 in., 194 lbs.), a driven guy, an earthy, passionate, volatile, funny, and profane guy, a talkative guy who tells it like it is, who grabs for gusto, who damns the torpedoes, and plunges full-speed ahead."
— _Time_ Magazine
"Lee Iacocca is an American hero.... Iacocca's candid analysis of what is right and wrong with the auto industry, big labor, government, and America is insightful and refreshing... _Iacocca_ provides readers with an unusual insight... into the inner workings of one of modern America's great characters."
— _Philadelphia Inquirer_
"Engaging.... Mr. Iacocca's book is a profile of a strong-minded corporate chief who moves on the balls of his feet... Mr. Iacocca drops some little bombshells that are certain to get attention in Detroit."
— _The Wall Street Journal_
"Iacocca describes how he assembled his team of disgruntled ex-Ford men and retired executives, cajoled his suppliers and battled his banks, cut and slashed at the company, wrenched a billion-dollar loan guarantee out of the federal government, became a media star, rolled out his K-cars, and saved the day. He did just that, by the way."
— _Chicago Tribune_
"Apparently the age of American industrial heroes in the computer age is not dead—at least not while there is a Lee Iacocca story like this one... This book is his story and it's a dilly—and here let me add a word of commendation to collaborator William Novak for letting Iacocca speak in his own true voice throughout.... Iacocca's is one of the great success stories of the decade and will be enjoyed by all his readers."
— _John Barkham Reviews_
IACOCCA
A Bantam Book
PUBLISHING HISTORY
Bantam hardcover edition published November 1984
Bantam mass market edition / July 1986
Bantam trade paperback edition / May 2007
Published by
Bantam Dell
A division of Random House, Inc.
New York, New York
All rights reserved
Copyright © 1984 by Lee Iacocca
Library of Congress Catalog Card Number: 84-45174
Bantam Books and the rooster colophon are registered trademarks of
Random House, Inc.
eISBN: 978-0-307-78868-9
www.bantamdell.com
v3.1
**_To my beloved Mary_ ,
_for your courage..._
_and your devotion to the three of us._**
# CONTENTS
_Cover_
_Title Page_
_Copyright_
_Dedication_
_Acknowledgments_
_Introduction to the Paperback Edition_
An Opening Word
Prologue
MADE IN AMERICA
I The Family
II School Days
THE FORD STORY
III Getting My Feet Wet
IV The Bean Counters
V The Key to Management
VI The Mustang
VII Encore!
VIII The Road to the Top
IX Trouble in Paradise
X 1975: The Fateful Year
XI The Showdown
XII The Day After
THE CHRYSLER STORY
XIII Courted by Chrysler
XIV Aboard a Sinking Ship
XV Building the Team
XVI The Day the Shah Left Town
XVII Drastic Measures: Going to the Government
XVIII Should Chrysler Be Saved?
XIX Chrysler Goes to Congress
XX Equality of Sacrifice
XXI The Banks: Trial by Fire
XXII The K-Car—And A Close Call
XXIII Public Man, Public Office
XXIV A Bittersweet Victory
STRAIGHT TALK
XXV How to Save Lives on the Road
XXVI The High Cost of Labor
XXVII The Japanese Challenge
XXVIII Making America Great Again
Epilogue: The Great Lady
_About the Author_
_Photo Insert_
# ACKNOWLEDGMENTS
It's customary for an author to thank all the people who helped him with his book. But since this is an autobiography, I want to begin by thanking some of the people who helped me with my life—my true friends who stuck by me when my world was falling apart: Bishop Ed Broderick, Bill Curran, Vic Damone, Alejandro deTomaso, Bill Fugazy, Frank Klotz, Walter Murphy, Bill Winn, and Gio, my barber. Also my doctor, James Barron, who helped me keep mind and body together.
I want to thank the gang that came out of cozy retirement to give me a hand at Chrysler—Paul Bergmoser, Don DeLaRossa, Gar Laux, Hans Matthias, and John Naughton—and the young Turks like Jerry Greenwald, Steve Miller, Leo Kelmenson, and Ron DeLuca, who left good and secure jobs to pitch in and help save a dying company.
In my thirty-eight years in the auto business, I was blessed with three secretaries who really made me look good. The first was Betty Martin, a woman so talented she made many of the Ford officers look bad by comparison. The second, Dorothy Carr, left Ford the day I was fired and came over to Chrysler out of sheer loyalty, even though she put her pension in jeopardy. And the third, my present secretary, Bonnie Gatewood, a veteran Chrysler employee, ranks right up there with them.
I am grateful to my old friends from Ford, those precious few who stayed my friends during the dark days: Calvin Beauregard, Hank Carlini, Jay Dugan, Matt McLaughlin, John Morrissey, Wes Small, Hal Sperlich, and Frank Zimmerman.
I want to thank Nessa Rapoport, my editor, who made sure this book would have no recalls; the people at Bantam Books who worked so hard, particularly Jack Romanos, Stuart Applebaum, Heather Florence, Alberto Vitale, and Lou Wolfe; and my invaluable collaborator, William Novak.
And, it goes without saying, my daughters, Kathi and Lia, who were really my whole life and still are.
# INTRODUCTION TO THE PAPERBACK EDITION
Nobody was more surprised than I was when this book jumped to number one on the best-seller list the first week it was published. People started asking me how a book with no sex, no violence, and no spies could sell so well. I honestly didn't know, and I was supposed to be a marketing genius.
After all, this is just a story about a kid from a good immigrant family who studied hard and worked hard, who had some big successes and some big disappointments, and who made out fine in the end because of the simple values he learned from his parents and teachers, and because he had the good luck to live in America.
This is not the kind of book that is supposed to set publishing records, but it did.
I found out why by reading my mail. I started getting as many as five hundred letters a day, and I grabbed a pile as I left the office every night.
I discovered that the secret to the book was simple: Most people who wrote had lived parts of my life themselves. I wasn't writing about a strange place like the bottom of the ocean or the surface of the moon; I was writing about somewhere they'd all been.
I got a lot of letters from people who, like me, had been fired after years of faithful service to one company, or who had recently lost a loved one.
Some people wrote and told me about how their parents had come through Ellis Island and built a great life in America (and many included checks to help restore the island and the Statue of Liberty). They told me about the debt they owed to the hard work and sacrifice of their parents, and about their determination to make things even better for their kids.
I got letters from people who said how much they loved America, but how scared they were that America's fiscal and trade policies were going to lead to disaster.
I heard from school kids and from people in their eighties, from corporate presidents and unemployed workers. The book seemed to touch all of them, in one way or another.
Thousands of people said they learned something from this book, but none of them learned as much as I did just reading their letters.
I learned that the real spirit of America is a kind of pragmatic optimism: Everything will turn out well in the end, but only if you struggle and sacrifice to make it happen.
The chapter "Making America Great Again" drew more comments than any other because it touched a raw nerve. Americans are not going to accept second-class status in the world. Maybe some of our leaders aren't too alarmed about our country's losing its ability to compete, but my mailbag has convinced me that the American people won't stand for it.
I was frustrated when I wrote that chapter because I saw America going down the tubes. But when I read my mail, I realized that there is too much common sense and determination in this country for that to happen.
I closed the book talking about the Statue of Liberty and what she meant to the millions of immigrants she had welcomed to America. Those people (our parents and grandparents) broke their backs to build an America that became the wonder of the world.
They left us a legacy to be proud of and an example to live up to. Sometimes I've had to wonder whether we've lost sight of their example and whether we're still worthy of them. But every night, after I put down a new batch of letters, I know that we really are the same kind of people.
# AN OPENING WORD
Wherever I go, people always ask me the same questions. How did you get to be successful? Why did Henry Ford fire you? How did you turn Chrysler around?
I've never had a good quick answer to these questions, so I've slipped into the habit of saying: "When I write my book, you'll find out."
Over the years, I've repeated that phrase so often that I've come to believe my own words. In the end, I had no choice but to write the book I've been talking about for so long.
Why did I write it? Certainly not to become famous. The television ads for Chrysler have already made me more famous than I ever wanted to be.
And I didn't write it to get rich. I already have every material thing a person could need. That's why I'm donating every penny I earn from this book to diabetes research.
And I didn't write this book to get back at Henry Ford for firing me. I've already done that the old-fashioned American way—by fighting it out in the marketplace.
The truth is that I wrote this book to set the record straight (and to keep my mind straight), to tell the story of my life at Ford and at Chrysler the way it really happened. While I was working on it and reliving my life, I kept thinking of all those young people I meet whenever I speak at universities and business schools. If this book can give them a realistic picture of the excitement and challenge of big business in America today and some idea of what is worth fighting for, then all of this hard work will have been worth something.
# PROLOGUE
You're about to read the story of a man who's had more than his share of successes. But along the way, there were some pretty bad times, too. In fact, when I look back on my thirty-eight years in the auto industry, the day I remember most vividly had nothing at all to do with new cars and promotions and profits.
I began my life as the son of immigrants, and I worked my way up to the presidency of the Ford Motor Company. When I finally got there, I was on top of the world. But then fate said to me: "Wait. We're not finished with you. Now you're going to find out what it feels like to get kicked off Mt. Everest!"
On July 13, 1978, I was fired. I had been president of Ford for eight years and a Ford employee for thirty-two. I had never worked anywhere else. And now, suddenly, I was out of a job. It was gut-wrenching.
Officially, my term of employment was to end in three months. But under the terms of my "resignation," at the end of that period I was to be given the use of an office until I found a new job.
On October 15, my final day at the office, and just incidentally my fifty-fourth birthday, my driver drove me to World Headquarters in Dearborn for the last time. Before I left the house, I kissed my wife, Mary, and my two daughters, Kathi and Lia. My family had suffered tremendously during my final, turbulent months at Ford, and that filled me with rage. Perhaps I was responsible for my own fate. But what about Mary and the girls? Why did they have to go through this? They were the innocent victims of the despot whose name was on the building.
Even today, their pain is what stays with me. It's like the lioness and her cubs. If the hunter knows what's good for him, he'll leave the little ones alone. Henry Ford made my kids suffer, and for that I'll never forgive him.
The very next day I got into my car and headed out to my new office. It was in an obscure warehouse on Telegraph Road, only a few miles from Ford's World Headquarters. But for me, it was like visiting another planet.
I wasn't exactly sure where the office was, and it took me a few minutes to find the right building. When I finally got there, I didn't even know where to park.
As it turned out, there were plenty of people around to show me. Someone had alerted the media that the newly deposed president of Ford would be coming to work here this morning, and a small crowd had gathered to meet me. A TV reporter shoved a microphone in my face and asked: "How do you feel, coming to this warehouse after eight years at the top?"
I couldn't bring myself to answer him. What could I say? When I was safely out of camera range, I muttered the truth. "I feel like shit," I said.
My new office was little more than a cubicle with a small desk and a telephone. My secretary, Dorothy Carr, was already there, with tears in her eyes. Without saying a word, she pointed to the cracked linoleum floor and the two plastic coffee cups on the desk.
Only yesterday, she and I had been working in the lap of luxury. The office of the president was the size of a grand hotel suite. I had my, own bathroom. I even had my own living quarters. As a senior Ford executive, I was served by white-coated waiters who were on call all day. I once brought some relatives from Italy to see where I worked, and they thought they had died and gone to heaven.
Today, however, I could have been a million miles away. A few minutes after I arrived, the depot manager stopped by to pay a courtesy call. He offered to get me a cup of coffee from the machine in the hall. It was a kind gesture, but the incongruity of my being there made us both feel awkward.
For me, this was Siberia. It was exile to the farthest corner of the kingdom. I was so stunned that it took me a few minutes before I realized I had no reason to stay. I had a telephone at home, and somebody could bring me the mail. I left that place before ten o'clock and never went back.
This final humiliation was much worse than being fired. It was enough to make me want to kill—I wasn't quite sure who, Henry Ford or myself. Murder or suicide were never real possibilities, but I did start to drink a little more—and shake a lot more. I really felt I was coming apart at the seams.
As you go through life, there are thousands of little forks in the road, and there are a few really big forks—those moments of reckoning, moments of truth. This was mine as I wondered what to do. Should I pack it all in and retire? I was fifty-four years old. I had already accomplished a great deal. I was financially secure. I could afford to play golf for the rest of my life.
But that just didn't feel right. I knew I had to pick up the pieces and carry on.
There are times in everyone's life when something constructive is born out of adversity. There are times when things seem so bad that you've got to grab your fate by the shoulders and shake it. I'm convinced it was that morning at the warehouse that pushed me to take on the presidency of Chrysler only a couple of weeks later.
The private pain I could have endured. But the deliberate public humiliation was too much for me. I was full of anger, and I had a simple choice: I could turn that anger against myself, with disastrous results. Or I could take some of that energy and try to do something productive.
"Don't get mad," Mary reminded me. "Get even." In times of great stress and adversity, it's always best to keep busy, to plow your anger and your energy into something positive.
As it turned out, I went from the frying pan into the fire. A year after I signed up, Chrysler came within a whisker of bankruptcy. There were many days at Chrysler when I wondered how I had got myself into this mess. Being fired at Ford was bad enough. But going down with the ship at Chrysler was more than I deserved.
Fortunately, Chrysler recovered from its brush with death. Today I'm a hero. But strangely enough, it's all because of that moment of truth at the warehouse. With determination, with luck, and with help from lots of good people, I was able to rise up from the ashes.
Now let me tell you my story.
# MADE
IN AMERICA
# I
# THE FAMILY
Nicola Iacocca, my father, arrived in this country in 1902 at the age of twelve—poor, alone, and scared. He used to say the only thing he was sure of when he got here was that the world was round. And that was only because another Italian boy named Christopher Columbus had preceded him by 410 years, almost to the day.
As the boat sailed into New York Harbor, my father looked out and saw the Statue of Liberty, that great symbol of hope for millions of immigrants. On his second crossing, when he saw the statue again, he was a new American citizen—with only his mother, his young wife, and hope by his side. For Nicola and Antoinette, America was the land of freedom—the freedom to become anything you wanted to be, if you wanted it bad enough and were willing to work for it.
This was the single lesson my father gave to his family. I hope I have done as well with my own.
When I was growing up in Allentown, Pennsylvania, our family was so close it sometimes felt as if we were one person with four parts.
My parents always made my sister, Delma, and me feel important and special. Nothing was too much work or too much trouble. My father might have been busy with a dozen other things, but he always had time for us. My mother went out of her way to cook the foods we loved—just to make us happy. To this day, whenever I come to visit, she still makes my two favorites—chicken soup with little veal meatballs, and ravioli stuffed with ricotta cheese. Of all the world's great Neopolitan cooks, she has to be one of the best.
My father and I were very close. I loved pleasing him, and he was always terrifically proud of my accomplishments. If I won a spelling contest at school, he was on top of the world. Later in life whenever I got a promotion, I'd call my father right away and he'd rush out to tell all his friends. At Ford, each time I brought out a new car, he wanted to be the first to drive it. In 1970, when I was named president of the Ford Motor Company, I don't know which of us was more excited.
Like many native Italians, my parents were very open with their feelings and their love—not only at home, but also in public. Most of my friends would never hug their fathers. I guess they were afraid of not appearing strong and independent. But I hugged and kissed my dad at every opportunity—nothing could have felt more natural.
He was a restless and inventive man who was always trying new things. At one point, he bought a couple of fig trees and actually found a way to grow them in the harsh climate of Allentown. He was also the first person in town to buy a motorcycle—an old Harley Davidson, which he rode through the dirt streets of our small city. Unfortunately, my father and his motorcycle didn't get along too well. He fell off it so often that he finally got rid of it. As a result, he never again trusted any vehicle with less than four wheels.
Because of that damn motorcycle, I wasn't allowed to have a bicycle when I was growing up. Whenever I wanted to ride a bike, I had to borrow one from a friend. On the other hand, my father let me drive a car as soon as I turned sixteen. This made me the only kid in Allentown who went straight from a tricycle to a Ford.
My father loved cars. In fact, he owned one of the first Model T's. He was one of the few people in Allentown who knew how to drive, and he was always tinkering with cars and thinking about how to improve them. Like every driver in those days, he used to get a lot of flat tires. For years he was obsessed with finding a way to drive a few extra miles with a flat. To this day, whenever there's a new development in tire technology, I always think of my father.
He was in love with America, and he pursued the American dream with all his might. When World War I broke out, he volunteered for the Army—partly out of patriotism, and partly, he admitted to me later, to have a little more control over his destiny. He had worked hard to get to America and to become naturalized, and he was terrified at the prospect of being sent back to Europe to fight in Italy or France. Luckily for him, he was stationed at Camp Crane, an army training center just a couple of miles from his home. Because he could drive, he was assigned to train ambulance drivers.
Nicola Iacocca had come to America from San Marco, about twenty-five miles northeast of Naples in the Italian province of Campania. Like so many immigrants, he was full of ambition and hope. In America he lived briefly in Garrett, Pennsylvania, with his stepbrother. There my father went to work in a coal mine, but he hated it so much that he quit after one day. He liked to say it was the only day in his life that he ever worked for anybody else.
He soon moved east to Allentown, where he had another brother. By 1921, he had saved up enough money doing odd jobs, mostly as an apprentice shoemaker, that he could return to San Marco to bring over his widowed mother. As it turned out, he ended up bringing over _my_ mother, too. During his stay in Italy this thirty-one-year-old bachelor fell in love with the seventeen-year-old daughter of a shoemaker. Within a few weeks they were married.
Over the years a number of journalists have reported (or repeated) that my parents went to Lido Beach in Venice for their honeymoon and that I was named Lido to commemorate that happy week. It's a wonderful story, except for one problem: it's not true. My father did take a trip to Lido Beach, but it was before the wedding, not after. And since he was with my mother's brother at the time, I doubt that his vacation was very romantic.
My parents' voyage to America wasn't easy. My mother came down with typhoid fever and spent the entire trip in the ship's infirmary. By the time they reached Ellis Island, she had lost all her hair. According to the laws, she should have been sent back to Italy. But my father was an aggressive, fast-talking operator who had already learned how to manage in the New World. Somehow he was able to convince the immigration officials that his new bride was merely seasick.
I was born three years later, on October 15, 1924. By this time, my father had opened a hot-dog restaurant called the Orpheum Wiener House. It was the perfect business for somebody without much cash. All he really needed to get started were a grill, a bun warmer, and a few stools.
My father always drilled two things into me: never get into a capital-intensive business, because the bankers will end up owning you. (I should have paid more attention to this particular piece of advice!) And when times are tough, be in the food business, because no matter how bad things get, people still have to eat. The Orpheum Wiener House stayed afloat all through the Great Depression.
Later, he brought my uncles Theodore and Marco into the business. To this day, Theodore's sons, Julius and Albert Iacocca, are still making hot dogs in Allentown. The company is called Yocco's, which is more or less how the Pennsylvania Dutch used to pronounce our name.
I came pretty close to going into the food business myself. At one point in 1952, I seriously considered leaving Ford to go into food franchising. Ford dealerships operated as independent franchises, and it occurred to me that anyone who could franchise a food operation would get rich in a hurry. My plan was to have ten fast-food outlets with one central buying location. This was long before McDonald's was even a gleam in Ray Kroc's eye, and I sometimes wonder if I missed my true calling in life. Who knows? Maybe today I'd be worth half a billion dollars, with a sign out front proclaiming: Over 10 billion served.
A few years later, I did open my own place, a little sandwich shop in Allentown called The Four Chefs. It served Philadelphia cheese steaks. (That's thinly-sliced steak with melted cheese on an Italian roll.) My father set it up, and I put in the money. It did very well—too well, in fact, because what I really needed was a tax shelter. We made $125,000 the first year, which raised my tax bracket to the point where I had to get rid of it. The Four Chefs was my first exposure to bracket creep and the progressive nature of our tax laws.
Actually I was in the food business long before I got involved with cars. When I was ten, one of the country's first supermarkets opened in Allentown. After school and on weekends, my little pals and I would line up at the door with our red wagons, like a row of taxicabs outside a hotel. As the shoppers came out, we would offer to take home their bags for a small tip. In retrospect, it makes a lot of sense—I was in the transportation end of the food business.
As a teenager, I had a weekend job in a fruit market run by a Greek named Jimmy Kritis. I used to get up before dawn to get to the wholesale market and bring back the produce. He paid me $2.00 a day—plus all the fruit and vegetables I could lug home after a sixteen-hour workday.
By this time, my father had other enterprises besides the Orpheum Wiener House. Early on, he bought into a national company called U-Drive-It, one of the very first car rental agencies. Eventually he built up a fleet of about thirty cars, mostly Fords. My father was also good friends with one Charley Charles, whose son, Edward Charles, worked for a Ford dealership. Later Eddie bought a dealership of his own, where he introduced me to the fascinating world of the retail car business. By the time I was fifteen, Eddie had convinced me to go into the automobile business. From that day forward, all my energies were directed to doing just that.
My father is probably responsible for my instinct for marketing. He owned a couple of movie houses; one of his theaters, the Franklin, is still in use today. Old-timers in Allentown have told me my father was such a great promoter that the kids who came down to the Saturday matinees used to get more excited about his special offers than about the movies. People still talk about the day he announced that the ten kids with the dirtiest faces would be admitted free.
I doubt there are any kids at the Franklin today. It's now called the Jenette, and instead of Tom Mix and Charlie Chaplin, it shows porno flicks.
Economically, our family had its ups and downs. Like many Americans, we did well during the 1920s. My father started making lots of money in real estate, in addition to his other businesses. For a few years we were actually wealthy. But then came the Depression.
No one who's lived through it can ever forget. My father lost all his money, and we almost lost our house. I remember asking my sister, who was a couple of years older, whether we'd have to move out and how we'd find somewhere else to live. I was only six or seven at the time, but the anxiety I felt about the future is still vivid in my mind. Bad times are indelible—they stay with you forever.
During those difficult years, my mother was very resourceful. She was a real immigrant mother, the backbone of the family. A nickel soupbone went a long way in our house, and we always had enough to eat. I remember that she used to buy squabs—three birds for a quarter—and kill the birds herself because she didn't trust the butcher to guarantee their freshness. As the Depression grew worse, she helped out in my father's restaurant. At one point she went to work in a silk mill, sewing shirts. Whatever it took to keep going, she did it gladly. Today she's still a beautiful woman—who looks younger than I do.
Like so many families in those days, our strong belief in God sustained us. We seemed to pray an awful lot. I had to go to Mass every Sunday and take Holy Communion every week or two. It took me a number of years to fully understand why I had to make a good confession to a priest before I went to Holy Communion, but in my teens I began to appreciate the importance of this most misunderstood rite of the Catholic Church. I not only had to think out my transgressions against my friends; I had to speak them aloud. In later years, I found myself completely refreshed after confession. I even began to attend weekend retreats, where the Jesuits, in face-to-face examinations of conscience, made me come to grips with how I was conducting my life.
The necessity of weighing right from wrong on a regular basis turned out to be the best therapy I ever had.
Despite some of the bad times, we had plenty of fun. There was no TV in those days, so people depended more on each other. On Sunday, after church, we'd always have a house full of family and friends, laughing, eating pasta, and drinking red wine. We also read a lot of books back then, and of course every Sunday night we'd gather around the old Philco radio to listen to our favorite shows, like Edgar Bergen and Charlie McCarthy, and _Inner Sanctum._
For my father, though, the Depression was the shock of his life. He couldn't get over it. After years of struggle he had finally made a pile of money. And then, almost overnight, it was all gone. When I was little, he used to tell me that I had to go to school to learn what the word "depression" meant. He himself had only finished the fourth grade. "If somebody had taught me what a depression was," he used to say, "I wouldn't have mortgaged one business on the next."
This was in 1931. I was only seven, but I knew even then that something serious had gone wrong. Later in college I would learn all about business cycles, and at Ford and Chrysler I would learn how to weather them. But our family's experience was an early inkling of things to come.
My parents were great picture-takers, and our family photo album told me a lot. From birth until I was six, I'm dressed in satin shoes and embroidered coats. My baby pictures show a silver rattle in my hand. Suddenly, around 1930, my clothes start to look a little ragged. My sister and I weren't getting new clothes anymore. I didn't really understand, and it wasn't the sort of thing my father could explain. How can you say to a kid: "I lost my shirt, son, but I don't know why"?
The Depression turned me into a materialist. Years later, when I graduated from college, my attitude was: "Don't bother me with philosophy. I want to make ten thousand a year by the time I'm twenty-five, and then I want to be a millionaire." I wasn't interested in a snob degree; I was after the bucks.
Even now, as a member of the working rich, I put most of my money away in very conservative investments. It's not that I'm afraid of being poor, but somewhere in the back of my mind there's still the awareness that lightning can strike again, and my family won't have enough to eat.
No matter how I'm doing financially, the Depression has never disappeared from my consciousness. To this day, I hate waste. When neckties went from narrow to wide, I kept all my old ones until the style went back to narrow. Throwing out food or scraping half a steak into the disposal still drives me crazy. I've managed to convey some of that awareness to my daughters, and I notice that they don't spend money unless they get a good deal—my goodness, they do go to a lot of sales!
More than once during the Depression, my father's checks were returned to him with that deathless line: Insufficient Funds. This would always throw him for a loop, because he felt a good credit rating was vital to the integrity of an individual or a business. He constantly preached his gospel of fiscal responsibility to Delma and me, urging us never to spend more money than we took in. He believed credit was insidious. Nobody in our family was allowed to have a credit card or to charge _anything_ —ever!
In this respect, my father was a little ahead of his time. He foresaw that buying things on time and getting into hock would undermine people's sense of responsibility about money. He predicted that easy credit would eventually permeate and sabotage our entire society and that consumers would get into trouble by treating their little plastic cards as if they were money in the bank.
"If you borrow anything," he used to tell me, "even twenty cents from a kid at school, be sure to write it down so you won't forget to pay it back." I often wonder how he would have reacted if he'd lived long enough to see me go into hock in 1981 to keep the Chrysler Corporation in business. This one was for a lot more than twenty cents: the total came to $1.2 billion. Although I recalled my father's advice, I had a funny feeling that this was one loan I'd remember even without writing it down.
They say that people vote with their pocketbooks, and certainly my father's political views shifted along with his income. When we were poor, we were Democrats. The Democrats, as everybody knew, were the party of the common man. They believed that if you were willing to work hard and not be a deadbeat, you should be able to feed your family and educate your kids.
But when times were good—before the Depression and then again when it was finally over—we were Republicans. After all, we had worked hard for our money and we deserved to hold on to it.
As an adult, I underwent a similar political transformation. As long as I was at Ford and all was right with the world, I was a Republican. But when I took over at Chrysler and several hundred thousand people were suddenly threatened with losing their jobs, the Democrats were the ones who were pragmatic enough to do what was necessary. If the Chrysler crisis had come up during a Republican administration, the company would have gone down the tubes before you could say Herbert Hoover.
Whenever times were tough in our family, it was my father who kept our spirits up. No matter what happened, he was always there for us. He was a philosopher, full of little sayings and homilies about the ways of the world. His favorite theme was that life has its ups and downs and that each person has to come to terms with his own share of misery. "You've got to accept a little sorrow in life," he'd tell me when I was upset about a bad grade in school or some other disappointment. "You'll never really know what happiness is unless you have something to compare it to."
At the same time, he hated to see any of us unhappy and would always try to cheer us up. Whenever I was worried about anything, he'd say: "Tell me, Lido, what were you so upset about last month? Or last year? See—you don't even remember! So maybe whatever you're so worried about today isn't really all that bad. Forget it, and move on to tomorrow."
During hard times, he was always the optimist. "Just wait," he'd tell me whenever things looked bleak, "the sun's gonna come out. It always does." Many years later, when I was trying to save Chrysler from bankruptcy, I missed my father's comforting words. I'd say, "Hey Pop, where's the sun, where's the sun!" He never let any of us surrender to despair, and I confess there was more than one moment in 1981 when I felt ready to throw in the towel. I kept my sanity in those days by recalling his favorite saying: "It looks bad right now, but remember, this too shall pass."
He was really a bird about performing up to your potential—no matter what you did. If we went out to a restaurant and the waitress was rude, he'd call her over at the end of the meal and give her his standard little speech: "I'm going to give you a _real_ tip," he'd say. "Why are you so unhappy in this job? Is anyone forcing you to be a waitress? When you act surly, you're telling everybody you don't like what you're doing. We're out for a nice time and you're wrecking it. If you really want to be a waitress, then you should work at being the best damn waitress in the world. Otherwise, find yourself another line of work."
In his own restaurants, he would immediately fire any employee who was rude to a customer. He'd say: "You can't work here, no matter how good you are, because you're scaring the customers away." He got right down to the heart of the matter, and I guess I'm the same way. I still think all the talent in the world doesn't excuse deliberate rudeness.
My father always reminded me that I should _enjoy_ life, and he practiced what he preached. No matter how hard he worked, he always made sure to leave enough room to have a good time. He loved bowling and poker as well as good food, drink, and especially good friends. He always made friends with my colleagues at work. During my career at Ford, I think he knew more people there than I did.
In 1971, two years before my father died, I threw a big party for my parents' fiftieth wedding anniversary. I had a cousin who worked in the U.S. Mint, and I commissioned him to sculpt a gold medal depicting my parents on one side and the little church in Italy where they had been married on the other. At the party, each guest was given a bronze version of the medal.
Later that year my wife and I took my parents back to Italy to visit their hometown and to see all their old friends and family. By this time we knew my father had leukemia. He was getting blood transfusions every two weeks and was steadily losing weight. When at one point we lost track of him for several hours, we were afraid he had lost consciousness or collapsed. We finally caught up with him in a tiny shop in Amalfi, where he was excitedly buying up ceramic souvenirs for all his friends back home.
Right up to the end, in 1973, he was still trying to enjoy life. He wasn't dancing as much or eating as much, but he sure was very brave and determined to live. Still, the last couple of years were rough on him, and all of us, too. It was difficult to see him so vulnerable—much less accept it.
Now when I look back on my father, I only remember a man of great vigor and boundless energy. Once I was in Palm Springs for a Ford dealer meeting and I invited my father to come out for a brief vacation. When the meeting was over, a couple of us went out to play golf. Although my father had never been on a golf course in his life, we asked him to come along.
As soon as he hit the ball, he began to chase after it—seventy years old and running all the way. I had to keep reminding him: "Pop, slow down. Golf is a game of walking!"
But that was my father for you. He always preached: "Why walk when you can run?"
# II
# SCHOOL DAYS
I was eleven before I learned we were Italian. Until then, I knew we came from a real country but I didn't know what it was called—or even where it was. I remember actually looking on a map of Europe for places named Dago and Wop.
In those days, especially if you lived in a small town, being Italian was something you tried to hide. Almost everybody in Allentown was Pennsylvania Dutch, and as a kid I took a lot of abuse for being different. Sometimes I got into fights with kids who called me names. But I always kept in mind my father's warning: "If he's bigger than you are, don't fight back. Use your head instead of your fists."
Unfortunately, the prejudice against Italians wasn't limited to people my own age. There were even a few teachers who called me "little wop" under their breath. My ethnic problems came to a head on June 13, 1933, when I was in the third grade. I'm sure of the date because June 13 is St. Anthony's day, a big event in our family. My mother's name is Antoinette, and Anthony is my middle name, so every year on June 13 we'd throw a big party at our house.
To mark the occasion, my mother would bake pizza. She comes from Naples, the birthplace of pizza. To this day, my mother makes the greatest pizzas in the country, if not the entire world.
That year we had an especially wonderful party with our friends and relatives. As usual, there was a big barrel of beer. Even at age nine I was allowed to swig a little—as long as I did it at home under strict supervision. Maybe that's why I never got pig-drunk in high school and college. In our house alcohol (usually homemade red wine) was accepted as part of life—but always in moderation.
Now, in those days, pizza was virtually unknown in this country. Today, of course, it's pushing hamburgers and fried chicken as one of America's favorite foods. But back then, nobody who wasn't Italian had ever heard of it.
The morning after the party, I started bragging to the other kids at school. "Boy, did we have a party last night!"
"Oh yeah?" somebody asked. "What kind of party?"
"A pizza party," I replied.
"A pizza party? What kind of dumb dago word is that?" And they all started laughing.
"Wait a minute," I said. "You guys like to eat pies." They were all pretty fat, so I knew I was on safe ground. "Well, that's what a pizza is. It's a pie made out of tomatoes."
I should have quit while I was ahead, because now they got hysterical. They didn't have the faintest idea of what I was talking about. But they knew that if it was Italian, it had to be bad. The only good thing about the whole incident was that it took place near the end of the school year. The pizza episode was forgotten over the summer.
But I never forgot it. Those guys grew up on shoofly pie, but I never once laughed at them for eating molasses pie for breakfast. Hell, you don't see shoofly pie huts all over America today. But to think that someday you'll be a trendsetter is no comfort for a nine-year-old kid.
I wasn't the only victim of bigotry in my class. There were also two Jewish kids; I was friendly with both of them. Dorothy Warsaw was always first in the class, and I was usually second. The other Jewish kid, Benamie Sussman, was the son of an Orthodox Jew who wore a black hat and a beard. In Allentown, the Sussmans were treated like outcasts.
The other kids kept their distance from these two as if they had leprosy. At first I didn't understand it. But by the time I was in the third grade, I began to get the message. As an Italian, I was seen as a cut above the Jewish kids—but not by much. I never saw a black person in Allentown until I was in high school.
Being exposed to bigotry as a kid left its mark. I remember it clearly, and it still leaves a bad taste in my mouth.
Unfortunately, I witnessed a lot of prejudice even after I left Allentown. This time it came not from schoolchildren but from men in positions of great power and prestige in the auto industry. In 1981, when I named Gerald Greenwald vice-chairman of Chrysler, I learned that his appointment was unprecedented. Until then, no Jew had ever reached the top ranks of the Big Three automakers. I find it a little hard to believe that none of them was qualified.
Looking back now, I remember certain episodes from my childhood that forced me to reckon with how the adult world operated. When I was in the sixth grade, there was an election for captain of the student patrol. The patrolmen all wore white belts with a silver badge, but the lieutenant and the captain got to wear special uniforms with special badges. In grade school, the captain of the student patrol was the equivalent of the high school quarterback. I loved the idea of wearing that uniform, and I was determined to be the captain.
When the vote came in, I had lost to another kid by a margin of twenty-two to twenty. I was bitterly disappointed. The following day I was at a Saturday afternoon matinee at the local theater, where we used to see Tom Mix movies.
In the row ahead of me sat the biggest kid in our class. He turned around and saw me. "You dumb wop," he said. "You lost the election."
"I know," I said. "But why are you calling me a dummy?"
"Because," he said. "There are only thirty-eight kids in the class. But forty-two kids voted. Can't you dagos even count?"
My opponent had stuffed the ballot box! I went to the teacher and told her that some kids had voted twice.
"Let's leave well enough alone," said the teacher. She covered it up. She didn't want any scandals. That incident had a profound effect on me. It was my first dramatic lesson that life wasn't always going to be fair.
In every other respect, however, school was a very happy place for me. I was a diligent student. I was also a favorite of many of my teachers, who were always singling me out to clap the erasers or wash the blackboards or ring the school bells. If you ask me the names of my professors in college or graduate school, I'd have trouble coming up with more than three or four. But I still remember the teachers who molded me in elementary and high school.
The most important thing I learned in school was how to communicate. Miss Raber, our ninth-grade teacher, had us turn in a theme paper of five hundred words every Monday morning. Week in and week out, we had to write that damn paper. By the end of the year, we had learned how to express ourselves in writing.
In class she would quiz us on the Word Power Game from _Reader's Digest_. Without any advance warning she'd rip it out of the magazine and make us take the vocabulary test. It became a powerful habit with me—to this day I still look for the list of words in every issue of the _Digest._
After a few months of these quizzes, we knew a lot of words. But we still didn't know how to put them together. At that point, Miss Raber started us on extemporaneous speaking. I was good at it, and as a result I joined the debating team, which was sponsored by Mr. Virgil Parks, our Latin teacher. That's where I developed my speaking skills and learned how to think on my feet.
At first I was scared to death. I had butterflies in my stomach—and to this day I still get a little nervous before giving a speech. But the experience of being on the debating team was crucial. You can have brilliant ideas, but if you can't get them across, your brains won't get you anywhere. When you're fourteen years old, nothing polishes your skills like arguing both sides of "Should capital punishment be abolished?" That was the hot issue in 1938—and I must have spoken for each side of the debate at least twenty-five times.
The next year was a turning point. I came down with rheumatic fever. The first time I had a palpitation of the heart, I almost passed out—from fear. I thought my heart was popping out of my chest. My doctor said: "Don't worry. Just put an ice pack on it." I panicked: What the hell was I doing with this chunk of ice on my chest? I must be dying!
Back then people _did_ die from rheumatic fever. In those days it was treated with birch bark pills to get the infection out of your joints. They were so strong you had to take antacid pills every fifteen minutes to keep from throwing up. (Today, of course, they use antibiotics.)
With rheumatic fever there's always a threat to the heart. But I was lucky. Although I lost about forty pounds and stayed in bed for six months, I eventually made a full recovery. But I'll never forget those crude splints with cotton wadding wet with oil of wintergreen to quiet down the lousy pain in my knees, ankles, elbows, and wrists. They actually alleviated the pain on the inside by giving you third degree burns on the outside. Sounds primitive today—but Darvon and Demerol weren't invented yet.
Before I got sick, I had been a pretty decent baseball player. I was a great Yankee fan, and Joe DiMaggio, Tony Lazzeri, and Frankie Crossetti—all Italian—were my real heroes. Like most boys, I dreamed of playing in the major leagues. But my long illness changed all that. I gave up sports and started playing chess, bridge, and especially poker. I still love poker, and I usually win. It's a great game for learning when to exploit an advantage, when to back off, and when to bluff. (It sure came in handy years later during tough union negotiations!)
Most of all, as I lay flat on my back, I turned to books. I read like crazy—everything I could get my hands on. I especially liked the stories of John O'Hara. My aunt had brought me _Appointment in Samarra_ , which was a pretty dirty book for those days. When the doctor saw it by my bed, he almost flipped. As far as he was concerned, this wasn't what a teenage boy with a palpitating heart ought to be reading.
Years later, when Gail Sheehy came to interview me for _Esquire_ , I happened to mention _Appointment in Samarra._ She pointed out that it was a novel about business executives and asked me whether I thought it had influenced my choice of a career. Hell no! All I could remember about the book was that it got me interested in sex.
I must have read my share of schoolbooks, too, because each year in high school I graduated near the top of my class, with straight A's in math. I was in the Latin club, and I won a prize for being the best kid in Latin for three years running. I haven't used a word of it in forty years! It did help me with my English vocabulary, and I was one of the few kids who could follow the priest at Sunday Mass. Then Pope John switched to English, and that was the end of that.
Being a good student was very important to me—but it wasn't enough. I was always heavily involved in extracurricular activities. In high school I was active in the drama club and the debating society. After my illness, when I could no longer participate in athletics, I became manager of the swim team. That meant I carried the towels and washed out the tank suits.
Back in seventh grade I had developed a passion for jazz and swing. This was the big-band era, and my friends and I spent every weekend going to hear the big bands. Usually I just listened, although I got pretty good at doing the shag and the lindy hop. We would go to the Empire Ballroom in Allentown and to Sunnybrook in Pottstown, Pennsylvania. When I could afford it, I slipped into the Hotel Pennsylvania, in New York, or Frank Daley's Meadowbrook on the Pompton Turnpike.
I once saw Tommy Dorsey and Glenn Miller in a Battle of the Bands—all for eighty-eight cents. In those days music was my life. I subscribed to _Downbeat_ and _Metronome_ , and I knew the name of every sideman in all of the major bands.
By this time I had started playing the tenor sax. I was even asked to play first trumpet in the school band. But I gave up music in order to go into politics. I wanted to be president of my class in seventh and eighth grade—and I was.
In ninth grade I ran for president of the whole school. Jimmy Leiby, my closest friend, was a genius. He became my campaign manager, and he created a real political machine. I won the election by a landslide and it went to my head. To use the vernacular of the day, I really thought I was hot shit.
But once I was elected, I lost touch with my constituency. I thought I was a cut above the other kids, and I started acting like a snob. I hadn't yet learned what I know now—that the ability to communicate is everything.
As a result, I lost the election in the second semester. It was a terrible blow. I had given up music to be in the student council, and now my political career had come to a halt because I forgot to shake hands and be friendly. It was an important lesson about leadership.
With all my extracurricular activities, I still managed to graduate twelfth in a class of over nine hundred. To show you the kind of expectations I grew up with, my father's reaction was: "Why weren't you first?" To hear him describe it, you'd think I flunked!
By the time I was ready for college, I had a solid background in the fundamentals: reading, writing, and public speaking. With good teachers and the ability to concentrate, you can go pretty far with these skills.
Years later, when my kids asked me what courses to take, my advice was always to get a good liberal arts education. Although I'm a great believer in the importance of learning from history, I really didn't care if they mastered all the dates and places of the Civil War. The key is to get a solid grounding in reading and writing.
Suddenly, in the middle of my senior year, Japan attacked Pearl Harbor. President Roosevelt's speeches had us all riled up, and the entire country was rallying 'round the flag. Overnight all of America was galvanized and united. I learned something from that crisis that has stayed with me ever since: it often takes a shot of adversity to get people to pull together.
Like most young men that December of 1941, I couldn't wait to join up. Ironically, the illness that had almost killed me may have ended up saving my life. To my enormous disappointment, I was classified 4F—a medical deferment—which meant I couldn't join the Air Corps and fight in the war. Although I had pretty well recovered and I felt terrific, the Army had decided not to take anybody with a history of rheumatic fever. But I didn't _feel_ sick, and a year or two later, when I had my first physical for life insurance, the doctor turned to me and said: "You're a healthy young fellow. Why aren't you overseas?"
Most of my classmates were called up, and many of them died. We were the class of '42, and the kids who were seventeen or eighteen went to boot camp and then straight across the Atlantic where the Germans were knocking the hell out of us. To this day I sometimes look through my high school yearbook and shake my head in sorrow and disbelief at all the students from Allentown High who died overseas, defending democracy.
Because World War II was nothing like Vietnam, younger readers may not fully understand how it felt to be unable to serve your country when it needed you most. Patriotism was at a fever pitch, and I wanted nothing more than to fly a bomber over Germany to take revenge on Hitler and his troops.
Being burdened with a medical deferment during the war seemed like a disgrace, and I began to think of myself as a second-class citizen. Most of my friends and relatives had gone over to fight the Germans. I felt like the only young man in America who wasn't in combat. So I did the only thing I could: I buried my head in my books.
By this time I had developed an interest in engineering, and I was looking into several colleges that specialized in the field. One of the finest in the country was Purdue. I applied for a scholarship there, and when I didn't get it I was crushed. However, Cal Tech, MIT, Cornell, and Lehigh also had top-rated engineering schools. I finally chose Lehigh because it was only half an hour's drive from my home in Allentown and I wouldn't have to leave my family too far behind.
Lehigh University, in Bethlehem, Pennsylvania, was a kind of satellite school for the Bethlehem Steel Company. Its departments of metallurgy and chemical engineering were among the best in the world. But being a freshman there was the academic equivalent of boot camp. Any student who didn't maintain a sufficiently high average by the end of his sophomore year was politely asked to leave. I had classes six days a week, including a course in statistics that met every Saturday morning at eight. Most of the guys cut it, but I got an A—not so much for my proficiency in statistics, but for my perseverance in showing up every week while the other guys were sleeping off their Friday-night binges.
I don't mean to imply that I had no fun at all during college. I liked to raise a little hell, and I went to my share of football games and beer parties. There were also trips to New York and Philadelphia, where I had a couple of girlfriends.
But with the war on, I was in no mood to goof off. As a little kid I had learned how to do my homework right after school so that I could play after supper. By the time I got to college, I knew how to concentrate and how to study without a radio or other distraction. I used to tell myself: "I'm going to give this my best shot for the next three hours. And when those three hours are up, I'll set this work aside and go to the movies."
The ability to concentrate and to use your time well is everything if you want to succeed in business—or almost anywhere else, for that matter. Ever since college I've always worked hard during the week while trying to keep my weekends free for family and recreation. Except for periods of real crisis I've never worked on Friday night, Saturday, or Sunday. Every Sunday night I get the adrenaline going again by making an outline of what I want to accomplish during the upcoming week. It's essentially the same schedule I developed at Lehigh.
I'm constantly amazed by the number of people who can't seem to control their own schedules. Over the years, I've had many executives come to me and say with pride: "Boy, last year I worked so hard that I didn't take any vacation." It's actually nothing to be proud of. I always feel like responding: "You dummy. You mean to tell me that you can take responsibility for an $80 million project and you can't plan two weeks out of the year to go off with your family and have some fun?"
If you want to make good use of your time, you've got to know what's most important and then give it all you've got. That's another lesson I learned at Lehigh. I might have had five classes the next day, including an oral quiz where I didn't want to look stupid, so I had to prepare. Anyone who wants to become a problem-solver in business has to learn fairly early how to establish priorities. Of course, the time frame is a little different. In college I had to figure out what I could accomplish in one evening. In business the time frame is more like three months to three years.
From what I've seen, you either get grounded in that kind of positive thinking early on in life or you don't. Establishing priorities and using your time well aren't things you can pick up at the Harvard Business School. Formal learning can teach you a great deal, but many of the essential skills in life are the ones you have to develop on your own.
It wasn't only my ability to concentrate that helped me at college. I was also lucky. As more and more students were drafted, the classes at Lehigh became smaller and smaller. A teacher who was accustomed to a lecture course for fifty was suddenly teaching a seminar of five. As a result, I had a very exclusive college education.
When you have small classes, everybody gets plenty of attention. A professor could afford to say: "Tell me why you can't do that machine design problem, and I'll help you understand it." So by an accident of history, I got terrific training. Right after the war, with the G.I. Bill, the same class at Lehigh might have had seventy guys. In that setting I wouldn't have learned half as much.
I was also motivated by the pressure from my father that was typical among immigrant families, where any kid who was fortunate enough to attend college was expected to compensate for his parents' lack of education. It was up to me to take advantage of all the opportunities they never had, so I had to be at the top of my class.
This, however, was easier said than done. I had an especially rough time during my first semester. When I failed to make the dean's list, my father got on my case—and quick! After all, he reasoned, if I was so smart in high school, where I graduated near the top of my class, how could I be so stupid only a few months later? He assumed that I was playing around. I couldn't get him to understand that college was completely different from high school. At Lehigh, _everyone_ was good—or they wouldn't have been there in the first place.
In my freshman year, I almost failed physics. We had a professor named Bergmann, a Viennese immigrant whose accent was so thick that I could hardly understand him. He was a great scholar, but he lacked the patience to teach freshmen. Unfortunately, his course was a requirement for anyone who majored in mechanical engineering.
Somehow, in spite of my difficulties in his class, I got to be good friends with Professor Bergmann. We would walk around the campus, and he would describe the latest developments in physics. He was especially interested in splitting atoms, which at that point seemed still in the realm of science fiction. It all sounded like Greek to me, and I understood only a fraction of what he was saying, although I managed to follow the main argument.
There was something mysterious about Bergmann. Every Friday he'd end the class abruptly and leave campus until the following Monday. It wasn't until several years later that I finally learned his secret. Given the nature of his interests, I probably should have guessed. He used to spend every weekend in New York working on the Manhattan Project. In other words, when Bergmann wasn't teaching at Lehigh, he was working on the atomic bomb.
Despite our friendship and despite the private tutorials, I managed no more than a D in freshman physics—my lowest grade at Lehigh. I had been a good math student in High school, but I simply wasn't prepared for the world of advanced calculus and differential equations.
Eventually I smartened up and switched my major from mechanical to industrial engineering. Before long, my grades started to improve. By my senior year I had moved away from the advanced sciences of hydraulics and thermodynamics and switched over to business courses such as labor problems, statistics, and accounting. I did much better in these subjects, finishing my last year with straight A's. My goal was a 3.5 grade average so I could graduate with high honors. I made it by a hair—ending up at 3.53. They say that this generation is competitive. You should have seen us at work!
In addition to all the engineering and business courses, I also studied four years of psychology and abnormal psychology at Lehigh. I'm not being facetious when I say that these were probably the most valuable courses of my college career. It makes for a bad pun, but it's true: I've applied more of those courses in dealing with the nuts I've met in the corporate world than all the engineering courses in dealing with the nuts (and bolts) of automobiles.
In one course we would spend three afternoons and evenings a week at the psychiatric ward of the Allentown State Hospital, about five miles from the campus. We saw them all—manic-depressives, schizophrenics, and even some violent types. Our teacher was a professor named Rossman, and to see him work with these mental patients was to watch a master in action.
The focus of the course was nothing less than the fundamentals of human behavior. What motivates that guy? How did this woman develop her problems? What makes Sammy run? What led Joe over there to act like an adolescent at the age of fifty? For our final exam we were introduced to a group of new patients. Our assignment was to make a diagnostic analysis of each one within a few minutes.
As a result of this training, I learned to figure people out pretty quickly. To this day, I can usually tell a fair amount about somebody from our first meeting. That's an important skill to have, because the most important thing a manager can do is to hire the right new people.
But there are two really important things about a candidate that you just can't learn from one short job interview. The first is whether he's lazy, and the second is whether he's got any horse sense. There's no qualitative analysis to check out whether he's got some fire in his belly, or whether he will have savvy—or street smarts—when it comes to decision time.
I wish there were some kind of machine that would measure these traits, because they're the ones that separate the men from the boys.
I completed my studies at Lehigh in eight straight semesters, which meant no summer vacations. I wish I had taken some time off to smell the flowers, as my father had always advised me. But the war was raging, and with my friends fighting—and dying—overseas, I had to run at full steam.
In addition to my studies, I got involved in lots of extracurricular activities. By far the most interesting was the time I spent on the school paper, _The Brown and White._ My first assignment as a reporter was to interview a professor who had rigged up a little car that ran on charcoal. (This was years before the energy crisis, of course.) I must have written a pretty good story, because it got picked up by the Associated Press and ran in a hundred papers.
On the strength of that story, I became the layout editor. This, I soon learned, was where the real power of the press resided. Years later, I read Gay Talese's book on _The New York Times_ , in which one of the editors said that the most powerful position on any paper is not the editor of the editorial page, but rather the editors in charge of headlines and layout.
That was a lesson I had already learned. As the layout editor, I figured out pretty quickly that most people don't read the stories. Instead, they rely on the headlines and subheads. That means that whoever writes _those_ has a helluva lot of influence on people's perception of the news.
In addition, I had to determine the length of each story, based on how much space was available. I did this with impunity, and I often lopped off two inches from a good story because I needed that space for the ads. I also learned how to screw our reporters through the judicious use of headlines and subtitles. Years later, I could see when I'd been had by the layout editors of the country's most prestigious newspapers and magazines. It takes one to know one!
Even before I graduated, I wanted to work for Ford. I drove a beat-up 1938 sixty-horsepower Ford, which is how I got interested in the company. More than once I'd be going up a hill when suddenly the cluster gear in my transmission would go. Some faceless executive at the Ford corporate headquarters in Dearborn, Michigan, had apparently decided they'd get better fuel economy by taking a V-8 engine down to only sixty horsepower. That was a fine idea—if they had restricted the car to places like Iowa. Lehigh was built on a mountain.
"Those guys need me," I used to joke to my friends. "Anybody who builds a car this bad can use some help."
In those days, owning a Ford was an excellent way to learn about cars. During the war, all the auto plants were kept busy making weapons; no new cars were manufactured. Even spare parts became scarce. People used to search for them on the black market or by visiting junkyards. If you were lucky enough to own a car then, you learned how to take good care of it. The wartime shortage of cars was so great that after graduation I sold that Ford for $450. When you consider that my father had bought me the car for only $250, I made out pretty well.
During my college days, gas was selling for only thirteen cents a gallon. But because of the war, there was a real shortage. As an engineering student, I was given a C-card, which meant that my studies were vital to the war effort. (Can you believe that!) It wasn't as patriotic as being overseas, but at least it was a small badge of honor that said I would make a contribution to my country—someday.
In the spring of my senior year, engineers were in great demand. I had about twenty job interviews, and I literally had my pick of where I wanted to work.
But cars were what I cared about. Since I still wanted to go to Ford, I made an appointment to see the company recruiter, whose name, unbelievably, was Leander Hamilton McCormick-Goodheart. He drove through the campus in a Mark I, one of those snazzy Lincoln Continentals that looked as if they were custom-built. That car really turned my head. One glimpse of it and one whiff of the leather interior were enough to make me want to work at Ford for the rest of my life.
Back then, Ford's recruitment policy was to visit fifty universities and select one student from each. This has always struck me as a little dumb. If Isaac Newton and Albert Einstein had been classmates, Ford could have accepted only one of them. McCormick-Goodheart interviewed several Lehigh students, but I was the one he picked for Ford, and I was on cloud nine.
After graduation and before starting the program, I took a brief vacation with my parents in Shipbottom, New Jersey. While we were there, I got a letter from Bernadine Lenky, the placement director at Lehigh. She enclosed a flyer offering a fellowship for graduate work at Princeton, a grant that covered tuition, books, and even spending money.
Bernadine told me that only two of these fellowships were awarded each year and suggested I apply. "I realize that you weren't planning on graduate school," she said, "but this one looks like a winner." I wrote to Princeton to ask for more details, and they wrote back for my records. The next thing I knew, I had won the Wallace Memorial Fellowship.
After one look at the campus I knew I wanted to be there. I figured that a master's degree after my name wouldn't hurt my career, either.
Suddenly I had two terrific opportunities. I called McCormick-Goodheart about my dilemma. "If they want you at Princeton," he told me, "by all means go and get your master's. We'll hold a space for you until you graduate." That was just what I hoped he would say, and I was on top of the world.
Princeton was a delightful place to go to school. Compared to Lehigh's frenetic pace it was almost laid back. I took my electives in politics, and a new field—plastics. Like Lehigh, Princeton had a very favorable teacher-student ratio due to the war. One of my professors, a man named Moody, was the most famous hydraulics expert in the world. He had worked on the Grand Coulee Dam and many other projects, yet there were only four of us in his class.
One day I went to hear Einstein give a lecture. I didn't really understand what he was talking about, but it was exciting just to be in his presence. The graduate school wasn't far from the Institute for Advanced Studies, where Einstein taught, and from time to time I would catch a glimpse of him taking a walk.
I was given three semesters to write my thesis, but I was so eager to begin working at Ford that I finished it in two. My project was to design and build, by hand, a hydraulic dynamometer. A professor named Sorenson offered to work with me. Together we built it and hooked it up to an engine that General Motors had donated to the university. I ran all the tests, completed my thesis, and had it bound—in leather yet, I was so proud of it.
Meanwhile, back in Dearborn, Leander McCormick-Goodheart had been drafted. Foolishly, I had neglected to stay in touch with him during my year at Princeton. Even worse, I had not gotten his promise to me in writing. By the time I was finished at Princeton, nobody at Ford had ever heard of me.
Finally I got McCormick-Goodheart's boss, Bob Dunham, on the phone and explained my predicament. "The training group is closed," he said, "and we already have our fifty guys. But considering the circumstances, it doesn't seem fair. If you can get yourself out here right away, we'll make you number fifty-one." The next day, my father drove me to Philadelphia, where I boarded the _Red Arrow_ for Detroit to begin my career.
It was an all-night trip, but I was too excited to sleep. When I arrived at the Fort Street Station, a duffel bag on my shoulder and fifty bucks in my pocket, I went outside and asked the first guy I met: "Which way to Dearborn?"
He said: "Go west, young man—go west about ten miles!"
# THE
FORD STORY
# III
# GETTING MY
FEET WET
In August, 1946, I began working at Ford as a student engineer. Our program was known as a loop training course, because the trainees made a complete circuit of the entire operation. We worked in the bowels of the company, spending a few days or a week in each department. When we finished, we were supposed to be familiar with every stage of manufacturing a car.
The company went to great lengths to give us hands-on experience. We were assigned to the famous River Rouge plant, the largest manufacturing complex in the world. The Ford Motor Company actually owned the coal and limestone mines, so we got to see the entire process, start to finish—from hauling the stuff out of the ground to making the steel and then turning the steel into cars.
Our tour of duty included the jobbing foundry, the production foundry, the ore boats, the tool and die shops, the test track, the forging plant, and the assembly lines. But not all of our experience was directly connected to manufacturing. We also spent time in the purchasing department and even in the plant hospital.
It was the best place in the world to learn how cars were really made and how the industrial process worked. The Rouge plant was the pride of the company, and visiting delegations from other countries were always coming over to have a look. It was long before the Japanese showed any interest in Detroit, but eventually they too would make a thousand pilgrimages to the Rouge.
I was finally seeing the practical application of everything I had read about in books. I had studied metallurgy at Lehigh, but now I was actually doing it, working at the blast furnaces and in the open hearths. In the tool and die department I got to run the machinery I had only read about, such as the planers, the milling machines, and the lathes.
I even spent four weeks on the final assembly line. My job was to attach a cap to a wiring harness on the inside of a truck frame. It wasn't hard work, but it was tedious as hell. My mother and father came to visit one day, and when my dad saw me in overalls, he smiled and said: "Seventeen years you went to school. See what happens to the dummies who don't finish first in their class?"
Our supervisors were pretty decent, but the workers treated us with suspicion and resentment. At first we thought the badges we wore, which said "Student Engineer," might be causing the problem. When we complained, our badges were changed to read "Administration." But that only made matters worse.
I soon learned enough history to understand what was going on. By this time, Henry Ford, the founder, had grown old. The company was being run by a group of his henchmen, notably Harry Bennett, who was known as a pretty tough cookie. Relations between workers and management were terrible, and the student engineers, with their "Administration" badges, were caught in the middle. Many of the workers were convinced we were spies who had been sent to keep an eye on them. The fact that we were just out of college and wet behind the ears didn't help.
Despite the tension, we did the best we could to have fun. We were a mix of fifty-one guys from different colleges who roomed together, drank beer together, and tried to enjoy life as much as possible when we weren't working. The training program was pretty disorganized, and if you wanted to take a couple of days off and drive to Chicago, nobody would know the difference.
Halfway through, we had an evaluation meeting with our supervisors. Mine said: "Ah, Iacocca—mechanical engineering, hydraulic dynamometers, automatic transmissions. Let's see, now. We're setting up a new automatic-transmission group. Well send you over there."
I was nine months into the program with another nine to go. But engineering no longer interested me. The day I'd arrived, they had me designing a clutch spring. It had taken me an entire day to make a detailed drawing of it, and I said to myself: "What on earth am I doing? Is this how I want to be spending the rest of my life?"
I wanted to stay at Ford, but not in engineering. I was eager to be where the real action was—marketing or sales. I liked working with people more than machines. Naturally, my supervisors in the program were not amused. After all, the company had hired me out of engineering school and had invested all this time and money in my training. And now I wanted to be in _sales_?
When I insisted, we settled on a compromise. I told them there was no point in my finishing the training course and that my masters degree from Princeton was equivalent to the second nine months of training. They agreed to let me go and try to find a job in sales. But I had to do it on my own. "We'd like to keep you at Ford," they told me. "But you've got to get out and sell yourself if you choose to go the sales route."
Right away I got in touch with Frank Zimmerman, my best friend in the training program. Zimmie had been the first guy accepted into the program, and he was the first to graduate. Like me, he had decided against engineering and had already talked himself into a sales position in trucks in the New York district. When I went East to visit him, we were like two little kids in the big city, racing to restaurants and nightclubs and taking in the splendor of Manhattan. "God," I thought, "I have just got to come back here." I was from the East, so this was really home.
The New York district manager happened to be out when I arrived in the office, so I had to meet with his two assistant managers. I was nervous. My background was in engineering, not sales. The only way I could possibly land a job here was to make a great impression in the interview.
I had brought a letter of recommendation from Dearborn, which I handed to one of the men. He reached out and took it without taking his eyes off his newspaper. In fact, he spent the entire half hour reading _The Wall Street Journal_ and didn't look up once.
The other guy was only slightly better. He glanced at my shoes and checked to see if my tie was straight. Then he asked me a couple of questions. I could tell he didn't like the fact that I had a college education and that I had spent some time in Dearborn. Maybe he thought I was there to check up on him. In any case, it was clear that he wasn't going to hire me. "Don't call us," he said. "We'll call you." I felt like I had just failed my Broadway audition. My only hope was to try another district sales office, so I made an appointment to see the manager of the sales office in Chester, Pennsylvania, not far from Philadelphia. This time I had better luck. The district manager was not only in that day—he was even willing to take a chance on me. I was hired for a low-level desk job in fleet sales.
In Chester, my job was to speak to fleet purchasing agents about the allocation of new cars. It wasn't easy. I was bashful and awkward in those days, and I used to get the jitters every time I picked up the phone. Before each call I'd practice my speech again and again, always afraid of being turned down.
Some people think that good salesmen are born and not made. But I had no natural talent. Most of my colleagues were a lot more relaxed and outgoing than I was. For the first year or two I was theoretical and stilted. Eventually I got some experience under my belt and started to improve. Once I had mastered the facts, I worked on how to present them. Before long, people started listening to me.
Learning the skills of salesmanship takes time and effort. You have to practice them over and over again until they become second nature. Not all young people today understand that. They look at a successful businessman and they don't stop to think about all the mistakes he might have made when he was younger. Mistakes are a part of life; you can't avoid them. All you can hope is that they won't be too expensive and that you don't make the same mistake twice.
Here again, as in college, my timing was lucky. There had been no car production during the war, so between 1945 and 1950, demand was high. Every new car was sold at list price—if not more. And all the dealers were looking for customers with used cars to trade, because even the most decrepit used car could be resold at a handsome profit.
Although I had a lowly position, the backlog for new cars gave my job a lot of clout. If I had wanted to cheat, I could have done very well for myself. There was plenty of shady dealing going on. Almost everywhere you looked, district employees were allocating cars to their friends in return for gifts or financial favors.
The dealers were getting rich. There was no such thing as a sticker price, so people paid what the market would bear. Some of the district guys wanted part of the action and played fast and loose with the rules to get it. As an idealistic, freshly scrubbed kid just a year out of college, I was shocked.
Eventually, I got out from behind the telephone. I went from the desk to the field, visiting dealers as a traveling truck and fleet representative to give them pointers on selling. I loved every minute of it. Finally I was out of school and into the real world. I spent my days driving around in a brand-new car, sharing my newly found wisdom with a couple of hundred dealers—each one hoping I could turn him into a millionaire.
In 1949, I became a zone manager in Wilkes-Barre, Pennsylvania. My job was to work closely with eighteen dealers. For me, this was a critical learning experience.
It's the dealers who have always been the guts of the car business in this country. While they have a working relationship with the parent company, they're really the quintessential American entrepreneurs. They're the ones who represent the heart of our capitalist system. And, of course, they're the guys who are actually selling and servicing all the cars the factory's turning out.
Because I started out by working directly with the dealers, I knew what they were worth. Later, when I became part of management, I worked hard to keep them happy. If you want to succeed in this business, you all have to operate as a team. And that means the home office and the dealers have to be playing on the same side.
Unfortunately, most auto executives I've known have failed to grasp this concept. The dealers, in turn, have been resentful because they're seldom invited to eat at the head table. To me, it's simple enough to understand: the dealers are really the _only_ customers a company has. So it's only common sense to listen very carefully to what they have to say, even if you don't always like what you hear.
During my years in Chester, I learned a great deal about the retail car business, most of it from a sales manager in Wilkes-Barre named Murray Kester. Murray was a real pro at training and motivating salesmen.
One of his little tricks was to call up every customer thirty days after he'd bought a new car. Murray would always ask: "How do your friends like it?" His strategy was simple. He reasoned that if you asked the customer how _he_ liked the car, he might feel obliged to think of something that was wrong with it. But if you asked him how his _friends_ liked it, he would have to tell you how great the car was.
Even if his friends didn't like his car, he wouldn't be able to admit it. At least not so soon! He still needed to justify in his own mind that he had made a smart buy. If you were really on the ball, you would ask the customer for the names and phone numbers of his friends. After all, they might be interested in buying a similar car.
Remember this: Anybody who ever buys anything—a house, a car, or stocks and bonds—will rationalize his purchase for a few weeks, even if he made a mistake.
Murray was also a great storyteller. He got most of his material from his brother-in-law, who happened to be Henny Youngman. One time he brought Henny down from New York to address a sales rally at the Broadwood Hotel in Philadelphia. Henny warmed up the crowd, and then I introduced the new cars. It was the first time I ever heard those famous words: "Take my wife—please!"
Following Murray's lead, I used to give the dealers a few tips myself. I would explain that they had to "qualify" a buyer, to ask the right questions that might lead to a sale.
If a guy wanted a red convertible, of course that's what you sold him. But many customers didn't really know what they wanted, and part of the salesman's job was to help them find out. I would say that buying a car isn't all that different from buying a pair of shoes. If you work in a shoe store, first you measure the guy's foot and then you ask whether he's interested in something sporty or dressy. The same thing applies to cars. You've got to learn what he wants to use the car for and who else in his family will be driving it. You've also got to figure out how much he can afford, so that you can put together the best finance plan.
Murray was always talking about the importance of closing the deal. We found that most of our people would do fine in the preliminary stages of selling but then were so afraid of rejection that they would often let potential customers walk right out the door. They just could never bring themselves to say: _Sign here._
Working in Chester, I came under the influence of another remarkable man, who would have more impact on my life than any person other than my father. Charlie Beacham was Ford's regional manager for the entire East Coast. Like me, he was trained as an engineer but later switched into sales and marketing. He was the closest thing I've ever had to a mentor.
Charlie was a Southerner, a warm and brilliant man, very large and imposing with a wonderful smile. He was a great motivator—the kind of guy you'd charge up the hill for even though you knew very well you could get killed in the process.
He had the rare gift of being tough and generous at the same time. On one occasion, out of the thirteen sales zones in our district, mine had come in last. I was depressed about it, and when Charlie saw me walking through the garage he came over and put his arm around me. "What are you so down about?" he wanted to know.
"Mr. Beacham," I replied, "there are thirteen zones and I ended up number thirteen in sales this month."
"Ah, hell, don't let _that_ get you down, somebody's got to be last," he said, and started to walk away. Just as he reached his car, he turned around. "But listen," he told me, "just don't be last two months in a row!"
He had a colorful way of speaking. One time there was talk of sending out some new recruits to visit the dealers in Philadelphia, who were a pretty rough group. Beacham thought that was a terrible idea. He said: "Those kids are so green that in the springtime the cows will eat 'em right up."
He could also be direct: "Make money," he used to say. "Screw everything else. This is a profit-making system, boy. The rest is frills."
Beacham used to talk about street smarts, the things you just _know_ , the basic lessons that can't really be taught. "Remember, Lee," he would say, "the only thing you've got going for you as a human being is your ability to reason and your common sense. That's the only real advantage we've got over the apes. Remember, a horse is stronger and a dog is friendlier. So if you don't know a dip of horseshit from a dip of vanilla ice cream—and a lot of guys don't—that's just too bad, because then you can never really make it."
He accepted mistakes, provided you took responsibility for them. "Always remember," he would say, "that everybody makes mistakes. The trouble is that most people just won't own up to them. When a guy screws up, he will never admit it was his fault, not if he can help it. He will try to blame it on his wife, his mistress, his kids, his dog, the weather—but never himself. So if you screw up, don't give me any excuses—go look at yourself in the mirror. Then come see me."
During sales meetings, Charlie would sometimes take a few minutes to list all the excuses he had heard recently on why cars weren't selling, so nobody would be tempted to use any of them. He respected people who faced up to their own failings. He didn't like the guys who were always making alibis or were still fighting the last war instead of the next one. Charlie was a street fighter and a strategist, always thinking ahead about what he could do next.
He was addicted to cigars, and even after the doctor made him stop smoking, he couldn't bear to part with them. Instead, he'd keep the unlit cigar in his mouth and chew on it. Every so often he would take out his pocket-knife and cut off the well-chewed end. When a meeting was over, you thought a rabbit had been in there with you—on your desk there were ten or fifteen little cigar pieces that looked remarkably like rabbit droppings.
Charlie could be a tough boss when he thought the situation called for it. At a dinner celebrating my election to the presidency of Ford in 1970, I finally got up the nerve to tell Charlie publicly what I thought of him. "There will never be another Charlie Beacham," I said. "He has a special niche in my heart—and sometimes I think he was carving it out by hand. He was not only my mentor, he was more than that. He was my _tor_ mentor, but I love him!"
As I became more confident and more successful, Charlie assigned me to teach dealers how to sell trucks. I even produced a little handbook called _Hiring and Training Truck Salesmen._ There was no doubt that I had made the right choice in leaving engineering. This was where the action was, and I loved being right in the middle of it.
As at college, my success in Chester wasn't all my own doing. Here, too, I was lucky enough to be in the right place at the right time. Ford was in the throes of reorganization. As a result, there was plenty of room for advancement. The opportunity was there, and I grabbed it. Before long, Charlie was sending me farther afield.
I would travel up and down the East Coast from city to city like a traveling salesman, lugging around the tools of my trade—slide projectors, posters, and flip charts. I'd get to town on a Sunday night and put on a five-day training course for the Ford truck salesmen in the area. I was talking all day. And like anything else, if you do enough of it, you eventually get the hang of what you're doing.
As part of my job, I had to make a lot of long-distance calls. In those days, there was no direct dialing, so that you always had to go through an operator. They'd ask for my name, and I'd say "Iacocca." Of course, they had no idea how to spell it, so there was always a struggle to get that right. Then they'd ask for my first name and when I said "Lido," they'd break out laughing. Finally I said to myself: "Who needs it?" and I started calling myself Lee.
Once, before my first trip to the South, Charlie called me into his office. "Lee," he said, "you're going down to my part of the country, and I want to give you a couple of tips. First, you talk much too fast for these guys, so slow it down. Second, they won't like your name. So here's what I want you to do. Tell them you have a funny first name—Iacocca—and that your family name is Lee. They ought to like that in the South."
They loved it. I started every meeting with that line, and they'd go wild. I would completely disarm all those Southerners. They'd forget that I was an Italian Yankee. Suddenly I was accepted as a good ole boy.
I worked hard on those trips, riding the trains to places like Norfolk, Charlotte, Atlanta, and Jacksonville. I got to know the dealers and the salesmen all over the South. I ate more grits and red-eyed gravy than I could stand. But I was happy. I had wanted to be in the people part of the car business, and now, at last, I was.
# IV
# THE BEAN COUNTERS
After a few good years in Chester, I suffered an unexpected setback. There was a mild recession in the early 1950s, and Ford decided to cut back drastically. One third of the sales force was fired—including some of my best buddies. I guess I was lucky to escape with only a demotion, but I certainly didn't _feel_ lucky. For a while I was pretty miserable. That was when I started thinking about the food business.
But if you really believe in what you're doing, you've got to persevere even when you run into obstacles. When I finished sulking, I doubled my efforts and worked even harder. In a few months I had my old job back. Setbacks are a natural part of life, and you've got to be careful how you respond to them. If I had sulked too long, I probably would have got myself fired.
By 1953, I had worked my way up to assistant sales manager of the Philadelphia district. Whether or not the dealers are moving them, the cars keep coming off the assembly lines and you've got to do something about it. You learn to scramble and move quickly. You learn to produce, or you get into trouble—fast!
When it rains, it pours, and for me it rained pretty hard in 1956. That was the year Ford decided to promote auto safety rather than performance and horsepower. The company introduced a safety package that included crash padding for the dashboard. The factory had sent along a film for us to show the dealers, which was supposed to explain just how much safer the new padding was in the event that a passenger hit his head on the dash. To illustrate the point, the narrator in the film claimed the padding was so thick that if you dropped an egg on it from a two-story building, the egg would bounce right off without breaking.
I was hooked. Instead of having the salesmen learn about the safety padding from the film, I would make the point far more dramatically by actually dropping an egg onto the padding. About eleven hundred men sat in the audience at the regional sales meeting as I began to make my pitch about the terrific new safety padding we were offering in our 1956 models. I had spread strips of the padding across the stage, and now I climbed up on a high ladder with a carton of fresh eggs.
The very first egg I dropped missed the padding altogether and splattered on the wooden floor. The audience roared with delight. I took more careful aim with the second egg, but my assistant, who was holding the ladder, chose this moment to move in the wrong direction. As a result, the egg bounced off his shoulder. This, too, was greeted with wild applause.
The third and fourth eggs landed exactly where they were supposed to. Unfortunately, they broke on impact. Finally, with the fifth egg, I achieved the desired result—and got a standing ovation. I learned two lessons that day. First, never use eggs at a sales rally. And second, never go before your customers without rehearsing what you want to say—as well as what you're going to _do_ —to help sell your product.
I had plenty of egg on my face that day, and it turned out to be a prophetic symbol for our 1956 cars. The safety campaign was a bust. Our campaign was well conceived and highly promoted, but the consumers failed to respond.
While sales of 1956 Fords were poor everywhere, our district was the weakest in the entire country. Shortly after the egg incident, I came up with another—and, I hoped, better—plan. I decided that any customer who bought a new 1956 Ford should be able to do so for a modest down payment of 20 percent, followed by three years of monthly payments of $56. This was a payment schedule that almost anyone could afford, and I hoped that it would stimulate sales in our district. I called my idea "56 for '56."
At that time, financing for new cars was just coming into its own. "56 for '56" took off like a rocket. Within a period of only three months, the Philadelphia district moved from last place in the country all the way to first. In Dearborn, Robert S. McNamara, vice-president in charge of the Ford Division—he would become secretary of defense in the Kennedy administration—admired the plan so much that he made it part of the company's national marketing strategy. He later estimated it was responsible for selling 75,000 extra cars.
And so, after ten years of preparation, I became an overnight success. Suddenly I was known and even talked about in national headquarters. I had toiled in the pits for a good decade, but now I had a big break. My future suddenly looked a lot brighter. As a reward, I was promoted to district manager of Washington, D.C.
In the midst of all this excitement, I also got married. Mary McCleary had been a receptionist in the Ford assembly plant in Chester. We had first met eight years earlier, at a reception following the introduction of our 1949 models at the Bellevue Stratford Hotel in Philadelphia. We dated on and off for several years, but I was constantly traveling, which made for a difficult and extended courtship. Finally, on September 29, 1956, we were married in Chester at St. Robert's Catholic Church.
Mary and I had spent several months looking for a house in Washington, but no sooner had we bought one than Charlie Beacham called me in and said: "You're getting moved." I said: "You gotta be kidding. I'm getting married next week and I just bought a house." He said: "I'm sorry, but if you want to get paid, your paycheck will be in Dearborn." Not only did I have to tell Mary that all of a sudden we were moving to Detroit, but I also had to tell her on our honeymoon that when we got back to our beautiful home in Maryland I would spend one night with her and then I was off!
Charlie Beacham, who himself had been promoted to head of car and truck sales for the Ford Division, brought me to Dearborn as his national truck marketing manager. Within a year I was head of car marketing, and in March of 1960 I took over both functions.
The first time that I met Robert McNamara, my new boss, we talked about carpeting. Although I was thrilled about the promotion to national headquarters, I was worried about the amount of money tied up in our new house in Washington. McNamara tried to put me at ease by explaining that the company would buy the house from me. Unfortunately, Mary and I had just spent two thousand dollars to install carpeting, a considerable sum of money in those days. I was hoping that Ford would reimburse me for that, too, but McNamara shook his head. "Just the house," he told me. "But don't worry," he added. "We'll take care of the rugs in your bonus."
That sounded fine to me, but when I got back to my office I had second thoughts. "Wait a minute," I said to myself. "I don't even know what the bonus would have been _without_ the carpeting, so how can I be sure I'm getting a good deal?" In retrospect, the whole incident seems ridiculous, and McNamara and I had a few laughs about it in later years. At the time, however, it wasn't prestige or power I wanted. It was money.
Robert McNamara had arrived at Ford eleven years earlier as one of the famous Whiz Kids. In 1945, when Henry Ford II came out of the Navy to take over his grandfather's huge but ailing company, what he needed most was managerial talent. As fate would have it, the solution to his problems fell into his lap. And he was smart enough to seize the opportunity.
Shortly after the war ended, Henry received an unusual and intriguing telegram from a group of ten young Air Force officers. They were interested in talking with him about "a matter of management importance," as they put it in the cable. As their reference, they named the secretary of defense. These ten officers, who had run the Air Force Office of Statistical Control, wanted to continue working as a team—this time in the private sector.
Henry Ford invited them out to Detroit, where their leader, Colonel Charles (Tex) Thornton, explained that his men could improve cost efficiency at Ford just as they had in the Air Force. Thornton also made clear that he was offering Henry a package deal. If he was interested, Henry would have to hire the whole gang. Wisely, Henry agreed. Although none of the men had a background in automobiles, two of them, McNamara and Arjay Miller, would eventually become presidents of Ford.
The Air Force officers came to Ford at the same time I joined up as a student engineer. They completed a loop course of their own, but instead of learning all about manufacturing, as we did, they studied the company's administration and management. They spent their first four months moving from one department to the next, and they asked so many questions that people started calling them the Quiz Kids. Later, when their success at Ford became obvious, they became known as the Whiz Kids.
Robert McNamara was noticeably different from the other Whiz Kids and also from his fellow executives at Ford. Many people thought he lacked warmth, and I guess he did project a degree of coolness. Certainly he didn't laugh very easily, except when he was with Beacham. Charlie relaxed him, and although the two men couldn't have been more different—or perhaps because of it—they got along famously. Despite McNamara's reputation as a human robot, he was really a very kind man as well as a loyal friend. But his intelligence was so formidable and so disciplined that it often overshadowed his personality.
He wasn't always easy to get along with, and his high standards of personal integrity could sometimes drive you crazy. Once, for a skiing vacation he planned, he needed a car with a ski rack. "No problem," I told him. "I'll put a rack on one of our company cars out in Denver, and you just pick it up." But he wouldn't hear of it. He insisted that we rent him a car from Hertz, pay extra for the ski rack, and send him the bill. He resolutely refused to use a company car on his vacation, even though we loaned out hundreds of courtesy cars every weekend to other VIPs.
McNamara used to say that the boss had to be more Catholic than the Pope—and as clean as a hound's tooth. He preached a certain aloofness, and he practiced what he preached. He was never one of the boys.
Whereas most auto executives lived in the residential suburbs of Grosse Pointe and Bloomfield Hills, McNamara and his wife lived in Ann Arbor, near the University of Michigan. Bob was an intellectual and preferred to socialize with academics, not car men. He was equally independent in his politics. In a world that automatically supported big-business Republicans, McNamara was both a liberal and a Democrat.
He was also one of the smartest men I've ever met, with a phenomenal IQ and a steel-trap mind. He was a mental giant. With his amazing capacity to absorb facts, he also retained everything he learned. But McNamara knew more than the actual facts—he also knew the hypothetical ones. When you talked with him, you realized that he had already played out in his head the relevant details for every conceivable option and scenario. He taught me never to make a major decision without having a choice of at least vanilla or chocolate. And if more than a hundred million dollars were at stake, it was a good idea to have strawberry, too.
When it came to spending large amounts of money, McNamara calculated the consequence of every possible decision. Unlike anyone else I've met, he could carry a dozen different plans in his head and could spin out all the facts and figures without ever consulting his notes.
Nevertheless, he taught me to put all my ideas into writing. "You're so effective one on one," he used to tell me. "You could sell anybody anything. But we're about to spend one hundred million dollars here. Go home tonight and put your great idea on paper. If you can't do that, then you haven't really thought it out."
It was a valuable lesson, and I've followed his lead ever since. Whenever one of my people has an idea, I ask him to lay it out in writing. I don't want anybody to sell me on a plan just by the melodiousness of his voice or force of personality. You really can't afford that.
McNamara and the other Whiz Kids were part of a new breed of managers who brought to Ford something the company urgently needed: financial controls. For many years, this area had been Ford's major weakness, dating from the time that old Henry Ford himself used to manage the accounts by scribbling numbers on the back of an envelope.
The Whiz Kids brought the Ford Motor Company into the twentieth century. They set up a system of controls so that for the first time each operation in the company could be measured in terms of profit and loss—and each manager could now be held responsible for the financial success or failure of his own area.
In addition to the Whiz Kids, Henry Ford II hired dozens of Harvard Business School graduates. Those of us in sales, product planning, and marketing thought of the financial planners as the longhairs—men with M.B.A.'s who formed an elitist group within the company. They had been brought in to clean up a bad mess, and they did their job well. By the time they were finished, however, they also held most of the power at Ford.
In the business world, financial men are often referred to as bean counters. McNamara was the quintessential bean counter, and he epitomized both the strengths and weaknesses of the breed. At their best—and Bob was as good as they came—the bean counters had great financial minds and impressive analytical skills. In the days before computers, these guys _were_ the computers.
By their very nature, financial analysts tend to be defensive, conservative, and pessimistic. On the other side of the fence are the guys in sales and marketing—aggressive, speculative, and optimistic. They're always saying, "Let's do it," while the bean counters are always cautioning you on why you shouldn't do it. In any company you need both sides of the equation, because the natural tension between the two groups creates its own system of checks and balances.
If the bean counters are too weak, the company will spend itself into bankruptcy. But if they're too strong, the company won't meet the market or stay competitive. That's what happened at Ford during the 1970s. The financial managers came to see themselves as the only prudent people in the company. Their attitude was: "If we don't stop them, these clowns are going to break us." They saw their mandate as saving the company from the wild-eyed dreamers and radicals who would spend Ford into oblivion. What they forgot was how quickly things can change in the car business. While their company was dying in the marketplace, they didn't want to make a move until next year's budget meeting.
Robert McNamara was different. He was a good businessman, but he had the mentality of a consumerist. He believed strongly in the idea of a utilitarian car, a car whose purpose was simply to meet people's basic needs. He looked upon most luxury models and options as frivolous and accepted them only because of the higher margins they commanded. But McNamara was so skillful a manager and so valuable to the company that he continued to rise in the system despite his ideological independence.
Although he had his eye on the presidency of Ford, he never expected to reach it. "I won't get there," he once told me, "because Henry and I don't see eye to eye on _anything."_ He was right in his assessment and wrong in his prediction.
But I don't think he would have been wrong in the long run. Bob was a strong man who fought hard for what he believed in. Henry Ford, as I would learn firsthand, had a nasty habit of getting rid of strong leaders. McNamara became president on November 10, 1960, and I was promoted the same day to fill his old position of vice-president and general manager of the Ford Division. Our appointments coincided with the election of J.F.K. A few days later, when Kennedy was putting together his cabinet, representatives of the President-elect flew to Detroit to meet with Bob. McNamara, who among his other accomplishments had been a professor at the Harvard Business School, was offered secretary of the treasury. He turned it down, but Kennedy was clearly impressed with him. When Kennedy later offered him the defense post, Bob said yes.
In 1959 McNamara had brought out his own car. The Falcon was the first American compact, and to quote a good line from the Subaru people, it was inexpensive—and built to stay that way. It was also extremely successful, selling a fabulous 417,000 units during the first year alone. This achievement was unprecedented in automobile history and more than enough to earn McNamara the presidency of Ford.
McNamara believed in basic transportation without gimmicks, and with the Falcon, he put his ideas into practice. Although I didn't care for the car's styling—I don't really think it had any—I had to admire its success. Here was a car priced to compete with the small imports, which were starting to come on strong and had already reached nearly 10 percent of the American market. But unlike the imports, the Falcon carried six passengers, which made it large enough for most American families.
We at Ford weren't the only ones to challenge the imports. Around the same time, General Motors came out with the Corvair, and Chrysler offered the Valiant. But the Falcon was the easy winner, in part because it carried the lowest price tag.
In addition to a good price, the Falcon also represented good value. Although fuel economy was certainly not a high-priority item in 1960, the Falcon had excellent mileage. More important, it boasted a fine reputation as a trouble-free, rattle-free, and carefree car. Its simple design made repairs relatively inexpensive when they did occur—so much so that insurance companies were willing to offer discounts to drivers who owned one.
But despite its enormous popularity, the Falcon did not bring in as much money as we had hoped. As an economical small car, its profit margin was limited. Nor did it offer many options, which would have greatly increased our revenues. After my promotion to head of the Ford Division, I began to develop my own ideas about doing a car that would be popular _and_ make us a ton of money. Within a couple of years, I would have the opportunity to put these ideas into practice.
# V
# THE KEY TO MANAGEMENT
At the age of thirty-six, I was the general manager of the biggest division in the world's second largest company. At the same time, I was virtually unknown. Half the people at Ford didn't know who I was. The other half couldn't pronounce my name.
When Henry Ford called me over to his office in December of 1960, it was like being summoned to see God. We had shaken hands a few times, but this was the first time we ever had a real conversation. McNamara and Beacham had already told me they had sold Henry on the idea of making me head of the Ford Division, but they asked me to play dumb. They knew that Henry would want to give me the impression it was his idea.
I was thrilled by the promotion, but I could see that it put me in a delicate position. On the one hand, I was suddenly running the company's elite division. Henry Ford had personally entrusted me with the crown jewels. On the other hand, I had bypassed a hundred older and more experienced people on my way up the ladder. Some of them, I knew, were resentful of my quick success. In addition, I still had no real credentials as a product man. At this point in my career there was no car that people could point to and say: "Iacocca did that one."
That left me with the area I did know: the people side of the business. I had to find out whether all my training in sales and marketing could be applied to working with people. I had to use everything I had learned from my father, from Charlie Beacham, and from my own experience and common sense. It was testing time.
One of my first ideas came from Wall Street. The Ford Motor Company had finally gone public only four years earlier, in 1956. Now we were owned by a large group of stockholders, who were keenly interested in our health and productivity. Like other publicly-held corporations, we sent those stockholders a detailed financial report every three months. Four times a year they kept tabs on us through these quarterly reports, and four times a year we paid them a dividend out of our earnings.
If our stockholders had a quarterly review system, why shouldn't our executives? I asked myself. I began to develop the management system I still use today. Over the years, I've regularly asked my key people—and I've had them ask _their_ key people, and so on down the line—a few basic questions: "What are your objectives for the next ninety days? What are your plans, your priorities, your hopes? And how do you intend to go about achieving them?"
On the surface, this procedure may seem like little more than a tough-minded way to make employees accountable to their boss. It is that, of course, but it's also much more, because the quarterly review system makes employees accountable to _themselves._ Not only does it force each manager to consider his own goals, but it's also an effective way to remind people not to lose sight of their dreams.
Every three months, each manager sits down with his immediate superior to review the manager's past accomplishments and to chart his goals for the next term. Once there is agreement on these goals, the manager puts them in writing and the supervisor signs off on it. As I'd learned from McNamara, the discipline of writing something down is the first step toward making it happen. In conversation, you can get away with all kinds of vagueness and nonsense, often without even realizing it. But there's something about putting your thoughts on paper that forces you to get down to specifics. That way, it's harder to deceive yourself—or anybody else.
The quarterly review system sounds almost too simple—except that it works. And it works for several reasons. First, it allows a man to be his own boss and to set his own goals. Second, it makes him more productive and gets him motivated on his own. Third, it helps new ideas bubble to the top. The quarterly review forces managers to pause and consider what they've accomplished, what they expect to accomplish next, and how they intend to go about it. I've never found a better way to stimulate fresh approaches to problemsolving.
Another advantage of the quarterly review system—especially in a big company—is that it keeps people from getting buried. It's very hard to get lost in the system if you're reviewed every quarter by your superior and, indirectly, by his boss and his boss's boss. This way, good guys don't get passed over. And equally important, bad guys don't get to hide.
Finally, and this is perhaps most important of all, the quarterly review system forces a dialogue between a manager and his boss. In an ideal world, you wouldn't need to institute a special structure just to make sure that kind of interaction takes place. But if a manager and his boss don't get along very well, at least four times a year they still have to sit down to decide what they're going to accomplish together in the months ahead. There's no way they can avoid this meeting, and over time, as they gradually come to know each other better, their working relationship usually improves.
During these quarterly meetings, it's the boss's responsibility to respond to each manager's plan. The boss might say: "Listen, I think you're shooting a little high, but if you think you can do all that in the next ninety days, why not give it a shot?" Or: "This plan makes good sense, but there are some priorities here that I don't agree with. Let's talk it over." Whatever the nature of the discussion, the boss's role begins to shift. Gradually he becomes less of an authority figure and more of an adviser and senior colleague.
If I'm Dave's supervisor, I might begin by asking Dave what he hopes to get done in the next three months. He might tell me he wants to raise our market penetration by half a point. At that point I'll say: "Fine. Now, how do you intend to do that?"
Before I ask that question, Dave and I have to agree on the specific goal he's working for. But that's rarely a problem. If there's any conflict between us, it's much more likely to center on _how_ rather than on _what._ Most managers are reluctant to let their people run with the ball. But you'd be surprised how fast an informed and motivated guy can run.
The more Dave feels he has set his own goals, the more likely it is that he'll go right through a brick wall in order to reach them. After all, he's decided on them himself, _and_ he has the boss's stamp of approval. And because Dave wants to do things his own way, he'll do his utmost to prove his way makes good sense.
The quarterly review system works equally well when Dave doesn't measure up. At that point the boss usually doesn't have to say anything. More often than not, Dave will bring it up himself, because his failure is so painfully obvious.
In my experience, after the ninety days are up, the guy who hasn't succeeded will usually come in and explain apologetically that he didn't make his goal before the boss says anything. If that happens for several quarters in a row, the guy begins to doubt himself. He comes to realize that this is _his_ problem—and not the boss's fault.
Even then, there's usually still time to take some constructive action. Often the guy himself will say: "Look, I can't handle my job. I'm in over my head. Can you move me somewhere else?"
It's far better for everybody when an employee comes to this decision on his own. Every company has lost good people who have simply been in the wrong job and who might have found more satisfaction as well as greater success if they could have been moved to another area instead of being fired. Obviously, the earlier you can detect this kind of problem, the better your chances of solving it.
Without a regular system of review, a manager who isn't working out in a particular area may build up resentment against his boss. Or the manager may imagine that the reason he failed to reach his target is that the boss holds a grudge against him. I've seen too many cases where somebody was in the wrong job for years. More often than not, there was no way for management to find that out until it was too late.
Normally, I'm not in favor of switching people around. I'm skeptical of the current fad of rotating people through various departments of a company as though all skills were interchangeable. They're not. It's like taking a cardiologist and saying: "He's a great heart surgeon. Next week, let's have him deliver a baby." He'll be the first to tell you that obstetrics is a completely different line of work and that having some expertise in one area doesn't translate into skill or experience in another. The same thing is true in the business world.
At Ford and later at Chrysler, I've always tried to get the people who worked for me to use my quarterly review system. "This is the way I control things," I explain. "And I'll show you how it works. I'm not saying you have to do it my way. But if you don't, you better find something else that produces the same results."
After using this system for many years, I've learned to watch for two potential problems. First, people sometimes bite off more than they can chew. In some cases that's a blessing in disguise, because it indicates that the guy is stretching, and for him, even a partial success may be worth a great deal. Any supervisor worth his salt would rather deal with people who attempt too much than with those who try too little.
The other problem is the boss's tendency to interfere too early. And as I came up through the ranks, I was one of the worst. I couldn't resist the temptation to get into a guy's hair, but through patience I learned. For the most part, the quarterly review system is self-regulating; it works best when I don't interfere. When it runs itself, it keeps people glued together in a constructive way, headed toward appropriate and agreed-upon objectives. You can't ask for more than that.
If I had to sum up in one word the qualities that make a good manager, I'd say that it all comes down to decisiveness. You can use the fanciest computers in the world and you can gather all the charts and numbers, but in the end you have to bring all your information together, set up a timetable, and _act._
And I don't mean act rashly. In the press, I'm sometimes described as a flamboyant leader and a hip-shooter, a kind of fly-by-the-seat-of-the-pants operator. I may occasionally give that impression, but if that image were really true, I could never have been successful in this business.
Actually, my management style has always been pretty conservative. Whenever I've taken risks, it's been after satisfying myself that the research and the market studies supported my instincts. I may act on my intuition—but only if my hunches are supported by the facts.
Too many managers let themselves get weighed down in their decision-making, especially those with too much education. I once said to Philip Caldwell, who became the top man at Ford after I left: "The trouble with you, Phil, is that you went to Harvard, where they taught you not to take any action until you've got _all_ the facts. You've got ninety-five percent of them, but it's going to take you another six months to get that last five percent. And by the time you do, your facts will be out of date because the market has moved on you. That's what life is all about—timing."
A good business leader can't operate that way. It's perfectly natural to want all the facts and to hold out for the research that guarantees a particular program will work. After all, if you're about to spend $300 million on a new product, you want to be absolutely sure you're on the right track.
That's fine in theory, but real life just doesn't work that way. Obviously, you're responsible for gathering as many relevant facts and projections as you possibly can. But at some point you've got to take that leap of faith. First, because even the right decision is wrong if it's made too late. Second, because in most cases there's no such thing as certainty. There are times when even the best manager is like the little boy with the big dog waiting to see where the dog wants to go so he can take him there.
What constitutes enough information for the decisionmaker? It's impossible to put a number on it, but clearly when you move ahead with only 50 percent of the facts, the odds are stacked against you. If that's the case, you had better be very lucky—or else come up with some terrific hunches. There are times when that kind of gamble is called for, but it's certainly no way to run a railroad.
At the same time, you'll never know 100 percent of what you need. Like many industries these days, the car business is constantly changing. For us in Detroit, the great challenge is always to figure out what's going to appeal to customers three years down the road. I'm writing these words in 1984, and we're already planning our models for 1987 and 1988. Somehow I have to try to predict what's going to sell three and four years from now, even though I can't say with any certainty what the public will want next _month._
When you don't have all the facts, you sometimes have to draw on your experience. Whenever I read in a newspaper that Lee Iacocca likes to shoot from the hip, I say to myself: "Well, maybe he's been shooting for so long that by this time he has a pretty good idea of how to hit the target."
To a certain extent, I've always operated by gut feeling. I like to be in the trenches. I was never one of those guys who could just sit around and strategize endlessly.
But there's a new breed of businessmen, mostly people with M.B.A.'s, who are wary of intuitive decisions. In part, they're right. Normally, intuition is not a good enough basis for making a move. But many of these guys go to the opposite extreme. They seem to think that every business problem can be structured and reduced to a case study. That may be true in school, but in business there has to be somebody around who will say: "Okay, folks, it's time. Be ready to go in one hour." When I read historical accounts of World War II and D-Day, I'm always struck by the same thought: Eisenhower almost blew it because he kept vacillating. But finally he said: "No matter what the weather looks like, we have to go ahead now. Waiting any longer could be even more dangerous. So let's move it!"
The same lesson applies to corporate life. There will always be those who will want to take an extra month or two to do further research on the shape of the roof on a new car. While that research may be helpful, it can wreak havoc on your production plans. After a certain point, when most of the relevant facts are in, you find yourself at the mercy of the law of diminishing returns.
That's why a certain amount of risk-taking is essential. I realize it's not for everybody. There are some people who won't leave home in the morning without an umbrella even if the sun is shining. Unfortunately, the world doesn't always wait for you while you try to anticipate your losses. Sometimes you just have to take a chance—and correct your mistakes as you go along.
Back in the 1960s and through most of the 1970s, these things didn't matter as much as they do now. In those days the car industry was like a golden goose. We were making money almost without trying. But today, few businesses can afford the luxury of slow decision-making, whether it involves a guy who's in the wrong job or the planning of a whole new line of cars five years down the road.
Despite what the textbooks say, most important decisions in corporate life are made by individuals, not by committees. My policy has always been to be democratic all the way to the point of decision. Then I become the ruthless commander. "Okay, I've heard everybody," I say. "Now here's what we're going to do."
You always need committees, because that's where people share their knowledge and intentions. But when committees replace individuals—and Ford these days has more committees than General Motors—then productivity begins to decline.
To sum up: nothing stands still in this world. I like to go duck hunting, where constant movement and change are facts of life. You can aim at a duck and get it in your sights, but the duck is always moving. _In order to hit the duck, you have to move your gun._ But a committee faced with a major decision can't always move as quickly as the events it's trying to respond to. By the time the committee is ready to shoot, the duck has flown away.
In addition to being decision-makers, managers also have to be motivators.
When I was general manager of the Ford Division, I was invited to speak to the Sloan Fellows at MIT's Alfred P. Sloan School of Management. The Sloan Fellows were a very talented group with a first-rate program that gave them a week in Europe studying the Common Market, a week on Wall Street, a week in the Pentagon, and so on.
Every Thursday night, a guest speaker from business or industry would meet with the students. When they asked me to address one of those gatherings back in 1962, I was honored but also a little nervous. "Just relax," I was told. "The students meet after dinner in the lounge. You'll say a few words about the car business, and then they'll ask you some questions."
So I spoke briefly about manufacturing and selling automobiles, and then I asked for questions and comments. With such a bright group, I was expecting some very abstract and theoretical queries, so I was surprised when somebody said to me: "How many people work in the Ford Division?"
"We have about eleven thousand people," I responded.
"Well," he said, "you're spending today and tomorrow here in Cambridge. While you're away from the office, who motivates those eleven thousand people?"
It was a very important question, and I still remember the face of the young man who asked it. He hit the nail on the head, because management is nothing more than motivating other people.
Obviously, I couldn't know the names of all eleven thousand people who worked for me. So there had to be something else in addition to the quarterly review system that was motivating them all.
The only way you can motivate people is to communicate with them. Although I was a member of the debating team in high school, I used to be afraid of public speaking. For the first few years of my working life, I was an introvert, a shrinking violet.
But that was before I took a course in public speaking at the Dale Carnegie Institute. At the time, I had just been appointed national truck training manager at Ford. The company sent a group of us to Dale Carnegie to learn the ins and outs of public speaking.
The course started off by trying to get us out of our shells. Some people—and I was one of them—can talk all day in front of one or two people, but speaking before a whole group makes them pretty nervous.
One exercise I remember was that we had to talk off the cuff for two minutes about something we knew nothing about—such as Zen Buddhism, for example. You could start off by saying you didn't know what it was, but then you'd have to keep going—and pretty soon you'd find _something_ to say. The point was to train you to think on your feet.
We learned some basic techniques of public speaking that I still practice. For example, you may know your subject, but you have to keep in mind that your audience is coming in cold. So start by telling them what you're going to tell them. Then tell them. Finally, tell them what you've already told them. I've never deviated from that axiom.
Another technique we learned was that you should always get your audience to _do_ something before you finish. It doesn't matter what it is—write your congressman, call your neighbor, consider a certain proposition. In other words, don't leave without asking for the order.
As the weeks went by, I started to feel more relaxed. Pretty soon I was willing to get up and speak without being asked. I liked the challenge. The whole point was to make us less inhibited, and in my case it certainly worked. Once I started speaking, I couldn't get enough of it. (I'm sure there are those who wish I hadn't learned to like it so much!)
To this day, I'm a great believer in the Dale Carnegie Institute. I've known a lot of engineers with terrific ideas who had trouble explaining them to other people. It's always a shame when a guy with great talent can't tell the board or a committee what's in his head. More often than not, a Dale Carnegie course would make all the difference.
Not every manager has to be an orator or a writer. But more and more kids are coming out of school without the basic ability to express themselves clearly. I've sent dozens of introverted guys to Dale Carnegie at the company's expense. For most of them it's made a real difference.
I only wish I could find an institute that teaches people how to _listen._ After all, a good manager needs to listen at least as much as he needs to talk. Too many people fail to realize that real communication goes in both directions.
In corporate life, you have to encourage all your people to make a contribution to the common good and to come up with better ways of doing things. You don't have to accept every single suggestion, but if you don't get back to the guy and say, "Hey, that idea was terrific," and pat him on the back, he'll never give you another one. That kind of communication lets people know they really count.
You have to be able to listen well if you're going to motivate the people who work for you. Right there, that's the difference between a mediocre company and a great company. The most fulfilling thing for me as a manager is to watch someone the system has labeled as just average or mediocre really come into his own, all because someone has listened to his problems and helped him solve them.
Of course, the more common way to communicate with your people is to talk to them as a group. Public speaking, which is the best way to motivate a large group, is entirely different from private conversation. For one thing, it requires a lot of preparation. There's just no way around it—you have to do your homework. A speaker may be very well informed, but if he hasn't thought out exactly what he wants to say _today, to this audience_ , he has no business taking up other people's valuable time.
It's important to talk to people in their own language. If you do it well, they'll say, "God, he said exactly what I was thinking." And when they begin to respect you, they'll follow you to the death. The _reason_ they're following you is not because you're providing some mysterious leadership. It's because you're following them.
That's what Bob Hope is doing when he sends an advance man to scout his audience so that he can make jokes that are special to them and their situation. If you're watching on television, you might not understand what he's saying. Nevertheless, the live audience always appreciates it when a speaker has taken the trouble to learn something about who they are. Not everyone can afford an advance man, but the message is clear: public speaking does not mean impersonal speaking.
Although I could probably speak off the cuff for two hours, I always work from a script. Speaking extemporaneously is simply too exhausting. I compromise by using a prepared text and deviating from it whenever I feel the need.
When I speak to a group at Chrysler, I'm less likely to be entertaining than when I'm on the dinner circuit. With my own people, my goal is to be as direct and as straightforward as possible. I've found that the best way to motivate them is to let them know the game plan so they can all be part of it. I have to explain my own goals, just as the other executives have to set their own objectives with their supervisors. And if they meet these objectives, they should be rewarded with more than kind words. Money and a promotion are the tangible ways a company can say: most valuable player.
When you give a guy a raise, that's the time to increase his responsibilities. While he's in a good frame of mind, you reward him for what he's done and, at the same time, you motivate him to do even more. Always hit him with more while he's up, and never be too tough on him when he's down. When he's upset over his own failure, you run the risk of hurting him badly and taking away his incentive to improve. Or, as Charlie Beacham used to say, "If you want to give a man credit, put it in writing. If you want to give him hell, do it on the phone."
Charlie Beacham would preach against trying to be a one-man band. "You want to do everything yourself," he used to say. "You don't know how to delegate. Now, don't get me wrong. You're the best guy I've got. Maybe you're even as good as two guys put together. But even so—that's still only two guys. You've got a hundred people working for you right now. What happens when you get ten thousand?"
He had foresight, because at the Ford Division I had eleven thousand. He taught me to stop trying to do everybody's job. And he taught me how to give other people a goal—and how to motivate them to achieve it.
I've always felt that a manager has achieved a great deal when he's able to motivate one other person. When it comes to making the place run, motivation is everything. You might be able to do the work of two people, but you can't _be_ two people. Instead, you have to inspire the next guy down the line and get him to inspire _his_ people.
Once, at a private dinner with Vince Lombardi, the legendary football coach and a friend of mine, I asked him about his formula for success. I wanted to know exactly what made a winning team. What he told me that evening applies as much to the business world as it does to sports.
"You have to start by teaching the fundamentals," Lombardi said. "A player's got to know the basics of the game and how to play his position. Next, you've got to keep him in line. That's discipline. The men have to play as a team, not as a bunch of individuals. There's no room for prima donnas."
He continued: "But there have been a lot of coaches with good ball clubs who know the fundamentals and have plenty of discipline but still don't win the game. Then you come to the third ingredient: if you're going to play together as a team, you've got to care for one another. You've got to _love_ each other. Each player has to be thinking about the next guy and saying to himself: 'If I don't block that man, Paul is going to get his legs broken. I have to do my job well in order that he can do his.'
"The difference between mediocrity and greatness," Lombardi said that night, "is the feeling these guys have for each other. Most people call it team spirit. When the players are imbued with that special feeling, you know you've got yourself a winning team."
Then he blurted out almost self-consciously: "But Lee, what am I telling _you_ for? You run a company. It's the same thing, whether you're running a ball club or a corporation. After all, does one man build a car all by himself?"
Lombardi told me he'd like to visit Ford and see how cars are made, and I promised to invite him out to Detroit. But shortly after our dinner together, he was hospitalized with a fatal illness. I had met him only a couple of times, but his words have stayed with me: "Every time a football player goes out to ply his trade, he's got to play from the ground up—from the soles of his feet right up to his head. Every inch of him has to play. Some guys play with their heads, and sure, you need to be smart to be number one in anything you try. But most important, you've got to play with your heart. If you're lucky enough to find a guy with a lot of head and a lot of heart, he's never going to come off the field second."
He was right, of course. I've seen too many guys come along who are smart and talented but who just can't play on a team. These are the managers about whom other people say: "I wonder why he didn't go further?" We all know such people, the ones who seem to have it all and yet never make much progress. I'm not talking here about the guys who don't really want to move ahead, or those who are just plain lazy. I'm thinking of the go-getters who followed a plan, went to school, got a good job, worked hard—and then nothing came of it.
When you speak to these guys, they'll often tell you that they've had some bad breaks or perhaps a boss who didn't like them. Invariably, they present themselves as victims. But you have to wonder why they had only bad breaks and why they never seemed to look for good ones. Certainly luck plays a part. But a major reason capable people fail to advance is that they don't work well with their colleagues.
I know a man who's been working in the car business all his life. He's highly educated and well organized. He's a brilliant strategist, probably one of the most valuable people in his company. Yet he's never risen to the top ranks, because he just doesn't have the ability to handle people.
Or look at my own career. I've seen a lot of guys who are smarter than I am and a lot who know more about cars. And yet I've lost them in the smoke. Why? Because I'm tough? No. You don't succeed for very long by kicking people around. You've got to know how to talk to them, plain and simple.
Now, there's one phrase that I hate to see on any executive's evaluation, no matter how talented he may be, and that's the line: "He has trouble getting along with other people."
To me, that's the kiss of death. "You've just destroyed the guy," I always think. "He can't get along with people? Then he's got a real problem, because that's all we've got around here. No dogs, no apes—only people. And if he can't get along with his peers, what good is he to the company? As an executive, his whole function is to motivate other people. If he can't do that, he's in the wrong place."
Then there's the prima donna. Nobody likes this type, although if he's sufficiently talented he may be tolerated. At Ford, there was one executive who wanted to have his office refurbished in antiques. He put through a request to have it redecorated to the tune of $1.25 million. (That's one room and half a bath!) I happened to see Henry Ford's response, and I could tell he was angry by the message he scrawled on the memo, which said simply: "Make do with three-quarters of a million." This executive knows a lot about the car industry, but in my opinion his style makes him ineffective as a manager.
I recall another case many years ago in which Ford hired a top executive to help straighten out the marketing department. Eventually he got himself fired by doing the unthinkable—he hired his own personal PR man. He tried to make it look as though the guy were coming in as a consultant, but the truth emerged soon enough. This executive's biggest concern was that his own accomplishments would be chronicled in the newspaper. Not surprisingly, he didn't last very long.
At the same time, a certain degree of self-promotion is natural and even necessary. I've seen managers who are too shy or too scared to deal with the press, or who don't want anyone to know how much they've done. Although General Motors has encouraged this kind of faceless personality with some success, it's not for me. If your top executives don't have some ego drive, how will your company stay stirred up and competitive?
There's a world of difference between a strong ego, which is essential, and a large ego—which can be destructive. The guy with a strong ego knows his own strengths. He's confident. He has a realistic idea of what he can accomplish, and he moves purposefully toward his goal.
But the guy with a large ego is always looking for recognition. He constantly needs to be patted on the back. He thinks he's a cut above everybody else. And he talks down to the people who work for him.
_The Wall Street Journal_ once said that I had "an ego as big as all outdoors." But if that were really true, I don't think I'd be effective in a business that depends so highly on the ability to work well with other people.
I've already said that I believe in writing things down. But this, too, can be carried to extremes. Some people seem to enjoy turning a company into a paper mill. In part, it's human nature. There are always situations in an office where some people feel a strong need to cover their ass by producing a memo for the file. True, putting your ideas on paper is usually the best way of thinking them through. But that doesn't mean everything you write should be circulated to your colleagues.
The best way to _develop_ ideas is through interacting with your fellow managers. This brings us back to the importance of teamwork and interpersonal skills. The chemistry among two or three people sitting down together can be incredible—and it's been a big part of my own success.
So I'm a great believer in having executives spend time together talking—not always in formal meetings but simply shooting the breeze, helping each other out, and solving problems.
People who visit my office at Chrysler are often surprised that I don't have a computer terminal on my desk. Maybe they forget that everything that comes out of a computer, somebody has to put in. The biggest problem facing American business today is that most managers have too much information. It dazzles them, and they don't know what to do with it all.
The key to success is not information. It's people. And the kind of people I look for to fill top management spots are the eager beavers. These are the guys who try to do more than they're expected to. They're always reaching. And reaching out to the people they work with, trying to help them do their jobs better. That's the way they're built.
Then there are the other guys, the nine-to-five gang. They just want to get along and be told what to do. They say: "I don't want to be in the rat race. It might affect my heartbeat."
Just because you get involved and excited and really tear into things doesn't mean you'll die of hypertension next week!
So I try to look for people with that drive. You don't need many. With twenty-five of these guys, I could run the government of the United States.
At Chrysler I have about a dozen. What makes these managers strong is that they know how to delegate and how to motivate. They know how to look for the pressure points and how to set priorities. They're the kind of guys who can say: "Forget that, it'll take ten years. Here's what we gotta do _now."_
# VI
# THE MUSTANG
My years as general manager of the Ford Division were the happiest period of my life. For my colleagues and me, this was fire-in-the-belly time. We were high from smoking our own brand—a combination of hard work and big dreams.
In those days, I couldn't wait to get to work in the morning. At night I didn't want to leave. We were continually playing with new ideas and trying out models on the test track. We were young and cocky. We saw ourselves as artists, about to produce the finest masterpieces the world had ever seen.
In 1960, the whole country was optimistic. With Kennedy in the White House, a fresh breeze was blowing across the land. It carried an unspoken message that anything was possible. The striking contrast between the new decade and the 1950s, between John Kennedy and Dwight Eisenhower, could be summed up in a single word—youth.
But before I could act on my own youthful dreams, there were other matters to take care of. After the spectacular success of the Falcon, Robert McNamara had authorized the development of another new car, a German-built compact known as the Cardinal. It was scheduled to be introduced in the fall of 1962, and when I took over the Ford Division, one of my responsibilities was to oversee its production.
Because McNamara was concerned with fuel efficiency and basic transportation, the Cardinal was conceived to be the American response to the Volkswagen. Like the Falcon, it was small, plain, and inexpensive. Both models expressed McNamara's deep conviction that a car was a means of transportation and not a toy.
A few months into my new job, I flew over to Germany to check on the progress of McNamara's car. It was my first time in Europe, and that alone was quite a thrill. But when I finally saw the Cardinal, I was underwhelmed.
It was a fine car for the European market, with its V-4 engine and front-wheel drive. But in the United States there was no way it could have sold the three hundred thousand units we were counting on. Among other problems, the Cardinal was too small and had no trunk. And while its fuel economy was great, that wasn't yet a selling point for the American consumer. In addition, the styling was lousy. The Cardinal looked like it was designed by committee.
As usual, McNamara was ahead of his time—ten years, to be exact. A decade later, after the OPEC crisis, the Cardinal would have been a world-beater.
In some industries, being ahead of your time is a great advantage. But not in Detroit. Just as the car industry can't afford to lag too far behind the consumer, it also can't afford to be too far ahead of him. Coming out with a new product too early is just as bad as being too late.
There's a widespread myth that those of us who run the car industry somehow manipulate the public, that we tell people what kind of cars they should buy—and that they listen. Whenever I hear this, I always smile and think: "If only it were true!"
The truth is that we can only sell what people are willing to buy. In fact, we follow the public far more than we lead it. Naturally, we do our best to persuade people to buy our products. But sometimes our best efforts aren't good enough.
I didn't need any reminder of that in 1960. The company was still reeling from the Edsel fiasco a couple of years back. This isn't the place to go into the various reasons for that sad story, but suffice it to say that the Edsel—which neither McNamara nor I had anything to do with—failed on so grand a scale that "Edsel" has come to be synonymous with failure.
When I returned from Germany I went straight to Henry Ford. "The Cardinal is a loser," I told him. "To bring out another lemon so soon after the Edsel would bring this company to its knees. We simply can't afford a new model that won't appeal to younger buyers."
I stressed the youth angle for two reasons. First, I was becoming increasingly aware of the economic power of the younger generation, a power that had not yet been recognized in our industry. Second, I knew that the boss liked to think of himself as a with-it guy, a swinger who understood what young people wanted.
Then I met with top management and our board of directors to discuss the fate of the Cardinal. In these talks, I got the impression that the entire company was confused about the car and that the senior people were only too pleased to have a young upstart like me make the decision for them. That way, none of them would have to take direct responsibility if stopping the Cardinal turned out to be a gigantic mistake. Although the company had already invested $35 million in the car, I argued that it wouldn't sell and that we should cut our losses and run.
I must have been convincing, because my decision was accepted with only two dissenters: John Bugas, head of our international operations, and Arjay Miller, our controller. Bugas, although he was my close friend, naturally wanted the Cardinal to come out because it was made overseas. Miller was concerned about the $35 million we had already invested. Like a true bean counter, he saw mainly the $35 million loss in that quarter.
With the Cardinal out of the way, I was free to work on my own projects. Right away, I brought together a group of bright and creative young guys from the Ford Division. We started getting together once a week for dinner and conversation at the Fairlane Inn in Dearborn, about a mile from where we worked.
We met at the hotel because a lot of people back at the office were just waiting for us to fall on our faces. I was a young Turk, a new vice-president who hadn't yet proved himself. My guys were talented, but they weren't always the most popular people in the company.
Don Frey, our product manager and now head of Bell and Howell, was a key member of that group. So was Hal Sperlich, who is still with me today in a top position at Chrysler. The others included Frank Zimmerman from marketing; Walter Murphy, our public-relations manager and my loyal friend throughout my years at Ford; and Sid Olson from J. Walter Thompson, a brilliant writer who was once a speech writer for F.D.R. and, among other things, coined the phrase "The Arsenal of Democracy."
The Fairlane Committee, as we called ourselves, had a lot on the ball. We were dimly aware that the car market would be stood on its ear in the next few years, although there was no way of knowing exactly how that would happen. We also knew that General Motors had taken the Corvair, an economy car, and transformed it into the hot-selling Corvair Monza simply by adding a few sporty accessories such as bucket seats, stick shift, and fancy interior trim. We at Ford had nothing to offer to the people who were considering a Monza, but it was clear to us that they represented a growing market.
Meanwhile, our public-relations department was receiving a steady stream of letters from people who wanted us to bring out another two-passenger Thunderbird. This was a surprise to us, because that car had not been very successful, selling only fifty-three thousand units over three years. But the mail was telling us consumer tastes were changing. Maybe the two-passenger Thunderbird was simply ahead of its time, we said to ourselves. We were starting to get the strong impression that if that car were still on the market, we'd be selling a lot more than eighteen thousand a year.
At the same time, our market researchers confirmed that the youthful image of the new decade had a firm basis in demographic reality. For one thing, the average age of the population was falling at an unusually rapid rate. Millions of teenagers born in the baby boom that followed World War II were about to surge into the national marketplace. The twenty- to twenty-four-year-old group would increase by over 50 percent during the 1960s. Moreover, young adults between eighteen and thirty-four would account for at least half the huge increase in car sales that was predicted for the entire industry during the next ten years.
The researchers added an obscure but interesting footnote. Not only would there be _more_ young people than ever before, but they would also be better educated than previous generations. We already knew that college-educated people bought cars at a much higher rate than their less-educated counterparts, and our projections showed that the number of college students was going to double by 1970.
There were equally interesting changes going on among older car buyers. We were now starting to see a perceptible shift away from the preoccupation with economy cars that had characterized the late 1950s and had helped the Falcon set new records. Consumers were beginning to look beyond the austere and the purely functional to consider more sporty and luxury models—just as they are again in 1984.
When we analyzed all this information, the conclusion was inescapable. Whereas the Edsel had been a car in search of a market it never found, _here was a market in search of a car._ The normal procedure in Detroit was to build a car and then try to identify its buyers. But we were in a position to move in the opposite direction—and tailor a new product for a hungry new market.
Any car that would appeal to these young customers had to have three main features: great styling, strong performance, and a low price. Developing a new model with all three would not be easy. But if it could be done, we had a shot at a major success.
We went back to the research and learned a little more about the changing market for new cars. First, there was an enormous growth in two-car families, with the second car typically smaller and more sporty than the first. Second, a growing number of cars were being bought by women, who preferred small cars with easy handling. Single people, too, were increasingly represented among new-car buyers, and they were choosing smaller and sportier models than their married friends. Finally, it was becoming clear that in the next few years, Americans would have more money than ever before to spend on transportation and entertainment.
As we processed this information, we began to look at the sales figures from the Falcon to see what we could find out about our own customers. The results were surprising. Although the Falcon was marketed as a low-priced economy car, far more customers than we expected were starting to order such options as automatic transmission, white-wall tires, and more powerful engines. This was my first inkling of an important fact about small cars that remains as true today as it was twenty years ago: the American car buyer wants economy so badly he'll pay almost anything to get it!
The Fairlane Committee began to get more specific about the car we wanted to build. It had to be small—but not _too_ small. The market for a two-seat car may have been growing, but it was still limited to around a hundred thousand, which meant that a two-seater would never have mass appeal. Our car, then, had to hold four passengers. For performance it also had to be light—twenty-five hundred pounds was our limit. And finally, it had to be inexpensive. Our goal was to have it sell for no more than $2,500 with equipment.
In terms of styling, I had an idea of what I wanted. I used to go home and pore through the pages of a book called _Auto Universum_ , which features pictures of all the cars ever built. The one that always jumped out at me was the first Continental Mark. That was everyone's dream car—or at least it had been mine ever since Leander Hamilton McCormick-Goodheart drove up to Lehigh in 1945. What distinguished the Mark was its long hood and short deck. The length of the hood gave the appearance of verve and performance, and that, I decided, was what people were looking for.
The more our group talked, the more concrete our ideas became. Our car had to be obviously sporty and distinctively styled, with just a dash of nostalgia. It had to be easy to identify and unlike anything else on the market. It had to be simple to maneuver but still capable of seating four people, with enough room left for a fair-sized trunk. It had to be a sports car but more than a sports car. We wanted to develop a car that you could drive to the country club on Friday night, to the drag strip on Saturday, and to church on Sunday.
In other words, our intention was to appeal to several markets at once. We had to broaden our base of potential customers because the only way we could afford to produce this car at a terrific price was to sell a ton of them. Rather than offer several different versions of the same product, we agreed that the only sensible course was to develop one basic car with a wide range of options. That way, the customer could buy as much economy, luxury, or performance as he wanted—or could afford.
But the question was: could _we_ afford the car? An all-new car from the ground up would cost $300 to $400 million. The answer lay in using components that were already in the system. That way we could save a fortune in production costs. The engines, transmissions, and axles for the Falcon already existed, so if we could adapt them, we wouldn't have to start from scratch. We could piggyback the new car onto the Falcon and save a fortune. In the end, we would be able to develop the new car for a mere $75 million.
All this sounded great, but not everyone thought it could be done. Dick Place, a product planner, said that making a sporty car out of a Falcon was like putting falsies on Grandma. Still, I assigned Don Frey and Hal Sperlich to play with the idea. They experimented with several different models but in the end concluded that the new car's design and exterior had to be completely original. We could keep the platform and the engine from the Falcon, but as we say in Detroit, the car needed a whole new skin and greenhouse—the windshield, side glass, and backlite.
By late 1961, we had a target date. The New York World's Fair was scheduled to open in April 1964, which sounded to us like the ideal place to launch our car. Although new models are traditionally introduced in the fall, we had in mind a product so exciting and so different that we would dare to bring it out in the middle of the season. Only the World's Fair had enough scale and drama for the car of our dreams.
There was one big piece missing from the puzzle: we still didn't have a design. During the first seven months of 1962, our styling people produced no less than eighteen different clay models, in the hope that one of them might be the car we were after. Several of these models were exciting, but none of them seemed exactly right.
By now I was growing impatient. If our new car was going to be ready in April 1964, we needed a design right away. There were twenty-one months left in which to get the idea approved, agree on a final styling model, decide on a plant, buy equipment, locate supply sources, and arrange for dealers to sell the finished product. We were well into the summer of 1962, and the only way we could still have a shot at the World's Fair was to come up with a fully approved clay model by September 1.
With time running out, I decided to stage a competition among our designers. On July 27, Gene Bordinat, our styling director, summoned three of his top stylists to his office. He explained that each of their studios would take part in an unprecedented open competition by designing at least one model of the small sports car we were determined to build.
The designers were told to have their clay models ready for review by top management on August 16. We were asking a great deal of these guys, because normally you can't design a car that quickly. But after two weeks of 'round-the-clock work, there were seven models to choose from on the day of the review.
The clear winner was designed by Dave Ash, the assistant to Ford studio head Joe Oros. When it was about half done, Joe had invited me down to have a look. As soon as I saw it, one thing hit me instantly: although it was just sitting there on the studio floor, this brown clay model looked like it was moving.
Because they saw their car as feline in nature, Joe and Dave had started calling it the Cougar. The model they had prepared for the August 16 showing was painted white with red wheels. The Cougar's back bumper turned up to form a bustling little rear end. The grille on the front had a stylized cougar inside, giving the model an aura that was both handsome and powerful.
Immediately after the presentation, the Cougar was rolled to the Ford studios for feasibility studies. At long last we had an active proposal under consideration. But we still didn't have a car. For that, we needed approval from the styling committee—which was made up of the top executives in the company.
I knew I was facing an uphill battle when I went in to try to sell the Cougar. To begin with, the senior executives were not yet convinced, as we were, that the youth market was real. And because the Edsel was still fresh in their minds, they were cautious and wary about introducing another new model. To make matters worse, they had already committed themselves to the huge expense of retooling the regular line of Ford products for 1965. There was some question as to whether the company could really afford another car—even one that could be produced for relatively little money.
Arjay Miller, who would soon become the new president, ordered a study of our proposal. He was somewhat optimistic about sales, but he worried about cannibalism—that the new car's success might come at the expense of other Ford products, especially the Falcon. The study he commissioned projected that the Cougar would sell eighty-six thousand units. That was a respectable figure, but it wasn't quite high enough to justify the huge expense of starting up a new model.
Fortunately, Henry Ford was now more receptive to the plan. This openness was in sharp contrast to his reaction the first time I had described the idea to a committee of high-level executives. In the middle of my pitch, Henry had suddenly said, "I'm leaving," and walked out of the room. I had never seen him so cold to a new idea. I went home and told Mary: "I got shot down today on my favorite project. Henry walked out on me."
I was really crushed. But the very next day, we learned that Henry's abrupt departure had nothing to do with my presentation. He had been feeling weak so he went home early—and spent the next six weeks in bed with mononucleosis. When he came back, he was feeling much better about everything, including the plans for our new car.
Later, as we were building the prototype, Henry came by one day to have a look. He climbed into the car and announced: "It's a little tight in the back seat. Add another inch for leg room."
Unfortunately, adding even an inch to the interior of a car can be a very expensive proposition. An extra inch also had implications for styling, and all of us were against the change. But we also knew that Henry's decisions were not open to debate. As he liked to remind us, his name was on the building. Besides, at that point we would have added another _ten_ inches if it would make the difference between doing the car and losing it.
Although he probably didn't know it at the time—and in fact, he may _still_ not know it—Henry also played a role in the new car's name. Before we decided to call it the Mustang, it was known by several other designations. During the early planning stages, we called it the Special Falcon. Then, after the Oros-Ash model was accepted, the Cougar. Henry wanted to call it T-Bird II, but nobody else liked that one.
At a product strategy meeting in May, we narrowed our choices down to Monte Carlo, Monaco, Torino, and Cougar. When we learned that the first two had already been registered with the Automobile Manufacturers Association by other companies, it came down to Torino and Cougar. Finally we settled on Torino, which happens to be the Italian spelling of the industrial city of Turin. Torino was also in keeping with the vaguely foreign flavor we had worked so hard to capture. As a kind of compromise, we decided to keep the stylized cougar as the Torino's emblem.
While we were preparing the ad campaign for the Torino, I got a call from the top guy in public relations, Charlie Moore. "You'll have to pick another name for your car," he said. He explained that Henry was in the midst of a divorce and was keeping company with Cristina Vettore Austin, an Italian jet-set divorcée he had met at a party in Paris. Some of Henry's underlings felt that giving the new car an Italian name would lead to unfavorable publicity and gossip, which would embarrass the boss.
We had to come up with another name in a hurry. When it comes to naming a car, there's always a battle. And for good reason: the name is often the toughest part of the car to get right. It's easier to design doors and roofs than to come up with a name, because the choice is inevitably subjective. Sometimes the process can get pretty emotional.
John Conley, who worked for J. Walter Thompson, our ad agency, was a name specialist. In the past, he had researched bird names for the Thunderbird and the Falcon. This time we sent him to the Detroit Public Library to look up the names of animals—from aardvark to zebra. John came up with thousands of suggestions, which we narrowed down to six: Bronco, Puma, Cheetah, Colt, Mustang, and Cougar.
Mustang had been the name of one of the car's prototypes. Curiously, it was not named for the horse but for the legendary World War II fighter plane. No matter. We all liked Mustang, and as the ad agency said: it "had the excitement of wide-open spaces and was American as all hell."
In my library at home, I still have a die casting of the emblem of the Cougar, which the designers sent me in a little walnut box with a scroll saying: "Please don't fool around. Don't name it anything but Cougar." It was a request I couldn't honor, but we did use the name Cougar a few years later for a fine new car in the Lincoln-Mercury division.
Ever since the Mustang was introduced, people have enjoyed pointing out that the emblem of the horse on the front of the car was facing the wrong way, because it gallops in a clockwise direction instead of counterclockwise, the way horses run on American racetracks. My answer to that has always been that the Mustang is a wild horse, not a domesticated racer. And no matter which way it was running, I felt increasingly sure that it was headed in the right direction.
Once we settled on the styling, we had to make some basic decisions about the interior. We were eager to provide for those customers who wanted luxury, but we didn't want to cut out the people who were more interested in performance or economy. At the same time, we didn't want to produce a totally stripped car. The Mustang was already being seen as a poor man's Thunderbird; there would be little point in bringing out a poor man's Mustang. We decided that even the economy model had to be comparable to the luxury and performance versions, and so we included such items as bucket seats, vinyl trim, wheel covers, and carpeting as standard features in each car.
Beyond that, we had in mind a kind of do-it-yourself car that would appeal to all segments of the market. If a customer could afford luxury, he could buy extra accessories and more power. If he loved luxury but couldn't afford these extras, he would still be happy because several options he'd normally have to pay for were available here at no extra charge.
Long before the car came out, we started doing market research. One of our final tests was especially encouraging. We invited a select group of fifty-two Detroit area couples to our styling showroom. Each of these couples already owned a standard-sized car and earned average incomes, which meant they were not prime candidates for a second car. We brought them in small groups into our styling studio to view the prototype of the Mustang, and we recorded their impressions on tape.
What we found was that white-collar couples were impressed by the car's styling, while blue-collar workers saw the Mustang as a symbol of status and prestige. When we asked them to estimate the price of the car, almost everybody guessed a figure that was at least $1,000 too high. When we asked if they would buy a Mustang, most said they wouldn't. They explained that it was too expensive, or too small, or too difficult to handle.
But when we told them the actual price of the car, a funny thing happened. Most people said: "The hell with my objections, I want it!" Suddenly their excuses vanished. They came up with all sorts of innovative reasons why this particular car made good sense after all. One fellow said: "If I parked that car in my driveway, all my neighbors would wonder what gravy train I fell into." Another one told us: "It doesn't look like an ordinary car—and at that price what you get is an ordinary car."
The lesson was clear. When it came time to market the Mustang, we had to make sure to emphasize its low price.
The final sticker price on the Mustang reflected our early decision to hold the price under $2,500. We ended up with a car that was an inch and a half longer than we had originally planned and 108 pounds heavier. But we held the line on price, and the Mustang sold for $2,368.
The good omens continued. By January 1964, only a few weeks from the launch, economic conditions had become unusually favorable. We would later learn that the first quarter of 1964 marked the highest level of auto sales in history. In addition, Congress was about to enact an income-tax cut, and disposable income was on the rise. All things considered, the national mood reflected high confidence and optimism.
On March 9, 1964, 571 days after the Oros-Ash Cougar had been selected over its six rivals, the first Mustang rolled off the assembly line. We had arranged to produce a minimum of 8,160 cars before introduction day—April 17—so that every Ford dealer in the country would have at least one Mustang in his showroom when the car was officially launched.
We promoted the Mustang to the hilt. We invited the editors of college newspapers to Dearborn, and we gave them a Mustang to drive for a few weeks. Four days before the car was officially launched, a hundred members of the press participated in a giant seventy-car Mustang rally from New York to Dearborn, and the cars demonstrated their reliability by breezing through the seven-hundred-mile trip without any problems. The press recorded its enthusiasm in a massive and lyrical outpouring of words and photographs that appeared prominently in hundreds of magazines and newspapers.
On April 17, Ford dealerships everywhere were mobbed with customers. In Chicago, one dealer had to lock his showroom doors because the crowd outside was so large. A dealer in Pittsburgh reported that the crush of customers was so thick he couldn't get his Mustang off the wash rack. In Detroit, another dealer said that so many people who had come to see the Mustang had arrived in sports cars that his parking lot looked like a foreign-car rally.
In Garland, Texas, a Ford dealer had fifteen potential customers bidding on a single Mustang in his display window. He sold it to the highest bidder—a man who insisted on spending the night in the car so that nobody else could buy it while his check was clearing. At a dealership in Seattle, the driver of a passing cement truck became so fascinated by the Mustang on display that he lost control of his vehicle and crashed through the showroom window.
The Mustang was destined to be an incredible hit. During the first weekend it was on sale, an unprecedented four million people visited Ford dealerships. The car's public reception was exceeding our wildest hopes.
The press played an important role in creating this excitement. Due to the tireless efforts of Walter Murphy in public relations, the Mustang was featured simultaneously on the covers of both _Time_ and _Newsweek._ This was an astounding publicity coup for a new commercial project. Both magazines sensed we had a winner, and their added publicity during the very week of the Mustang's introduction helped make their prediction a self-fulfilling prophecy. I'm convinced that _Time_ and _Newsweek_ alone led to the sale of an extra 100,000 cars.
The twin cover stories had the effect of two gigantic commercials. After telling its readers that my name "rhymes with try-a-Coke-ah," _Time_ noted that "Iacocca has produced more than just another new car. With its long hood and short rear deck, its Ferrari flair and openmouthed air scoop, the Mustang resembles the European racing cars that American sports-car buffs find so appealing. Yet Iacocca has made the Mustang's design so flexible, its price so reasonable, and its options so numerous that its potential appeal reaches toward two-thirds of all U.S. car buyers. Priced as low as $2,368 and able to accommodate a small family in its four seats, the Mustang seems destined to be a sort of Model A of sports cars—for the masses as well as the buffs." I couldn't have said it better myself.
The automotive press was no less enthusiastic. "A market which had been looking for a car has it now," began the story in _Car Life._ Even _Consumer Reports_ , generally no great fan of Detroit, noted the Mustang's "almost complete absence of poor fit and sloppy workmanship in a car being built at a hell-for-leather pace."
But we hadn't been counting on the press to do our advertising for us. On introduction day we ran full-page ads in twenty-six hundred newspapers. We used what I call the Mona Lisa approach: a simple profile of the car in white, listing the price along with a simple line, "The Unexpected." When the product is right, you don't have to be a great marketer.
We also blanketed the television networks with Mustang commercials. J. Walter Thompson produced a whole series of ads using a Walter Mitty theme, based on the James Thurber character who dreams of being a race driver or a jet pilot. In one of these ads, Henry Foster, a conservative, mild-mannered antiques dealer, leaves his shop carrying a lunch bag. "Have you heard about Henry Foster?" asks the lady in the next store. Henry walks around the corner and gets into his red Mustang. He throws away his derby and replaces it with a sporty tweed hat from his bag. Then he takes off his coat to reveal a bright red vest. Finally he exchanges his old-fashioned glasses for racing goggles.
"Something's happened to Henry," the lady's voice continues.
"A Mustang's happened to Henry," announces another woman. She's young, attractive, and waiting for Henry in a green meadow with a picnic lunch and a bottle of wine.
We also ran hard-hitting national promotion programs. We displayed Mustangs in fifteen of the country's busiest airports and in the lobbies of two hundred Holiday Inns from coast to coast. At the University of Michigan football games, we contracted for several acres of space in the parking lot and put up huge signs that said: "Mustang Corral." We also did a lot of direct mail, sending out millions of pieces to small-car owners across the country.
After only a few weeks it became clear to me that we had to open up a second plant. The initial assumption had been that the Mustang would sell seventy-five thousand units during the first year. But the projections kept growing, and before the car was introduced we were planning on sales of two hundred thousand. To build even that many cars, we had to convince top management to convert a second plant, in San Jose, California, into producing more Mustangs.
Because the cars were in such short supply, it was hard to know how many we could really sell. So a few weeks after the Mustang was introduced, Frank Zimmerman arranged for an experiment in Dayton, Ohio, known as a GM town because GM had several plants in the area.
He met with the Ford dealers in Dayton and told them: "Look, you guys are in a tough, competitive market here, and the Mustang's a hot car. We want to see how hot it really is, so we're going to give each of you ten cars to put in stock and we'll honor your retail orders as quickly as you get them."
The results were amazing. We got something like 10 percent of the entire car market in Dayton. That was all the ammunition we needed, and by September we were starting to convert the San Jose plant.
Our annual capacity was now 360,000 cars, and soon we were converting a third plant, in Metuchen, New Jersey. These two conversions represented an expensive risk, but we had been burned on the Falcon when we'd set our sights too low and then didn't have the capacity to produce all the cars we needed. We weren't going to make that mistake twice.
People were buying Mustangs in record numbers. The options and accessories were moving just as quickly. Our customers reacted to the long list of options like hungry lumberjacks at a Swedish smorgasbord. Over 80 percent ordered white sidewall tires, 80 percent wanted radios, 71 percent took eight-cylinder engines, and 50 percent bought the automatic transmission. Every tenth Mustang was sold equipped with a tachometer and a clock that comprised a special "Rallye Pack." For a car that cost $2,368, our customers were spending an average of $1,000 each just on options!
I had a target in mind for the first year. During _its_ first year, the Falcon had sold a record 417,174 cars, and that was the figure I wanted to beat. We had a slogan: "417 by 4/17"—the Mustang's birthday. Late in the evening of April 16, 1965, a young Californian bought a sporty red Mustang convertible. He had just purchased the 418,812th Mustang, and we finished our first year with a new record.
The bean counters went back into the bunkers muttering that there was evidently more than one way to build a car. It was the styling that did it, which was something they hadn't counted on. But they weren't shy when it came time to count the money. In the first two years alone, the Mustang generated net profits of $1.1 billion. And that's in 1964 dollars!
Within weeks of the Mustang's introduction, we were flooded with letters from satisfied customers. I always read customer mail, so I'm well aware that most people write to the manufacturer only when there's a problem. With the Mustang, however, people wrote to express their gratitude and their enthusiasm. Just about the only complaint I got had to do with the scarcity of Mustangs and the long waiting list.
One of my favorite letters came from a Brooklyn man only four days after the car was launched. "I'm not much on cars," he wrote, "and I haven't been since most cars got pregnant. Furthermore, New York is no place to have a car. Pet owners urge their dogs to urinate on the wheels. Slum kids steal the hubcaps. Cops give parking tickets. Pigeons roost on the car, and worse. Streets are always torn up. Buses crush you, taxis bump you, and inside parking requires a second mortgage on the house. Gas costs 30 percent more than anyplace else. The insurance rates are incredible. The garment district is impassable, the Wall Street area impenetrable, going to New Jersey impossible."
And here's his final line: "So as soon as I can raise the nut, I'm buying a Mustang."
When we surveyed the ranks of Mustang owners, we found that their average age was thirty-one, but that one in every six owners was in the forty-five-to-fifty-four group, which meant that the car wasn't limited to young people. Almost two thirds of the buyers were married, and more than half of them had been to college.
Before the first year was over, there were Mustang clubs—hundreds of them—as well as Mustang sunglasses, key chains, and hats, along with toy Mustangs for kids. I knew we had it made when somebody spotted a sign in a bakery window that read: "Our hotcakes are selling like Mustangs."
I could easily devote the rest of this book to Mustang stories, but I'll add just one more.
During one of my fifty-two round trips to Europe, I was asleep on the company plane one Sunday morning over the iceberg route—where the _Titanic_ sank. Beneath us was a weather ship with one poor, godforsaken soul giving weather reports to airplanes. When our guys went over the ship, they radioed down: "How're things?"
"I can't stand up," the weatherman answered. "It's such a rough day, the swells are twelve feet high."
They kibitzed about it, and then the guy found out who we were. "I got a Mustang," he said immediately. "You got Iacocca on board?"
While they were crackling this out, a KLM plane crossed our path and their pilot said: "Hold it. Is that the Ford plane with Iacocca? I'd like to talk to him."
Just then a Pan Am plane flew by and _their_ guy jumped in.
This all happened while I was asleep. Our pilot comes in and says to me: "You're wanted on the phone. We've got a ship and two airplanes all wanting to talk to you at the same time."
I said: "Is nothing sacred? It's Sunday morning, I'm in the middle of nowhere, and I can't get away from this Mustang mania!"
I'm generally seen as the father of the Mustang, although, as with any success, there were plenty of people willing to take the credit. A stranger asking around Dearborn for people who were connected with the Edsel would be like old Diogenes with his lantern searching for an honest man. On the other hand, so many people have claimed to be the father of the Mustang that I wouldn't want to be seen in public with the mother!
They say all good things must come to an end, and the Mustang was no exception. In 1968, at Ford's annual meeting, one of our stockholders took the floor to voice a complaint: "When the Thunderbird came out," she said, "it was a beautiful sports car. Then you blew it up to the point where it lost its identity. The same thing is happening to the Mustang. Why can't you leave a small car small? You keep blowing them up and then starting another little one, blowing that one up and starting another one."
Unfortunately, she was right. Within a few years of its introduction, the Mustang was no longer a sleek horse. It was more like a fat pig. In 1968, Bunkie Knudsen came in as the new president of Ford. Right away he added a monster of an engine with double the horsepower to the Mustang. To support the engine, he had to widen the entire car. By 1971, the Mustang had grown eight inches longer, six inches wider, and almost six hundred pounds heavier than the original 1965 model.
It was no longer the same car, and our declining sales figures were making the point very clearly. In 1966, we sold 550,000 Mustangs. By 1970, sales had plummeted to 150,000—a disastrous decline. Our customers had abandoned us because we had abandoned their car. Instead of the original $2,368, the Mustang was now closer to $3,368, and not all of that rise could be blamed on inflation.
Late in 1969 we began planning the Mustang II, a return to the small car that had been so successful. A lot of people in Detroit could hardly believe we were doing this, because it violated an unwritten rule that an established car could only be made bigger—never smaller. To put out a smaller Mustang was tantamount to admitting we had made a mistake.
Of course we had. To plan Mustang II, I turned once more to Hal Sperlich, who had played a major role in creating the original Mustang. Hal and I flew over to Italy to visit the Ghia studios in Turin, where we met with Alejandro deTomaso, the studio head. Within two months, deTomaso's prototype arrived in Dearborn, and we had ourselves a terrific design.
Mustang II was very successful, although it wasn't quite the hit that the original had been. But then, as we knew only too well, that was a tough act to follow.
# VII
# ENCORE!
The success of the Mustang was apparent so quickly that even before its first birthday I was given a major promotion. In January 1965, I became vice-president of the corporate car and truck group. I was now in charge of the planning, production, and marketing of all cars and trucks in both the Ford and Lincoln-Mercury Divisions.
My new office was in the Glass House, which is how everybody at Ford referred to World Headquarters. I was finally one of the big boys, part of that select group of officers who ate lunch every day with Henry Ford. Until now, as far as I was concerned, Henry had simply been the top boss. Suddenly I was seeing him almost every day. Not only was I part of the rarefied atmosphere of top management, but I was also the new kid on the block, the young comer who was responsible for the Mustang.
Moreover, I was His Majesty's special protégé. After McNamara left in 1960 to join the Kennedy administration, Henry had more or less adopted me, and he kept a close eye on what I was up to from the start.
As a group vice-president, I had a number of new assignments and responsibilities, especially in the area of advertising and promotion. But my chief mandate, as Henry made clear, was to "rub some of that Mustang ointment onto the Lincoln-Mercury Division."
For years, Lincoln-Mercury had been the weak sister of the Ford family and a burden to the rest of the company. The division had been started in the 1940s, but twenty years later it still hadn't come into its own. There had even been talk of dropping the Lincoln and selling off that part of the company.
This was the division that featured high-priced, upscale cars. The company's hope and expectation had been that the customer who had purchased a Ford Division product would eventually "graduate" to a Mercury or a Lincoln, much as a General Motors customer might trade up from a Chevrolet or Pontiac to a Buick or Oldsmobile.
So much for theory. In practice, most Ford owners ended up jumping ship. Those who could afford to trade up were more likely to graduate to a Buick, Oldsmobile, or Cadillac rather than a Mercury or Lincoln. All we were doing was growing future customers for GM's luxury cars.
When I took a good look around the Lincoln-Mercury Division, I understood why. The cars simply weren't exciting. It's not that they weren't _good;_ they just weren't distinctive. The Comet, for example, was really only a fancy Falcon, while the Mercury resembled an oversized Ford. What Lincoln-Mercury cars were lacking was their own unique style and identity.
Over the years, sales had languished. The Lincoln was supposed to be competing with Cadillac, but it was consistently outsold by Cadillac by something like five to one. The Mercury suffered a similar fate and was unable to mount much of an assault on GM's duo of Buick and Oldsmobile. Now, in 1965, the Lincoln-Mercury Division was virtually dead and in urgent need of a resurrection.
It would have been easy enough to blame the dealers, but that would have been grossly unfair. In fact, those dealers who were able to survive until 1965 _had_ to be good, because they didn't have the benefit of a first-rate product. Still, they suffered from low morale. They needed motivation. They needed a new team of district sales managers. And they needed somebody in the Glass House who could really look after their interests.
But most of all, they needed new products. We got right to work, and by 1967 we were ready with two new entries. The Mercury Cougar was a luxury sports car designed to appeal to the Mustang driver who was ready for something a little plusher. The Mercury Marquis was a full-sized luxury car to compete with Buick and Oldsmobile.
It was symptomatic of our problems that Gar Laux, the head of the Lincoln-Mercury Division, didn't even want the Marquis to carry the Mercury name. As far as he was concerned, the Mercury name was the kiss of death, so bad that it would drag down even a great car. I had to convince him that by starting with the new Marquis, we were going to upgrade Lincoln-Mercury's image.
To create a sense of excitement about these two new cars, it was important to unveil them to the dealers in the most dramatic way. Until around ten years ago, the annual introduction of new-car models from Detroit was a major event for both the dealers and the general public. As introduction day approached, the dealers would keep their new cars under wraps. All across the land, kids would peek into the windows in the hope of getting an early glimpse of the new Fords or Chevys. Today that ritual is just a fond memory.
Also long gone are the big dealer shows, which we used to arrange each year in Las Vegas. Every summer we would wine them and dine them and spend millions on a spectacular show where we would introduce the new models. There would be cars coming out of fountains, girls jumping out of cars, lots of smoke bombs and strobe lights, and all sorts of dazzling displays. These shows were sometimes better than Broadway, but here the cars were the stars.
We also used to run dealer incentive programs. Back then, the Big Three were rolling in big bucks. Everything we did was first class. When it came to impressing the dealers, the sky was the limit. Many of them were making $1 million a year, and even the guys who weren't so good were doing well.
During the 1960s, we used to run a lot of trips as incentives and bonuses for the dealers. No matter how wealthy they were, there was something about a well-planned trip to an exotic spot that was very difficult to pass up. These trips were always a big hit, and many of the dealers became very friendly with each other, which raised their morale even higher and gave them a heightened sense of purpose and belonging.
Sometimes I used to go along as an official host. For me, the trips were a perfect opportunity to touch base with a lot of dealers over a short time. They were also an ideal way of combining work with a good time, and Mary and I always had fun.
In September 1966, Lincoln-Mercury scheduled a spectacular cruise for those dealers who had reached a certain sales quota. We leased the S. S. _Independence_ at a cost of $44,000 a day and set sail from New York for the Caribbean, where we planned to show our new models. At sunset on the second day, we assembled all the dealers at the stern of the ship. At a predetermined moment we released hundreds of helium balloons, which floated skyward to reveal the 1967 Mercury Marquis. Together with Matt McLaughlin, who had become head of the division, I introduced the car and described its features.
Two nights later, on the island of St. Thomas, we unveiled the new Cougar. At a beach lit by clusters of brilliant torches, a World War II landing craft pulled up to the shore and lowered its ramp. The audience was breathless as a shining white Cougar drove onto the sand. The door opened, and out stepped singer Vic Damone, who began to entertain. I've seen some pretty fancy dealer introductions in my time, but this one really took the cake.
The dealers hadn't had anything to get excited about in years. They went nuts over the Cougar. Like the Mustang, it had a sporty look, with a long hood and a short deck. As the dealers expected, it was an immediate success and soon became the most visible part of the Lincoln-Mercury Division. Today a 1967 Cougar in good condition is a collector's item.
A lot of the credit for these spectacular introductions has to go to Frank Zimmerman, our resident promotion genius. Zimmie, who is now retired in South Carolina, is an unforgettable character—thin as a reed, endlessly energetic, and very funny.
Working with Zimmie was a joy, but it presented its own special challenge because he used to have a new idea every five minutes. About 10 percent of his ideas were splendid, but some of the rest bordered on the absurd.
To promote the Cougar, for example, Zimmie wanted to have a trained bear drive the car from New York to California. According to one scenario, a trainer would sit in front beside him. Another plan called for a midget to crouch under the dash and do the driving using special equipment. The way Zimmie described it, the car would make dozens of stops each day as the public crowded around and the press took pictures. "Think of the headlines," said Zimmie. "Bear Drives Cougar Coast to Coast!"
I love bold ideas, but this one was a little wild even for me. Some years later, Henry Ford received a letter from a guy who claimed to have trained his horse to drive a Lincoln Continental. The horse even blew the horn by pressing on it with its nose! Henry passed the letter on to me, and I gave it to Zimmie. That was the last I heard of it, which is probably just as well.
We did use a live animal to promote the Cougar. At the suggestion of Kenyon & Eckhardt, the advertising agency for Lincoln-Mercury, we tried the obvious—a real cougar. The agency's New York office was charged with the awesome responsibility of finding a trained cougar and filming it on top of a Lincoln-Mercury sign. This was no easy task, but within about a month we had a few precious seconds of film depicting a growling cougar on top of the logo. The Ford Division had been successful with a wild horse. Now Lincoln-Mercury would see what a wild cat could do.
The cougar turned out to be such an effective symbol that the ad agency recommended we use "the sign of the cat" to represent the entire division. We did, and it became a vital step in creating a new identity for Lincoln-Mercury. Before long, the picture of the cougar perched on top of the sign became almost as widely known as Ford's oval and Chrysler's pentastar.
Whenever you're trying to promote a brand name, your first task is to make clear where the brand is available. That's why the McDonald's arch is so effective. Even a little kid knows that's where you go to get a hamburger. Before the cougar went up on the signs, most people had never heard of Lincoln-Mercury. Today almost everybody knows what it is.
Meanwhile, Zimmie was continuing to come up with promotion ideas. At one point he scouted the country for people with the same names as famous explorers, like Christopher Columbus or Admiral Byrd. When he tracked them down, he hired them to appear in our ads, which would claim, for example, that "Christopher Columbus has just discovered the new Mercury."
Kenyon & Eckhardt did a great job in advertising the Cougar. With the Marquis, we all decided the strong selling point was the smoothness of its ride. The Marquis had achieved a new level in ride engineering, and the result was the softest, plushest ride in the world.
But how could we get this across to the public? Our engineers had told the advertising people that the ride of the Marquis was better than the competition's more expensive cars. The agency's response was: "Prove it!" So the engineers invited a group from the agency to our test track, blindfolded them, and then drove them around in Oldsmobiles, Buicks, Cadillacs, and Marquis. All but one guy voted for the Marquis as the best ride of them all.
Eventually the blindfold test found its way into the advertising campaign. Kenyon & Eckhardt made several commercials where blindfolded consumers, and in one case chauffeurs, were asked to rate the cars on smoothness and quiet.
Before long, the agency came up with other commercials that made the point equally well. In one ad, a container of dangerous acid was suspended over an expensive fur coat. In another, a record was playing on a phonograph that was sitting on the front seat. In a third, Bart Starr, the football player, was being shaved by a barber. Then there was the one that showed a container of nitroglycerin on the back seat. To show that it was real, at the end of the commercial we blew up the car!
In the most famous commercial of all, the agency filmed a Dutch diamond cutter busy at his craft while the car twisted its way down some pretty bumpy roads. Those too young to remember that ad might have seen a classic parody of it that appeared a few years later on _Saturday Night Live._ In this version, the diamond cutter was replaced by a rabbi about to perform a ritual circumcision on an infant while being driven in the rain over bad country roads. Believe me, the suspense in the diamond-cutter ad was nothing compared to the tension in this one.
With the Marquis and the Cougar in place, the Mercury line was now in pretty good shape. But we still had nothing special at the high end. We needed a new Lincoln that would really give Cadillac a run for the money.
One night when I was in Canada for a meeting, I was lying in bed in my hotel room unable to sleep. Suddenly I had an idea. I put through a call to Gene Bordinat, our chief stylist. "I want to put a Rolls-Royce grille on the front of a Thunderbird," I told him.
At the time, we had a four-door Thunderbird that was dying in the marketplace. My plan was to create a new car using the same platform, engine, and even the roof, but to make enough changes so that the car really _looked_ new and not like a spinoff of the T-Bird.
While I was trying to imagine this new luxury car, I remembered a good precedent. Some years earlier, in the late 1930s, Edsel Ford had produced the Mark, a quiet and understated luxury car that appealed to a small, discriminating audience. In the middle 1950s, his son William Clay had built the Mark II, a derivative of the original Mark. Both of these cars were classics, the Rolls-Royce of American automobiles. They were the kind of car that most people dreamed about but only a select few could afford.
I decided it was time for us to revive the Mark line with a Mark III, based on our Thunderbird but with enough changes to make it fresh and different. The Mark III had a very long hood, a short rear deck, a powerful V-8 engine, and the same continental spare tire in the back that had been part of the original Marks. It was big, dramatic, and very distinctive. I had mixed feelings when one reporter compared it to a German staff car from World War II.
We brought out the Mark III in April 1968, and in its very first year it outsold the Cadillac Eldorado, which had been our long-range goal. For the next five years we had a field day, in part because the car had been developed on the cheap. We did the whole thing for $30 million, a bargain-basement price, because we were able to use existing parts and designs.
Our initial plan was to introduce the Mark III at Cartier's, the prestigious Fifth Avenue jeweler in Manhattan. The management of Cartier's was very interested, so Walter Murphy flew to New York to meet with them. We wanted to stress the elegance and good taste of the car by inviting the press to a midnight supper right in the store. So far, so good. But when Walter explained that we'd have to tear down a couple of walls and expand a window or two to get the car in, Cartier's had second thoughts. (They did agree to let us use their name on the Mark III's clock.)
Instead, we brought out the Mark III in several different cities. In Hollywood, we put it on a stage on the set of _Camelot_ , so people had to walk up the steps as though they were paying homage to a king. In Detroit, we unveiled the car at a dinner of American newspaper publishers. Rather than placing the car on a turntable, which was the normal way of introducing a new model, we put the _publishers_ on a turntable. As their viewpoint shifted, they saw a series of historic Lincolns and Marks. Finally the curtains opened and there was the new Mark III. The publishers were so impressed that many of them ordered one on the spot.
Before the Mark III, the Lincoln-Mercury Division was actually losing money on every luxury car. We were selling only about eighteen thousand Lincolns a year, which wasn't enough to amortize the fixed costs. In our business, these costs are enormous. Whether you produce one car or a million, you've got to have a plant and you have to develop the dies to stamp out the metal. If your volume projections are wrong and you don't hit your objective, you have to pay off these fixed expenses over a smaller number of cars. Simply stated: you lose your shirt.
The old cliché is certainly true: bigger cars do mean bigger profits. We made as much from selling one Mark as we did from ten Falcons. Our profit worked out to an astonishing $2,000 per car. Moreover, the money started coming in so quickly we could barely keep track of it. In our best year, we made almost $1 billion from the Lincoln Division alone, which is as big a success as I've ever had in my career.
We followed with the Mark IV in 1971. Ford is still making the series—they're currently up to the Mark VII. The Mark is Ford's biggest moneymaker, just as Cadillac is for General Motors. It's the Alfred Sloan theory: you have to have something for everybody. To hedge your bets, you always need a poor man's car—that's all the first Henry Ford ever envisioned—but then you need upscale cars, too, because you never know when the blue-collar guy is going to be laid off. It seems that in the United States the one thing you can count on is that even during a depression, the rich get richer. So you always have to have some goodies for them.
# VIII
# THE ROAD TO THE TOP
By 1968, I was the odds-on favorite to become the next president of the Ford Motor Company. The Mustang had shown I was someone to watch. The Mark III made it clear I was no flash in the pan. I was forty-four, Henry Ford had taken me under his wing, and my future never looked better.
But just as it seemed that nothing could stop me, fate intervened. General Motors presented Henry with an opportunity he couldn't resist.
In those days, GM had a highly regarded executive vice-president named Semon Knudsen, known to the world as "Bunkie." Knudsen was an MIT graduate in engineering who had been made head of the Pontiac Division at the age of forty-four. This made him the youngest division head in GM's history—the kind of distinction that definitely gets noticed in Detroit.
One reason for Knudsen's notability was that his father had once been president of GM. Many people expected Bunkie to follow in the elder Knudsen's footsteps. But when, despite Bunkie's strong reputation as a product man, GM chose Ed Cole as its next president, Bunkie soon understood that he had reached the end of his career at GM.
As Avis watches Hertz, as Macy's watches Gimbel's, we at Ford always kept a close eye on General Motors. Henry in particular was a great GM watcher and admirer. For him, the sudden availability of Bunkie Knudsen was a gift from heaven. Perhaps Henry believed that Knudsen had all of that famous GM wisdom locked in his genes. In any event, he wasted no time in making his approach. When Henry heard that Bunkie was thinking of resigning, he called him immediately.
Henry couldn't very well ask Bunkie to come to the office, because there are no secrets in the Glass House. Within half an hour, the press would have known all about the visit. And he ruled out inviting Bunkie home when he realized his Grosse Pointe neighbors might notice. But Henry loved intrigue, so he rented an Oldsmobile from Hertz, put on a raincoat, and in his best 007 style, he drove over to Bunkie's house in Bloomfield Hills.
A week later, they had a deal. Knudsen would take over immediately as president at an annual salary of $600,000—the same as Henry's.
To make room for Knudsen, Henry had to get rid of Arjay Miller, who had been our president for the past five years. Miller was abruptly kicked upstairs to become the vice-chairman, a new position created especially for the occasion, A year later, he resigned and went on to become dean of the Business School at Stanford University.
Bunkie was hired during the early winter of 1968, while I was away on a skiing vacation with my family. In the middle of the trip, I got a call from Henry's office asking me to come in the next day. The company even sent a DC-3 to bring me back.
On the day after my return, I went in to see the boss. Henry knew I would be upset that he was bringing in Bunkie as president, and he wanted to explain his reasons. He was sure that the addition of a high-level GM man to our team at Ford would make a big difference in the next few years. And he took pains to assure me that Bunkie's arrival did not mean my career was over. On the contrary. "Look," he told me, "you're still my boy. But you're young. There are things you have to learn."
As Henry saw it, Bunkie would be bringing in a wealth of information about the GM system. I was twelve years younger than Knudsen, he reminded me, asking me to be patient. He made it clear he didn't want to lose me. And he strongly implied that my patience now would be amply rewarded in the future.
A few days later, I got a call from Sidney Weinberg, one of our senior board members and a legendary Wall Street wizard. He had been Henry's mentor for years, but he was also a big fan of mine. He always called me "Lehigh."
Over lunch in his New York apartment, Weinberg told me that he assumed I was angry about Knudsen's arrival. But he advised me to sit tight. Sidney had heard the same rumors I had: that GM was secretly delighted to be rid of Knudsen. Weinberg had gotten the word straight from a top executive at GM, who said: "You solved one helluva problem for us. We didn't know what to do with Knudsen until good old Henry picked him up. We couldn't be more grateful."
"If Bunkie's as bad as they say," Sidney told me, "your turn will come soon enough."
I wasn't so sure. In those days I was in a mad rush to the top. Despite Henry's reassurances, Bunkie's arrival was a big blow to me. I wanted the presidency badly, and I didn't agree I had much left to learn. As I saw it, I had been exposed to every test the company had to offer. And I had passed each one with flying colors.
For a few weeks I seriously considered resigning. There had been an attractive offer from Herb Siegel, a Lehigh graduate who was head of ChrisCraft. Herb wanted to expand ChrisCraft into a small conglomerate in the leisure business. He liked me and respected what I had accomplished at Ford.
"Look," said Herb, "if you stay here, you're always going to be at the mercy of Henry Ford, and if he was dumb enough to pass you over for president, he'll probably zap you again."
I was tempted. I even went so far as to look for houses in New York and Connecticut. Mary, too, liked the idea of going back East. "If nothing else, we can get fresh seafood again," she said with a twinkle in her eye.
In the end, I decided to stay at Ford. I loved the car business and I loved the Ford Motor Company. I really couldn't imagine being anywhere else. With Henry on my side, the future still looked bright. I was also counting on the prospect that Bunkie would not work out as president and that my turn would come sooner rather than later.
In Detroit, Knudsen's move from GM to Ford was the talk of the town. In our industry, jumping ship and going to work for a competitor has always been pretty rare. It was almost unheard of at GM, which even by Detroit standards had a reputation for being inbred.
What made the story even more appealing was that Bunkie wasn't the first Knudsen to work for the Ford Motor Company. More than half a century earlier, William Knudsen, Bunkie's father, had worked for Henry's grandfather. The elder Knudsen had supervised the establishment of fourteen Model T plants in two years, including the famous River Rouge plant. After World War I, he was sent over to Europe, where he was instrumental in developing Ford's operations overseas.
After rising to the top ranks of the company, the senior Knudsen ran into problems with the senior Ford, who fired him in 1921. When Knudsen left Ford, he was making $50,000 a year, a huge salary in those days. A year later, he signed on with General Motors.
And now the Knudsen-Ford relationship had come full circle. Detroit loved the drama of the Knudsen hiring, and the press had a field day with Bunkie's appointment. It made for a great story: Henry Ford, the grandson of the man who had fired William Knudsen, was now bringing back Knudsen's son as _his_ president.
When Bunkie's appointment was first announced, many of us in top positions at Ford were resentful that a GM man was going to be our boss. I was especially concerned, as there were rumors that Knudsen was going to bring in John Z. DeLorean to put me in my place. (In those days, DeLorean was a creative young maverick at GM who had worked with Bunkie in the Pontiac Division.)
My colleagues and I were pretty sure that the GM system of management wouldn't work very well at Ford. But as Henry saw it, the mere presence of Bunkie Knudsen in the Glass House would cause some of GM's great success to rub off on us.
It never happened. Ford had its own way of doing things. We liked to move quickly, and Bunkie seemed to have trouble keeping up. Besides, administration was not his strong point. It soon became clear to me that GM probably had a good reason for passing him over as president.
Knudsen was always suspicious of me. He assumed that I had been after the presidency before he came and that I was still gunning for it after he arrived. He was right on both counts. Fortunately, we were both too busy to spend much time on office politics. But we did have our share of disagreements, especially about the styling of new models.
As soon as Knudsen arrived at Ford, he began adding weight to the Mustang and making it bigger. He was a racing nut, but he failed to understand that the heyday of racing had already passed. Knudsen also took it upon himself to redesign our Thunderbird so that it would look like a Pontiac, which was a complete disaster.
As a leader, Bunkie Knudsen had little impact on the company. Among other things, he failed to bring over any of his top people from GM to help him put his plans into operation. Nobody at Ford felt much loyalty to Knudsen, so he was without a power base. As a result, he found himself alone in an alien atmosphere, never really accepted. A decade later, when I went to Chrysler, I made sure not to repeat that mistake.
The press has often reported that I led a revolt against Knudsen. But his failing had little to do with me. Bunkie Knudsen tried to run Ford without using the system. He ignored the existing lines of authority and alienated me and a lot of other top people by making policy in areas that were ours to decide.
From the very start, Ford and GM have been completely different companies. GM has always been clubby and genteel, with dozens of committees and multiple levels of management. Ford, by contrast, has a more competitive environment. We always made decisions more quickly, with less staff review and more of an entrepreneurial spirit. In the slow, well-ordered world of GM, Bunkie Knudsen had flourished. At Ford, he was a fish out of water.
Knudsen lasted only nineteen months. Henry Ford had achieved a great publicity coup by hiring a top GM man, but he soon learned that success in one car company does not always guarantee success in another.
I wish I could say that Bunkie got fired because he ruined the Mustang or because his ideas were all wrong. But the actual reason for the firing was nothing like that. Bunkie Knudsen was fired because he used to walk into Henry's office without knocking. That's right—without knocking!
Ed O'Leary, one of Henry's aides, used to say: "That drives Henry nuts! The door opens, and there's Bunkie just standing there."
Of course, this minor transgression was merely the last straw in a relationship that had never been very good to begin with. Henry was a king who could tolerate no equals, a point Bunkie never seemed to grasp. He tried to get palsy-walsy with Henry, and that was a big mistake. The one thing you could never do at Ford was to get too close to the throne. "Give Henry a wide berth," Beacham had advised me years earlier. "Remember, he has blue blood. Yours is only red."
The way that Henry Ford fired Bunkie Knudsen makes for a good story. It also reveals a great deal about Henry. On Monday evening of the Labor Day weekend, he sent Ted Mecke, his vice-president of public relations, to Bunkie's house. Mecke's assignment; to let Knudsen know he was about to be fired.
But Mecke couldn't bring himself to spill the beans. All he could say was: "Henry sent me here to tell you that tomorrow will be a rough day at work."
"Wait a minute," said Florence Knudsen, a very strong-willed lady. "What is it you're really here for? Who sent you and what's your message? Did you come to fire my husband?" She guessed the truth instantly, and Mecke had no choice but to confirm it.
The next morning Henry came running down the hall. He was looking for an ally, and he knew that I'd be pleased to see Knudsen go. But Henry still hadn't told Bunkie he was fired.
Finally Mecke said to Bunkie: "I guess you're supposed to see Mr. Ford."
When Bunkie went in to Henry's office, Henry asked him: "Did Mecke talk to you?"
"Now, what the hell's going on here?" demanded Bunkie. "Are you firing me?"
Henry nodded. "Things just didn't work out," he said. That land of vague statement was vintage Henry.
A few minutes later, Henry came into my office again. "Bunkie's calling a press conference," he said.
"What happened?" I asked. By this time I had a pretty good idea, but I wanted to hear it from the horse's mouth.
Henry tried to tell me that he had just fired Bunkie. But as I stood there looking at him, he couldn't seem to get the words out. Finally he said: "Bunkie doesn't understand. We've got problems here."
It was Keystone Kops time. The next thing I knew, Bunkie was in my office, saying: "I think I've been fired, but I'm not sure."
As soon as Knudsen left, Henry came back in, asking: "What did he tell you?"
A few minutes later, Henry returned again. "What are we going to do?" he said. "Bunkie's going to hold his press conference right here!"
"Well," I replied, "if he's been canned, he's got to say something."
"Sure he's been canned," said Henry. "But I think he should have his press conference at a hotel, not right here in the building."
I had mixed feelings about the whole episode. On the one hand, I was delighted that Bunkie was out. At the same time, I felt real compassion for him. I didn't want anybody's term as president of the company to end like _this._
But Henry Ford could never bring himself to fire anybody directly. He always had a hatchetman do the dirty work for him.
I couldn't help but wonder: is this what lay in store for me? I spent that evening talking with Mary. "Why don't you pack it in?" she said. Once again I was tempted. And once again I decided to stay on.
The day Bunkie was fired there was great rejoicing and much drinking of champagne. Over in public relations, one of our people coined a phrase that soon became famous throughout the company: "Henry Ford [the first] once said that history is bunk. But today, Bunkie is history."
Even with Bunkie gone, Henry was still not ready to offer me the job. Instead, he set up a three-man office of the president. I was in charge of Ford's North American operations, which made me first among equals. Robert Stevenson was head of Ford International, and Robert Hampson led nonautomotive operations.
Fortunately, the troika didn't last very long. The following year, on December 10, 1970, I finally got what I was waiting for: the presidency of Ford.
A few days before he made the announcement, Henry came into my office to tell me what he had in mind. I remember thinking: "This is the greatest Christmas present I've ever had!" We just sat there for a moment or two, he with a cigarette and me with a cigar, and blew smoke at each other.
The moment Henry walked out the door I called my wife. Then I called my father in Allentown to tell him the good news. During his long and active life my father had a lot of happy moments, but I'm sure my phone call that day ranks near the top.
When I became president, the Ford Motor Company had approximately 432,000 employees. Our total payroll came to more than $3.5 billion. In North America alone, we were building close to 2.5 million cars a year and 750,000 trucks. Overseas, the combined total came to another 1.5 million vehicles. Our total sales for 1970 added up to $14.9 billion, on which we made a profit of $515 million.
Now, while $515 million was certainly nothing to sneeze at, it represented only 3.5 percent of total sales. In the early 1960s, our return on sales had never dipped below 5 percent. I was determined to get it back up.
As everyone knows, there are only two ways to make more money: you can sell more goods or spend less on overhead. I was satisfied with our sales—at least for the moment. But the closer I looked at our operations, the more I was convinced we could do a lot more to reduce our expenses.
One of the first moves I made as president was to convene a meeting of top managers to establish a cost-cutting program. I called it "four fifties," as its purpose was to cut operating expenses by $50 million in each of four areas—timing foul-ups, product complexity, design costs, and outmoded ways of doing business. If we could reach our goal within three years, we could improve our profits by $200 million—a gain of almost 40 percent—even before selling a single additional car.
There was plenty of room for improvement. For example, it took us two weeks out of each year to prepare our factories for the production of the next year's models. During that time the factories were simply not operating, which meant that both the machinery and the workers were idle.
Through more vigorous computer programing and more sophisticated scheduling, it was possible to reduce the changeover period from two weeks to two days. Of course that kind of change doesn't take place overnight. But by 1974, we had reached the point where our plants were converted during the course of a single weekend—when production lines were down anyway.
Another area where we cut costs was shipping. Freight came to only a small percentage of our total expenses, but at over $500 million a year, it was still a figure worth a second look. This wasn't something I had ever thought about before. But when I checked into it, I found that the railroads were really taking us for a ride. They were charging us by volume rather than weight, and we weren't planning accordingly.
We began packing the freight cars much more tightly. At one point, I recall, we trimmed a fender design by two inches to allow a few more cars to fit onto each train. With huge sums of money at stake, the last thing I wanted was to be shipping air. When you're dealing with figures like $500 million for freight, even a minuscule saving of half of one percent came to $2.5 million.
I also instituted a program called Shuck the Losers. In a company as large as ours, there were dozens of operations that either lost money or made only minimal profits. I've always believed that every operation in a car company could be measured in terms of its profitability. Each plant manager knew—or should have known—whether his operation was making money for the company, or whether the parts he was building cost more than they could be purchased for on the outside.
And so I announced that managers had three years to either make their departments profitable or sell them off. It was simple common sense, like a large department store whose manager says: "We're losing a ton of money in that boutique over there, so let's close it."
Many of our biggest losers were part of Philco-Ford, the appliance and electronics firm we had bought in 1961. Philco was a terrible mistake, and it lost millions of dollars a year for ten years before finally starting to turn a profit. Many in top management had argued against buying it, but Henry had insisted. And at Ford, what Henry wanted, Henry got.
We ended up dropping close to twenty major losers in the early 1970s. One of them was an operation that made laundry equipment. To this day, I don't know what on earth we were doing in laundry equipment. But somehow it had taken us ten years to bite the bullet on that one, which had never earned us a dime.
These programs to reduce expenses and cut losses represented a new area for me. Until now I had concentrated on selling, marketing, and design. But as president my first concern was the relatively unglamorous task of searching out hundreds of different ways to cut costs and increase profits. As a result, I was finally earning the respect of the one group that had always been suspicious of me—the bean counters.
I now had so many diverse responsibilities that I had to learn a different style of operating. I didn't like to admit it, but I no longer had the stamina of the Mustang years, when I thought nothing of grabbing a hamburger for dinner and staying at the office until midnight.
The Ford Motor Company had close to half a million employees around the world, and I had to keep in mind that I was only one of them. Sometimes this meant that I wouldn't be able to return a phone call for a couple of weeks. But I decided it was more important to preserve my mental health than to give everybody curb service.
Instead of driving home a different car every night to become more familiar with our various products, I now had a driver. I used the commuting time to read and answer my mail. But I continued to follow my old weekly routine. Unless I was out of town, my weekends were devoted to the family. I wouldn't open my briefcase until Sunday night. At that point I would sit in my library at home, do the serious company reading, and plan out the week ahead. By Monday morning I was ready to hit the ground running. I expected no less of the people who worked for me: I've always found that the speed of the boss is the speed of the team.
During my years as president of Ford, I was constantly meeting people who would tell me: "I wouldn't want your job for all the money in the world." I never knew how to respond to that kind of remark. I loved my job, even though many people viewed it as the kind of position that grinds you up and kills you off. But I never saw it that way. To me, it was sheer excitement.
Actually, after reaching the presidency I experienced a certain letdown. I had spent years climbing the mountain. When I finally made it to the top, I started to wonder why I had been in such a hurry to get there. I was only in my mid-forties, and I had no idea what I would do for an encore.
I certainly enjoyed the prestige and the power of my position. But being a public figure was definitely a mixed blessing. This was brought home to me very dramatically one Friday morning as I was riding to work. The radio was on and I was half listening when suddenly the announcer interrupted the regular program with a special bulletin. Apparently a group of the nation's top business leaders, myself included, had been marked for assassination by the Manson "family."
This cheerful news had come from Sandra Good, roommate of "Squeaky" Fromme, the young lady who had been arrested for trying to kill President Ford in Sacramento. If you ever want a quick waker-upper in the morning, all you've got to hear is that you've made somebody's hit list!
But I don't want to complain too much about one of the best jobs in the world. If Henry was king, I was the crown prince. And there was no question that the king liked me. Once he and his wife, Cristina, came to our house for dinner. My parents were there, too, and Henry spent half the night telling them how great I was and that without me there wouldn't be a Ford Motor Company. On another occasion, he took me to meet his good friend L.B.J. Henry really thought of me as his protégé, and he treated me that way.
Those were the days of wine and roses. All of us who constituted top management in the Glass House lived the good life in the royal court. We were part of something beyond first class—royal class, perhaps, where we had the best of everything. White-coated waiters were on call throughout the day, and we all ate lunch together in the executive dining room.
Now, this was no ordinary cafeteria. It was closer to being one of the country's finest restaurants. Dover sole was flown over from England on a daily basis. We enjoyed the finest fruits, no matter what the season. Fancy chocolates, exotic flowers—you name it, we had it. And everything was served up by those professional waiters in their white coats.
At first we paid all of $2.00 each for those lunches. The price had started at $1.50, but inflation hiked it to $2.00. When Arjay Miller was still vice-president in charge of finance, he complained about the cost. "We really shouldn't have to pay for these lunches," he said one day. "Feeding employees is deductible for the company. A lot of companies feed their people without charging them at all. But if we pay for it ourselves, it's after-tax money." We were all in the 90 percent bracket, so every time we spent $2.00 we had to earn $20.
At that point a few of us got into a discussion of how much those lunches really did cost the company. In typical Ford style, we ran a study to determine the real expense of serving lunch in the executive dining room. It came out to $104 dollars a head—and this was twenty years ago!
You could order anything you wanted in that room, from oysters Rockefeller to roast pheasant. But Henry's standard meal was a hamburger. He rarely ate anything else. One day at lunch he turned to me and complained that his personal chef at home, who was earning something like $30,000 or $40,000 a year, couldn't even make a decent hamburger. Furthermore, no restaurant he had ever been to could make a hamburger the way he liked it—the way it was prepared for him in the executive dining room.
I like to cook, so I was fascinated by Henry's complaint. I went into the kitchen to speak to Joe Bernardi, our Swiss-Italian chef. "Joe," I said, "Henry really likes the way you make hamburgers. Could you show me how?"
"Sure," said Joe. "But you have to be a great chef to do it right, so watch me very carefully."
He went over to the fridge, took out an inch-thick New York strip steak, and dropped it into the grinder. Out came the ground meat, which Joe fashioned into a hamburger patty. Then he slapped it onto the grill.
"Any questions?" he asked.
Then he looked at me with a half smile and said: "Amazing what you can cook up when you start with a five-dollar hunk of meat!"
# IX
# TROUBLE IN PARADISE
Until I became president, Henry Ford had always been a pretty remote figure. But now my office was right next to his in the Glass House, and we saw quite a lot of each other, although only in meetings. The better I got to know Henry Ford, the more I worried about the company's future—and my own.
The Glass House was a palace, and Henry reigned supreme. Whenever he entered the building, the word would go out: _The king has arrived_. Executives would linger in the halls, hoping to run into him. If they were lucky, Mr. Ford might notice them and say hello. At times he might even deign to speak to them.
Each time Henry walked into a meeting, the atmosphere changed abruptly. He held the power of life and death over all of us. He could suddenly say "off with his head"—and he often did. Without a fair hearing, one more promising career at Ford would bite the dust.
It was the superficial things that counted for Henry. He was a sucker for appearances. If a guy wore the right clothes and used the right buzz words, Henry was impressed. But without the right veneer, forget it.
One day Henry ordered me to fire a certain executive who was, in his judgment, "a fag."
"Don't be silly," I said. "The guy's a good pal of mine. He's married and has a kid. We have dinner together."
"Get rid of him," Henry repeated. "He's a fag."
"What are you talking about?" I said.
"Look at him. His pants are too tight."
"Henry," I said calmly, "what the hell do the guy's pants have to do with anything?"
"He's queer," said Henry. "He's got an effeminate bearing. Get rid of him."
In the end, I had to demote a good friend. I moved him out of the Glass House and into the boondocks, hating every minute of it. But the only alternative was to fire him.
This arbitrary use of power wasn't merely a character flaw. It was something Henry actually _believed_ in.
Early in my presidency, Henry told me his management philosophy. "If a guy works for you," he said, "don't let him get too comfortable. Don't let him get cozy or set in his ways. Always do the opposite of what he expects. Keep your people anxious and off-balance."
Now, one might wonder why on earth the chairman of the Ford Motor Company, one of the most powerful men in the world, would behave like a spoiled brat? What made him so insecure?
Perhaps the answer is that Henry Ford never had to work for anything in his life. Maybe that's the bane of rich kids who inherit their money. They go through life tripping through the tulips, wondering what they would have become without Daddy. Poor people complain that nobody gave them a break, but the rich guy never knows if he's accomplished anything on his own. Nobody ever tells him the truth. They only tell him what he wants to hear.
It seemed to me that Henry Ford II, grandson of the founder of the Ford Motor Company, had spent his whole life worrying that he would screw things up.
Maybe that's why he seemed to feel so threatened. And why he was always on the lookout for palace revolts. He'd see two guys talking together in the hall, and right away—they must be planning a conspiracy!
I don't want to play psychiatrist here, but I had a theory about where his fears came from. When Henry was young, his grandfather was fanatically frightened of kidnappers. Those kids grew up with locked gates and bodyguards, wary of everyone who wasn't part of their immediate family.
So Henry got a little paranoid about some things. For example, he hated to put anything in writing. Although the two of us ran the company together for nearly eight years, almost nothing in my archives from those days carries his signature. Henry actually used to boast that he never kept any files. Every now and then he would burn all his papers.
"That stuff can only hurt you," he'd tell me. "Any guy who holds on to his own files is asking for trouble. Eventually the wrong person will read them and you or the company will pay the price."
He was even worse after Watergate, which had a deep effect on him. "See?" he said. "I was right—look what can happen to you!"
Once on one of his rare visits to my office, he glanced around at my various scrapbooks and files. "You're nuts," he said. "Some day you could be crucified for keeping all this stuff."
He lived by his grandfather's motto: "History is bunk." It became an obsession with him. His attitude was: destroy everything you can.
At one point during my presidency, Henry sat for a portrait by Karsh of Ottawa, the great Canadian photographer. As always, Karsh's work was superb. The photograph was so flattering that Henry sent out autographed copies to his friends and relatives.
One day Ted Mecke, Henry's aide, saw me admiring the portrait.
"What do you think of the boss's new picture?" he asked.
"It's outstanding," I replied. "By the way," I added, "I don't have any pictures of Henry. Do you think I could have one of these?"
"Sure," said Ted. "I'll get him to sign it."
A few days later Mecke told me: "Mr. Ford didn't want to sign that picture right away, so I left it with him."
The next time I went in to see Henry, I noticed one of the prints on his desk. "That's a great picture," I said.
"Thank you," he replied. "Actually, this one is for you. I just haven't gotten around to signing it yet."
He never mentioned it again, and I never received the picture. It just evaporated. For Henry, autographing that picture was too intimate a gesture—even for his own president.
Henry didn't seem to want any lasting, concrete reminders of our friendship—even though in those days we were still friends. It was as if he knew that someday he would have to turn against me, and he didn't want any evidence that we were once on good terms.
Even during those first years we had our share of disagreements. But I always took great care to exercise restraint. If I had any major problems with him, I just blocked them out. If we had any serious arguments, I made sure to air them only in private, when I thought he would give me a fair hearing.
As president I couldn't afford to waste energy on petty disputes. I had to think of the big picture. Where was the company going to be five years from now? What were the major trends we had to pay attention to?
After the Arab-Israeli war of 1973 and the subsequent oil crisis, the answers to those questions became very clear. The world had turned upside down, and we had to respond immediately. Small, fuel-efficient, front-wheel-drive cars were the wave of the future.
You didn't have to be a genius to figure this out. All you had to do was read the sales figures for 1974, a terrible year for Detroit. Sales at GM dropped by a million and a half vehicles. Sales at Ford were off by half a million. The Japanese had most of the small cars, and they were selling like crazy.
Gearing up to produce small cars in the United States was a very expensive proposition. But there are times when you have no choice but to make a big investment. General Motors was spending billions of dollars to "downsize" the entire company. Even Chrysler was investing a small fortune in fuel-efficient models.
But for Henry, small cars were a dead end. His favorite expression was "minicars, miniprofits."
Now, it's true that you can't make money on small cars—at least not in this country. And it's becoming more true every day. The margins on small cars just aren't high enough.
But that didn't mean we shouldn't be building them. Even without the prospect of a second oil shortage, we had to keep our dealers happy. If we didn't provide them with the small cars people wanted, those dealers would drop us and sign up with Honda and Toyota, where the action was.
It's a simple fact of life that you've got to take care of the low end of the market. And if there's an energy crisis to boot, that clinches the argument. For us not to be offering small, fuel-efficient cars was like owning a shoe store where you tell the customer: "Sorry, we only handle size nine and up."
Small cars became the bone in Henry's throat. But I insisted that we had to do a small, front-wheel-drive car—at least in Europe. There, gas prices were much higher and the roads were narrower. Even Henry could tell that a small car in Europe made good sense.
I sent Hal Sperlich, our top product planner, across the Atlantic. In only a thousand days, Hal and I put together a brand-new car. The Fiesta was very small, with front-wheel drive and a transverse engine. And it was fabulous. I knew we had a winner.
For twenty years, the bean counters at Ford had given us reasons why we should never build this car. Now even the top people in our European Division opposed the Fiesta. My vice-president of international operations told me that Phil Caldwell, then president of Ford of Europe, was violently against it, saying that I must be smoking pot, because the Fiesta would never sell, and even if it did, it would never make a dime.
But I knew we had to go for it. I went to Henry's office and confronted him. "Look," I told him, "our guys in Europe don't want to do this car. So you've got to back me up. I don't want any second-guessing like you did on the Edsel. If you're not with me heart and soul, let's just forget it."
Henry saw the light. He finally agreed to spend $1 billion to do the Fiesta. And it's a good thing he did. The Fiesta was a tremendous hit. Whether Henry knew it or not, it saved him in Europe and was as important to our turnaround there as the Mustang had been to the Ford Division in the 1960s.
Right away, Sperlich and I started talking about bringing the Fiesta over to America for the 1979 model year. We saw the Japanese imports on the rise. We knew GM front-wheel-drive X-cars were well on the way. Chrysler was coming out with its Omni and Horizon, and Ford had nothing to offer.
As it stood, the Fiesta was a little too small for the American market. So Hal and I decided to modify it by expanding the sides a little to add more room in the interior. We called our car the "blown Fiesta." Its code name was the Wolf.
By this time, however, a combination of Japanese trade advantages and impossibly high labor rates had made it almost impossible for an American company to build small cars on a competitive basis. It would have cost us $500 million just to build new plants for the four-cylinder engines and transmissions. And Henry wasn't willing to take the gamble.
But Sperlich and I were too hot on this project to give it up without a fight. There just had to be some way to build the Wolf and still make a profit.
On my next trip to Japan, I set up a meeting with the top management of Honda. Back then, Honda didn't really want to make cars. They preferred to stay with motorcycles. But they were already equipped to make small engines and they were eager to do business with us.
I got along wonderfully with Mr. Honda. He invited me to his house and he threw a great party, with a massive display of fireworks. Before I left Tokyo, we had worked out a deal. Honda would supply us with three hundred thousand power trains a year at a price of $711 each. It was a fantastic opportunity—$711 for a transmission and engine in a box, ready to drop into any car we wanted to make.
I was on fire when I came back from Japan. The Wolf just couldn't miss. This was going to be the next Mustang! Hal and I put together a black-and-yellow prototype that was a smash. This car would have knocked the country on its ear.
But when I told Henry about the deal with Honda, he promptly vetoed it. "No car with my name on the hood is going to have a Jap engine inside!" he said. And that was the end of a great opportunity.
Henry may not have liked the Japanese, but he was crazy about Europe. Back home, especially after Vietnam, there was less and less respect for authority. More to the point, there was less and less respect for the Ford name. But Europe was altogether different. Over there, family money still meant something. Europe still had its old class system. It was the home of the landed aristocracy, of palaces and royal families. In Europe people still cared who your grandparents were.
One night to remember, I was with Henry in Germany at a castle on the Rhine. Money was no object when it came to entertaining Henry Ford. When we pulled up, my eyes popped. There was a brass band—all these guys in lederhosen—lined up to welcome him. As Henry walked slowly across the moat and up the steps of the castle, the band followed close behind, serenading. I kept waiting for them to strike up "Hail to the Chief."
Wherever Henry went in Europe, he met with royalty. He hobnobbed with them, drank with them, and loved to hang around them. He was so crazy about Europe that he often talked of retiring there. Once at a party of jet-setters in Sardinia, he came with an American flag sewed to the seat of his pants. Even the Europeans were offended. But Henry thought it was just jolly good fun.
That's why my success with the Fiesta may have been a nail in my coffin. In America, my achievements weren't threatening. But Europe was his domain. When they started applauding me in the great halls of the Old Country, he got worried.
Henry never said so explicitly, but certain constituencies were definitely off limits. Europe was one of them. Wall Street was another.
In 1973 and early 1974, we started making a ton of money, even after the OPEC crisis. Our top management went to New York to speak to a group of a hundred key bankers and stock analysts. Henry was always opposed to these meetings. "I don't want to go touting the stock," he used to say. But _every_ public company used to hold meetings with members of the financial community. It was a routine part of business.
When Henry got up to speak at that meeting, he was well into his cups. He actually started to babble about how the company was unraveling. Ed Lundy, our top finance guy, leaned over to me and said: "Well, Lee, you better do your darnedest now. Try to save the day for us, or we'll all look like idiots."
I got up and spoke, which may have been the beginning of the end for me.
The next morning Henry called me in. "You're talking to too many people outside," he said. What he meant was it was all right for me to talk to the dealers or suppliers, but steer clear of Wall Street. Otherwise, they might think I was running the company, and that didn't sit too well with him.
That same day, similar meetings scheduled for Chicago and San Francisco were canceled. "That's it," Henry said. "We're never doing that again. No more going out to tell the world what we're up to."
Henry didn't mind if I got publicity—as long as it was tied to product. When I was featured on the cover of _The New York Times Magazine_ , he sent a cable of congratulations to my hotel in Rome. But when I got praised in his spheres of influence, he couldn't handle it.
Now, just about everybody in this world is accountable to somebody. Some people are accountable to their parents—or their children. Others are accountable to their spouses, or their bosses, or even their dogs. Still others see themselves as accountable to God.
But Henry Ford has never been accountable to anyone. In a publicly held company, the chairman is morally accountable to his employees and his stockholders. He's legally accountable to his board of directors. But Henry always seemed to get his way with them.
The Ford Motor Company had gone public in 1956, but Henry never really accepted the change. As he saw it, he was like his grandfather, the rightful owner—Henry Ford, Prop.—and the company was his to do as he pleased. When it came to the board, he, more than most CEO's, believed in the mushroom treatment—throw manure on them and keep them in the dark. That attitude, of course, was fostered by the fact that Henry and his family, with only 12 percent of the stock, held on to 40 percent of the voting rights.
His attitude toward the government was not very different from his attitude toward the company.
One day he said to me: "Do you pay any income tax?"
"Are you kidding?" I replied. "Of course!" No matter how I sliced it, I was paying 50 percent of everything I earned.
"Well," he said, "I'm getting worried. This year I'm paying eleven thousand dollars. And that's the first time in six years that I'm paying _anything_!"
I was incredulous. "Henry," I said, "how on earth do you do it?"
"My lawyers take care of it," he replied.
"Look," I said, "I'm not against using whatever loopholes the government allows us. But the guys who work in our factories are paying almost as much as you are! Don't you think you should be paying your way? What about the national defense? What about the Army and the Air Force?"
But he didn't see the point. While I have no reason to believe he was breaking the law, as far as he was concerned, the name of the game was: take the government for all you can.
In all the years we worked together, I never saw him spend a penny of his own money. Eventually a group of Ford stockholders hired Roy Cohn, the prominent New York attorney, to represent them in a suit charging that Henry had used corporate funds for all sorts of personal expenses. On trips to London, for example, when he stayed at his own house there, he still billed the company. In fact, he went out of his way to ask me what the company was paying for my suite at Claridge's—just so his charges wouldn't be out of line.
The Roy Cohn suit also charged that Henry had used company planes to fly his own furniture from Europe to Detroit, to transport his sister's dogs and cats whenever she felt her pets needed a trim or a shampoo, and to take Dom Perignon champagne and Château Lafite wine from one home to another.
I don't know if all these charges were true, but I once did carry a fireplace on the company plane from London to Grosse Pointe for him.
Henry had a real thing about airplanes. At one point the company bought from Nippon Airways a 727 jet that Henry converted into a luxury cruiser. The lawyers told Henry it was improper for him to use the plane for his vacations and his jaunts to Europe—unless he paid for the trips himself. But he'd sooner _swim_ to Europe than agree to reimburse the company out of his own pocket.
I, meanwhile, was using the 727 regularly for my business trips overseas. That plane became a thorn in Henry's side. He just hated to see me flying in it when he couldn't.
One day Henry suddenly gave an order to sell the plane to the Shah of Iran for $5 million.
The guy in charge of our fleet was shocked. "Shouldn't we at least get bids on it?" he asked.
"No," said Henry. "I want that plane out of here _today_!" The company lost a bundle on the deal.
After an internal audit, Henry had to pay back $34,000 to the company. He had been caught with his hand in the cookie jar, and not even his own auditing people would let him off the hook. Henry's only defense was to hold his wife responsible, but the fact that he admitted to _any_ wrongdoing was remarkable in itself.
Ultimately the Roy Cohn suit was settled out of court. Although the stockholders didn't get anything, Cohn collected his legal fees for the effort—some $260,000. Henry got off easy once again.
But all of this was small stuff compared to Renaissance Center.
RenCen, as it's commonly known, is a dazzling complex of office buildings, stores, and the world's tallest hotel. It was designed as an elaborate plan to save downtown Detroit, which had become increasingly bleak and dangerous as more and more businesses had moved out to the suburbs.
Henry decided he would construct this monument to himself and raise the money for it. The official Ford commitment was $6 million—from corporate funds, of course. This was soon doubled to $12 million. Eventually the company funding swelled to about $100 million. At least that was the official story. But all told, I would estimate that we probably invested another couple of hundred million dollars in RenCen—when you count the costs involved in moving hundreds of our employees downtown to try to fill those huge office towers. Naturally, only a fraction of our huge investment was ever made public.
I was plain disgusted. We should have been spending that money on keeping up with General Motors. Instead of fancy real estate, GM was putting _its_ profits into small cars. Several times, in private, I let Henry know how I felt. But he ignored me.
Henry's involvement in RenCen would have been very different if he had operated along the lines of the Carnegies, the Mellons, or the Rockefellers. These families used a lot of their own money for the public good.
But unlike the great philanthropists, Henry's generosity too often seemed to come from _other people's money_ —money that belonged not to him but to the company and its stockholders. Not surprisingly, the stockholders were never consulted.
From the very start, RenCen was a failure. By 1974, when it was only half complete, it was already short by $100 million.
To make up the difference, Henry assigned Paul Bergmoser, vice-president in charge of purchasing, to fly around the country putting pressure on other companies to "invest" in RenCen. Fifty-one companies put up the money. Of these, thirty-eight depended on the auto industry and Ford in particular for a lot of their business.
Bergmoser would go to see the heads of companies such as U.S. Steel and Goodyear. With a straight face, he'd have to say to them: "Now, I'm not here in my capacity as head of purchasing"—even though we were doing millions of dollars of business with these companies each year. "I'm coming to you as the personal representative of Henry Ford," he'd tell them, "and my visit here has nothing to do with the Ford Motor Company."
The executives of companies such as Budd, Rockwell, and U.S. Steel would burst out laughing at Bergie's disclaimer. Ed Speer, the chief executive of U.S. Steel, told Bergie that the only proper symbol for Renaissance Center was a twisted arm.
Because of the Ford name, some of the finest stores in the United States and Europe agreed to come into RenCen. But they all insisted on financial guarantees by the company. This led to the totally ridiculous situation of the Ford Motor Company's having to be in the boutique or jewelry or fancy chocolate business and cover their losses for the first couple of years. And losses they were.
As I write these words, RenCen is on the verge of economic collapse. Today it offers little more than confusing architecture and a very ordinary shopping mall—with high-priced parking to boot. Oh, yes—there is also a $2.7 million office, complete with a winding staircase and a fireplace, that was built for Henry Ford as a downtown office.
I often wonder: Where was the press? There was a lot of talk about investigative reporting in those days, but nobody in Detroit was digging for the real story behind Renaissance Center.
One reason is that Henry made for good copy, and everybody indulged his excesses. Besides, we were a major advertiser. Nobody in Detroit—or anywhere else, for that matter—wanted to run the risk of offending such a big spender.
The way I saw it, Henry was always a playboy. He never worked hard. He _played_ hard. What he cared about was wine, women, and song.
Actually, I always thought he hated women—except for his mother. When Henry's father died, Eleanor Clay Ford had taken over the family and put her son Henry in charge. She also kept him somewhat in line.
But when she died in 1976, his whole world came tumbling down. The only woman in his life he had any respect for was gone. Henry was the ultimate chauvinist, who believed that women were put on earth only for the pleasure of men.
He once complained to me that women would take over the Ford Motor Company one day—and wreck it. That's what happened at Gulf Oil, he would say. He added that the thirteen grandchildren at Ford now held more voting power than he and his brother and sister. But the really sad part, he felt, was that of the thirteen grandchildren, seven were girls and only six were boys. And that was the problem, he'd tell me: women can't run a damn thing.
As usual, Mary was wise to him from the very beginning. She used to say to me: "Liquor destroys all inhibitions and out comes the real man. So beware: this guy is _mean_!"
Actually, Mary was one of the few women he didn't scorn. Once, at a fiftieth birthday party for a close friend of ours, Katie Curran, Henry and Mary got into a long discussion while everyone else was getting bombed. At the time, Henry was on the wagon, and Mary didn't drink because she had diabetes.
They were talking about meetings of top management, which generally took place in fancy resorts. When Mary told Henry that the wives should be invited, too, Henry disagreed. "You girls just try to outdo each other," he said. "All you care about are your clothes and your jewels."
"You're totally wrong," she told him. "When the wives are there, your guys get to bed on time. They aren't out fooling around. The liquor bill is cut in half, and in the morning, guys get to the meetings when they're supposed to. You'll accomplish a lot more if you invite the wives along."
He really listened to her. Afterward, he said to me: "Your wife has horse sense." You had to get to Henry in those moments of sobriety. You had to grab him by the nose and twist it. Mary was always able to do that without getting into trouble.
Henry tried to be sophisticated and European. He knew how to be charming. He even knew something about wine and art.
But it was all a façade. After the third bottle of wine, all bets were off. He would change before your eyes from Dr. Jekyll to Mr. Hyde.
Because of his drinking, I kept my distance from him on social occasions. Beacham and McNamara, my two mentors, had both warned me. "Stay away from him," they said. "He'll get drunk, and you'll find yourself in trouble over nothing."
Ed O'Leary gave me similar advice. "You'll never get fired for losing a billion dollars," he told me. "You'll get fired some night when Henry's drunk. He'll call you a wop and you'll get into a fight. Mark my words—it will be over nothing. So always stay out of his line of fire."
I tried to. But Henry began to reveal himself as more than merely crude.
For me, a turning point in seeing the man for what he was came in 1974, at a management meeting on the equal opportunity program. Each division was asked to report its progress in hiring and promoting blacks. After listening to the reports, which were not impressive, Henry got angry. "You guys are only giving this thing lip service," he told us.
He then proceeded to make an impassioned plea for us to do more on behalf of blacks. He even said that executive bonuses might soon be tied to our progress in this area. "That way," he concluded, "you'll be sure to get off your asses and do what needs to be done for the black community."
His remarks at that meeting were so moving that they literally brought tears to my eyes. "Maybe he's right," I said to myself. "Maybe we really aren't doing enough. Maybe I'm dragging my feet. If the boss feels that strongly, I guess we ought to make a bigger push."
When the meeting was over, we all went up to the penthouse for lunch in the executive dining room. As usual, I was sitting at Henry's table. As soon as we sat down, he started spouting off about the blacks. "Those goddamn coons," he said. "They drive up and down Lake Shore Drive in front of my house. I hate them, I'm scared of them, and I think I'll move to Switzerland, where there just aren't any."
It was one of those moments I'll never forget. My antennae shot up. The guy had practically made me cry, and one hour later he was raving against the blacks. It had all been for show. Deep down, he must have hated their guts.
That's when I realized I was working for a real bastard.
Bigotry is bad enough, as I had learned in Allentown. At least the kids in my school didn't pretend to be anything else. But Henry was more than a bigot. He was also a hypocrite.
Publicly, he tried to be the world's most progressive businessman, but behind closed doors he showed disdain for just about everybody. Until 1975, the only group that Henry hadn't slandered in my presence were the Italians. But before long, he would be making up for lost time.
# X
# 1975: THE FATEFUL YEAR
In 1975, Henry Ford started his month-by-month premeditated plan to destroy me.
Until then, he had pretty well left me alone. But in that year he started having chest pains, and he really didn't look well. It was then that King Henry began to realize his mortality.
He turned animal. I imagine his first impulse was: "I don't want that Italian interloper taking over. What's going to happen to the family business if I get a heart attack and die? Before I know it, he'll sneak in here one night, take my name off the building, and turn this place into the Iacocca Motor Company. Where does that leave my son, Edsel?"
When Henry thought I'd steal the family jewels, he had to get rid of me. But he didn't have the guts to just go ahead and do his own dirty work. Besides, he knew he'd never get away with it. Instead, he played Machiavelli, determined to humiliate me into quitting.
Henry dropped his first bomb while I was away. Early in 1975, I was out of the country for a couple of weeks on a whirlwind tour of the Middle East, part of a delegation of business leaders brought over by _Time_ magazine to get a better understanding of Israel and the Arab world.
When I returned to the United States on February 3, I was surprised to find Chalmers Goyert, my executive assistant, waiting for me at J.F.K. Airport in New York.
"What's up?" I asked.
"We've got big problems," he told me.
We sure did. I listened as Goyert outlined the incredible events that had taken place during my absence. Just a few days earlier, while a group of us had been meeting with King Faisal in Saudi Arabia, King Henry had suddenly called a special meeting of top management.
The effects of that meeting are still being felt today. Henry was worried about the OPEC situation. The man who had taken the credit for turning the Ford Motor Company around after World War II was beside himself with fear. The Arabs had come charging up the hill, and he just couldn't take it.
Convinced that a major depression was imminent, he ordered $2 billion scratched from future product programs. With this decision, he summarily eliminated many of the products that would have made us competitive—such necessities as small cars and front-wheel-drive technology.
During the meeting, Henry had announced: "I am the Sewell Avery of the Ford Motor Company." It was an ominous reference.
Sewell Avery had been the head of Montgomery Ward, an ultraconservative manager who had decided not to allocate any money for future development after World War II. He was sure the world was coming to an end and America was doomed. His decision proved to be a disaster for Montgomery Ward, because Sears started knocking the hell out of them.
Henry's announcement had similar implications for us.
As for me, it wasn't hard to read the writing on the wall. Henry had waited until I was thousands of miles away in order to call a meeting where he usurped my power and responsibility—and where he also went against everything I believed in.
Henry did enormous damage to the company that day. Ford's Topaz and Tempo, the small, front-wheel-drive cars that finally went on sale in May of 1983, should have been ready four or five years earlier when the public was clamoring for small cars. But Ford's response to the 1973 oil crisis wasn't even _planned_ until 1979.
I was furious. OPEC had already made clear that without small cars we were dead. GM and Chrysler were working fast and furious to bring out their own subcompacts. And while this was going on, the head of the Ford Motor Company had stuck his head in the sand.
Every month like clockwork, after the board meeting, I used to get a visit from Franklin Murphy, the dean of our board, former chancellor of UCLA, chairman of the board of the _Los Angeles Times-Mirror_ Company—and senior confidant of Henry Ford.
Murphy was always giving me sincere advice, not on how to run the company, but on how to handle Henry. "He's under a lot of pressure," he told me one day. "You have to be charitable. He's having a helluva time with his wife."
We all knew that Henry's marriage to Cristina was coming apart. He had just been arrested for drunk driving in Santa Barbara—together with his girlfriend, Kathy DuRoss—while Cristina was off in Katmandu with her good friend Imelda Marcos, the first lady of the Philippines.
Just a few days later, I was home sick with the flu and fatefully missed a meeting about an amazing event.
On February 14, while I was absent, Henry called a summit meeting to discuss "the Indonesian situation." Henry had apparently authorized Paul Lorenz, an executive vice-president and one of the top officers of the company, to pay a "commission" of $1 million to an Indonesian general. In return, Ford was to get a $29 million contract to build fifteen satellite ground stations.
But when word of the "commission" leaked out, Henry sent two of our guys from Dearborn to Djakarta to tell the general this wasn't the way we did business.
Lorenz worked for me. When I learned of the incident I called him into my office. "Paul," I said, "why the hell did you offer that general a million bucks?"
Paul was a very proper and competent guy. He was also loyal, and he didn't want to get anyone in trouble. "It was a mistake," he told me.
"A mistake?" I said. "Nobody gives away a million bucks by mistake!"
Paul was silent. When I persisted, he said: "You don't think I'd do something like that on my own, do you?"
"What do you mean by that?" I asked. "Do you mean to tell me that somebody told you to do it?"
Paul replied: "Well, no, but the chairman sort of winked at it and said: 'That's how things are done over there.' "
Now, it's true that American corporations doing business in Third World countries sometimes offered bribes. But as far as I knew, a thing like that could never happen at Ford.
As soon as the press got wind of the attempted bribe, a full-scale cover-up went into operation within the company. It was at least as impressive as anything that went on during Watergate. There was an internal purging of the files. There were even special meetings to coordinate excuses on why we did it.
We had no choice but to fire Paul Lorenz, and, as usual, I was assigned the task of doing it. "I'll go quietly if there's no stigma on my record," he told me. "But I'm taking the rap for this. You know I wouldn't have done it without approval from the highest levels." I knew Paul well and I believed he was telling the truth.
A few days later, Henry made a confession of sorts. "I think I might have led Lorenz to believe that the payoff was all right," he said to me. "Maybe I led the poor bastard astray."
A full year and a half later, I was looking over the bonus sheet. To my shock, I saw that Henry had decided to give Paul Lorenz $100,000.
" _I_ fired the guy," I said to Henry. "How can _you_ give him a hundred grand as a bonus?"
"Well," said Henry, "he wasn't a bad fellow." It was almost like Watergate all over again. Lorenz took the rap, and the boss was taking care of him.
Here, too, the press was very easy on Henry. And so were the courts. A couple of years later, I was called down to the Justice Department to give a deposition on the matter. Henry never gave one. I don't know how he got away with it.
During that same winter, we announced our fourth-quarter losses for 1974, which came to $12 million. As losses go, this was a small one. Compared to what the auto industry went through between 1979 and 1982, a loss of $12 million might have been a cause for celebration.
Still, this was the first time since 1946 that the Ford Motor Company had experienced a losing quarter. So in addition to his failing health and his crumbling marriage, Henry had one more thing to worry about. As a result, he became more paranoid than ever.
In those days my secretary was a terrific woman named Betty Martin. If it weren't for the chauvinism built into the system, Betty would have been a vice-president—she was better than most of the guys who worked for me.
Betty always knew when something fishy was going on. One day she came to me and said: "I've just learned that every time you make a call on the company credit card, a record of it goes to Mr. Ford's office."
A couple of weeks later she told me: "Your desk is always pretty messy, so sometimes before I go home I try to organize it for you. I always remember exactly where I put everything, but the next morning, everything's moved around. It happens a lot, and I thought you should know about it. I don't think the cleaning ladies would touch it."
I went home and said to Mary: "Now I'm worried." Betty Martin was a no-nonsense woman. She hated gossip. She wouldn't have told me these stories if she didn't think they were important. Something bad was in the air, and, as usual, the secretaries were the first to know.
After that, things got stranger and stranger. On April 10, at our monthly board meeting, we responded to our recent losses by cutting our quarterly dividend by twenty cents. That alone saved us $75 million a year.
But that same day Henry raised the directors' fees from $40,000 to $47,000 a year. That's what I call neutralizing the board.
Later that month we announced our first-quarter losses of $11 million after taxes, which meant that we now had two losing quarters in a row.
Henry was starting to come apart at the seams. On July 11, he went public with his madness. That day he called a meeting of the top five hundred managers. He gave no advance indication—not even to me—as to the purpose of this extraordinary gathering.
When everyone had assembled in the auditorium, Henry proceeded to give a speech in which he announced: "I am the captain of this ship." Our management, he said, was going about things all wrong. I was the top manager, so there was no question about whom he had in mind. It was an unprecedented meeting. Henry was rambling and often incoherent. People walked out of there asking each other: "Hey, what was _that_ all about?"
After this meeting, we all started to wonder if Henry was losing his mind. Everybody got nervous. The whole company was frozen. Nobody was doing a thing. Instead, people were busy trying to figure out what Henry was up to—and whose side to take.
Although the press was mostly unaware of these squabbles, our dealers were getting the distinct impression that something was rotten in Denmark. On February 10, 1976, there was a meeting of Ford Division dealers in Las Vegas. The minutes read: "There appears to be too much politics within the leadership of Ford Motor Company and it is blunting the effectiveness of the leaders.... Henry Ford II is not at this time offering the type of quality leadership that his dealers expect from him."
The dealers also expressed their concern about the lack of new products from Ford and the fact that they now felt in a "catch-up" position with respect to GM.
During my struggles with Henry, the dealers made it very clear that they sided with me. This only made matters worse. Every statement of support from the dealers was more ammunition for Henry. The Ford Motor Company was not a democracy, so the very fact of my popularity among the troops was enough to convince him I was dangerous.
But all these events were small potatoes compared to the really big news of that year.
In the fall of 1975, Henry called in Paul Bergmoser and grilled him about doing business with Bill Fugazy, who ran a limousine and travel company in New York and arranged our dealer incentive programs.
"Aren't you afraid of Fugazy?" Henry asked. "Aren't you scared of ending up in the East River with a pair of cement boots?"
Shortly after that, Henry called me in. "I know Fugazy's a good friend of yours," he said. "But I'm starting a full investigation of him."
"What's the problem?" I asked.
"I think he's mixed up with the Mafia," said Henry.
"Don't be ridiculous," I said. "His grandfather started the travel business in 1870. Besides, I've had dinner with Bill and Cardinal Spellman. He's connected to all the right people."
"I don't know about that," said Henry. "He's got a limousine company. Limousine and trucking companies are always Mafia fronts."
"Are you kidding?" I said. "If he's involved with the Mafia, why is he losing so much money?" That line didn't seem to register, so I took another tack. I reminded Henry that it was Bill Fugazy who had arranged for Pope Paul to ride in a Lincoln instead of a Cadillac when the Pope came to New York.
But Henry was adamant. The next thing I knew, Fugazy told me files had been removed from his office without his knowledge. He was convinced his telephones were tapped, too, but nothing incriminating was ever found.
Very soon it became clear that the Fugazy affair was really a cover. The real subject of Henry's probe wasn't Bill Fugazy at all. It was Lee Iacocca.
The investigation, which ended up costing the company close to $2 million, began in August 1975. Inspired by Watergate, Henry even appointed a special prosecutor—Theodore Souris, a former justice of the Michigan Supreme Court.
The investigation began by focusing on a Ford dealer meeting in Las Vegas. Wendell Coleman, head of our San Diego branch sales office, was in charge of expense accounts for the Las Vegas meeting. He was called in for an interrogation in which they verbally beat the hell out of him. He was so outraged by what happened that he wrote down a full account and sent it to me.
Coleman was asked to come to World Headquarters on December 3, 1975, where he was "interviewed" by two men from the finance staff. They began by advising him of his rights. They then told him that this was not a Ford Division audit review but rather a review done at the request of World Headquarters, and they asked him not to discuss the interview with anyone else in the company.
The interview began with a detailed review of several Ford dealer dinners in Las Vegas. Coleman was asked whether there were any women in the party of executives at one fancy restaurant. He was specifically asked if there were any women with me. Then they grilled him on why he'd given a generous tip to the maître d', whether Fugazy had been part of our group, if certain executives had done any gambling, and if Coleman had supplied them with money for that purpose.
"It was a witch-hunt," Coleman told me. "They were looking for something—anything—gambling, girls, whatever." When Coleman objected to the line of questioning, he was asked outright: "Did you at any time give money to Iacocca to gamble with?"
"No."
"Did any executives ask for money to gamble with?"
"No."
Coleman had the impression that the investigators believed he stood around handing out wads of cash to the top officers of the company.
Under the guise of an audit of the travel and expense accounts of top executives, Henry conducted nothing less than a full-scale investigation of both my business and my personal life. The "audit" consisted of something like fifty-five interviews, which were conducted not only with Ford executives but also with many of our suppliers, such as U.S. Steel and Budd, as well as our advertising agencies.
Despite an incredible effort, the investigation failed to turn up a single damaging item about me or my people.
A full report was made to Franklin Murphy, who came to see me and said: "You have nothing to worry about. The whole thing is over."
I was outraged. "Why didn't any of you guys on the board get involved in this while it was going on?" I asked.
"Forget about it," said Frank. "You know Henry. Boys will be boys. Anyway, he came in with a cannon and went out with a peashooter."
After spending $2 million and coming up with nothing, a normal person might have apologized. A normal person might have shown a little remorse. A normal person might have said: "Well, I checked out my president and some of my vice-presidents, and they're as clean as a whistle. And I'm proud of them because that investigation was relentless."
It sure was. During those months, we found ourselves leaving the building to make phone calls. Henry had gone to Japan, and he was a real nut about the new, high-powered electronic gadgets he saw over there. We were all afraid our offices were tapped. Bill Bourke, one of our vice-presidents, told us that he was with Henry when he bought a $10,000 device that could pick up conversations from another building. Knowing Henry, nobody doubted it was true.
The impact of all this on our top management is hard to believe. We started to pull the drapes and talk in whispers. Ben Bidwell, who later became president of Hertz before joining me at Chrysler, used to say he was even afraid to walk in the halls. Grown men were quaking in their boots, afraid the king would condemn them to death.
It was incredible. One man with inherited wealth was making a shambles of everything, launching a company on three years of hell just because he felt like it. He was playing with people's lives. Guys were drinking too much. Their families were falling apart. And nobody could do a thing about it. This juggernaut was running amok.
That was the atmosphere in the Glass House in 1975.
And that was when I should have quit.
Certainly Henry must have expected me to leave. Originally, he had probably figured: "I'll find something on the guy. He's going on all these trips, he's living off the fat of the land. If I dig hard enough, I'm bound to hit pay dirt."
But he never did. When the investigation was finally done, my friends said: "Thank God it's over."
"No," I said. "Henry came up empty. He looks like a fool. Now our real troubles begin."
# XI
# THE SHOWDOWN
I often ask myself why I didn't quit at the end of 1975. Why did I accept the fate Henry was dishing out? How could I let a guy take my destiny and pummel it?
Looking back, I don't know how I lived through those years. My life was so crazy that I started writing everything down. Mary always said: "Keep track of this stuff. Someday you might want to write a book. Nobody would believe what we're going through."
So why didn't I just take a walk?
First, like anybody who's in a bad situation, I hoped that things would get better. Maybe Henry would come to his senses. Or the board would get its back up.
Another scenario I imagined was that his brother Bill, who owned twice as much stock as Henry, would say one day: "Look, my brother's gone nuts. We've got to replace him." I know that the idea had certainly crossed Bill's mind. But he never acted on it.
Why did I stay? In part because I couldn't imagine working anywhere else. I had spent my whole adult life at Ford, and that's where I wanted to be. The Mustang, the Mark III, and the Fiesta were my babies. I also had a lot of allies. The suppliers kept getting big orders. The dealers said: "We've never done this well." The managers were making huge bonuses. Unless I was some kind of swami who had a magic hold on all these people, I have to conclude that my popularity was due to my performance. Despite my troubles with Henry, I got a lot of satisfaction from my success.
I never expected a showdown, but if it came to that, I was ready. I knew how valuable I was to the company. In terms of everything that really counted, I was far more important than Henry. In my naïveté, I held out the hope that because we were a publicly held company, the better man would win.
I was also greedy. I enjoyed being president. I liked having the president's perks, the special parking place, the private bathroom, the white-coated waiters. I was getting soft, seduced by the good life.
And I found it almost impossible to walk away from an annual income of $970,000. Although I was the number two man at the number two company, I was actually earning more than the chairman of General Motors. I wanted that $1 million a year so much that I wouldn't face reality.
Of the seven deadly sins, I'm absolutely convinced that greed is the worst.
Deep down in my character there must have been a weakness. People say I'm decisive and hard-as-nails when the chips are down. But where were those qualities when I really needed them?
Maybe I should have fought back. Mary always wanted to punch Henry out. "If you give me the word," she used to say, "I'd like to take him apart. I know it'll mean your job, but at least we'll all feel better."
Meanwhile, Henry was still determined to get rid of me. When his investigation failed to do the trick, he must have thought: "This guy is not quitting, so I'll have to try something else. I can't fire him because he's too popular. So I'll have to go with the stiletto treatment. I'll slice off his limbs one at a time and he won't even know they're gone."
As it turned out, these limbs were real people. It was rumored that Henry had a hit list of Iacocca cronies. I soon learned it was a lot more than a rumor.
One day, for no apparent reason, Henry picked up the phone and called Leo-Arthur Kelmenson, president of Kenyon & Eckhardt, the ad agency that handled the Lincoln-Mercury account.
"Kelmenson!" he roared. "Fire Bill Winn."
Now, Bill Winn was one of my closest friends. We had once been roommates in Ann Arbor. Only two days before Henry's call, Bill had been hired by Kenyon & Eckhardt to work on special promotions. Before that, he had run his own production company. He had often worked with us on our spectacular annual dealer shows and had always done a superb job.
When Kelmenson reached me with the news that Bill had been fired, I was about to give a speech to a group of business executives at a conference sponsored by Michigan State University. During my talk that night, my mind kept going back to Bill.
I couldn't understand why Henry had done it. Bill Winn was a very easy fellow to get along with. There was nothing controversial about him. Henry couldn't have had a fight with Bill, because he had never even met him. Moreover, Bill had always done an outstanding job in everything we'd given him.
Then it came to me. Henry's arbitrary decision to fire Bill Winn was nothing more than a clumsy and indirect attack on Lee Iacocca.
The Bill Winn affair was the opening salvo of a prolonged war of attrition that really escalated during 1976. If I had any doubts about that, Henry's subsequent assault on Harold Sperlich would give me all the evidence I needed.
Hal Sperlich is one of those legendary Detroit types about whom people say: "He has gasoline in his veins." As an engineer and product planner, he worked with me all through the 1960s and 1970s. He played a critical role in the creation of several new cars—especially the Mustang and the Fiesta.
Hal is so talented that it's difficult to praise him too highly. He may be the best car man in Detroit. He's fast as a whip, with an uncanny ability to get to the root of a problem—and to get to it first.
As president of Ford, one of my duties was to chair the committee on product planning. In the meetings, Hal Sperlich sat on my left, and Henry sat on my right. Every now and then, Henry would give a nod or a grunt. He never talked much at these meetings, but his gestures and noises spoke volumes. In fact, people generally paid more attention to Henry's facial expressions than to whatever ideas were being presented at the time.
It was clear that Henry didn't like Sperlich or his proposals. Hal was brash, and he didn't show much deference to the king. He tried to be diplomatic about it, but anyone could see what was happening: Sperlich, who knew a great deal about cars and had incredible instincts about the future, kept pushing us in the direction of smaller models—which was about the last thing in the world Henry wanted to hear.
One day, after a product committee meeting, Henry called me into his office. "I hate that goddamn Sperlich," he said, "and I don't want him sitting beside you. He's always pissing in your ear. I don't want the two of you ganging up on me like that."
I had little choice but to call in Sperlich and tell him the news. "Hal," I said, "I know this sounds ridiculous, but you can't sit next to me anymore." That was as far as I was willing to go. Hal was easily the most valuable player on the team, and there was no way on earth that I was going to bench him.
Eventually the only thing I could do to save Hal was to move him completely out of Henry's line of vision. I assigned him to a number of projects in Europe, and he soon became a regular transatlantic commuter. No matter what the problem was, Hal would go in and get the job done. The Fiesta was his greatest coup, but almost everything he touched turned to gold.
Shortly thereafter Henry called me and ordered me to fire Hal Sperlich.
"Henry," I said, "you gotta be kidding. He's the best we've got."
"Fire him now," said Henry.
It was the middle of the afternoon. I was about to leave the office to catch a flight to New York. I asked Henry if it could wait until I returned.
"If you don't can him right now," Henry replied, "you'll go out the door with him."
I knew it was hopeless. Still, I tried to reason with him. "Sperlich did the Mustang," I told Henry. "He made us millions."
"Don't give me any bullshit," said Henry. "I don't like him. You're not entitled to ask why. It's just a feeling I have."
Hal took it very hard. Although both of us could see it coming, you always live in the hope that if you do your job well, justice will prevail. Hal genuinely believed that his talent was enough to keep him at Ford, even if the boss didn't like him. But he forgot that we worked in a dictatorship.
"This is a chickenshit outfit," I told Sperlich. "And I should probably be getting out with you. I'm higher up than you are, but I have to put up with the same garbage. Maybe Henry's doing you a favor," I said. "In a more democratic environment, your talent will be recognized and rewarded. It's hard to believe right now, but you might look back on this day and be grateful that Henry kicked you out."
I guess I was prophetic. Shortly after Hal was fired, the president of Chrysler took him to lunch. Early in 1977, Hal started working at Chrysler. He immediately took a leading role in the planning of their small cars, where he did everything he had wanted to accomplish at Ford.
Less than two years later, Hal and I were working together again. Today he's president of Chrysler. And in a delicious turn of events, his front-wheel-drive cars, especially the new T115 minivans—the cars that Henry never let him do at Ford—are inexorably eating into Ford's share of the market.
At the beginning of 1977, Henry declared war. He brought in McKinsey & Company, the management-consultant people, to reorganize our top administration. When the project was over, an executive high in the company left a little note on my desk that said, in effect: "Hang in there, Lee. But it won't be easy. Your boss is an absolute total dictator and I don't know how you guys put up with it."
After months of study and a couple of million dollars in fees, McKinsey issued its recommendation. The plan called for a troika—a three-member office of the chief executive—to replace the standard structure of chairman and president.
The new arrangement was formally established in April. Henry, of course, remained as chairman and chief executive officer. Phil Caldwell was named vice-chairman, while I continued as president.
We each had our own areas of responsibility, but the key change—and the obvious reason for the new arrangement—was spelled out in a memo issued by Henry, which specified that "The Vice Chairman is the Chief Executive Officer in the absence of the Chairman." In other words, if Henry was first among equals, Phil Caldwell was now second.
Making Caldwell number two brought my fight with Henry out in the open. Until then, it had been guerrilla tactics. But now Henry was getting bolder. The entire management shift was no more than an ornate and expensive way to defuse my power in a socially acceptable manner. Without having to confront me directly, Henry had succeeded in installing Caldwell above me.
It was a real crack in the face. Every time there was a dinner, Henry hosted table one, Caldwell hosted table two, and I was shoved down to three. It was public humiliation, like the guy in the stockade in the center of town.
He tore me up inside. He tore up my wife and my kids. They knew I was under great pressure, but I didn't tell them all the details. I didn't want them to go crazy. I was killing myself but I wouldn't yield. It might have been pride, it might have been stupidity, but I was not going to crawl out of there with my tail between my legs.
The office of the chief executive was a three-headed monster. It was ridiculous that Caldwell, who used to work for me, was suddenly above me for no apparent reason except malice. Privately, I told Henry that his new plan was a big mistake. But in typical fashion, he tried to reassure me with platitudes. "Don't worry," he said. "It will all work out in the end."
Although I was boiling inside, in public I defended the new structure. I reassured all the people who worked for me that the new arrangement was perfectly fine.
Not surprisingly, the office of the chief executive didn't last very long. In June of 1978, fourteen months after it was established, Henry announced another shift in top management. Instead of three members, our little team would now have four. The new arrival was William Clay Ford, Henry's younger brother. Bill was brought in to maintain a Ford family presence in the event of Henry's illness or death.
Now I had dropped to fourth in the pecking order. Moreover, I was reporting not to Henry but to Phil Caldwell, who was named deputy chief executive officer. To make the humiliation complete, Henry didn't even bother to tell me about this new restructuring until the day before it was announced.
When he finally gave me the news, I said: "I think you're making a mistake."
"That's my decision and the board's," he snapped.
It was salami-slicing time—one slice at a time. I was getting cut up. Each day I found another part of my body missing. I put out the word that I wasn't going to take it.
Four days later, on June 12, Henry met with our nine outside board members and told them he was about to fire me. This time the board drew the line. They said: "No, Henry, you're doing this wrong, let's cool it. We'll talk to Lee. We'll work things out. You go in and apologize to him."
"I lost my board today," he told Franklin Murphy.
The next day Henry came to my office for only the third time in eight years. "Let's bury the hatchet," he said.
The board had decided that I should get together with some of its members to try to iron out the problems. Over the next couple of weeks, I met separately with Joseph Cullman, chairman of Philip Morris in New York, and George Bennett, president of the State Street Investment Corporation in Boston. There was nothing secret about these meetings. It was their idea. I flew to see each of them on the company plane and I submitted expense accounts, so they were all a matter of record.
The false peace lasted one month. On the evening of July 12, 1978, Henry had dinner with the outside board members, as he did every month on the eve of the board meeting. Again he announced that he was going to fire me. Now he claimed I was ganging up on him by going to the outside directors behind his back—even though they had asked for the meeting with me. He also said that the personal chemistry between the two of us had never been right. It seems to have taken Henry Ford thirty-two years to decide he didn't get along with me.
This time, too, several of the board members challenged him. They cited my loyalty and my value to the company. They asked Henry to reinstate me to my former position as number two man.
Henry was livid. He wasn't used to backtalk from the board. "It's him or me," he growled. "You have twenty minutes to make up your minds." Then he stormed out of the room.
Until this point he had not dared to fire the guy who was making him all this money, who was the father of the Mustang and the Mark and the Fiesta, and who was so popular in the company. I think he had doubts as to whether he could get away with it.
But finally, in frustration, he just blew his stack. "It's taken three whole years," he must have been thinking, "and this bastard's still here!" When he couldn't get me to quit, he finally decided to move in and occupy the land. He could always justify it later.
That same night I received a telephone call from Keith Crain. Crain was the publisher of _Automotive News_ , the trade weekly of the car industry. "Say it isn't so," he said.
I had no doubt as to what he meant. Crain was a close friend of Henry's son, Edsel, and my guess is that Henry had instructed Edsel to leak the story to him. That way, I could learn about my own firing indirectly, through the press.
It was classic Henry. He wanted the news of my firing to reach me through a third party. Henry was a pro at turning the screws. This move also ensured that the king wouldn't have to get his hands dirty with messy affairs of state.
The next morning I went to work as usual. At the office there was no indication anything was wrong. By lunchtime I was beginning to wonder whether Keith Crane had been misinformed. But just before three o'clock, Henry's secretary summoned me to his office. "This is it," I thought.
When I walked into the inner sanctum, Henry and his brother Bill were sitting at a marble conference table with an "I smell shit" look on their faces. They were tight and nervous. In a strange way I was relaxed. I had already been tipped off. I knew what was about to happen. The meeting was just to make it official.
I hadn't expected Bill to be there for the firing, but it made good sense. His presence was a way of letting me know that this was not just Henry's decision but the family's. Bill was the company's biggest individual shareholder, so his being there carried a political message as well. If Bill went along with his brother's decision, I would have no recourse.
Henry also wanted a witness. Normally, he delegated his dirty work by getting other people—especially me—to do his firings for him. But this time he was on his own. Having Bill there by his side probably made it easier for him to let me go.
The fact that Bill was there also made _me_ feel better. He was a great fan of mine as well as a good friend. He had already promised me that when push came to shove—as we both knew it would—he would fight for me. I knew I couldn't totally count on his support, because Bill had never stood up to Henry in his life. Still, I held out some hope that he would intervene.
As I took my seat at the table, Henry hemmed and hawed. He had never fired anyone, and he didn't know how to begin. "There comes a time when I have to do things my way," he finally said. "I've decided to reorganize the company. This is one of those things that you hate to do, but you have to do it anyway. It's been a nice association"—I looked at him in disbelief—"but I think you should leave. It's best for the company."
At no point during our entire forty-five-minute meeting did he ever use the word "fired."
"What's this all about?" I asked.
But Henry couldn't give me a reason. "It's personal," he said, "and I can't tell you any more. It's just one of those things."
But I persisted. I wanted to force him to give me a reason because I knew he didn't have a good one. Finally, he just shrugged his shoulders and said: "Well, sometimes you just don't like somebody."
I had only one card left to play. "What about Bill over here?" I said. "I'd like to know what he thinks."
"I've already made the decision," said Henry.
I was disappointed but not really surprised. Blood is thicker than water, and Bill was part of the dynasty.
"I do have certain rights," I said, "and I hope there won't be any quarrel over that." I was concerned about my pension and my deferred compensation.
"We can work that out," said Henry. We agreed that the record would show I was resigning from the company effective October 15, 1978—my fifty-fourth birthday. Had I left any earlier, I would have forfeited a lot of benefits.
Up to this point, our conversation had been remarkably calm. Then I took over. For Henry's benefit, I recited a list of my accomplishments on behalf of the Ford Motor Company. I reminded Henry that we had just completed the two best years in our history. I wanted him to know exactly what he was throwing away.
When I finished my speech, I said: "Look at me." Until this point he had not been able to look me in the eye. My voice was rising now as I realized that this would be our final conversation.
"Your timing stinks," I said. "We've just made a billion eight for the second year in a row. That's three and a half billion in the past two years. But mark my words, Henry. You may never see a billion eight again. And do you know why? Because you don't know how the fuck we made it in the first place!"
It was true. Henry was an old pro at spending money, but he never understood how it all came in. He just sat in his ivory tower and said: "My God, we're making money!" He was there every day to throw his weight around, but he never knew what made the place tick.
Near the end of the meeting, Bill made an honest effort to change his brother's mind. But it was too little, too late. As we left Henry's office, Bill had tears running down his face. "This shouldn't have happened," he kept saying. "He's ruthless."
Then he composed himself. "You were so cool in there," he said. "You've been with us thirty-two years, and he didn't even give you a reason. You really laid him out. Nobody in his life ever took him on the way you just did. I'm surprised he held still for it."
"Thanks, Bill," I said. "But I'm dead, and you and he are still alive!"
Bill is a good man, but it's always been the Fords against the world. Still, he and I remained friends. I know that he genuinely wanted me to continue as president—just as he genuinely believed there was nothing he could do about it.
When I returned to my office, I began getting phone calls of inquiry from some of my friends and colleagues. Apparently, word of my firing had already spread. Before the day was over, Henry issued a cryptic memo to top executives that said simply: "Effective immediately you will report to Philip Caldwell."
Some people received that memo in their office. But most found it waiting on the front seat of their cars in the executive garage. Somebody told me later that Henry himself had come down and put them there. That was probably the only way he could know for sure that the deed was finally done.
Leaving the office that afternoon, I felt a great sense of relief. "Thank God the bullshit is over," I said to myself in the car. If I had to get fired, at least my timing was good. We had just finished the best six months in our history.
When I got home, I received a call from Lia, my younger daughter, who was at tennis camp—her first time away from home. She had heard about the firing on the radio, and she was in tears.
When I look back on that awful week, what I remember most clearly is Lia crying on the telephone. I hate Henry for what he did to me. But I hate him even more for the way he did it. There had been no opportunity to sit down and talk to my kids before the whole world knew. I'll never forgive him for that.
Lia wasn't only sad. She was also angry that I hadn't told her in advance that I was about to be fired. She couldn't believe I hadn't known it was about to happen.
"How could you not know?" she asked. "You're the president of this big company. You always know what's going on!"
"Not this time, honey."
She had a very hard week. I think there were kids who took some sadistic pleasure that the president's daughter, who always had the best of everything, was finally getting her comeuppance.
It soon became clear that Henry had made his decision to fire me on impulse, even if it was inevitable in the long run. That same week, the company had mailed out an advance press kit for the 1979 Mustang. Inside was a photograph of me standing in front of the new car. But when the Mustang was introduced a few weeks later at the Dearborn Hyatt Regency, it was Bill Bourke who represented the company.
They say that the bigger you are, the harder you fall. Well, I fell a great distance that week. I instantly identified with every person I had ever fired.
When I moved to Chrysler a few months later, I had to lay off hundreds of executives in order to keep the company alive. I tried my best to do it with some degree of sensitivity. For the first time in my life, I learned how terrible it felt to be let go.
After I was fired, it was as if I ceased to exist. Phrases such as "father of the Mustang" could no longer be used. People who had worked for me, my colleagues and friends, were afraid to see me. Yesterday I had been a hero. Today I was somebody to be avoided at all costs.
Everybody knew that Henry was prepared to carry out a major purge of Iacocca supporters. Anyone who failed to break off complete diplomatic and social relations with me risked being fired.
My former friends stopped calling me because my phone might be tapped. They would notice me at an auto show and look the other way. The really courageous ones would come up and give me a quick handshake. Then they'd get out of sight before the photographer from the _Detroit Free Press_ could capture the moment. After all, Henry might see the picture in the paper. And then he might execute the offender for being seen in public with the pariah.
The week I was fired, Walter Murphy, who had been my close associate and executive director of the company's worldwide public relations staff for twenty years, received a phone call from Henry in the middle of the night.
"Do you love Iacocca?" Henry wanted to know.
"Sure," said Walter.
"Then you're fired," said Henry.
Henry rescinded the order the next day, but it shows you how crazy he got.
Several months later, Fred and Burns Cody, two old friends of mine, gave a party for me. Only a couple of Ford guys showed up, and only one of the officers—Ben Bidwell. He took a hell of a chance. The next day, when Bidwell went to work, he was called on the carpet. "We want to know who was at that party," they said to him.
It didn't stop. The company masseur, a great friend of mine, kept coming to my house for a year or two. Then one Sunday he didn't show. He said he was tied up, and I never saw him again. Somebody must have put out the word that he was seen coming to my house to give me a rubdown, and he couldn't afford to lose his job. Almost four years after I was fired, the chief stewardess of the company fleet got moved out and demoted because she was still friendly with my wife and kids.
For me, the pain continued long after the deed was done. One of my best friends in the company had been close to my family for twenty-five years. We had played poker together every Friday night. Our families went on vacations together. But after I was fired, he never even called. And when Mary died in 1983, he didn't even come to her funeral.
My father always used to say that when you die, if you've got five real friends, you've had a great life. I found out in a hurry what he meant.
It was a bitter lesson. You can be friends with someone for decades. You can share all the good times and bad with him. You can try to protect him when the going gets rough. And then you have some rough luck yourself and you never hear from the guy again.
It really makes you ask yourself the big questions. If I could do it over, could I have protected my family better? The pressure on them was awful. You watch your wife get sicker—Mary had her first heart attack less than three months after I was fired—and you wonder. A cruel man and cruel fate intervene and change your life.
I was hurting pretty bad after the firing, and I could have used a phone call from somebody who said: "Let's have coffee together, I feel terrible about what happened." But most of my company friends deserted me. It was the greatest shock of my life.
To some extent, I can understand their attitude. It wasn't their fault that the corporation was a dictatorship. Their jobs really _were_ on the line if they continued to associate with me. They had their mortgages and their kids to worry about.
But what about the board? These guys were the illustrious guardians of the Ford Motor Company. They were supposed to constitute the system of checks and balances to prevent the flagrant abuse of power by top management. But it seemed to me their attitude was: "As long as we're taken care of, we'll follow the leader."
When Henry ordered the board to choose between himself and me, why did they let him fire the guy they had such great faith in? They may not have been able to prevent it, but at least some of them could have resigned in protest. Nobody did. Not one person said: "This is a disgrace. This guy is making us a couple of billion a year, and you're firing him? Then I'm leaving, too."
That's one mystery I want to unravel before I die: How can those board members sleep at night? Why didn't Joe Cullman and George Bennett and Frank Murphy and Carter Burgess really stand up to Henry Ford? To this day, I can't figure out how the board members can defend their decision, to themselves or to anyone else.
After I left the company, the only ones I ever heard a word from were Joe Cullman, Marian Heiskell, and George Bennett. The day I signed on with Chrysler, Marian called to wish me well. She was a real lady.
I stayed on good terms with George Bennett of State Street Investment. He said: "You know, if I'd had any guts I should have quit with you. But I handle a pension fund for Ford and I'd lose it in an instant if I followed you to Chrysler."
After Mary died, I got a letter from Bill Ford and a note from Franklin Murphy. But that was it. For all the years of our working together, that was the first and last I ever heard from the board during my time of grief.
In the annual meeting that followed my firing, Roy Cohn stood up to Henry and asked: "By firing Iacocca, how did you help the stockholders?"
But Henry just smiled and replied: "Well, the board supported me, and that's privileged information."
The firing got a lot of attention in the outside world. Walter Cronkite reported the details on _The CBS Evening News_ , commenting that "it all sounds like something from one of those enormous novels about the automobile business." _The New York Times_ , in a front-page story, called the firing "one of the most dramatic shakeups in the history of the Ford Motor Company." Given our turbulent history, that was saying a great deal.
I was especially pleased with an editorial in _Automotive News._ It mentioned my $1 million annual income and said that "by all standards, he earned every penny." Without directly criticizing Henry, the editorial said: "The best ballplayer in the business is now a free agent."
A number of editorial writers and columnists found the firing disturbing—and difficult to believe. Jack Egan, writing in the financial pages of the _Washington Post_ , wrote that the way it all happened "raises questions about how much an enterprise as large as Ford Motor is run like a private duchy by the whim of one man."
In Warren, Rhode Island, the local paper made a similar point. Quoting a _Wall Street Journal_ story that explained my firing by saying I "flew too close to Air Force One," a columnist observed: "That's a little scary when you think that Ford is so big in America that what Ford does affects everybody. And what goes on at Ford is apparently under the control of one arrogant old man who isn't responsible to anybody. He simply does as he pleases."
Nicholas Von Hoffman, the syndicated columnist, went even further. Calling Henry a "60-year-old adolescent," he concluded: "If a guy like Iacocca's job isn't safe, is yours?"
# XII
# THE DAY AFTER
As soon as they heard the news, the Ford dealers were up in arms. Ed Mullane, a dealer in Bergenfield, New Jersey, who was president of the twelve-hundred-member Ford Dealer Alliance, was especially upset.
Mullane had already figured out I was in trouble. On his own, he had written a letter supporting me to Henry and all of the directors. Henry wrote back telling him to mind his own business. Once I went by Henry's office and heard him yelling on the phone: "Iacocca went to see Mullane, the son-of-a-bitch, and put him up to this." Of course I never did.
After the firing, Mullane led a campaign to get me back and to have a dealer named to the board of directors. He calculated that the dealers had a combined investment of close to $10 billion in their various franchises and that I represented the best way to protect that investment. Later that summer, he actually tried to bring about an organized protest on the part of dealers who were also stockholders in the company, but the plan fizzled.
Although Mullane was unsuccessful in his efforts to have me reinstated, there were indications that the company was worried about its dealer base in the wake of my departure. The day after I was fired, Henry sent off a letter to every Ford dealer in the country, trying to reassure them all that they wouldn't be neglected:
"The Company has a strong and experienced management team. Our North American Automotive Operations are headed by talented executives who are well known to you and who are fully attuned to your needs and the needs of the retail market." Of course, if that were really true, there would have been no need for the letter.
I received a great many phone calls and letters of support from our dealers. Their concern and good wishes meant a lot to me. In the press I'm often described as "demanding," "tough-assed," or lacking in compassion. But if that were so, I don't think the dealers would have rallied on my behalf. We had our share of disagreements, but I always treated them fairly. While Henry was running with the jet set and raising hell, I was paying attention to them as people. I also helped quite a few of them become millionaires.
Meanwhile, back at the office, Henry had appointed Bill Ford and Carter Burgess, a board member, to decide upon my compensation. I told them how much I had coming to me, but they were bastards to the bitter end. To get what I deserved, I hired Edward Bennett Williams, the best lawyer I knew. In the end, I got about 75 percent of what I was entitled to.
Looking back on this episode, what sticks in my craw is Carter Burgess and Henry Nolte, Ford's chief counsel, mouthing platitudes about how they wanted to be fair but couldn't set any precedents on financial settlements because of "stockholder interests." Bill Ford, on the other hand, just sat there and bit his lip.
I did get a lot of letters of support from fellow employees. These letters were all written by hand, of course, so that there would be no record they had been sent. There were also letters and phone calls from headhunters eager to help me find a new job.
I think that morning of exile in the parts depot had a major influence on my decision, two weeks later, to accept the presidency of Chrysler. Had it not been for the humiliation of the warehouse, I might have taken some time off, played a little golf, or gone away on a vacation with my family.
But I was so enraged by what had happened that it's a good thing I found myself a new job right away. Otherwise, I might have burned myself out, just stewing in my own anger.
A curious sidelight to the firing was that I could now invite Pete and Connie Estes to our house for dinner. Pete, who lived a couple of doors away, was president of General Motors. In all the years we knew each other, we had never been together socially.
For as long as I was working for Ford, we both had to obey the unwritten rule that if a Ford and a GM guy were seen playing tennis or golf together, it was a sure sign they were price-fixing or otherwise plotting the overthrow of our free enterprise system. GM executives were especially careful, because their company was always under the threat of being broken up for being a monopoly. As a result, those of us in positions of power at the Big Three rarely even said hello to our counterparts.
This change was a special bonus for Mary, because she liked Connie Estes and now they wouldn't have to socialize on the sly. It sounds funny, but that was the code of conduct in Grosse Pointe and Bloomfield Hills in the 1970s.
My newly found friendship with Pete Estes was all too brief. The moment I signed on with Chrysler, we had to become strangers again.
Not long after I was dismissed, a story ran in one of the Detroit papers in which a "family spokesman" from Ford was quoted as saying that I had been fired because I "lacked grace," was too "pushy," and that "the son of an Italian immigrant born in Allentown, Pennsylvania, is a long way from Grosse Pointe."
That was an awful slur, but it wasn't really surprising. To the Fords I would always be an outsider. Hell, even Henry's wife, Christina, was always an outsider. Everyone in the family called her "The Pizza Queen."
Given how Henry felt about Italians, the comments were par for the course. For the past few years he had been convinced I was in the Mafia. I guess _The Godfather_ was enough to persuade him that all Italians were linked to organized crime.
He would have _really_ trembled if he had known about an unexpected phone call I received after those anonymous words appeared in the paper. A guy with an Italian accent called me at home and said: "If what we're reading in the papers is true, we want to do something about that no-good SOB. He destroyed the honor of your family. I'm gonna give you a number to call. Whenever you tell us, we'll break his arms and legs for you. It will make us feel better. And it will certainly make _you_ feel better."
"No, thanks," I said, "that's really not my style. If you guys did it, I wouldn't get any satisfaction out of it. If I'm going to get violent, I'd want to break his legs _myself"_
During the 1975 investigation, Henry had continually implied that I had Mafia connections. To the best of my knowledge, I had never met a Mafia guy in my life. But now Henry had created a self-fulfilling prophecy. Suddenly I had access to just about the only people in the world who could really throw the fear of God into him.
It's not that I believe in turning the other cheek. Henry Ford destroyed a lot of lives. But I got revenge without resorting to violence. Because of my pension, he still pays me a lot of money to go to work every morning to see if I can knock his block off. It must drive him crazy.
After the initial shock of the firing wore off, I started to think about what had happened between Henry and me. In some respects, it doesn't matter much whether you're the president of the company or the janitor. Being fired is still a terrible blow, and you immediately start to wonder: what did I do wrong?
Certainly I never had any illusions about becoming number one. I made my peace with that very early. If I had wanted to be the CEO of a company, I had plenty of opportunities to go elsewhere. But as long as I remained at Ford, I knew that a member of the family would always be at the head of the company, and I accepted that. If being a CEO had been one of my undying ambitions, I would have left long ago. But until 1975 I was very happy where I was.
I was fired for being a threat to the boss. Henry was infamous for dropping his number two men under unpleasant circumstances. To him, it was always the uprising of the peasants against their lord and master. Still, I had always clung to the idea that I was different, that somehow I was smarter or luckier than the rest. I didn't think it would ever happen to me.
I should have thought a little more about the company's history. I _knew_ that Ernie Breech was put out to pasture in Slobbovia, where I would follow him one day. I _knew_ that Tex Thornton and McNamara couldn't wait to get out after they had come in as Whiz Kids. I _knew_ that Beacham said every day: This guy's a nut and you better get ready for rainy days. Arjay Miller, Bunkie Knudsen, and even Henry's good friend John Bugas ended up the same way. All I had to do was review history and my autobiography was staring me in the face.
Then there was Henry's illness. He was convinced that if anything happened to him, I would somehow manipulate the family and take over the company. "When I got angina in January 1976," he told a reporter from _Fortune_ , "I suddenly discovered I wasn't going to live forever. I asked myself, 'Where does the Ford Motor Company end up without me?' I came to the conclusion that Iacocca could not succeed me as chairman." That evil man has never explained that line to me, to his board, and probably not even to himself.
The Fords are one of America's last great family dynasties. In any dynasty, the first instinct is self-protection. Anything, _anything_ —good, bad, or indifferent—that might affect the dynasty becomes a potential problem in the mind of the man who heads it.
Henry has never hidden his intention of having his son, Edsel, succeed him, and he believed that I stood in the way of those plans. As a friend of mine likes to say, "Lee, you weren't touched by the first Edsel fiasco. But you sure as hell got creamed by the second one!"
I saw Henry only once after I was fired. Four and a half years later, Mary and I were invited by Katharine Graham to one of the fiftieth-anniversary parties for _Newsweek_ , which were held in several cities across the country. In Detroit, ironically for me, the celebration took place in the ballroom of the Renaissance Center.
This was a few months before Mary's death. She wasn't feeling very well, so I was at her side the whole evening. We were sitting at a table with Bill Bonds, our premier newscaster in Detroit and a great guy. At one point, while Mary and Bill were talking, I looked over and noticed Henry and his wife coming through the receiving line.
"Uh-oh," I said. Mary turned around. "Uh-oh," she said. This was a moment I had often thought about. I'm a pretty serene guy, but I had always wondered what would happen if I ever saw Henry after I'd had a couple of drinks. I wondered if I would flip out. I had fantasized for so long about kicking him where it hurts, I really wasn't sure I could handle it.
Our eyes met. I nodded, and I knew that he had three choices. The first was to nod and say hello, and then get lost in the crowd. That would be holding his ground.
His second alternative was to come over and say a few words. We could shake hands, and he could even put his arm around me. This would be letting bygones be bygones. It would be the decent thing to do, which meant that it would be expecting too much.
His third option was to run like hell. And that's what he did. He grabbed his wife, Kathy, and he _ran._
And that was the last I ever saw of Henry Ford.
A lot has happened since July 13, 1978. The scars left by Henry Ford, especially on my family, will be lasting, because the wounds were deep. But the events of recent years have had a healing effect. So you move on.
# THE CHRYSLER STORY
# XIII
# COURTED BY CHRYSLER
If I'd had the slightest idea of what lay ahead for me when I joined up with Chrysler, I wouldn't have gone over there for all the money in the world. It's a good thing God doesn't let you look a year or two into the future, or you might be sorely tempted to shoot yourself. But He's a charitable Lord: He only lets you see one day at a time. When times get tough, there's no choice except to take a deep breath, carry on, and do the best you can.
As soon as the firing was announced, I was approached by a number of companies in other industries, including International Paper and Lockheed. Charles Tandy, who owned Radio Shack, asked me to come and work for him. Three or four business schools, including NYU, wanted me as their dean. Some of these offers were very tempting, but I had trouble taking them seriously. I had always worked in the car business, and that's where I wanted to stay. As far as I was concerned, it didn't make much sense to be changing careers at this point in my life.
At fifty-four, I was too young to retire but too old to start working in a completely new business. Besides, cars were in my blood.
I've never gone along with the idea that all business skills are interchangeable, that the president of Ford could be running any other large corporation just as well. To me, it's like a guy who plays the saxophone in a band. One day the conductor says to him: "You're a good musician. Why don't you switch over to the piano?" He says: "Wait a minute, I've been playing the sax for twenty years! I don't know beans about the piano."
I did have one offer from a car company. Renault, over in France, was interested in hiring me as a worldwide automotive consultant. But I'm not the consultant type. I flourish where the action is. I like hands-on responsibility. If it works, give me the credit. If it doesn't, I'll take the rap.
Besides, the entrepreneur in me was getting restless. During this interim period in the summer of 1978, I got obsessed with an idea I called Global Motors. This plan was a biggie, not exactly the sort of project you could do overnight. My dream was to put together a consortium of car companies in Europe, Japan, and the United States. Together, we'd create a major force that could challenge the dominance of General Motors. I envisaged myself as the new Alfred Sloan, the man who reorganized GM between the wars—and, in my opinion, the greatest genius ever in the auto business.
The partners I had in mind for Global Motors were Volkswagen, Mitsubishi, and Chrysler, although the plan could also work with a different partner, such as Fiat, Renault, Nissan, or Honda. But Chrysler was the logical American choice. GM was too big to join up with anybody else, or so I thought at the time. Ford was out of the question—for obvious reasons.
Chrysler, however, could provide a solid engineering base for Global Motors. Engineering may have been Chrysler's only strength, but it was a vital one.
I asked a friend of mine—Billy Salomon of Salomon Brothers, the New York investment bankers—to do some research about what such a merger might involve. In the process I learned a great deal about several car companies, including Chrysler. To be more precise, I learned a great deal about their balance sheets. But as I would soon find out, there's a hell of a difference between what a company looks like on paper and how it actually operates.
According to Salomon Brothers, the biggest obstacle to Global Motors was the American antitrust laws. What a difference five years makes! At the moment, the White House is embracing a cooperative venture between General Motors and Toyota, the two biggest auto companies in the world. Back in 1978, even a merger between Chrysler and American Motors would have been impossible. It goes to show you how the world changes.
Ever since I was fired from Ford, there were rumors around town that I might be headed for Chrysler. I was available, Chrysler was in trouble, so people put two and two together. The first overture came through Claude Kirk, the ex-governor of Florida and a personal friend of mine, who asked me if I'd have lunch in New York with Dick Dilworth and Louis Warren, two of Chrysler's board members. Dilworth ran the financial empire of the Rockefeller family, and Warren was a Wall Street lawyer who had been associated with Chrysler for thirty-five years. I agreed to the meeting. For some reason, I still remember what we ate for lunch: raw clams on the half shell. They were so good I ate two dozen of them.
This was a getting-to-know-you meeting rather than anything official, and our conversation remained pretty general. Dilworth and Warren made it clear that they were talking to me as private individuals, not official representatives of the company. They did speak with deep concern about the auto business—and especially about Chrysler. But for the most part, it was only an exploratory discussion, more social than business.
Meanwhile, I had remained in touch with George Bennett. I soon learned that he had been my one real friend on the Ford board. Besides serving there, George was also on the board of Hewlett-Packard. And Bill Hewlett, the cofounder of that company and a likeable genius, was a member of the Chrysler board. Hewlett knew that Bennett and I were friends, and when they talked, George had the honesty to tell him how valuable I had been at Ford.
A little later I got a call from John Riccardo, chairman of the board of Chrysler. He and Dick Dilworth wanted to meet me down at the Hotel Pontchartrain, just a few blocks from Henry's Renaissance Center. The purpose of the meeting was to talk in general terms about the possibility of my coming to Chrysler.
We kept the meeting as quiet as possible. I drove my own car and entered the hotel through a side door. Even Gene Cafiero, the president of Chrysler, was kept in the dark. Riccardo and Cafiero had been feuding so openly that the whole town knew about it.
At the meeting, both Dilworth and Riccardo were still pretty vague. "We're thinking of making a change," Riccardo said. "Things aren't going right."
That was about as specific as they wanted to get. Both of them were trying to offer me a job without actually coming out and saying it. That sounded like baloney to me, so I put it to them directly: "What are we really here to talk about?"
"About hiring you," Riccardo said. "Would you be interested in coming back into the auto business?"
I told them that before we could talk specifics, I had a number of questions about Chrysler's current situation. I wanted to know exactly what I'd be getting into.
"I don't want to go into this blind," I said. "I need to know how bad things are. I need to know where the company stands. How much cash you have. What your operating plan is for next year. What your future products look like. And especially whether you guys really think you can make it."
Our next two meetings were held at the Northfield Hilton in suburban Detroit. Riccardo painted a bleak picture, but one that I thought could be turned around in a year. I really don't think that John or anyone else at Chrysler was trying to pull the wool over my eyes. One of Chrysler's biggest problems, as I soon learned, was that even its top management didn't have a very good idea of what was going on. They knew Chrysler was bleeding. What they didn't realize—and what I would soon find out—was that it was hemorrhaging.
That fall it sounded like a good, tough challenge. I went home from these meetings and talked things over with Mary. She said: "You won't be happy doing anything except cars. And you're too young to sit around the house. Let's give that bastard Henry a shot he'll always remember." She was feisty that way. I also talked it over with my kids. Their attitude was: "If it makes you happy, go for it!"
The only remaining question was whether Chrysler could afford me—and I don't just mean financially. What I wanted now was to be my own man. At this point in my life, I had no interest in working for somebody else. I had been number two for too long. If I took the Chrysler job, I had to be _número uno_ within a year or so—or no dice!
That was my going-in price to even discuss coming to Chrysler. It wasn't just my experience with Henry, although that was part of it. It was also that I needed a completely free hand to be able to turn the company around. I already knew that my way of doing things was totally different from theirs. Unless I had full authority to put my management style and my policies into effect, going over to Chrysler would be a major exercise in frustration.
I had the impression that Riccardo wanted me to be president and chief operating officer, with himself as chairman and chief executive officer. But when I told him what I wanted, I found out I was wrong. "Listen," he said. "I'm not going to stay in this job much longer. There's only room for one boss here. If you come with us, you'll be it. Otherwise, we wouldn't have gone to all the trouble of setting up these meetings."
It was sad in a way, because he hadn't even been pushed by Chrysler's board of directors to approach me. He did it on his own. He obviously realized that the company was in deep trouble and that he wasn't going to be able to nurse it back to health. He would get rid of Cafiero to bring me in, knowing full well that if I joined, his own days as chairman were numbered. We agreed that I would come in as president but would become chairman and CEO on January 1, 1980. As it turned out, Riccardo resigned a few months early, and I became the boss in September of 1979.
John Riccardo and his wife, Thelma, were two of the finest people I've ever met. Unfortunately, the crisis at Chrysler was so severe that I never really got to know them. But one thing was perfectly clear: John was sacrificing himself to save the company. He was over his head and he knew it. Although it meant the end of his own career, he bent over backward to make sure that the transition would go as smoothly as possible. He blew himself out of the water to bring Chrysler back to life. And that is the test of a real hero.
The next step in the hiring process was a meeting with Chrysler's compensation committee in the Chrysler suite at the Waldorf Towers in New York. This time, by way of discretion, I took the elevator up to the thirty-fourth floor, where Ford had its suite, and then walked up two flights to the Chrysler suite. Riccardo followed in a separate elevator.
We had to be that careful. If Iacocca, who was still in the news because he was just fired from Ford, was seen talking to Riccardo and the Chrysler board, the press would jump the gun and I'd find myself hired before we had come to any decision. But the story never did leak out. There was some light speculation in _New York_ magazine a week before the announcement, but generally the security was first-rate.
The announcement that I would be joining Chrysler in November must have been a real jolt to Henry Ford. Normally in these situations, the man who's fired takes his pension and goes off quietly to Florida, never to be heard from again. But I stayed within the walls of the city, and that really got to him. When word got out that I was going to Chrysler, I heard from good sources that Henry was getting sloshed every night. He was always a big drinker, but I'm told that he really got bad during this period. Rumor had it that he was putting away two bottles of Château Lafite-Rothschild a night. At $120 a bottle, that's an expensive nightcap! But based on past experience, I imagine the Ford stockholders were still picking up the tab.
When Henry fired me, my settlement with Ford included severance pay of $1.5 million. But there was one important catch—Ford's very restrictive contract included a competitive clause which stipulated that if I worked for another car company I would forfeit the money.
"Don't worry about that," Riccardo told me. "We'll make you whole." When my appointment to Chrysler was made public, the press made a big fuss about how I had been given a bonus of $1.5 million just for signing up with Chrysler. In reality, I didn't get a nickel for signing. I had earned that money over many years at Ford, through deferred compensation as well as retirement and pension benefits. Chrysler was simply matching it. In effect, they were buying out my contract.
At Ford, my official salary had been $360,000, although in good years my bonuses raised that total to as much as $1 million. I knew that Chrysler couldn't afford to pay me more than that, so I told the committee that I'd accept the same salary I was earning when I was fired.
Unfortunately, Riccardo's own salary at the time was only $340,000. This made things a little awkward, because I was starting out as the president, and he was still the chairman. It wouldn't look right if I was earning more than he was. The board solved the problem by granting Riccardo an immediate raise of $20,000, which made us even.
I've never had any qualms about getting a high salary. I'm not a big spender, but I appreciate the achievement a high salary represents. Why does a guy want to be president? Does he enjoy it? Maybe, but it can make him old and tired. So why does he work so hard? So he can say: "Hey, I made it to the top. I accomplished something."
My father always said: "Be careful about money. When you have five thousand, you'll want ten. And when you have ten, you'll want twenty." He was right. No matter what you have, it's never enough.
Still, I'm an entrepreneur at heart. At Ford, I used to watch with some envy as the car dealers made the really big bucks. It's not that I wasn't earning a good living. For a couple of years in the 1970s, Henry Ford and I were listed as the two highest-paid businessmen in America. My mother and father thought that was terrific, a real badge of honor.
Yet I know guys in real estate in New York who can make that much money in a single day. But unlike the big dealmakers, my income is public knowledge. I get more mail and more requests for money than I can handle. Which brings me to another of my father's favorite sayings. "You think _making_ money is hard? Wait until you try giving it away!" It's true. Everybody writes me and wants me to share the wealth. Every college, every hospital, every good cause on the face of the earth. Seems it's a full-time job to do it right.
When I worked at Ford, I barely knew that Chrysler existed. It was GM that we followed and nobody else. We never thought much about Chrysler. Their products didn't even show up on the monthly sales sheets that measured how well our cars were doing against the competition.
I can think of only two occasions at Ford when we were forced to pay attention to Chrysler. The first was over the logo. In the early 1960s, Lynn Townsend, Chrysler's chairman, made an extended trip to visit Chrysler dealers across the country. When he came back, he told one of his colleagues that he had been amazed by the number of Howard Johnson outlets in the United States. He was even more amazed when his colleague replied that there were actually more Chrysler dealerships in America than there were Howard Johnsons.
Townsend started to think about the bright orange roofs that identify Hojos. He decided that to increase their visibility Chrysler dealerships ought to have a symbol, too. The company commissioned a New York firm to create a logo for Chrysler. Before long, the white pentastar on a blue background was popping up all over.
The Chrysler logo was so successful that within a year we at Ford were forced to respond. We already had our famous blue oval. Now we started putting it up on the dealers' signs. But we blew it. Chrysler used the pentastar with the dealer's name under it. GM put the dealer's name right in the sign. Ford Division dealers had the oval in Ford script and then another "Ford" next to it in block letters, but there was no place for the dealer's name in that sign. It prompted many a dealer to complain that if Henry Ford could use his name twice, the dealer was at least entitled to use his name once.
The other time we followed Chrysler was on their extended warranty in 1962. Until then, Ford had the best warranty in the business—twelve months or twelve thousand miles. At the time we didn't pay much attention to Chrysler's decision to take the warranty all the way up to five years or fifty thousand miles. But within about three years, Chrysler's market share had gone up so much that we at Ford had to come up with a similar program.
The so-called warranty wars among the Big Three automakers lasted for about five years. Eventually we all discontinued the plans because they were too expensive. In those days, our cars weren't really good enough for us to back them for half a decade.
Then there was Chrysler's great reputation for engineering. The engineers at Chrysler have always been a cut above their counterparts at Ford and GM. I assumed it was because of the Chrysler Engineering Institute, and I was always after Henry to set one up, although he never did. Over the years we stole a few of their best people. In 1962, I had raided Chrysler and brought over a dozen of their top engineers. Several of them rose to the highest ranks at Ford.
But ever since Ford had surpassed Chrysler in the early 1950s, all our attention was directed toward General Motors. I was and still am a devoted GM-watcher. They're like a country unto themselves, and I envy their tremendous brute power.
Still, I was familiar with the history of the auto industry, and I knew a little about the origins of the Chrysler Corporation and the man who founded it. When the car business started, there was just one key figure: Henry Ford. With all his quirks and his idiosyncrasies—and with all his bigotry—the original Henry Ford was an inventive genius. He started by tinkering with cars and eventually he learned how to mass-produce them.
Henry Ford often gets credit for the assembly line, but actually that was the creation of others. Where the old man was truly innovative was in coming up with the $5.00 day in 1914. Five bucks was more than double what workers had been making, and the publicity from this announcement was overwhelming.
What the public hasn't always realized was that Ford didn't make his offer to the workers out of any great generosity or compassion. It wasn't their standard of living he cared about. Henry Ford never hid his real reason for the $5.00 day: he wanted his workers to earn enough so that they could eventually buy their own cars. In other words, Henry Ford was creating a middle class. He realized that the industry—and therefore the Ford Motor Company—could only be truly successful if its cars appealed to the workingman as well as the wealthy.
The next major figure in the industry was Walter P. Chrysler. He was an innovator in engines, transmissions, and mechanical components, and his company has been strong in those areas ever since. Walter P. left General Motors in 1920, when the chairman, William Durant, wouldn't give him the freedom to run the Buick Division the way he wanted. This guy was my kind of maverick!
I have a special interest in the next part of the story. Three years later, Walter Chrysler comes out of retirement to reorganize the Maxwell and Chalmers Motor Car Companies, which are dying. So what does he do? He brings out new models and promotes them aggressively. _He even appears in some of the advertising!_ By 1925, he has reorganized a joke of a company into the Chrysler Corporation.
But he didn't stop there. In 1928, he bought out Dodge and Plymouth. His own company was now one of the big boys, and it has remained there ever since. When Walter Chrysler died in 1940, the company had surpassed Ford and was second only to General Motors, with 25 percent of the domestic market. Oh, how I'd love to repeat his achievement! To get 25 percent of the market and knock off Ford? I'd give my eyeteeth.
Although they were having a hell of a tough time by the late 1970s, Chrysler did have that long tradition of design and engineering innovation you could build on. Frederick Zeder, Chrysler's chief engineer during the 1930s, was the first man to figure out how to get the vibrations out of cars. His solution? He mounted their engines on a rubber base. Zeder also invented the high-compression engine, the oil filter, and the air filter.
I learned that Chrysler engineers in Michigan had designed the world's most sophisticated tank. Their engineers in Alabama designed the world's first electronic ignition for cars. Chrysler people designed the first lock-up torque converter for greater fuel efficiency, the first modern electronic voltage regulator, the first hydraulic brakes, and the first under-the-hood computer. I already knew that Chrysler had the best engines and transmissions in the business.
So there was no question that Chrysler had a respectable past. I was also convinced it had a future. The company already had a solid dealer organization, as well as engineers second to none. The only trouble was that they weren't given the resources to build good products.
I was equally confident of my own abilities. I knew the car business, and I knew I was good at it. In my heart I honestly believed that the place would be humming within a couple of years.
But the opposite happened. Everything collapsed. We had the Iranian crisis, and then we had the energy crisis. In 1978, nobody could have imagined that by the next spring there would be havoc in Iran and the price of gas would suddenly double. Then, to top it off, came the biggest recession in fifty years.
All this took place only a few months after I had signed on at Chrysler. It made me wonder whether my destiny had caught up with me. Maybe when God—the real God, not Henry—had me fired from Ford, He was trying to tell me something. Maybe I had been fired at the perfect time, right before everything fell apart, and I was just too stupid to accept my good fortune.
For a variety of reasons, Chrysler turned out to be a hell of a lot more than I bargained for. But once I was in, once I had decided what it was I wanted to do, I never thought seriously of leaving.
Of course, that's not always the best policy. People sometimes die with that attitude. They get swamped and overtaken by events, and they're still holding on as the waters rise up above them. When I signed on for my new job, I couldn't imagine that anything in the automobile business could be _that_ bad. I was wrong. In retrospect, I have to admit there were several times at Chrysler when I came close to drowning.
# XIV
# ABOARD A SINKING SHIP
On November 2, 1978, the _Detroit Free Press_ carried two headlines: CHRYSLER LOSSES ARE WORST EVER, and LEE IACOCCA JOINS CHRYSLER. Great timing! The day I came aboard, the company had announced a third-quarter loss of almost $160 million, the worst deficit in its history. "Oh, well," I thought, "from here things can only get better." Despite the huge losses, Chrysler's stock closed up three eighths that day, which I took as a vote of confidence in my new administration. Ha, ha!
On my first day on the job, I had a little trouble getting to the office. To be honest, I wasn't exactly sure where it _was._ I knew that Chrysler headquarters were in Highland Park, just off the Davison Expressway. But beyond that I had to ask for directions. I didn't even know what ramp to get off.
I had been to Chrysler only once, when I was president of Ford. But in those days I had a driver, and I didn't pay much attention to the route we followed. Every three years, the heads of the Big Three used to get together for what we called summit meetings, to prepare a joint strategy for labor negotiations. Henry Ford and I had gone to one of those meetings over in Highland Park. We were joined there by Lynn Townsend and John Riccardo of Chrysler as well as by the GM people and all the lawyers.
By the way, the union would get uptight about these meetings. They were sure that we were conspiring against them. Little did they know that these talks were always an exercise in total futility. As the marginal producer, Chrysler could never afford the possibility of a strike, so all our tough talk about dealing with the union came to naught.
When I got there that morning, Riccardo showed me around the place and introduced me to some of the officers. There was a meeting with a few of the top people, and, as usual, I lit up a cigar. Riccardo turned to his group and said: "You guys know I've always had a fetish about no cigar smoking in meetings. As of this morning, we've just rescinded that rule." I took it as a good omen. From everything I had heard about Chrysler, rescinding some of the house rules sounded like a super idea.
Before the day was over, I noticed a couple of seemingly insignificant details that gave me pause. The first was that the office of the president, where Cafiero worked, was being used as a thoroughfare to get from one office to another. I watched in amazement as executives with coffee cups in their hands kept opening the door and walking right through the president's office. Right away I knew the place was in a state of anarchy. Chrysler needed a dose of order and discipline—and quick.
Then there was the fact that Riccardo's secretary seemed to be spending a lot of time taking personal calls on her own private phone. When the secretaries are goofing off, you know the place has dry rot. During the first couple of weeks in a new job, you look for telltale signs. You want to know what kind of fraternity you've joined. These are the signs I remember, and what they told me about Chrysler made me apprehensive about what I was getting myself into.
It turned out that my worries were justified. I soon stumbled upon my first major revelation: Chrysler didn't really function like a company at all. Chrysler in 1978 was like Italy in the 1860s—the company consisted of a cluster of little duchies, each one run by a prima donna. It was a bunch of mini-empires, with nobody giving a damn about what anyone else was doing.
What I found at Chrysler were thirty-five vice-presidents, each with his own turf. There was no real committee setup, no cement in the organizational chart, no system of meetings to get people talking to each other. I couldn't believe, for example, that the guy running the engineering department wasn't in constant touch with his counterpart in manufacturing. But that's how it was. Everybody worked independently. I took one look at that system and I almost threw up. That's when I knew I was in really deep trouble.
Apparently these guys didn't believe in Newton's third law of motion—that for every action there's an equal and opposite reaction. Instead, they were all working in a vacuum. It was so bad that even this description doesn't begin to do it justice.
I'd call in a guy from engineering, and he'd stand there dumbfounded when I'd explain to him that we had a design problem or some other hitch in the engineering-manufacturing relationship. He might have the ability to invent a brilliant piece of engineering that would save us a lot of money. He might come up with a terrific new design. There was only one problem: he didn't know that the manufacturing people couldn't build it. Why? Because he had never talked to them about it.
Nobody at Chrysler seemed to understand that interaction among the different functions in a company is absolutely critical. People in engineering and manufacturing almost have to be sleeping together. These guys weren't even flirting!
Another example: sales and manufacturing were under the same vice-president. This was inconceivable to me because these were huge and primarily separate functions. To make matters worse, there was virtually no contact between the two areas. The manufacturing guys would build cars without ever checking with the sales guys. They just built them, stuck them in a yard, and then hoped that somebody would take them out of there. We ended up with a huge inventory and a financial nightmare.
The contrast between Chrysler's structure and Ford's was simply amazing. Nobody at Chrysler seemed to realize that you just can't run a big corporation without calling some pregame sessions to do blackboard work. Every member of the team has to understand what his job is and exactly how it fits in with every other job.
But instead of tying the loose ends together and looking at the larger picture, Riccardo and Bill McGagh, the treasurer, had to spend their time visiting all the banks that had lent Chrysler money. They were continually running from one bank to the next just to keep the outstanding loans intact. That meant they were dealing with the day-to-day crises, always focusing on next month instead of next year.
A couple of months after I arrived, something hit me like a ton of bricks. We were running out of cash! Before I came to Chrysler, I had been vaguely aware of a number of problems there, ranging from poor management techniques to skimping on research and development. But the one area where I had some degree of confidence was financial controls. After all, everybody in Detroit knew that Chrysler was run by financial men. We all assumed, therefore, that financial controls were given top priority.
But I soon discovered to my horror that Lynn Townsend (who had retired a couple of years earlier) and John Riccardo were basically a couple of accountants from the Detroit auditing firm of Touche Ross. What's more, they hadn't brought in any serious financial analysts. Their attitude seemed to be: "We'll handle that stuff ourselves." But there was no way they could do that in a company the size of Chrysler.
Gradually I was finding that Chrysler had no overall system of financial controls. To make matters worse, nobody in the whole place seemed to fully understand what was going on when it came to financial planning and projecting. Even the most rudimentary questions were impossible for them to answer. But never mind the answers: these guys didn't even know the questions!
At Ford, as soon as I became president I had asked for a list of all the plants, marked with the rate of return on investment for each one. But talking this way at Chrysler, I might as well have been speaking a foreign language. I couldn't find out _anything._
This was probably the greatest jolt I've ever had in my business career. When I thought about it, I was bereft. (That's a euphemism for feeling lower than whale shit!) I already knew about the lousy cars. I was well aware of the bad morale and the deteriorating factories. But I simply had no idea that I wouldn't even be able to get hold of the right numbers so that we could begin to attack some of Chrysler's basic problems.
Lynn Townsend always enjoyed a good reputation as a financial man, but I think his decisions, like those of many businessmen, had more to do with the next quarter's profits than with the long-range good of the company. For years, Chrysler had been run by men who didn't really like the car business. And now the chickens were coming home to roost.
As a result, the company had begun to play follow the leader. As the smallest of the Big Three, Chrysler could have and should have been the industry front-runner when it came to developing new cars. But engineering, which had always been Chrysler's ace in the hole, became a low priority under Lynn Townsend. When profits started to fall, it was engineering and product development that paid the price.
Instead of concentrating on good cars, Lynn Townsend and his group started to expand overseas. In their zeal to become an international company, they bought European firms that were dead on their feet—companies that were dogs, such as Simca in France and Rootes in England. They were babes in the woods when it came to international operations. I began to think there were Chrysler people who didn't even know that the British drove on the left-hand side of the street!
Lynn Townsend was always popular with the stockholders, and as one of them, he himself became rich. But I don't think he ever really understood the fundamental business of the company. At one point during his administration, Chrysler was actually running marginal or losing operations on every continent except Antarctica.
Townsend did do some good things at Chrysler, such as establishing Chrysler Financial, a subsidiary that was designed to provide credit for both the dealers and the retail customers. Today Chrysler Financial is a model of its kind. So Townsend certainly doesn't deserve all the blame for Chrysler's weak position. I often wondered: where the hell was the board when all of this was going on?
When I went to my first board meeting, I began to understand the problem. Chrysler's board of directors had even less information than their counterparts at Ford—and that's saying a mouthful. There were no slides and no financial reviews. Riccardo was giving a little pitch from the back of an envelope. This was hardly the way to be running the tenth largest corporation in the country.
When I became chairman, I moved in on the board members very gradually. I wasn't crazy enough to point my finger at a group that had just hired me and tell them: "It's your fault." But once or twice I did ask the board, as politely as I could: "How did management ever get their plans past such a distinguished group of businessmen? Didn't you guys get any information?"
Within the ranks, Chrysler's problems were not confined to top management. All through the company, people were scared and despondent. Nobody was doing anything right. I had never seen anything like it. The vice-presidents were all square pegs in round holes. Townsend and his people had taken guys who had performed well enough in one area and had moved them around at will. Their attitude was that a guy with talent could climb any mountain. After a few years of being shuffled around, everybody at Chrysler was doing something he wasn't trained for. And believe me, it showed.
The guy who ran parts and service in South America had been brought in as controller and he hated it. When I had to let him go, he was actually relieved. The guy who used to run the European operations had been shipped over here and been made vice-president of purchasing, although he'd never been in purchasing in his life. It was pathetic.
I felt terrible, because in their own environment these guys might have been great. They tried to explain their predicament by saying: "Hey, I never asked for this job. You're asking questions of a controller, and I don't know the answers. What I know about is parts and service. I'm really a catcher, but these guys have me playing shortstop. Hell, I don't know how to play shortstop. I could learn, but I need more time."
They all knew that I was coming in to clean house, and each one was afraid he was going to be the target. They had no certainty in their lives. They were living in fear—and for good reason. Over a three-year period I had to fire thirty-three out of the thirty-five vice-presidents. That's one a month!
In a few cases, I tried to resurrect some of the executives. But it didn't work—they just couldn't cut it. Charlie Beacham used to say that once a guy is over twenty-one, you'll never really change his style or his habits. You may think you can, but his self-image is locked in. Nobody is ever humble enough to learn after he's grown up.
Unfortunately, Beacham was right—as usual. When Paul Bergmoser came in, I remember saying to him: "Try to save some of these guys." He worked with them for six months. "It's impossible," he then told me. "These people have learned the Chrysler way of running their own show. They will never adjust. It's too late."
Problems always lead to other problems. When you have a guy who isn't very sure of himself on the job, the very last thing he wants is a guy backing him up who _is_ sure of himself. He figures: "If the next guy is too good, he'll show me up—and eventually replace me." As a result, one incompetent manager brings along another. And all of them hide behind the overall weakness in the system.
Don't get me wrong. I don't mean that if somebody went to school to study accounting, he has to be dubbed an accountant for the rest of his career, no matter what his other skills may be. My point is simply that each guy has to have a management development plan early in his career. He has to be given enough time on a job to prove that he really learned that particular area.
You don't want to overdo specialization, because if you carry it to extremes, you'll never have general managers. Still, not everybody should be trained for general management.
All of Chrysler's problems really boiled down to the same thing: nobody knew who was on first. There was no team, only a collection of independent players, many of whom hadn't yet mastered their positions.
Now, it's one thing to say all that and to understand in theoretical terms what it means. Believe me, it's quite another matter to see it unfold in front of you in living color. It's pretty scary to witness one of the world's largest corporations, playing for billions of dollars, going down the tubes without anybody being able to stop it. This was a tremendous shock to me. And each day brought more bad news.
The only parallel I could think of was the situation that Henry Ford II had faced thirty-two years earlier. When young Henry came out of the Navy to join his grandfather's company, it was in ruins. In one department, so the story goes, expenses were estimated by weighing the invoices.
The Ford Motor Company had become a disaster because the old man ran it so poorly. He knew nothing about sound business practices. In those days, companies were routinely run by swashbuckling entrepreneurs rather than planners and managers.
But Chrysler was even worse. Chrysler couldn't blame its condition on its founder, who came from another era. The Chrysler fiasco had occurred after thirty years of postwar, scientific management. That in 1978 a huge company could still be run like a small grocery store was incomprehensible.
These problems didn't develop overnight. In Detroit auto circles, Chrysler's reputation had been sinking for years. The place had become known as a last resort: if somebody couldn't hack it elsewhere, he could always go to Chrysler. Chrysler executives had a better reputation for their golfing abilities than for any expertise with cars.
Not surprisingly, morale in Highland Park was very low. And if morale is low, the place becomes a sieve. All kinds of secrets start flowing out. When guys are upset and worried about going bankrupt and losing their jobs, then you've tripled your chances for leaks.
Industrial spying in the auto business is something that the press enjoys talking about—and occasionally indulging in. Spying had sometimes been a problem at Ford. One day in the early 1970s, a friend of mine from Chrysler showed me a packet of confidential materials from Ford that one of his people had purchased from one of ours. I showed the papers to Henry, who got very upset. He tried to put in a system to see how deep this spying and industrial espionage really went and to determine what, if anything, we could do about it.
But it's almost impossible to counter that stuff. We started installing shredding machines and giving out numbered copies of certain reports: 1 was Henry, 2 was Iacocca, and so on. Even then, there would be leaks. You could call in the twelve guys who had access to the report and say: "Somebody in this room is lying," but it wouldn't get you anywhere. I tried it a couple of times, but I never plugged those holes.
I've known a few cases where a company has gone to great lengths to get early photographs, grainy as they are, of somebody else's future cars. But generally, such pictures aren't very useful to the competition. For example, I've always assumed that General Motors had pictures of the Mustang two years before the car went on sale. But what did they really know? They wouldn't want to copy it until it hit the market, when they could see for themselves how well it was doing.
On the other hand, there are times when you might have some engineering work going on that's pretty exclusive. Or maybe you've had a breakthrough to get better fuel economy. Before you know it, the other guy's already got your results in his hands. These are the ones that really hurt.
At Chrysler, bad morale and security leaks were showing up on the balance sheets. They were the reasons why the company was doing so poorly while the rest of the auto industry was ending its best year in history. GM and Ford were reporting record sales and profits in 1978. GM alone sold close to 5.4 million cars, while Ford sold 2.6 million. Chrysler, as usual, was a distant third, with less than 1.2 million. More important, our share of the American car market had dropped from 12.2 percent to 11.1 percent within a single year—a tremendous decline. Our share of the truck market had dropped just as badly, from 12.9 percent to 11.8 percent.
Even worse, Chrysler had lost 7 percent in owner loyalty during the past two years. When I arrived on the scene, our owner loyalty rate was down to 36 percent. By comparison, Ford was at 53 percent, and that was a huge drop for them. GM was always pretty steady at around 70 percent.
We were already having trouble getting people to consider our products. Now the research was telling us that almost two thirds of the people we did attract were unhappy with us. They didn't expect to return and buy another Chrysler product.
Another point troubling me about our sales figures was that Chrysler had long been known as an older guy's car. When I came aboard, the median age for Dodge and Plymouth buyers was higher than that of Buick, Oldsmobile, Pontiac, or even Mercury customers. Our surveys continued to show that Chrysler owners were more likely to be blue-collar, older, less educated, and more concentrated in the northeastern and the midwestern industrial states than those who bought competing brands.
The demographics made clear what I already knew: Chrysler products were perceived as staid and a little boring. We needed some innovative cars in a hurry. If you stand still in this business, you get run over very quickly.
Fortunately, I wouldn't be starting from scratch. Chrysler had a long tradition of innovation, a tradition I was eager to continue. Not too many years earlier, a lot of young people had wanted a Chrysler because it was a hot item. Chrysler had Chargers and Dusters that ran down Main Street quicker than anybody's. Racing cars like high-winged Dodge Daytonas, the Chrysler 300 series, the Satellites and Barracudas were the ones that were clustered around drive-ins and hamburger stands from Maine to California.
Chrysler was also responsible for the ultimate street racer of them all, the Road Runner, with its 426-cubic-inch "Hemi" engine. This was a classic of the late 1960s—loud, fast, and almost as powerful as a locomotive. Every evening these muscle cars would race up and down Detroit's Woodward Avenue, where they were occasionally joined by professional engineers and car executives on their way back to the suburbs.
Yet now Chrysler was weak in the sunbelt, with its younger and more affluent drivers. We were especially weak in California—and that's the place that really counts. Although the car industry was born in Michigan, it came of age in California. California gave us our first vast system of freeways. It was the entry point for the youth market—with muscle cars and four on the floor and exotic wheel covers and live-in vans and crazy cars and various other permutations of the basic automobile that began in a factory in Michigan.
California has also contributed some things that we in Michigan aren't too happy about. One is the import boom. Californians buy more imported cars than the residents of any other state. Second, they've given us some supercharged emission standards that have almost transformed California itself into a foreign country.
It's been said many times before, but it's worth saying again: California is really the mirror into the future. Sometimes we don't like everything we see when we gaze into that mirror, but we'd be crazy if we didn't take a good, hard look.
We needed to succeed in California, but before we could do that, we had to change the product.
It wasn't only the style of Chrysler products that had a bad reputation. The company had also run into big problems with quality. Among the worst examples were the Aspen and Volaré, the successors to the highly acclaimed Dart and Valiant. The Dart and the Valiant ran forever, and they never should have been dropped. Instead they had been replaced by cars that often started to come apart after only a year or two.
Aspen and Volaré were introduced in 1975, but they should have been delayed a full six months. The company was hungry for cash, and this time Chrysler didn't honor the normal cycle of designing, testing, and building an automobile. The customers who bought Aspens and Volarés in 1975 were actually acting as Chrysler's development engineers. When these cars first came out, they were still in the development phase.
Looking back over the past twenty years or so, I can't think of any cars that caused more disappointment among customers than the Aspen and the Volaré. The Edsel was a different case: people just didn't want it. But with these cars, customers bought them in large numbers and got fooled. They went for the styling, especially the wagon, which Ford and GM didn't have in 1976.
But the Aspen and the Volaré simply weren't well made. The engines would stall when you stepped on the gas. The brakes would fail. The hoods would fly open. Customers complained, and more than three and a half million cars were brought back to the dealers for free repairs—free to the customer, that is. Chrysler had to foot the bill.
But then even cars that were mechanically sound started rusting. The Volaré's rusted fender program cost us $109 million—in 1980, when we could ill afford it. The fenders had rusted through because somebody wasn't paying enough attention to the process of rustproofing them. We weren't asked to recall them, but we had an obligation to our customers to fix them. Even though we stood behind them, the resale value of these cars plummeted, which hurt Chrysler's image badly.
Ford had gone through a similar problem. In 1957, we had come up with a beautiful car, the Fairlane 500, a styling gem that sold like hotcakes. But like the Volaré, it was poorly made. Francis Emerson, my fleet manager in Philadelphia, had one of the first four-doors to show to the managers of the major fleet accounts. The car was so poorly constructed that the rear doors would pop open when he hit a hard bump in the road. He licked the problem by tying the doors together from the inside with a clothesline. "I'm having a hell of a wild time demonstrating this car," he used to tell me. "They like the styling, but I can't let them get in the back seat!"
In those days, the typical Ford customer used to trade in his car every three years. Unfortunately, in 1960 we came up with another clinker, and I thought: "Now we've really got problems. A guy will tolerate one lemon. But what about the '57 customer who bought a new car because he liked the style and then found out the car was lousy? If he stuck with us and bought a '60 Ford, he got burned twice in a row. That guy will never come back. He probably went over to GM or the imports."
The '75 Volaré was in that same category. Of course, GM has had its fiascos, too, like the Corvair. Here I find myself in rare agreement with Ralph Nader: the Corvair really was unsafe. The Vega, with its pancake aluminum engine, was another disaster. The Vega and the Corvair were both terrible cars, but GM is so big and powerful that it can withstand a disaster or two without suffering any major damage. Little Chrysler couldn't afford any.
I can't talk about bad cars without a few words on the Ford Pinto. We brought out the Pinto in 1971. We needed a subcompact, and this was the best one you could buy for under $2,000. A lot of people must have agreed—we sold over four hundred thousand Pintos in the first year alone. This made the car a great success and put it in the category of the Falcon and the Mustang.
Unhappily, the Pinto was involved in a number of accidents where the car burst into flames after a rear-end collision. There were lawsuits—hundreds of them. In 1978, in a major trial in Indiana, the Ford Motor Company was charged with reckless homicide. Ford was acquitted, but the damage to the company was incalculable.
There were two problems with the Pinto. First, the fuel tank was located behind the axle, so if the car got hit hard enough from behind, there was the possibility of a fire.
The Pinto was not the only car with this problem. In those days, _all_ small cars had the fuel tank behind the axle. And all small cars were occasionally involved in fires.
But the Pinto also had a filler neck on the fuel tank that sometimes, in a collision, was ripped out on impact. When that happened, raw gas spilled out and frequently ignited.
We resisted making any changes, and that hurt us badly. Even Joan Claybrook, the tough director of the National Highway Traffic Safety Administration and a Nader protege, said to me one day: "It's a shame you can't do something about the Pinto. It's really no worse than any other small car. You don't have an engineering problem as much as you have a legal and public-relations problem."
Whose fault was it? One obvious answer is that it was the fault of Ford's management—including me. There are plenty of people who would say that the legal and PR pressures involved in such a situation excuse management's stonewalling in the hope the problem will go away. It seems to me, though, that it is fair to hold management to a high standard, and to insist that they do what duty and common sense require, no matter what the pressures.
But there's absolutely no truth to the charge that we tried to save a few bucks and knowingly made a dangerous car. The auto industry has often been arrogant, but it's not that callous. The guys who built the Pinto had kids in college who were driving that car. Believe me, nobody sits down and thinks: "I'm deliberately going to make this car unsafe."
In the end, we voluntarily recalled almost a million and a half Pintos. This was in June 1978, the month before I was fired.
Meanwhile, at Chrysler, my initiation included one more major problem. In my first week on the job, I attended an informal meeting where ten thousand cars were taken out of the production schedule. A week later there was a more formal meeting. This time, _fifty thousand_ cars were promptly withdrawn from the first-quarter schedule for 1979.
I was puzzled and distressed. What kind of profit mentality was this—taking cars willy-nilly out of production? I was horrified to discover that we didn't have dealer orders to build these cars, and there was no room to add any more cars to the already bulging factory inventory. This inventory was known as Chrysler's sales bank, which was nothing more than an excuse to keep the plants running when we didn't have dealer orders for the cars.
At regular intervals the Manufacturing Division would tell the Sales Division how many and what types of vehicles they were going to produce. Then it would be up to the Sales Division to try to sell them. This was completely ass backwards in my book. The company had recruited bright young college graduates who were sitting in hotel rooms day after day with their fingers stuck in a telephone, trying to peddle iron out of the sales bank to the dealers. And the system had been operating this way for years.
Most of the excess cars were kept on huge lots in the Detroit area. I'll never forget visiting the Michigan State Fairgrounds, jammed with thousands of unsold Chryslers, Dodges, and Plymouths, vivid evidence of the company's structural weakness. The volume would vary, but the number of cars was usually far and above what we could hope to sell.
In the summer of 1979, when Chrysler first approached the government for help, the sales bank contained eighty thousand unsold vehicles. At one point the number reached as high as a hundred thousand units, representing about $600 million in finished inventory. At a time when our cash was dwindling anyway and interest rates were high, the costs of carrying this inventory were astronomical. But even worse, the cars were just sitting there in the great outdoors and slowly deteriorating.
Building cars had become a gigantic guessing game. It had nothing to do with a customer ordering what he wanted on the car, or a dealer ordering what the customer was likely to ask for. Instead, it was some guy in the zone office saying: "I'll put power steering on this one and automatic transmission on that one. I'll make a thousand blues and a thousand greens." If a customer wanted red, too bad!
Something had to be done about all those cars, so at the end of every month the zone offices used to "move the iron" by running a fire sale. The zone guys used to spend at least one week a month on the phone just trying to move cars out of inventory. And the dealers got used to it. They soon learned that if they waited until the last week of the month, somebody from the zone office would call them and try to package ten cars for a special price. One way or another, the dealers could always get something off the regular wholesale price. At Ford, we had run occasional fire sales when inventories got too large. But here it was a way of life.
Like Pavlov's dogs, the dealers became dependent on these sales. They knew the day was coming, and they waited. They'd hear that bell ring and their hearts would start to beat faster because now they could buy their cars a little cheaper.
I knew that Chrysler would never be profitable unless we got rid of this system—permanently. I also knew it wouldn't be easy. A lot of people in the organization had become accustomed to the sales bank. They counted on it. Some were even addicted to it. When I vowed to wipe it out, they thought I was dreaming. At Chrysler, the sales bank was so big and so much a part of doing business it was hard to imagine life without it.
I talked tough to the dealers. I explained to them that the sales bank was destroying the company. I told them there was no place for a sales bank in our operation, that the phrase should be struck from the corporate vocabulary. I told them that from now on, they—not we—would be carrying the inventory. I also made it clear that we weren't going to build a car unless we had a specific order for it and that both the company and the dealers would benefit from running things right.
But it wasn't enough to improve our procedures in the future. We were still stuck with all those cars in the sales bank right now. As I explained to the dealers: "We can't sell these cars and trucks to Sears or J. C. Penney. You are our only customers, and somehow you're going to have to buy these products from us—and I mean _now_. I can't unbuild them and put the pieces back. And you can't leave me sitting with half a billion dollars tied up in inventory—no matter how it happened—while you selectively order the cars you think you would like to market and to hell with the rest."
It didn't happen overnight, but eventually the dealers took up the slack and we finally cleaned up the sales bank. It was incredibly difficult. Dealer inventories were already large, and interest rates were high. But the dealers did what was necessary, and within a couple of years we were finally running our plants to firm dealer orders.
Under our new system, salespeople sit down with each of our dealers. Together they plan the dealer's order for the next month, and they estimate his needs for the following two months. We get a firm commitment from the dealer, and that becomes our building schedule.
The dealer has to come through on his end, and we keep our part of the bargain. This means that we build the order right, keep the dealer posted, and deliver a quality product on time.
Today the system has integrity. We might go to a dealer and tell him that to participate in a certain rebate program he has to buy a hundred cars. He can then take it or leave it. But there's no way to fool around with that number, and there's no fire sale at the end of the month. As a result, we no longer operate in a daily panic. Today, unless a customer chooses to buy the car out of the dealer's inventory, his purchase is made to order and he can pick it up within a few weeks.
The sales bank was bad enough, but I also learned that Chrvsler had been running the world's largest leasing company. Instead of selling cars to Hertz and Avis, we had been leasing them. And every six months we were buying them back. Without protest we became used-car brokers. Our dealers didn't want these cars, so we had to dump them at auctions. The first year I was at Chrysler, I wrote off $88 million in used-car losses!
We chose the alternative: to sell the cars to the rental companies, even if the profit margin was minimal. Let _them_ worry about how to get rid of the cars later. Sixty thousand used cars were about the last thing we needed.
The rental companies drive a hard bargain, but especially for Chrysler it's essential to be represented in their fleets. The average Hertz car is out with two or three guys a week, which means I've got two or three product demonstrations of one of my cars that week—to people who may never have driven a Chrysler product before. They get in and they ask: "Who builds this car?" We get a tremendous amount of mail from the rental customers saying: "Why don't you promote this car? Where has it been hiding? I rented a Reliant to drive from Seattle to San Francisco and I was amazed."
The rental cars get us exposure. They attract the youth market, the more affluent crowd, the professional, upscale guy who traditionally hasn't even considered one of our cars. We need much greater penetration in the Southwest and in California, and that's where the rental business is especially important.
Between the sales bank and the rental cars and various other problems, we had to write off $500 million in management mistakes before we could even begin to enjoy the lousy market that was prevailing in those days.
There was so much to do and so little time! I had to eliminate the thirty-five little duchies. I had to bring some cohesion and unity into the company. I had to get rid of the many people who didn't know what they were doing. I had to replace them by finding guys with experience who could move fast. And I had to install a system of financial controls as quickly as possible.
These problems were urgent, and their solutions all pointed in the same direction. I needed a good team of experienced people who could work with me in turning this company around before it completely fell apart. My highest priority was to put that team together before it was too late.
# XV
# BUILDING THE TEAM
In the end, all business operations can be reduced to three words: people, product, and profits. People come first. Unless you've got a good team, you can't do much with the other two.
When I came to Chrysler, I brought along my notebooks from Ford, where I had tracked the careers of several hundred Ford executives. After I was fired, I had prepared a detailed list of everything I wanted to remove from my office. Those black notebooks were clearly mine, but it could be argued that they belonged to the company. I didn't want to take any chances. Henry and I were not on speaking terms, so I brought the list to Bill Ford and he gave me his permission to take the books home.
I went back to those notebooks as soon as I learned that Chrysler was in urgent need of first-rate financial people. A few months earlier, as president of Ford, I had asked J. Edward Lundy, our top finance man, for a report on the best financial talent in the company. Lundy had been one of the original Whiz Kids, and he, as much as anyone else, was responsible for Ford's excellent financial system.
On the surface, my request was perfectly routine. But in retrospect I wonder if I knew on some unconscious level that I might soon be in a position where this information would be valuable. As it turned out, Lundy's list was a godsend.
I opened the notebooks and started reading down the names. Lundy had ranked everybody A, B, or C. There were about twenty names on the A list, but I wasn't sure I wanted any of them. I respected Lundy, but his priorities and mine were different. The A list consisted of first-rate bean counters. What I was looking for was a little more than that.
Looking through the B list, I noticed the name of Gerald Greenwald. He was only forty-four, but he had already accomplished a great deal. I had met Greenwald on a number of occasions and I liked him. I remembered that he was always trying to get out of finance. Once I had helped him expand his range of skills by sending him over to Paris to take over Richier, a farm and construction equipment company we had bought. The company failed, but that wasn't Greenwald's fault. It was simply a bad operation, and eventually we had to sell it.
Next we had sent Greenwald to Ford of Venezuela. He was an aggressive manager, to the point where Ford's market share in Venezuela for both cars and trucks was higher than any other Ford subsidiary. At the time, gas in Venezuela was fourteen cents a gallon, and I've always kidded jerry that under those conditions he couldn't miss. In France he had drawn the bad end of the stick. In Venezuela he got the golden end. But the truth is that he showed real business savvy in both jobs—he was obviously more than just a bean counter.
Jerry's background is highly unusual for the auto business. He's Jewish, the son of a chicken farmer from St. Louis. He got himself a good education in economics at Princeton and then came to Ford with the intention of working in labor relations.
"We have a better idea," they told him. Greenwald was assigned a position in a new division—Edsel. Within a few months of that fiasco he was thinking: "I'm just out of school. How could I have been so lucky?"
Jerry has the talent and the know-how of the entrepreneur who can analyze a problem and then move on to solve it. He doesn't talk things to death—he _acts._ He had always wanted to go beyond finance, and it was clear from his work in Venezuela that his talents extended to other areas as well. I wanted Jerry Greenwald because he was a good businessman, period.
In December of 1978, I called Greenwald in Venezuela. Jerry and his wife were out at a party, so I left a message at their house. When they got back, Glenda Greenwald immediately guessed why I'd called. "Don't call him back!" she told her husband. The Greenwalds were living the good life in Caracas, where Jerry was a big fish in a little pond. The prospect of moving to Detroit to work for a failing company could not have been very appealing.
But Jerry did call back, and we decided to meet in Miami. He showed up with a beard. He wasn't at all sure he wanted to come to Chrysler, and he went to great lengths to keep our talks secret.
Our second meeting was in Las Vegas, where I was attending a Chrysler dealer convention. When Jerry arrived at the hotel, he was jolted to find that a Ford meeting was going on at the same time. He spent the entire time up in his room to avoid running into anyone he might know from Ford. We talked all evening. Jerry had an early plane to catch the next morning, and at 5:30 A.M. he called my room and asked, "Are you up?"
"Are you out of your mind?" I replied. He said that he hadn't slept all night and that he needed to ask a few more questions before he could make his decision. I told him to come right over to my room. As I sat there in my bathrobe, he told me about his doubts. "All my life I fought to get out of that bean-counter syndrome at Ford," he said. "And at Chrysler I'd be coming right back into it."
I explained that I needed him to set up the financial controls, but that when that was taken care of, he could move into other operations. As he left my room and started walking down the hall, I called after him: "Wait a minute, Jerry. You may end up as president sooner than you think." He gave me a skeptical look, as though I were trying to give him the hard sell. But I was serious. Within two years, Jerry became the number two man at Chrysler.
After he agreed to make the move, Jerry flew up to Ford headquarters in Dearborn to give them the news. To his surprise, Henry asked to meet with him. Both Henry and Bill Ford knew Jerry was a prize, and they tried to talk him out of going to Chrysler. Jerry explained to Henry that he just couldn't pass up the excitement Chrysler represented—the opportunity to be involved in turning around a big, ailing company. Henry of all people ought to appreciate his motivation, he said, because Henry had faced a similar challenge when he came into his grandfather's company in 1946. That silenced Henry, so apparently the analogy hit home.
One of Greenwald's first responsibilities was to centralize the accounts payable. Coming from Ford, he probably went into shock when he discovered that bills were being paid from about thirty different locations.
In his first few days on the job, he talked at length to the people involved in running the controller's office. Predictably, he learned that they had no idea how to evaluate from a financial perspective what management was doing and that they couldn't project the consequences of our corporate decisions. He had a hell of a time finding anybody who could be identified as having a specific responsibility for anything. They would tell him: "Well, everyone is responsible for controlling costs." Jerry knew very well what that meant—in the final analysis, nobody was.
One of several disaster areas Greenwald uncovered was Chrysler's handling of warranty costs, which were running as high as $350 million a year. Greenwald immediately asked for a list of the top ten warranty problems with somebody's name next to each one, and a specific plan for correcting the deficiencies and reducing the costs. To his dismay, he quickly learned what I already knew. At Chrysler, to get the financial data in order to address a problem, you had to first put in a system to get the data!
Jerry never let me forget he wanted to be more than a controller. After a few months, when I saw how effective he was, I made him an offer: "If you can find somebody else as good as you are, I'll free you up to do other things."
Greenwald promptly brought in Steve Miller, who had been his main financial man in Venezuela. As our chief financial officer, Miller has been a brilliant addition to the team. During our seemingly endless negotiations with hundreds of banks during 1980 and 1981, Miller's work was absolutely critical. Amazingly, both he and Greenwald managed to stay calm and cool through those chaotic times. Chrysler could not have survived without them.
Hal Sperlich was already at Chrysler when I arrived, having come over when Henry fired him in 1977. Having Hal at Chrysler was like finding a tall, cold beer in the middle of a desert. Thank you Henry!
Whenever I added someone to the team, I felt a little guilty. In order to recruit these guys, I'd have to lie to myself. If I had really been honest, I would have told them the truth: "Stay away from this place—you can't imagine how bad it is!" But I couldn't do that. I had to tell them what I desperately hoped was true: that if we got the right group together, we could save the company.
With Sperlich, however, I didn't have this problem. He was at Chrysler a couple of years before I arrived and he knew perfectly well how bad things were. More than once I said to him: "You son of a bitch, why did you let me take this job? Why didn't you warn me?" He too had lied to himself in order to get me to Chrysler.
But I forgave Hal because his experience at Chrysler gave him a big advantage over my new recruits: he already knew the place. Hal was like my advance man. Riccardo could tell me about the balance sheets, but it was Sperlich who really knew the nuts and bolts of the operation.
As a result, he was able to unearth a lot of good people who had been passed over by the previous management. Many of them were down a few layers, so Hal had to do some serious digging. He discovered a number of bright young men who had been hidden under bushel baskets. They had the talent and the enthusiasm—they just needed to be discovered.
Fortunately, the cancer at Chrysler did not reach all the way down. Although I had to replace almost all the officers, there was plenty of dynamic young talent beneath them. As we started getting rid of the less competent people, it was a lot easier to find the good ones. To this day, I can't believe that the former management didn't notice them. I'm talking about people with fire in their eyes: you can practically tell they're good just by looking at them.
I quickly elevated Sperlich to vice-president in charge of product planning. Before long, I promoted him to head of all North American operations. As I saw it, Hal had a hand in everything that had gone right at Ford during the 1960s and 1970s. More recently, the same has been true at Chrysler.
Hal's a visionary, but a very pragmatic one. He understands how to ring the cash register and he doesn't fool around with trivia. He tolerates a fair share of facts and study, but only up to a certain point. Then he says; "Okay, what are we trying to do here?" And he does it. He's a guy who knows how to move.
Hal's also got that uncanny ability to see into the future, to know what people will want three or four years down the road. We've worked together ever since the Mustang and we test our hunches on each other. Both of us are given a lot of credit for clairvoyance. I'd say that between the two of us, we're at least as good as any _one_ top auto guy in the world!
We have our disagreements, too, but that's part of our working relationship. Hal likes to kid me. He says I'm getting too old to know about the youth market. Maybe he's right. Maybe that's why I still listen to him. But hell, not always! He's only five years younger than I. He's beginning to look older, but after twenty-four years of abuse from me, that's only natural.
From the start, Greenwald and Sperlich were terrific, but two guys do not a management team make. I still needed more help in a hurry. And I knew where to get it. There was one pool of people who had a body of experience and proven ability that was completely going to waste: retired Ford executives. I needed to pick their brains and use their street smarts to get things organized.
Gar Laux had worked in both the marketing and the dealer side of operations at Ford. When the Mustang was introduced, he had been sales manager of the Ford Division. Later he was my general manager in the Lincoln-Mercury Division.
During the Knudsen era at Ford, Gar had left the company to head the Dallas Chamber of Commerce. Within a few years he had another job—as Arnold Palmer's partner in a Cadillac dealership in North Carolina. But it wasn't only Gar's experience that appealed to me. His personality was just as important. He's one of those guys everybody likes to go out and drink with and confide in, and I knew he'd be terrific at building better relations with our dealers. God knows we needed it.
The bad feelings between Highland Park and the dealers-were astounding. I was amazed and appalled by the way the two sides were talking to each other and by the angry and insulting letters that were being exchanged between the dealers and Chrysler headquarters. At Ford I had always been on very good terms with the dealers, but it took me twenty years to win their confidence. Getting to know a whole new group of dealers was different—and I sure didn't have twenty years to do it. I couldn't build all the bridges myself. Gar Laux was the man for the job.
I brought him in to help both sides lower their voices and start listening to each other. After all, what's good for Chrysler is good for the dealers, and vice versa. Instead of allowing the two sides to harbor grudges or take potshots at each other, we needed to create an environment where somebody from top management could sit down with the dealers and go over all of their complaints and problems, one by one.
And the dealers certainly had plenty to say. They had every right to be angry with management, because they hadn't been treated well at all. For years the company had been shipping them junk and expecting them to sell it. Chrysler's quality had been so poor that the dealers got into the habit of expecting to rebuild the cars when they received them. Under those conditions, how could we ask them to be courteous and enthusiastic? How could we ask them to _trust_ us?
We were flooded with letters from unhappy customers who had visited Chrysler showrooms, letters that said: "I can't get the time of day from these guys," or: "I saw a commercial that said come in and compare. I went in to compare, but there was nobody to talk to. The salesmen all seemed to be drinking coffee or reading _The Daily Racing Form._ So what am I supposed to do?"
Every time I read one of those letters I got mad. I was furious that we were losing sales from people who really wanted to do business with us—if only to help us out.
So I sent Gar to hold seminars with the dealers and remind them of a few fundamentals: when a guy comes through your door, love him. Talk to him. Give him the information he needs to make a $10,000 purchase. He's not always too sure of what he wants. He might not know what a transaxle is or what front-wheel-drive does for him. And the hims have now given way to the hers. Over 50 percent of cars are now bought by women, and they don't always know about the technical side of things. They need some courteous help. Dealing with customers takes knowledge, time, and patience—after all, if salespeople don't have that, they should look for another line of work. (I always remembered my father's admonition to those waitresses.)
Gar informed the dealers that the new administration was going to bring a sense of discipline to all areas of our operations. He said that we recognized the quality problem and were determined to fix it. He explained that we intended to honor our commitments, operate within budgets, and keep to schedules. He told the dealers that the whole company was being turned around and that from now on they could count on us.
Originally, Gar had agreed to come up as a consultant for a few months while maintaining his dealership in North Carolina. Before long, we persuaded him to stay on for a couple of years to be in charge of sales and marketing.
When it came to a quality image, Chrysler had a really serious problem. With something so important, you can't just wave a wand and presto! Even if your product gets better right away, it takes time for the public to realize it. It's like the bad girl in town who changes her ways and goes straight. For the first couple of years, nobody believes her.
Styling and value are what sells cars, but quality is what keeps them sold. When it comes to the public's perception of quality, advertising can't do the job for you. Neither can press conferences or other public appearances. The only solution is to build good products, price them competitively, and then go out and service them. If you can do those things, the public will start beating a path to your door.
To give us a hand on quality, I brought Hans Matthias out of retirement and hired him as a consultant. Hans used to be my chief engineer at the Ford Division and later was in charge of manufacturing for the whole Ford Motor Company. His specialty was quality control; until he retired in 1972, he had done more than anyone else to improve Ford's quality. In two years at Chrysler, he did the same.
Matthias worked with Sperlich to put some discipline into the manufacturing system. Sperlich was always working on future models that were still three years away. "Don't skimp," I told him, "no matter how bad things are right now. The only way we'll ever survive is if we stay in business during alterations." Today our quality is equal to or better than any American-made cars. And we're fast closing in on the Japanese.
The public has become pretty cynical about big business and for good reason. Sometimes our cars were so bad, they felt we built them that way on purpose. Most people don't realize that it's in the company's interest to build cars right the first time. If we catch a problem at the factory, it might cost us $20 an hour to fix it. But if we let that problem go and the dealer has to fix it, it's going to cost us $30 an hour under warranty. As much as I hate paying $20 an hour, it sure as hell beats paying $30.
Good design always involves a delicate balance: what does a customer want, and how can we give it to him without compromising the other things he wants?
Cars are very complex machines, more so each year. Take air conditioning, for example. If you're paying an extra $700 to keep cool in the summer, you want your money's worth. Whoever designs the air-conditioning system has to remember: it's no good if it takes 30 minutes to cool down the car, because most trips are over by then. So you need to install high-speed blowers. But they can't be too noisy, because the guy driving the car wants to listen to his $300 stereo while the air conditioning is on. The air-conditioning guy can't say: "That's not my problem. I just want to cool him down." He's got to integrate his part into the total system of the car.
The designer has to keep several things in mind. First, the part has to be low in weight, because like anything else in the car, if it's heavy, it will affect the mileage. Second, it should be low in cost—for obvious reasons. Finally, it should be easy to manufacture. Assembling two pieces is always easier and more reliable than assembling three.
Easy to manufacture— _that's_ the key to quality. "My design is super." That's a line I've heard for years. And I always think: "Yeah, it's so super that I can't build the thing."
Of course, quality doesn't stop with the engineer. It has to be part of the consciousness of the workers in the plants. Through the establishment of "quality circles," our plant workers have become far more involved than they used to be in the building process. We sit them down in a room and we say: "How about this operation? Can you do it? The engineer says you can, and the manufacturing guy says you can. But you're the ones who have to build the thing. What do you say?"
So off they go to try it for a couple of days. If it doesn't work, they come back and tell us: "That's a bad idea. Here's a better way to do it." The word gets around pretty quickly that management is listening, that we really care about quality, that we're open to new ideas, we're not just a bunch of dummies. That may be the most important consideration of all when it comes to quality—that the worker believes his ideas will be heard.
We also set up a joint UAW-Chrysler Management Quality Program that says: "Look, we'll argue about everything else, but when it comes to quality, we're not going to fight each other. Quality cannot get mixed up with other bargaining and be compromised by the usual adversarial relationship between workers and management."
At Ford, Hans Matthias had made quality really mean something. When I asked him to help us, he couldn't wait to get cracking. In a year and a half he brought discipline into the Chrysler system of manufacturing. Moreover, he did all this as a consultant, and everybody knows that consultants aren't supposed to do anything!
Matthias and I understood each other. Within ten minutes at Chrysler he was saying: "Do you know what you've got here? You've got a mess we may never unravel." But he did. He would go to the plants every morning and pull five units at random off the line. Then he'd bring in a new Toyota and ask the guys to look at the difference. Pretty soon he had the foreman saying: "Hey, our cars are really bad."
Then there's George Butts, who was there when I arrived. George has done a great job in improving the quality of Chrysler products. I've made it very clear to everybody in the company that quality is our top priority, and I think the message has filtered down. I set up a separate department for George to oversee quality. He's the watchdog for me—and my top manager on all quality issues.
During the height of the loan guarantee debate in 1979 when we were cutting costs right and left, Matthias and Butts came to me with a proposal to bring 250 new people into the plants for improved quality control. We couldn't afford it. But I approved the plan anyway because if Chrysler was going to have any future at all, we had to have a quality product.
I can't talk about quality without also mentioning Steve Sharf, who is now head of all manufacturing. He too was at Chrysler when I got there. He's a diamond in the rough, one of those guys who had been kept under a bushel basket for years. Given new responsibilities, he really made good things happen.
Then there was Dick Dauch, who came to Chrysler after working at GM and Volkswagen. Dauch proceeded to bring us fifteen top guys from his two alma maters. This is a point that's often overlooked by people trying to understand our comeback. I took all the guys from Ford that I knew in marketing, finance, and purchasing, but when it came to quality car building I went for the best GM and Volkswagen people. So I had the old and the new, the line and the staff, and the retirees—and they all got along. It was that unique melting pot that turned our quality around so quickly.
Together, Matthias, Butts, Sharf, and Dauch have brought integrity to our manufacturing system. It is this commitment to quality manufacturing—along with a brilliant group of designers and engineers led by Don DeLaRossa and Jack Withrow—that allows us to be the only car company in the world to offer a five-year, fifty-thousand-mile warranty.
That warranty is no sales gimmick. It can't be. In the fourth and fifth years, when those cars start to age, it would be too expensive to repair all those engines and transmissions if they didn't hold up. The liability would kill us.
Fortunately, quality and productivity are two sides of the same coin. Everything you do for quality improves your productivity. When you improve quality, warranty costs go down, and so do inspection and repair costs. If you're doing the job right the first time, engineering and tooling costs go down, too, and owner loyalty starts to rise.
In addition to Gar Laux and Hans Matthias, I brought another ex-Ford man out of retirement to join Chrysler. Paul Bergmoser had worked at Ford for thirty years as vice-president in charge of purchasing. He's tough and innovative, and I knew I could count on him to figure out a dozen ways to do what everybody else said was impossible.
"Listen, Bergie," I told him on the phone, "I'm all alone over here." I tried to explain how Chrysler didn't have any of the systems and organizations we had been so used to at Ford. He too agreed to come aboard—first as a consultant, and later, for a year or so, as president of the company.
When Paul arrived in Highland Park, he was amazed at what he found. He used to come in and say to me: "You know, I'm doing the digging for you, but what is under the rocks I'm overturning you just aren't going to believe." Sometimes we would laugh, it was so wild. After a year at Chrysler, he complained to me: "Lee, I have a terrific accountant's report that tells me we lost a billion dollars this year. What I don't have is an analysis to tell me how we lost it!" All I could say was: "Paul, welcome to Chrysler."
Like all of us who had worked at Ford, Bergie was used to a highly systematic way of working. At Chrysler, he found almost no systems in place in the purchasing department, which even by the lax standards of Chrysler was known for its inefficiency. Unfortunately, Chrysler was more dependent on outside suppliers than either GM or Ford, both of whom build many of their own parts.
And as the smallest of the Big Three, Chrysler wasn't always in a position to get the best prices. To make matters worse, the company had failed to treat its suppliers well, and over the years they had reciprocated in kind. As a result, we couldn't always depend on a steady flow of parts. Bergie had his work cut out for him.
As I've already mentioned, Laux, Matthias, and Bergmoser all came out of retirement to help me. I would have been lost without these guys. Each of them had many years of experience as well as the desire to put that experience to work.
Why did they do it? Was it, as some people speculated, because of my great salesmanship? Of course not. These were my friends. I knew they were the kind of people who would respond to the challenge, who would be willing to give a hand. They thought it could be fun. When it wasn't any fun, they stuck with it anyway. They had that essential quality—inner strength.
That's true, by the way, of everybody who joined our team. Only guys of a certain temperament could hack it. It was more than a challenge—it was an adventure. And in all the travail, nobody ever got weak in the knees. There was no self-doubt. There was no wringing of hands. There was no asking: "Why did I give up a promising career with a good company to take this on?" These were spirited men, men of character and mettle. I'm grateful to every one of them and I will never forget them.
Still, I owe a special debt to the guys who came out of retirement. Let's face it: mandatory retirement is a terrible idea. I've always felt it was ridiculous that when a guy reaches sixty-five, no matter what shape he's in, we retire him instantly. We should be depending on our older executives. They have the experience. They have the wisdom.
In Japan, it's the older guys who are still running things. On my last trip over there, the youngest guy I talked to was seventy-five. I don't think this policy has done Japan much harm in recent years, either.
If you can still come to work at the age of sixty-five and do a good job, why should you have to leave? The retired executive has been there before and he's seen it all. He's learned a lot over the years. What is wrong with old age if the guy is healthy? People forget that our health standards have improved dramatically. If a man's okay physically and has the stamina to do the job, why wouldn't I want to use his expertise?
I've seen too many executives announce that they'll retire at fifty-five. Then when they turn fifty-five, they feel compelled to carry it through. They've said it so often that they're committed, even if they're not crazy about the idea. I think that's tragic.
Many of these guys fall apart when they retire. They've become used to the tough grind, with lots of excitement and high risks—big successes and big failures. Then they suddenly find themselves playing golf and going home for lunch. I've seen a lot of men die only a few months after they retire. Sure, working can kill you. But so can not working.
Well, you might say I finally had my battery and my infield in place. But I still needed an outfield. To complete the new team, I had to buy some marketing talent. Marketing is my specialty, and I wasn't impressed by what I found at Chrysler. I solved the problem in a slightly unusual way. On March 1, 1979, I called a press conference in New York to announce a very important acquisition: we were replacing Chrysler's two ad agencies, Young & Rubicam, and BBDO, with Kenyon & Eckhardt, the New York-based agency that had been so effective for the Lincoln-Mercury Division at Ford.
Even by the standards of Madison Avenue, firing our agencies was a ruthless act. It also represented the single largest account change in the history of advertising. This was a $150 million decision, and it told the business world we weren't afraid to take the bold steps that were essential if we were going to turn our company around.
At the time, K&E still had the $75 million Lincoln-Mercury account at Ford. In order to join us, they had to drop it immediately. I'm sure Henry was none too pleased to hear the news, which must have come as a shock to him. Our announcement had been planned very carefully, and the Ford people were informed only about two hours in advance. Security surrounding the deal had been terrific, and virtually nobody in Detroit knew about the switch before it was announced. After the shake-up, Young & Rubicam became the new agency for Lincoln-Mercury. A couple of years later, when we had grown too big for one agency, BBDO got back the Dodge account. So the whole thing ended up as a high-stakes game of musical chairs.
The two agencies that I replaced were perfectly okay. But I already had so much on my plate that I had to simplify things. I just didn't have the year it would take to deal with two entirely new groups. I didn't have time to teach them my philosophy—or my way of operating. Instead, I brought in familiar professionals who knew me so well that when I gave half an order, they already knew what the other half would be.
In my view, K&E are the best in the business. At Ford they had given us "Ford has a better idea," although some people at Ford actually objected to that phrase. They thought it should have read, "Ford has the _best_ idea."
"Ford has a better idea" was the brainchild of John Morrissey, who until recently was chairman of the domestic board of Kenyon & Eckhardt. John started out with J. Walter Thompson and then moved over to work for Ford before joining K&E. He's a very creative guy, and we go back a long way together.
It was K&E that had come up with "the sign of the cat," which was a critical component in building up the Lincoln-Mercury Division. K&E's record in helping to double Lincoln-Mercury's market share during the 1970s speaks for itself. Lincoln-Mercury was a tough assignment, and it's during those years that I learned that Kenyon & Eckhardt could operate in a crisis mode, under pressure.
Because K&E had been involved with Ford for thirty-four years, we offered them a five-year contract, which was unprecedented in the short-term world of advertising. We also offered them the opportunity to become far more involved than any agency had in the past.
With every new car, public perception is half the battle. The deeper the agency gets involved, the better it is for both sides. K&E people were our active partners. They became members of our most important company committees, including product planning and marketing. They became an integral part of Chrysler, the closest thing to a house agency we could have. In effect, they became our marketing and communications arm.
Such a close association between the agency and the client had never been tried before in the automobile business. But I've always felt that if you're going to spend $100 million on a new car, you can't expect your advertising people to get creative overnight. They've got to be in on the whole process of developing the car. They've got to be at the meetings where the car is being thought up. They've got to give you their best advice as early as possible, such as "This won't sell because..." or "Don't name it that because..."
A big advantage of this setup is the speed with which we can now operate. One Thursday at four in the afternoon we decided to offer our retail customers a new financing rate of 10.9 percent. K&E immediately started filming a commercial. By five the next morning it was finished. By Saturday it was on the air. When something has to be done, I like to move fast. I need an agency that can keep up with the pace.
One of K&E's first decisions was to bring back the symbol of the ram, which had been used years ago by Dodge trucks and then abandoned. K&E's research showed that what people really wanted in a truck was a tough, durable, dependable, no-nonsense product. So they resurrected the ram with the theme "Dodge trucks are ram-tough" and put the word and the symbol back on the trucks and in the ads. Before long, our trucks were perceived as being in the same league as Chevrolet and Ford. We were soon getting consideration from people who until now hadn't even been thinking of a Dodge product.
At one point when sales were very low, the agency came up with a program in which we said to the public: "We want to get you to consider a Chrysler product. Come in and test-drive one of our cars. If you do, and if you then end up buying a car from one of our competitors, we'll give you fifty bucks just for considering us."
Admittedly, this idea was a little far out. Many of our dealers rebelled. They said it would be abused. But they were wrong: we got a lot of people into the showroom, and we sold a lot of cars.
Still, the dealers continued to see it as a gimmick, even though the company, and not the dealers, was putting up the fifty bucks. After a few months we dropped the plan because of the lack of dealer support. But I still think it was a hell of an idea.
Another marketing first we put together with K&E was the money-back guarantee. "Buy one of our cars," we said. "Take it home, and within thirty days, if you don't like it _for any reason_ , bring it back and we'll refund your money." The only catch was a depreciation charge of $100, since we couldn't sell the car as new.
We tried this one in 1981, and all of Detroit thought we were nuts: "What if a guy simply doesn't like the car? What if he changes his mind? What if his wife hates the color?"
If any of those things had happened more than occasionally, we'd have been swamped by customers coming in to get their money back. The paperwork alone could have killed us.
But to the surprise of the skeptics, the program worked very well. Most people play fair; very few took advantage. We had estimated that 1 percent of our customers might bring back their cars. Amazingly, the total number of returns worked out to less than two tenths of one percent.
This one, too, was a revolutionary idea, and I'm glad that we tried it. The important thing to remember is that we were trying everything possible to assure potential buyers that we stood behind what we said.
With Kenyon & Eckhardt on our team, we were now ready to play ball. Unfortunately, the season was half over, and we were deep in last place. Even so, I thought it was only a matter of time before we would be back in the race. I failed to realize that before we could ever resemble the New York Yankees of old, we had to go through a long period of looking more like the old Chicago Cubs.
# XVI
# THE DAY THE SHAH LEFT TOWN
Once I had my team in place, I was confident that Chrysler's recovery would only be a matter of time. But then I hadn't counted on the economy to fall apart. And I certainly hadn't counted on Iran. As it turned out, neither had Jimmy Carter.
Right after I came in, our share of the market headed due south. We started to hit numbers as low as 8 percent, which was pretty dismal even by Chrysler's modest standards. I was beginning to realize that it might take years before this company was back on its feet again.
During my career at Ford, I had taken great pride in my strong family life. No matter what was going on at work, I was always able to leave behind the concerns of the office. But that was before I came to Chrysler. Now I started waking up in the middle of the night. My mind never got settled. I was working constantly. There were times when I wondered about my sanity, about whether I could keep it all together. You can run sprints only so long before you're out of breath.
Thank God I had a wife who understood me. Yet after twenty-five years with me in the auto business, even she started worrying.
I was losing my ass out there, and it was a new experience. Ralph Nader used to claim that Iacocca was such a marketing whiz that he could make people buy cars they really didn't want. Nader complained that the monstrous Big Three, with all their power and leverage, could brainwash the public into buying whatever we told them.
But if that was true, where was this special power now that I really needed it? Where was my great marketing genius when nobody was buying our cars? I could have used some of that magic in 1979, when I was having a terrible time selling anything.
By now, Chrysler's problems were so serious that our precarious position was well known. So in addition to everything else, we had to deal with the nasty rumors of our imminent demise. When a guy puts down $8,000 or $10,000 for a new car, it's a major investment. He has to worry about whether the company is going to be around in a couple of years to provide parts and service. If he's always reading about the potential bankruptcy of Chrysler, he's not going to rush out and buy one of our cars.
It got to the point where Chrysler was fast becoming a one-word joke. The nation's cartoonists were having a field day. So was Johnny Carson:
CARSON: | "Boy, is he mean."
---|---
AUDIENCE: | "How mean is he?"
CARSON: | "Why, he's so mean that this morning he called up Chrysler and asked, 'How's business?' "
Or: "I don't know what's going on at Chrysler, but it's the first time I ever heard anybody make a conference call to Dial-A-Prayer!"
I had been at Chrysler less than three months when all hell broke loose. On January 16, 1979, the Shah left town. Within a few weeks, the price of gas doubled. The energy crisis hit California first, and in May _Newsweek_ featured it as a cover story. A month later, the crisis came East. During the last weekend in June, you had to be lucky to find a gas station open for business.
All of this had a devastating effect on sales of our larger cars as well as recreational vehicles (RVs). Chrysler was a leader in RVs and motor homes, and these huge gas-guzzlers were the first victims when the panic began. By June of 1979, the chassis and the engines we were supplying to the RV industry had virtually stopped selling. And sales of our vans, another big part of our operation, had dropped by half.
One of the public's favorite criticisms of the auto industry is that we should have anticipated the post-Iran oil shortage. But if our own government had no idea about what was going on over there, how should _I_ have known?
No, we weren't prepared for Iran. But we sure responded to it. In 1979, we planned our 1983 models with the very rational assumption that by the time they came out, gas would be selling for $2.50 a gallon. Then somebody yelled, "April Fool's! Gas is cheap again, so give us big cars!"
If anybody had told me that gas prices would double in 1979 and that four years later they would still be at the same price regardless of inflation, I would have said he's nuts. There's no way in the world that we could have anticipated either the Iranian crisis or its aftermath.
There's a widespread myth that American car companies had all the wrong kinds of cars, whereas foreign carmakers had just what people wanted when the oil crisis hit. But that's not true. Until the Shah was overthrown, there were long waiting lists of customers who wanted big cars with big V-8s—in fact, there weren't enough gas-guzzlers to go around.
As for the Japanese, did they really anticipate the American demand for small cars? For thirty years, they've been building nothing else. _Whenever_ the shift occurred, they would have been ready.
We all had small cars, but in 1978 we couldn't give them away. As late as January 1979, just a few weeks before the Iranian explosion, Datsun was offering rebates. Toyota and Honda weren't selling anything. We ourselves had thousands of unsold Omnis and Horizons. And our small Colt, built by Mitsubishi, was not selling even with a $1,000 rebate.
All of that changed overnight. Just two months earlier, gas had been selling for sixty-five cents a gallon. Our full-size car plants were working overtime. The Japanese had seven hundred thousand small cars sitting on the docks in San Diego and Baltimore. But by April, those seven hundred thousand little Japanese cars were gone, snapped up by Americans who wanted instant fuel economy. And many of them had been sold at black-market prices, $1,000 over the sticker price. It wasn't that Ford, GM, and Chrysler couldn't anticipate the American market. _Nobody_ could.
GM was lucky. They had planned to be previewing their new X-body cars in April. The Chevrolet Citation was a down-sized, front-wheel-drive, fuel-efficient car. In the first two days it was offered, GM sold every Citation in existence and took orders for twenty-two thousand more.
Chrysler was less fortunate. After the first oil crisis had subsided in 1974, Americans had gone back with a vengeance to big cars. As usual, Chrysler had followed the market. That meant we didn't have nearly enough subcompacts ready when the public suddenly had its mind changed again.
I vividly remember the images we saw every night on the evening news—pictures of gas lines in California, in Washington, and of actual riots at some service stations in New York. People got scared. They started topping off their tanks whenever they could. Some drivers even started carrying an extra five-gallon can in their trunk or putting a fifty-gallon tank in their garage—and to hell with safety.
Congress started talking about gas rationing. Magazines ran cover stories about how Detroit got caught with its pants down. And sure enough, whether it was panic over the availability of gas or simply the sharp rise in prices, the market for family cars, V-8 engines, vans, trucks, and recreational vehicles dried up instantly.
In a period of five months in 1979, the small-car share of the market rose from 43 percent to nearly 58 percent—a swing of 15 percent. In our business, a move of 2 percent in a single year represents a major shift. A swing of 15 percent is catastrophic. In a single month—May 1979—van sales fell by 42 percent. Never before in the history of the car business had there been such a violent change in the market as the one that occurred that spring.
As damaging as that revolution was, we at Chrysler knew that we could adapt to this new reality. We also knew we could get there before anybody else in Detroit. It wouldn't take much. All we had to do was double our investment in new plants and products over the next five years and hope we were still alive!
But just as we were starting to take those first expensive steps, the country nosedived into a recession. We were still staggering from the first punch. When the second one came, it almost knocked us out. The annual rate of car sales in this country dropped to almost half of what it had been. No industry in the world can survive in an economy that calls for double the investment with only half the revenues. For us, all bets were off. There were no rules, because we were in an unprecedented situation. These were uncharted waters.
Until then you could always say: Go look in the manual. GM originated it, Ford copied it, and Chrysler had pieces of it. I don't mean this literally. It's just that between 1946, when I came into the business, and March of 1979, there was never much doubt about how to run a successful operation.
But suddenly we had to stay loose and change our minds every week. To put it mildly, this was a very new and novel way of doing business. Everybody talks about "strategy," but all we knew was survival. Survival was simple. Close the plants that are hurting us the most. Fire the people who aren't absolutely necessary or who don't know what's going on.
I felt like an Army surgeon. The toughest assignment in the world is for the doctor who's at the front during a battle. In World War II, my cousin was a medic at a M*A*S*H-type hospital in the Philippines. He came back with some pretty ugly stories about triage. It's a question of priorities, he used to say. There'd be forty badly injured guys, and the medical staff had to think fast. "We have three hours. How many guys can we save?" They would pick the ones who had the best chance of survival—and the rest had to be left for dead.
It was the same at Chrysler. We had to do radical surgery, saving what we could. When times are good and you have a marginal plant, you can study it for two years, going over every pro and con. Ford is terrific at that. They'll study the thing to death.
But when you're in a crisis, there's no time to run a study. You've got to put down on a piece of paper the ten things that you absolutely have to do. That's what you concentrate on. Everything else—forget it. The specter of dying has a way of focusing your attention in a big hurry.
At the same time, you've got to make sure you've got something left when the immediate crisis is over. That sounds simple enough, but it's much easier said than done. It takes gritting your teeth. It takes discipline. You hope and you pray that it works, because you're doing the best you can. You're concentrating on the future, meaning you hope you'll be alive tomorrow.
We began by closing some of our plants, including a trim plant in Lyons, Michigan, and our oldest plant, Dodge Main, in Hamtramck, the Polish section of Detroit. There was a great deal of protest from the community when we closed down this inner-city factory, but we had absolutely no choice.
At the same time, we had to keep the suppliers shipping their stuff to us, even when we didn't have enough money to pay them. The first thing we needed to do was convince them that we weren't heading into bankruptcy. You can't fool suppliers. They know your business very well. We brought them in. We showed them our future products. We let them know we were here to stay. We asked them to stand by us.
To save money, we set up a system where parts would be shipped at the last possible moment. This is known as "just in time" inventory, and it's a good way to cut costs. The Japanese have been doing it for years, and they probably learned it from us. As far back as the 1920s, when the ore boats used to arrive at Ford's River Rouge plant, that ore was turned into steel and then to engine blocks within twenty-four hours. But during the boom years between 1945 and 1978, the American car industry fell into some bad habits.
One of the many changes we made was to speed up the way our parts and supplies reached the assembly plants. For example, we used to ship transaxles by train from Kokomo, Indiana, to Belvidere, Illinois. By switching to trucks, we got them there the same day, which streamlined the whole operation.
After a few months, our just-in-time system became so efficient that when our Detroit engine plant staged a wildcat strike, our assembly plant in Windsor ran out of engines four hours later!
We saved money wherever we possibly could. When we designed the K-cars, we deliberately kept them under 176 inches long so that we could fit more of them on a standard freight car. In normal times, nobody notices things like that. But in a crisis, you look for every possible way to cut costs.
When it came time to produce our 1979 annual report, we decided to forego the traditional glorious full-color magazine that most companies send to their shareholders. Instead, our two hundred thousand owners received a brief, plain-looking document printed with black ink on plain white recycled paper. It saved us quite a bit—and it gave our stockholders a message: anything so austere had to mean we were close to impoverished. And we were!
But saving money wasn't enough. We also had to raise a bundle of cash just to pay our bills. At one point we were losing money so badly that we sold all the dealership real estate we owned to a Kansas company called ABKO. Included were a couple of hundred downtown properties that ensured we'd have Chrysler dealers in strategic locations around the country. But we were scrambling for cash and we needed the money, which came to $90 million. Later, to keep our dealers where we needed them, we had to buy back about half of those properties—for twice the price.
In retrospect, selling the real estate looks like an enormous mistake. On the other hand, we needed the cash. At the time, that $90 million looked like a billion to me!
Before he retired, John Riccardo did his best to undo some of the company's more serious mistakes. He made a deal with Mitsubishi for our operations in Australia. He sold our Venezuela operations to GM, and our Brazil and Argentina operations to Volkswagen. He negotiated a deal with Peugeot for our European operations, in return for $230 million and a 15 percent stake in Peugeot, an arrangement that made Peugeot the largest automobile company in Europe. When it was all over, Chrysler had operations in the United States, Canada, and Mexico. And nowhere else.
Sometime later, I concluded that we had no choice but to sell our tank operation to General Dynamics for $348 million. That was a very tough decision, because the Defense Division was the one part of the company that was virtually guaranteed its profit of $50 million a year by the U.S. government. But we needed the cash as a buffer to get the suppliers to give us an extension on our payments to them.
I made that decision reluctantly, in part because I was selling the only business where by law the Japanese couldn't compete. Actually, I was tempted to sell off the car business and keep the tanks! Financially, that would have made a lot more sense. But building tanks was not our main line of business. If Chrysler was going to have a future, it would have to be as a car company.
Even so, it was a painful decision. Our Tank Division was a very strong subsidiary, with plenty of great people. We had forty years of history tied up in the tank business. During World War II, we had been part of the "Arsenal of Democracy." Our people had designed and built the best battle tank in the entire world, and just a few months earlier I had personally driven the first M-l turbine-powered tank off the line. We had some very exciting and profitable new products on the drawing boards. And some of the best talent in the whole company was running the place.
Nobody wanted to give up all that. But in the end, we had to balance our attachment to that division against our urgent need to build a substantial cash cushion with which to ride out the recession. We had no choice but to concentrate our efforts on cars and trucks.
At the time, interest rates were so high that if we hadn't needed all that cash to stay alive, we could have made $50 million a year just by putting what General Dynamics paid us into a money market fund. And $50 million was almost as much as we had been making on the Tank Division itself. It was then that I was first struck by the idea of buying a bank. You could make more money on money than you could on cars, trucks—or tanks!
There's an interesting sidelight to this story. Our contract with the UAW covered tanks as well as cars. In order to survive, we had negotiated an agreement with the union whereby we paid the workers a little over $17 an hour instead of the $20 an hour they had been getting. The tank workers didn't ratify the contract, but they were stuck with it. As a result, the Defense Department got a big break. I went to the Army and said: "Here's a refund of $62 million—my gift to you as a patriotic American." At $1 million a tank, it was like giving them sixty-two tanks free!
All of the measures we took to keep Chrysler alive were difficult. But none was more difficult than the mass firings. In 1979 and again in 1980, we had to lay off thousands of workers, blue-collar and white-collar alike. At one point, in April 1980, we cut our white-collar ranks by seven thousand people, a move that saved us over $200 million a year. A few months earlier, we had laid off eighty-five hundred salaried workers. These two moves alone cut out $500 million in annual costs! These cuts were across the board, including the chiefs as well as the Indians.
The firings were just tragic, and there's no way to pretend otherwise. Among the senior people, I handled most of the firings personally. That's not something you should delegate. You have to tell the truth. Having been fired myself, I had become an instant expert on what _not_ to do. I certainly wouldn't say I just didn't like them! I always made sure to explain the reasons and to offer the guy the best possible pension he was entitled to. In some cases I even tried to bend the rules a little.
Firings are never pleasant, so you have to handle them with as much compassion as you can muster. You have to put yourself in the other guy's shoes and recognize that no matter how you dress it up, it's a pretty bad day in anyone's life. It's especially hard when the person feels it's not really his fault, that he's the victim of bad management, or that the top people never really cared about him.
I'm sure we made a lot of mistakes. Especially in the first year, there were probably guys who got laid off for the wrong reasons. Perhaps the boss didn't like them. Maybe they were too candid or outspoken. We had to move fast, and in the process it was inevitable that some good people got blamed unfairly. I'm sure we have some blood on our hands. But this was an emergency, and we tried to do the best we could.
Most of the people we fired found other jobs gradually. Some stayed in the auto business. Others found jobs with suppliers, or as teachers and consultants. It hurt me to let them go. As a group they were friendlier and nicer than the crew I had known at Ford. But in the end, that wasn't enough.
Watching people get kicked around had a big impact on me. It made me think a lot more about social responsibility, a lesson I had never learned at Ford. There, like the rest of top management, I was above it all. Also, we never had a crisis of this magnitude. In the past, I never had to do much laying off. It's not that I suddenly got religion. It's just that I reached a point where I had to say: "I wonder if I'm doing right by all these people who depend on me."
One of the luxuries we had to eliminate was a large staff. Ever since Alfred P. Sloan took over the presidency of General Motors, all management functions in our industry have been divided into staff and line positions—just like the Army. Line guys are in operations. They have hands-on involvement and specific responsibilities, whether it's in engineering, manufacturing, or purchasing.
The staff guys are the overall planners. They're the ones who integrate the work of the line guys into a workable system. Virtually the only way that a staff guy can be effective is if he's come up through the line. Yet the tendency, especially at a place like Ford, is to take a Harvard Business School graduate who may not know his ass from his elbow and make him staff. He's never run anything, but now he's telling the line guy, who's been doing his job for thirty years, that he's doing it all wrong. I've spent too much time in my career refereeing staff/line disputes that should never have come up in the first place.
You do need a staff—so long as you don't overdo it. At Ford, when Henry was trying to get rid of me, he brought in the consulting firm of McKinsey & Company. In addition to forming the office of the chairman, McKinsey also set up a superstaff of about eighty people. Its purpose was to check all the other staff and line people to make sure everybody was doing his job. Over the years, this group has become like a sovereign power at Ford—a company unto itself.
When Chrysler got hit, I had to let most of the staff go. I've been a line guy all my life, which might have made it easier. But my thinking was simple: I needed somebody to build the cars and sell the cars. I couldn't afford to have a guy who says that if we had done this or that, we could have built that car a little better. Even if he was right, we didn't have the luxury to consider it. When the bullets start to fly, the staff is always first out the door.
With all the firings, we ended up stripping out several levels of management. We cut down the number of people who needed to be involved in important decisions. Initially we did it out of the sheer necessity to survive. But over time we found that running a large company with fewer people actually made things easier. With hindsight it's clear that Chrysler had been top-heavy, far beyond what was good for us. That's a lesson our competitors have yet to learn—and I hope they never do!
# XVII
# DRASTIC MEASURES: GOING TO THE GOVERNMENT
As early as the summer of 1979, it was clear that only drastic measures could save the Chrysler Corporation. We were doing all we could—and then some—to reduce our expenses, but the economy was getting worse and our losses were continuing to mount. By now we were drifting into dangerous waters. If we were going to survive, we needed help. We no longer had the means to save ourselves from drowning.
I could see only one way out of this mess.
Believe me, the last thing in the world I wanted to do was turn to the government. But once I made the decision, I went at it with all flags flying.
Ideologically, I've always been a free-enterpriser, a believer in survival of the fittest. When I was president of Ford, I spent almost as much time in Washington as in Dearborn. Then I went to the capital for only one reason—to try to get the government off our backs. So naturally, when I was back in Washington as chairman of Chrysler to make the case for government help, everybody said: "How can you? How dare you?"
"What choice do I have?" I answered. "It's the only game in town."
We had already tried absolutely everything else. During 1979 and 1980, there had been more than a hundred meetings with potential investors. Most of these people turned out to be phonies, con men, or well-intentioned but naïve Samaritans. Still, I met with anybody who might have been able to help us, however unlikely the prospect.
Then there were the middlemen purporting to represent wealthy Arabs. I knew there were a lot of rich Arabs, but this was ridiculous. We had to follow up 156 separate Arab leads alone. I used to say to our Treasury Department, "Aren't we out of rich Arabs yet?" I must have met a dozen promising-looking guys with Arab connections, most of whom turned out to be hustlers. Each one explained that he had access to an Arab prince who was going to come up with the big bucks. But they were all dead ends.
A noteworthy exception was Adnan Khashoggi. He's a zillionaire from Saudi Arabia who made a huge bundle from the inflow of oil money. Khashoggi is a savvy guy who got an American education. He's a broker who gets involved in all kinds of deals for war matériel and capital investment goods in return for a handsome commission.
I tried to sell him on the fact that the Arab world was in disrepute because of OPEC. I told him that in terms of public relations, whether he was representing Yasir Arafat or King Faisal, an investment in Chrysler could only help the Arab image. But nothing ever came out of my talks with Khashoggi or anyone else from the Arab world.
My discussions with Toni Schmuecker, head of Volkswagen, were far more serious. Toni and I have known each other as good friends for over twenty years, ever since he worked for me as a purchasing agent in Ford of Germany. We had a few hush-hush discussions about a partnership between Volkswagen and Chrysler, which we called the Grand Design. The plan was that we'd both manufacture the same car. Chrysler would sell it on the American side, and Volkswagen would sell it in Europe. Earlier we had arranged to buy three hundred thousand Volkswagen four-cylinder engines a year for our Omnis and Horizons, which had a lot in common with the Rabbit. So in a way, we had already taken the first step.
There were some obvious advantages to the plan. Our dealer network would increase dramatically. Our purchasing power would be much greater. We could spread our fixed costs over a much larger volume of cars. It really was a marriage made in heaven. And it was so simple a baby could have figured it out.
When I joined Chrysler, I hadn't stopped thinking about the idea of Global Motors. From time to time, Hal Sperlich and I continued to talk about it. A merger between Chrysler and Volkswagen would have represented a real beginning, and both Hal and I were tremendously excited about the possibility. If we succeeded in merging with Volkswagen, we could have added on a Japanese partner without too much difficulty.
Our talks with Volkswagen got pretty specific. It was a very interesting episode at a time when we were dying. But that was the problem—we really _were_ dying. Once Volkswagen studied our balance sheet, they pulled back. We were deeply in debt, and we weren't making any money. At the time the plan was much too risky. Instead of their lifting us up, we might have pulled them down.
As our talks were ending, word of the meetings leaked out. The rumor of an imminent merger between Volkswagen and Chrysler was leaked by _Automotive News_ , the weekly trade journal of the car industry. That was proof enough for Wall Street, where our stock jumped from $11 to $14. According to the rumors, Volkswagen had decided to buy out Chrysler for $15 a share.
When the "news" broke, Riccardo was in Washington, meeting with Stuart Eizenstat of the Carter staff and Michael Blumenthal, secretary of the Treasury. Both Eizenstat and Blumenthal urged him to accept the offer. Unfortunately, there was no offer to accept.
Schmuecker had certainly been interested, but Werner Schmidt, their vice-president for marketing, had opposed it strongly. Schmidt, who had once been a trainee in my office at Ford, was a big German fellow who proceeded to tell me in no uncertain terms why Volkswagen could never join up with Chrysler: our image was bad, our cars were lousy, and our dealer organization wasn't strong enough. I must have trained him well, because Schmidt summed up the case against the merger in a few brash words.
Four years later, in 1983, we had further talks with Volkswagen. Ironically, our positions were reversed. Now it was _their_ dealer organization that was having trouble: nobody was buying Rabbits anymore.
Because our government still doesn't have an energy policy, any company that makes only small cars is at the mercy of fluctuating gas prices. And because Volkswagen produces _only_ small cars, the Japanese were walking all over them. For one thing, the German mark, like the dollar, can't compete against the controlled yen. For another, whether Rabbits are made in Germany or in Pennsylvania, the labor costs are very high. On top of that, Volkswagen had to absorb the cost of shipping their cars from Germany, which is another big expense. That's why they finally started to build some of them in the United States.
Volkswagen was our most serious suitor, but there were others, including John Z. DeLorean. DeLorean, who had started his own automobile company after leaving General Motors, came to see me about the possibility of merging his company into Chrysler.
At the time of John's visit, both our companies were in deep trouble. "My father told me never put two losers together," I told him. "So either you make it or I will, and then we'll come back and talk."
DeLorean is a first-rate auto man. I knew him when he was a super engineer for Pontiac and later when he was the top guy at the Chevrolet Division. We were great competitors, going at it head-to-head. When I was on the cover of _Time_ in 1964 for the Mustang, he used to kid me: "Why did you make the cover of _Time_ , and not me with the GTO?" In 1982, when he made the cover of _Time_ for his alleged part in the drug bust, I thought: "Well, John, you finally made it." I felt bad for him, because he had more than enough talent to get there the right way.
After the merger idea didn't pan out, John came to see me again. This time he wanted me to consider an R&D tax shelter, which became known as a "DeLorean Shelter." This project, which he had masterminded with a couple of his associates, got a lot of publicity in _Fortune._ It involved selling off limited partnerships, which are then written off against the government.
He thought Chrysler should go that route, and he had prepared a huge study for me that cost him something like fifty or sixty thousand dollars. I said: "John, I appreciate it. But even if it worked"—and it might have worked in a modest way—"the IRS would flip if I took them for a couple of billion dollars." That's one shelter that would be thrown out—because of sheer size.
Finally, after many more meetings with possible saviors, we ran out of alternatives. And that's when we finally went to the government. But our approach to Washington did not begin with a request for loan guarantees.
Like me, John Riccardo was getting more frantic by the day. Technically he was still the chairman, although he was on his way out and I was running the company. Riccardo could see that we were going down the tubes in a hurry unless something happened soon. That's when _he_ started traveling to Washington.
First he tried to line up congressional support for a two-year freeze on government regulations. That way we could spend our money on new fuel-efficient cars instead of squeezing the very last gram of hydrocarbons out of the tailpipe. But nobody in Washington would listen.
Riccardo had the right approach. Although many of Chrysler's problems were the direct result of bad management, the government had to share at least part of the blame for our situation. After setting some tough, ill-considered regulations for automotive safety and emission controls, it then said to the American automakers: "You guys aren't allowed to get together for joint research and development on these problems. You each have to do it on your own." Mind you, Japan was pursuing the opposite strategy. Since they didn't have to conform to U.S. antitrust laws, they could pool all their genius.
Now, we can do some pretty dumb things in Washington when we work at it. Regulated items should not be competitive. If one of the companies develops a more effective, more efficient, less costly way of controlling emissions, it should be shared. I don't mean the company has to give it away. Let them sell the thing.
But until recently, we couldn't talk about it in the same room without going to jail. We couldn't even hear General Motors describe its system. We literally had to get up and leave, or we'd be guilty under the consent decree by which all of us were operating.
As I write these words, Washington is finally starting to change its tune. It's getting the message that our antitrust laws have been too severe and that we can't be competitive with the Japanese until those laws are reconstituted. Unfortunately, the government's new attitude seems to be starting with a marriage between Toyota and General Motors, the two giants of the industry. We need that like a hole in the head.
At any rate, because of the antitrust laws, General Motors, Ford, American Motors, and Chrysler each had to set up, staff, and finance separate facilities to work on the same problems—problems whose solutions would be of no economic benefit to any of us.
Ever since the Motor Vehicle Safety Act of 1966, all the various gadgets and devices designed to protect motorists from hurting each other came to a cost of around $19 _billion._ General Motors can spread that cost over five million cars a year. Ford spreads it over two and a half million, and Chrysler over about a million.
You don't need a calculator to see that if GM's expenses on a particular item were $1 million and they sold a hundred thousand cars, each buyer paid an additional $10. And if Chrysler's costs were the same but we had only twenty thousand buyers, each one would pay an additional $50.
But that's only for research and development. Then we have to _manufacture_ the stuff. Here the same disproportion applies, except with larger numbers. GM, with its huge sales volume, can build them cheaper and sell them cheaper than we can. And so the gap widens.
Another factor that slowed us down was the sheer volume of staff time and paperwork necessary to report on our EPA regulatory confirmations. In 1978 alone we had to file 228,000 pages to the EPA!
There are any number of studies by widely respected economic institutions that prove beyond a shadow of a doubt that the application of the government's safety, emission, and environmental controls on automobiles and trucks is discriminatory and retrogressive. That's why both Riccardo and I came to the same conclusion. The government helped get us into this mess, so the government should be willing to help get us out.
But Riccardo's proposal for a freeze on regulations fell on deaf ears. At that point he began to lobby for a refundable tax credit. According to this plan, the money we spent on meeting government safety and pollution standards would be refunded to us, dollar for dollar. The total amount came to $1 billion—$500 million in 1979, and another $500 million in 1980. We would repay the debt from higher taxes on our future earnings.
We would not have been the first to ask. In 1967, American Motors had received a special tax credit of $22 million. Volkswagen had received a tax break of $40 million from the state of Pennsylvania in order to set up a plant there. Oklahoma had recently provided tax relief for General Motors. Renault, which is wholly owned by the government of France, had just been given a loan of $135 million for the assembly of new cars in an American Motors plant in Wisconsin. Michigan and Illinois have been known to engage in bidding wars to compete for new business. The city of Detroit has itself given tax relief to Chrysler. And in a number of European countries, American car companies routinely receive outright grants and subsidies from the host government.
Riccardo proposed that companies should get some tax benefits while they're in a loss position. When you're losing money, you can't write anything off. Everything costs you more, from air bags to robots. With all the government regulations to contend with, as well as the energy crisis, the guy in a loss position was really getting a raw deal.
Riccardo went down to Washington to try to get some congressional action, but once more they threw him out. He was a good fellow, but he wasn't an effective communicator. He had a short fuse and a hot temper, and those qualities don't get you very far in the halls of Congress.
John knew there was no viable alternative to government help. We were losing money, and we weren't cutting our overhead fast enough. Volume was going to hell due to the international oil crisis. And because gas prices had just doubled, we had to switch over to front-wheel-drive and high-fuel-efficiency cars in a big hurry. Chrysler had to commit $100 million a month—$1.2 billion a year—just to provide for the future.
Moreover, every Friday we had to come up with $250 million to meet the payroll and pay for the parts we had bought the previous week. It didn't take much foresight to realize where we were headed.
On August 6, 1979, G. William Miller left his position as chairman of the Federal Reserve Board to become secretary of the treasury. It was an important move. As head of the Fed, Miller had told Riccardo that Chrysler should go into bankruptcy rather than approach the government for help. But in his new position, Miller apparently changed his mind. His first official act was to announce that he favored government support for Chrysler as being in the public interest. Miller rejected the idea of tax credits. But he said that the Carter administration would be willing to consider loan guarantees if we submitted an overall plan for our survival.
Only then did we decide to ask for a loan guarantee. Even so, we went through some pretty tough soul-searching in Highland Park. Sperlich in particular was dead set against it. He was convinced that government involvement would ruin the company, and I wasn't sure he was wrong. But I didn't see any other option. "Fine," I said. "You don't want to go to the government? Neither do I. Show me a better way out."
But there wasn't any. Someone else brought up the case of British Leyland, the English car company. When they went to the government, it destroyed people's confidence in the company. Their market share was cut in half, and they never recovered. It wasn't an encouraging precedent, but there was no other choice except bankruptcy. And bankruptcy was no choice at all.
With great reluctance, we decided to proceed with an application for government loan guarantees.
I knew that this proposal would be highly controversial, so I made sure I did my homework. I found that there were a number of precedents for what we were asking. In 1971, Lockheed Aircraft had received $250 million in federally guaranteed loans after Congress decided to save its workers and suppliers. Congress established a loan-guarantee board to oversee the operation, and Lockheed repaid its loans, including an additional $31 million in fees, to the federal treasury. The city of New York had also received guaranteed loans, and it, too, was still in business. But these were merely the best-known examples.
Loan guarantees, I soon learned, were as American as apple pie. Among those who had received them were electric companies, farmers, railroads, chemical companies, shipbuilders, small-businessmen of every description, college students, and airlines.
In fact, a total of $409 billion in loans and loan guarantees was outstanding when we made our $1 billion request. But nobody knew this. They all said that loan guarantees to Chrysler would set a dangerous precedent.
Over and over, I told editors and reporters about the $409 billion in previous loan guarantees—it's now grown to more than $500 billion. Setting a precedent? On the contrary. We were only following the crowd.
Who had received all those guaranteed loans? Five steel companies under the Import Relief Act of 1974, including $111 million to Jones & Laughlin alone. More recently, the Wheeling-Pittsburgh Steel Corporation had been granted $150 million in loan guarantees for plant modernization and the installation of antipollution equipment.
Then there's the housing industry. And subsidies for tobacco farmers. And loans for keeping up our marine freight capability—the maritime industry literally floats on government subsidies. Loans for airlines, such as People Express. Loans from the Farmers Home Administration, the Export-Import Bank, and the Commodity Credit Corporation. Loans guaranteed by the Farmers Home Administration, the Small Business Administration, and the Department of Health and Human Services.
There were even loan guarantees for the Washington subway. The Metro had received $1 billion so that senators, congressmen, and their aides could get around town better.
Up on Capitol Hill, they didn't like it when I talked about that one. But I don't think they'll ever see that money again.
"Let's face it," I said. "The subway is just a showpiece for the capital."
"Showpiece?" they said. "This is a transportation system!"
"Fine," I replied. "What the hell do you think Chrysler is?"
But nobody seemed to remember these other loan guarantees. At least the media should have reported that side of the story. Even today, most people are surprised to learn that our case wasn't totally without precedent.
To be honest, when I was president of Ford, I don't think I would have listened to these arguments either. I probably would have said to Chrysler: "Leave the government out of this. I believe in survival of the fittest. Let the marginal guy go broke."
Back then I had a very different view of the world. But if I had known about some of the guaranteed loans that never got much publicity and if I had followed the arguments in the great national debate that accompanied our approach to Congress, I might have come to see things another way. At any rate, I'd like to think so.
To anyone who would listen, I continually stressed that Chrysler wasn't an isolated case. Instead, we were a microcosm of what was going wrong in America and a kind of test lab for everybody else. No industry in the world got hit harder than autos. Government regulation, the energy crisis, and the recession were almost enough to put us away.
As the weakest link in the chain, Chrysler got hit first. But what happened to us, as I explained again and again, represented only the tip of the iceberg when it came to the problems facing American industry. I predicted flatly that GM and Ford would soon join us in the loss column. (I didn't know they'd join us to the tune of $5 billion. But they did. Within six months they were in the ditch to keep us company.)
What I had to say wasn't what people wanted to hear. It was so much easier to find a scapegoat. And who was a better candidate than the tenth-largest industrial corporation in America—a corporation that had the nerve to approach its own government for help?
# XVIII
# SHOULD CHRYSLER BE SAVED?
From the very start, the prospect of government-backed loans for Chrysler was opposed by just about everybody. Predictably, the greatest outcry came from the business community. Most business leaders came out strongly against the plan, and many of them went public with their views, including Tom Murphy of General Motors and Walter Wriston of Citicorp.
For most of them, federal help for Chrysler constituted a sacrilege, a heresy, a repudiation of the religion of corporate America. The aphorisms started flowing like water as all the old cliches got dusted off. Ours is a profit-and-loss system. Liquidations and closedowns are the healthy catharsis of an efficient market. A loan guarantee violates the spirit of free enterprise. It rewards failure. It weakens the discipline of the marketplace. Water seeks its own level. Survival of the fittest. Don't change the rules in the middle of the game. A society without risk is a society without reward. Failure is to capitalism what hell is to Christianity. Laissez-faire forever. And other assorted bullshit!
The National Association of Manufacturers came out strongly against federal loan guarantees. And at its meeting on November 13, 1979, the policy committee of the Business Roundtable approved the following statement on the Chrysler situation:
A fundamental premise of the market system is that it allows for both failure and success, for loss as well as profit. Whatever the hardships of failure may be for particular companies and individuals, the broad social and economic interests of the nation are best served by allowing this system to operate as freely and fully as possible.
The consequences of failure and reorganization under the revised statutes [bankruptcy, in other words], while serious, are not unthinkable. The loss of jobs and production would be far from total. Under reorganization, the many viable components of the business could be expected to operate more effectively while other elements might be sold off to other producers. It is at this stage that a better case can be made for targeted Federal assistance to deal with any resulting social problems.
At a time when government, business, and the public are becoming more and more aware of the costs and inefficiencies of government intervention in the economy, it would be highly inappropriate to recommend a course of even deeper involvement. Now is the time to reaffirm the principle of "no federal bailouts."
This statement made me furious. I tried to find out exactly who in the group had voted for it, but everybody I checked with seemed to have been out of town at the time. Nobody wanted to take responsibility for zapping us.
In reply, I sent the following letter:
Gentlemen:
I was deeply disturbed to learn that on the same day I testified in Washington on behalf of Chrysler Corporation's request for loan guarantees, the Business Roundtable, of which Chrysler is a member, issued a press release against "federal bailouts."
I have several observations to make.
First—the basic charter of the Roundtable is to contain inflation. Its goals have since been extended to a discussion of other economic issues of national importance. These discussions have traditionally taken place in an open and free atmosphere in which all points of view are considered. The fact that we did not have an opportunity to present the facts of the Chrysler case to the members of the Policy Committee runs directly counter to that tradition.
Second—it is ironic that the Roundtable took no similar position on federal loan guarantees to steel companies, to shipbuilders, to airlines, to farmers, and to the housing industry. Nor did it protest the establishment of "trigger prices" on foreign steel, or the provisions for federal assistance to American Motors.
Third—the Roundtable statement invokes the principles of the free market system which "allows for both failure and success." It totally ignores the fact that government regulatory intrusion into the system has contributed greatly to Chrysler's problem. It is in fact entirely consistent with the workings of a free market system for the government to offset some of the adverse effects of federal regulation. Federal loan guarantees to steel companies were made precisely for that reason.
Fourth—the Roundtable statement is wrong in its declaration that reorganization under the new bankruptcy statute is practical. Our need is not to scale down debt, but to raise huge amounts of new capital. It would be impossible for us to raise the necessary amounts of capital during a bankruptcy proceeding. We have consulted with one of the nation's leading experts on bankruptcy, Mr. J. Ronald Trost, of Shutan and Trost, whose analysis of the new law led him to testify that bankruptcy is not practical for Chrysler and would lead quickly to liquidation.
Your own Roundtable staff has indicated that no bankruptcy experts were consulted during the preparation of your statement. If they had been, I feel sure the statements would have been considerably less confident on the subject of the virtues of bankruptcy.
Fifth—it is most unfortunate that the Roundtable has chosen to engage in sloganeering in this campaign. To proclaim a policy of "no federal bailouts" in a press release is to reduce the discussion to its lowest level. The hundreds of thousands of workers across the country who depend on Chrysler for employment deserve far better in the debate over their future.
Finally, I believe my acceptance of your current invitation to become a member of the Roundtable would be a source of embarrassment to the other members. I had looked forward to joining a business forum that openly discusses vital economic and social issues in an atmosphere of mutual trust and respect. The Roundtable's press release indicates that such an opportunity does not exist in the Policy Committee. Therefore, please accept my sincere regrets and the resignation of Chrysler Corporation from Business Roundtable membership.
That was what I told the Business Roundtable. This is what I would have _liked_ to tell them: "You guys are supposed to be the business elite of this country. But you're a bunch of hypocrites. Your group was founded by some steel guys who've spent their whole lives trying to screw the government. Remember President Kennedy blowing his cool with Big Steel and calling them a bunch of SOBs? You're against federal help for Chrysler? Where were you when loan guarantees were made available for steel companies, shipbuilders, and airlines? Why didn't you speak up about trigger prices on foreign steel? I guess it depends on whose ox is being gored!"
In all these prior cases, the Business Roundtable had been silent. But when I came in asking for federal loan guarantees, they put out a manifesto! As long as it benefits them, they really don't object to a little government interference. But when it comes to saving Chrysler, they suddenly stand on principle.
Even some of our major suppliers joined in the chorus of gloom. We were isolated, captives of an outmoded ideology.
Let me be clear where I stand. Free-enterprise capitalism is the best economic system the world has ever seen. I'm 100 percent in favor of it. All things being equal, it's the only way to go.
But what happens when all things are _not_ equal? What happens when the real-life causes of a company's problems are not determined by free enterprise but by its opposite? What happens when one company—because of the industry it's in and because of its size—is driven into the ground by the unequal effects of government regulation?
That's what happened to Chrysler. Certainly, past management errors were a big part of the problem. Chrysler never should have built all its products on speculation. It shouldn't have tried to expand overseas. It never should have been in the used-car business. It should have paid more attention to quality.
But what ultimately brought the company to its knees was the relentless lash of more and more government regulation.
I had a week of hell in Congress trying to explain that.
They kept saying: "Why do you keep coming down here and crying, 'Regulation!'?"
I said: "Because you guys made the regulations, but you're pointing the finger at us."
Then they would turn around and say: "It was stupid management."
Finally I'd had enough. "Okay," I told them, "let's stop this crap. It's fifty percent your fault—regulation—and fifty percent our fault, because I know all the management sins. What do you want me to do? Crucify the guys who aren't here? They made mistakes. Now let's get back to the matter at hand: you guys helped us get into this mess!"
Why is our free-enterprise system so strong? Not because it stands still, frozen in the past, but because it has always adapted to changing realities. I'm a great advocate of free enterprise, but that doesn't mean I live in the nineteenth century. The fact is that free enterprise no longer means exactly what it used to.
First, the free-enterprise system adapted to the industrial revolution. In 1890, it adapted to Samuel Gompers and the labor movement. The corporate executives all fought against the new movement, but they were the ones who were really responsible for it. They had set up the sweatshops, kept small children working all day at the sewing tables, and created a hundred other injustices that needed to be corrected.
If you go back and read the history books, you'll see that the businessmen of that era were convinced that the new labor unions spelled the end of free enterprise. They thought capitalism was finished and that the specter of socialism in America lurked just around the corner.
But they were completely wrong. They failed to understand that free enterprise is flexible and organic. Free enterprise adapted to the labor movement. And the labor movement adapted to free enterprise—so well, in fact, that in some industries labor has become almost as successful and as powerful as management.
Free enterprise also survived the Great Depression. Here, too, our business leaders thought it was the end of the road for capitalism. They were furious when Franklin Roosevelt decided to create work for people who had lost their jobs. But while the business leaders were only theorizing, F.D.R. was playing with live ammunition. He did what had to be done. And when he was finished, the system was stronger and more successful than ever.
Whenever I praise F.D.R., I hear the business leaders mumbling: "Iacocca's a turncoat. He's lost his mind. He _loves_ F.D.R." But they forget where they'd be without his amazing vision. F.D.R. was fifty years ahead of his time. The SEC and the FDIC are just two of the agencies he set up to prevent the terrible things that happen when business cycles go haywire.
These days, free enterprise has to make further adjustments. This time, it has to adapt to a new world—a world which now includes a formidable rival, Japan, and a world where nobody else is playing by the rules of pure laissez-faire.
While all these ideological arguments were raging, the nation's tenth-largest corporation was falling apart. Obviously, that's not the time to talk ideology. When the wolf is at the door, you get pragmatic in a big hurry.
You certainly don't have the luxury of saying: "Now, wait a minute. I wonder how they would argue this one down at the Union League Club in Philadelphia? What would they say: Free enterprise forever!"
But what is free enterprise really about? Competition. And competition was something the loan guarantees stood to provide a lot more of. Why? Because they would guarantee that Chrysler would still be around to compete with GM and Ford.
Competition is something that the auto industry both needs and understands. During the great debate over the future of Chrysler, a Ford dealer wrote a letter to _The New York Times:_ "For the past twenty-five years, I have been a competitor of Chrysler. Yet I take basic issue with the editorials you have written against Chrysler's request for Federal assistance.... The proper role of the federal government in a democratic free-enterprise system is not to aid the survival of the fattest [sic], but to preserve competition. If Chrysler fails, as the industry strains to reinvent the automobile more quickly than anyone expected, can Ford be far behind?"
Another dealer, in Oregon—this time for Chevrolet—ran a full-page ad in his hometown paper with the headline, "If we can't sell you a Chevrolet or a Honda, buy a Chrysler!" The ad went on to say: "Competition is good for us, good for the industry, good for the country, and good for you, the consumer."
In addition to preserving competition, saving Chrysler would also preserve jobs—lots of them. Altogether, counting our workers, dealers, and suppliers, six hundred thousand jobs were at stake.
Some people believed that if we went under, our workers could have found positions with Ford and General Motors. But that wasn't the case. At the time, both Ford and CM were selling just about all the small cars they could manufacture. It wasn't as if they had empty factories and were looking for additional workers to fill them. If Chrysler folded, almost all our workers would have been unemployed.
Only the imports could have met America's sudden and insatiable demand for small cars. And so if Chrysler went under, America wouldn't only be importing more small cars. We would also be exporting jobs.
We were asking: "Would this country really be better off if Chrysler folded and the nation's unemployment rate went up another half of one percent overnight? Would free enterprise really be served if Chrysler failed and tens of thousands of American jobs were lost to the Japanese? Would our free-market system really be more competitive without the million-plus cars and trucks that Chrysler builds and sells each year?"
We went to the government and we said: "If it makes sense to have a safety net for individuals, it makes sense to have a safety net for their companies. Work, after all, is what keeps individuals alive."
So we argued about competition and we argued about jobs. But most important of all were our arguments about economics. Quite simply, we bottom-lined them. The Treasury Department had estimated that if Chrysler collapsed, it would cost the country $2.7 billion during the first year alone in unemployment insurance and welfare payments due to all the layoffs.
I said to the Congress: "You guys have a choice. Do you want to pay the $2.7 billion now, or do you want to guarantee loans of half that amount with a good chance of getting it all back? You can pay now or you can pay later."
That's the kind of argument that causes people to sit up and take notice. And it brings up an important lesson for young people who may be reading this book— _always_ think in terms of the other person's interests. I guess that's my Dale Carnegie training, and it's served me well.
In this case, I had to talk in terms of the representative sitting in Congress. On ideological grounds, he might be against helping us. But he sure changed his mind fast after we did our homework and provided a district-by-district breakdown of all the Chrysler-related jobs and businesses in his state. When he realized how many people in his constituency depended upon Chrysler for their living, it was farewell, ideology.
While the battle was being fought in and out of Congress, I was busy doing everything I could to raise money, including selling debentures to other companies. I felt like a rug merchant who needed to raise some cash in a hurry. And my spirits were low because wherever I turned, there was nobody saying, "Give it a go, you can make it."
During the debate, the bankruptcy "solution" for Chrysler was very popular. Under Chapter 11 of the Federal Bankruptcy Act, we'd be protected against our creditors until we got our house in order. A few years later, we would supposedly emerge as a smaller but healthier company.
But when we called in all kinds of experts, they told us, as we already knew, that in our case bankruptcy would be catastrophic. Our situation was unique. It wasn't like Penn Central. It wasn't like Lockheed. It wasn't like dealing with the government on defense contracts they've already given you. And it wasn't like the cereal business. If Kellogg's were known to be going out of business, nobody would say: "Well, I won't buy their corn flakes today What if I get stuck with a box of cereal and there's nobody around to service it?"
But cars are different. Just the whisper of bankruptcy would shut off the cash flow to the company. We'd see a domino effect. Customers would cancel their orders. They'd worry about future warranty coverage and the availability of parts and service—not to mention the resale value of the car.
Here there was an instructive precedent. When the White Truck Company declared bankruptcy, they thought they could strong-arm their lenders by hiding under the rules of Chapter 11. Technically it might have worked. Except for one problem. Every one of their customers said: "Oh, no, they've gone bankrupt! I think I'll buy somebody else's truck."
Some of the banks wanted us to go that route. "What are you messing around with the government for? Go declare bankruptcy, and run your company out of bankruptcy." They'd give us examples of other companies that had done that. But we kept saying: "Look, we're a major consumer company in a consumer industry. We wouldn't survive for two weeks trying that."
In a bankruptcy, our dealers would lose their ability to finance purchases from the factory. Nearly all dealer vehicle financing would be shut off within a day or two by the banks and the finance companies. We estimated that about half our dealers would themselves be forced into bankruptcy. Many others would be recruited by GM and Ford, leaving us without outlets in major markets.
Suppliers would demand payment in advance—or on a COD basis. Most of our suppliers are small businesses with fewer than five hundred employees. The strain of a Chrysler bankruptcy would be impossible for thousands of small companies who depended on us for their very existence. Many of them, too, would have to declare bankruptcy, which in turn would deprive us of essential parts.
And forget about Chrysler. What would the largest bankruptcy in American history have done to the nation? A study by Data Resources estimated that the demise of Chrysler would ultimately cost the taxpayers $16 billion in unemployment, welfare, and other expenses.
So much for the bankruptcy option.
During the national debate over Chrysler's future, everybody was taking potshots at us. Writing in _The New York Times_ , columnist Tom Wicker said that Chrysler should suddenly devote its energies to building mass transit instead of automobiles. Editorial cartoonists had a marvelous time with the story that Chrysler was asking the government for help.
But _The Wall Street Journal_ was particularly relentless. They went crazy on the subject of loan guarantees, which they called, in a memorable editorial headline, "Laetrile for Chrysler."
Their objections to government help for Chrysler went far beyond the editorial pages. They just wouldn't leave us alone. They duly reported every single item of bad news but neglected to report any of the more hopeful signs. Even after we had received the loan guarantees, they pointed out that although we had enough money, although we had a restructured company, although we had new management, the right product, and great quality, lightning _could_ strike. The economy _could_ get worse. Car sales _could_ be even lousier.
It seemed that almost every day the _Journal_ would run a negative article about the Chrysler situation. And whenever that happened, we'd have to spend some of our limited energy trying to control the damage to public opinion.
For example, in the first quarter of 1981, Ford lost $439 million. Chrysler was improving but we still lost close to $300 million. What was the _Journals_ headline? "Ford Has Narrower-Than-Expected Loss While Chrysler's Is Wider Than Forecast." That was the only way you could possibly write a headline that made us look worse than Ford. The numbers just didn't support it.
A couple of months later, our monthly sales showed a 51 percent gain over the previous year. But the _Journal_ felt compelled to point out that "the comparison is distorted, however, because Chrysler's year-earlier sales had plunged to rock-bottom levels." Fine. But the previous year, do you think the _Journal_ had excused our low sales by statements to the effect that business had been great the year before?
It reminds me of an old Jewish joke. Goldberg gets a call from the bank that his account is overdrawn by $400.
"Look up last month's statement," he says.
"You had a balance of nine hundred dollars," says the bank official.
"And the month before that?" says Goldberg.
"Twelve hundred dollars."
"And the month before that?"
"Fifteen hundred."
"Tell me," says Goldberg. "All those other months, when I had plenty of money in my account—did I call _you_?"
That's how I felt about _The Wall Street Journal._
In college, as one of the editors of the school paper, I had learned firsthand how much power the headline writer has. Since most people don't read the whole story unless they're especially interested in the subject, for the majority, the headline _is_ the story.
In the middle of the loan guarantee crisis, after we had borrowed only part of what we were entitled to under law, the _Journal_ ran an editorial suggesting that Chrysler be "put out of its misery." It was their now-famous "Let Them Die With Dignity" editorial, which should go down in history as a classic—if only as an example of how abusive freedom of the press can get in this country. I know, I know, the First Amendment guarantees them that right.
I was furious. I fired off a letter to the editor in which I said: "In effect, you have announced that because the patient has not yet been restored to full health by the ingestion of half the prescribed medicine, he should be put to death. I'm grateful you are not my family physician."
I think _The Wall Street Journal_ is living in the last century. Unfortunately, it's the only game in town. The _Journal_ is a monopoly and it's become arrogant, like General Motors.
Incidentally, the _Journal'_ s snipings didn't stop when Chrysler recovered. On July 13, 1983, I announced at the National Press Club that we would repay all of our government-backed loans by the end of the year. Two days later, _The New York Times_ —which had opposed the loan guarantees—ran a story called "Chrysler's Sharp Turnaround." According to the article, "It is hard to overstate the magnitude of the turnaround.... How was it possible to turn such a desperately sick company around so quickly?"
That same day, _The Wall Street Journal_ also ran a big story about Chrysler. Its headline? "Chrysler, Having Cut Muscle as Well as Fat, Is Still in a Weak State." Could there be any doubt that the _Journal_ carries a bias? They have a right to their opinions, but opinions belong on the editorial page. They could at least have said something like: "It's too bad they had to do it _this_ way, but what a great job Chrysler's done!"
With that kind of coverage in the nation's business press, it's not surprising that so much of the public had trouble understanding what was really going on.
A big part of the problem was the language being used to describe our situation. "Bailout" is a colorful metaphor. It conjures up images of a leaky boat foundering in rough seas. It implies that the crew was inadequate. At least "bailout" is a better phrase than "handout," which was also being tossed around. We didn't ask for any free gifts, and we sure didn't get any.
One popular view was that we were a big, monolithic company that didn't deserve help. To counter this myth, we explained that we're really an amalgam of little guys. We're an assembly company. We have eleven thousand suppliers and four thousand dealers. Almost all of these people are small-businessmen, not fat cats. We needed a helping hand—not a handout.
Many people didn't even know _that._ They thought we were asking for a gift. They seemed to think that Jimmy Carter sent me a get-well card with $1 billion in laundered tens and twenties tucked inside. Many well-intentioned Americans were apparently under the impression that Chrysler had received $1 billion in cash in a brown paper bag and that we never had to pay it back.
If only it were true!
# XIX
# CHRYSLER GOES TO CONGRESS
To say the least, testifying before congressional and Senate committees has never been my idea of fun and games. Believe me, it was the last thing in the world I ever wanted to do. But if we had even the slightest chance of getting Congress to approve the loan guarantees, I knew I would have to appear in person to state our case. No delegating this time!
The Senate and House hearing rooms are designed to intimidate the witness. The committee members sit at a semicircular table a couple of feet above the floor, looking down. The witness is at a real psychological disadvantage, because he's always looking up at the questioner. And to make matters worse, there are those television lights in your eyes.
I was referred to as the witness, but that's a misnomer. In reality, I was the defendant. Hour after hour I had to sit in the box and go on trial before Congress and the press for all of Chrysler's so-called sins of management—both real and imagined.
At times it was like a kangaroo court. The ideologues lined up and said: "We don't care what you're saying. We want to break you." I was on my own in those hearings. I had to ad-lib everything. The questions came fast and furious, and they were always loaded. Staff members were constantly passing notes to the senators and congressmen, and I had to respond to everything off the cuff. It was murder.
We were scolded for not having the foresight of the clever Japanese to build cars that get thirty miles per gallon, even though the American consumer had continually demanded bigger cars. We were lectured for not being prepared for the overthrow of the Shah of Iran. I had to point out that neither Carter, Kissinger, David Rockefeller, nor the State Department had anticipated that event, although they were all far better informed than I on these matters.
We were excoriated for not having prepared for the screwed-up fuel allocation system devised by the Department of Energy and for the subsequent riots at the gas pumps. Never mind that gas had been sixty-five cents a gallon one month earlier. Never mind that its price had been artificially depressed because of government price controls, which sent precisely the wrong signals to the American consumer. Never mind that we were investing the bulk of our capital in meeting government regulations. In the minds of Congress and the media, we had sinned. We had missed the market, and we deserved to be punished.
And punished we were. During the congressional hearings, we were held up before the entire world as living examples of everything that was wrong with American industry. We were humiliated on the editorial pages for not having the decency to give up and die gracefully, We were the object of scorn by the nation's cartoonists, who couldn't wait to paint us into the grave. Our wives and kids were the butt of jokes in shopping malls and schools. It was a far higher price to pay than just closing the doors and walking away. It was personal. It was pointed. And it was painful.
On October 18, I made my first appearance before the House Subcommittee on Economic Stabilization of the Committee of Banking, Finance, and Urban Affairs. All of the members showed up, which in itself was unusual. Normally, hearings are held without most of the members, who always have a dozen other commitments at the same time. The real work is usually done by the congressional staff.
I began my testimony by stating our case very simply: "I am sure you know that I do not speak alone here today. I speak for the hundreds of thousands of people whose livelihood depends on Chrysler remaining in business. It is that simple. Our one hundred forty thousand employees and their dependents, our forty-seven hundred dealers and their one hundred fifty thousand employees who sell and service our products, our nineteen thousand suppliers, and the two hundred fifty thousand people on their payrolls, and, of course, the families and dependents of all those constituents."
Because there was so much confusion about what kind of help we were asking for, I made it clear that we were not requesting a handout. We were not asking for any gifts. I reminded the committee that we were petitioning for the guarantee of a loan, every last dollar of which would be repaid—with interest.
In my opening statement, I outlined seven essential points to the committee. First, our problems were due to a combination of bad management, excessive regulation, the energy crisis, and the recession. We had completely changed our management, but the other three factors were beyond our control.
Second, we had already taken prompt and decisive steps to solve our problems. We had sold off our marginal assets. We had raised a significant amount of new money. We had reduced our fixed costs by almost $600 million a year. We had lowered the salaries of our top seventeen hundred executives. We'd suspended all merit pay increases. We had cut out our employee stock purchase plan. We had eliminated the dividend on our common stock. We had gained new and important commitments from our suppliers, our bankers, our dealers, and our workers, as well as state and local governments.
Third, in order to remain profitable, we had to remain a full-line producer of cars and light trucks. We could not survive as a one-product company. We could not stay in business and manufacture only small cars. The profit margins on subcompact cars are about $700 each, which was not enough to keep us in business—not with the Japanese enjoying low labor rates and favorable tax advantages.
Fourth, we would not be able to survive a bankruptcy.
Fifth, we had no offers to merge with other companies, either American or foreign. And unless we received the loan guarantees, it wasn't likely that anyone was going to ask us to dance.
Sixth, despite our reputation for building gas-guzzlers, Chrysler already had the best average fuel economy of the Big Three. We offered more models with at least twenty-five miles per gallon than GM, Ford, Toyota, Datsun, or Honda.
Finally, I asserted that our operating plan for the next five years was sound and that it was based on conservative assumptions. We knew that we could improve our market share and soon become profitable once again.
Later in the hearing I elaborated on each of these points in much greater detail.
The questions and the accusations were endless. Some of the committee members just could not get it through their heads that Chrysler was now under new management. Not surprisingly, most of them didn't want to consider the real costs of federal regulation. So they continually pointed a finger at the mistakes made by the previous management team and asked me to defend them.
CONGRESSMAN SHUMWAY OF CALIFORNIA: "My concern is what assurances can you give this subcommittee and give the government that you are not going to repeat the mistakes of yesteryear? You assert that some of the fallacies that have pervaded management in the company now have been resolved and you are on your way toward profitability. I frankly do not see the kind of answers that would really convince me that that is the case."
MR. IACOCCA: "Congressman, I couldn't convince you. You will have to take my word for it. I put together a new team at Chrysler. They are the best automobile men in the United States, in my opinion. We have got a track record. We have been through all that. We know how to build small cars. We have been at it for thirty years and we're saying we can do it. That is all we can say to you. You go on track records, you go on experience. We offer ours up to you. That is all I can say."
MR. SHUMWAY: "The track record of Chrysler is not what you're relying on today to persuade us."
MR. IACOCCA: "People make companies. I think we are doing enough to help ourselves. You just watch us. You will see a lot of action at Chrysler. You will see better cars and you will see better service and better quality. And that, in the end, is all that is going to matter."
Everybody was looking for a scapegoat, but I refused to blame the previous Chrysler administration for all our problems. After all, during the third quarter of 1979, the Ford Motor Company had lost $678 million. Even GM had a third-quarter loss of $300 million. What about those numbers? We couldn't have _all_ gotten stupid at the same time! Obviously there had to be other, more compelling reasons for these unprecedented losses. And so I talked a great deal about regulation.
And I talked about the common misconception that Chrysler built gas-guzzlers rather than fuel-efficient small cars. I pointed out that Chrysler was the first American producer of small, front-wheel-drive cars, ahead of both GM and Ford. At the time of my testimony, there were more than half a million Omnis and Horizons on the road—more small, front-wheel-drive cars than any other American manufacturer could offer. Moreover, the new K-car was due out within the year.
No, I explained, the problem wasn't that we had too many gas-guzzlers. In reality, we didn't have _enough_. Big cars are where the profits are, for the same reason that in a butcher shop there's a bigger markup on steak than on hamburger.
I said that General Motors makes 70 percent of all the big cars, including Cadillac Sevilles, which sell at a profit of $5,500 a pop. We had nothing to compare. To make as much money as GM did on one Seville, we had to sell eight Omnis or Horizons. Moreover, GM is the price leader. They're not going to raise their prices on small cars by $1,000 just so Chrysler can break even.
I talked about all these things and more. But when I look back on the hearings, it's other voices I hear. I vividly remember Congressman Richard Kelly from Florida, our most outspoken opponent. He began by saying: "I think that you are trying to put a con on us. I think that you have made your presentation in the open market, and the people out there, acting on a voluntary basis—not the people of the quality you see sitting up here, but the kings of industry that really know how to make the thing hum—they have told you to get lost.
"And they told you to get lost because, in the same conditions in which they survived, you could not make it. So now you are coming here, and you are expecting this bunch of dummies here on this subcommittee to fall for this baloney about human suffering."
Kelly was smart. He manipulated the media by using the right words to titillate people on the evening news. He lashed out at us again and again. "The Chrysler bailout will be the beginning of a new era of irresponsibility in government. The Chrysler bailout is a rip-off of the American worker, American industry, and the taxpayer and consumer. The Chrysler charity is the most blatant con job in our time."
Kelly lectured us about how Chrysler had failed to compete. He repeatedly urged us to declare bankruptcy and opposed federal loan guarantees in every way, shape, and form.
A couple of years later, by the way, Congressman Kelly, the great defender of the American way of life, was convicted twice in the Abscam affair and sentenced to a term in jail. He lost the election, and went out in disrepute. Poetic justice!
Kelly wasn't our only opponent. In the midst of the debate, Congressman David Stockman, from our own Michigan delegation, wrote a major article for the _Washington Post Magazine_ entitled "Let Chrysler Go Broke." A few weeks earlier, he had written a piece for _The Wall Street Journal_ called "Chrysler Bailout: Rewarding Failure?" Stockman, who later became the budget director, was the only member of the Michigan delegation to vote against us. He was a former divinity student, but I guess he was playing hooky the day they learned about compassion.
Fortunately, not everybody was hostile. Stewart McKinney, the ranking minority member on the committee, was very supportive. Here I got a break, as McKinney was a friend whom I knew from my days at Ford. As a Republican from a silk stocking district in Connecticut, he took a lot of flak from his more doctrinaire colleagues.
McKinney favored us from the beginning, mostly because the alternative to federal help was so bad. His position was: "I know autos, and I know what this guy did at Ford. He'll make it work." At one point in the hearings, he said: "If you do for Chrysler what you did for Ford, we're going to have to put up a statue."
To which I thought: "And you know what happens to statues—the pigeons shit all over them!"
McKinney had done his homework, which is more than I can say for some of his colleagues. Henry Reuss, chairman of the House Banking Committee, proposed at one point that Chrysler ought to be building railroad cars! We couldn't afford to maintain the facilities we had, but this guy thought we should be getting into a whole new line of vehicles. This little project would have entailed an investment of a couple of billion dollars—at a time when we were already broke.
Our other big supporter on the subcommittee was Michigan Congressman Jim Blanchard, author of the loan guarantee bill, who later went on to become governor of Michigan. Blanchard was the number two Democrat on the committee, and he and McKinney were a great team.
Tip O'Neill was our real point man in the Congress. Early on, I had a meeting with him to explain our position. He listened carefully, and he understood what he heard. As soon as he turned on his lights to help us, the tide started to turn.
Tip set up a Speaker's task force, a group of about thirty who lobbied their colleagues. There was also a small ad hoc support group on the Republican side—their job was much more difficult.
There were similar hearings in the Senate. There my chief nemesis was William Proxmire, chairman of the Banking Committee. Proxmire was tough, but he was always straightforward and fair. He told us from the beginning that he was totally opposed to loan guarantees. But he was scrupulous in letting us make our case. He promised only to vote against us—not to do any lobbying.
I had a good sparring session with Proxmire, because for all his talk about free trade, he had previously agreed to some special help for American Motors.
In 1967, American Motors had received a federal tax credit that resulted in a cash rebate of $22 million.
In 1970, American Motors was granted special permission to purchase emissions control technology from GM as an exception to a federal court consent decree.
In 1974, American Motors was designated a small business by the federal government in order to give it preferential treatment on its requests for government contracts.
In 1977, American Motors was given the right to request a two-year waiver from the final emissions standards for oxides of nitrogen.
In 1979, American Motors' request for a waiver was granted by the EPA. A similar waiver for Chrysler, by the way, could have saved us over $300 million.
Proxmire has made himself quite a reputation out of ridiculing government expenditures he disagrees with. But he made a blatant exception for American Motors. Why? Because Proxmire happens to be a senator from Wisconsin, where American Motors has a major assembly plant.
I went head to head with him. I said: "I remember you were the prime mover for loan guarantees for American Motors, and they're owned by the French. So you were aiding and abetting the French government." We were fighting for our lives, and by that time I really didn't care whether I was polite.
Proxmire struck back. He raked me over the coals for being inconsistent in my own ideology. "More than any other executive in Detroit," he said, "you have led the anti-Washington campaign, and what you said has made a lot of sense. I would support it and other members might support it more vigorously." He then went on to say that if the guarantees were passed, the government would be deeply involved with Chrysler. "Doesn't this fly in the face of what you have been preaching so eloquently for so long?"
"It sure does," I replied. "I have been a free-enterpriser all my life. I come here with great reluctance. I am between a rock and a hard place. I cannot save the company without some kind of guarantee from the federal government.
"I am not going to preach to you," I continued. "You gentlemen know this better than I do, that we are setting no precedent. There are already four hundred nine billion dollars of loan guarantees on the books, so don't stop now, men. Go to four hundred ten billion dollars for Chrysler because it is the tenth biggest company in the U.S. and there are six hundred thousand jobs involved here."
When I talked about precedents, even the adversarial guys had a hell of a time. The best they could come up with was to say: "Well, just because we've done some stupid things in the past doesn't make this one right."
At the end of my long testimony and the subsequent interrogation, Senator Proxmire paid me a high compliment. "As you know," he said, "I am opposed to your request. But I have rarely heard a more eloquent, intelligent, well-informed witness than you have been today. You did a brilliant job and we thank you. We are in your debt." I thought: "No, no, you've got it backwards. We're trying to get in _your_ debt!"
After Proxmire's great compliment, I smiled for a moment. But then he made clear that he was going to fight me down to the last shot—and he made good on his word.
Another opponent on the Senate committee was Senator John Heinz, Republican of Pennsylvania, who went out of his way to be hostile. He had it in for our stockholders, and he wanted them to suffer. We had to point out that Chrysler stock was not held by institutions. Thirty percent of our shareholders were employees. The rest were private individuals. They had already seen the value of their stock erode considerably.
But Heinz wanted us to issue another fifty million shares immediately, which would reduce the value of our stock from $7.50 to $3.50—a price it later reached quite nicely on its own. He couldn't get it through his head that with the shape we were in, nobody out there had any interest in buying Chrysler shares at _any_ price.
The House and Senate hearings were only part of the story. I spent most of my time in small, private meetings. I had a good talk with Kansas Senator Nancy Kassebaum, the only woman in the Senate. I made a strong case, and I thought she was coming around. But in the end, she voted against us.
I had better luck with the Italian caucus in the House. Congressman Pete Rodino of New Jersey brought me in and said: "I want you to talk to my pals here." There were thirty-one guys, (well, actually, thirty guys and Geraldine Ferraro, a representative from Queens), and all but one voted for us. Some were Republicans, some were Democrats, but in this case they voted the straight Italian ticket. We were desperate, and we had to play every angle. It was democracy in action.
There wasn't time for a meeting with the black caucus, but I did meet with its leader, Congressman Parren Mitchell of Maryland. In 1979, 1 percent of the black payroll in the entire United States was paid by the Chrysler Corporation. Blacks comprised an important part of the coalition that made the loan guarantees possible.
Coleman Young, the black mayor of Detroit, came to Washington several times to testify on our behalf. He minced no words in outlining what a Chrysler bankruptcy would do to Detroit. Young had been an early supporter of Jimmy Carter, and he spoke forcefully to the President about the Chrysler situation.
During the last three months of 1979, the pressure on me was tremendous. I was going to Washington a couple of times a week and trying to run Chrysler at the same time. Meanwhile, Mary was sick with periodic diabetic attacks. On two or three occasions I had to drop everything and run back to Detroit to be with her.
Every time I went to Washington, I was on a crazy schedule of eight or ten meetings a day. Each time I went, I had to make the same speech, outline the same points, present the same arguments. Repeated, repeated, one at a time.
Once I was walking down one of the marble corridors in Congress and I just didn't feel right. It was as if I were walking on eggs. I was dizzy and close to fainting. I was also seeing double.
They took me to the surgeon general's office and then to the House infirmary, where they checked me out. It was vertigo, something I had experienced only once before, twenty years earlier. Back then, I had been walking down the corridor at Ford with McNamara, and I started bumping into the wall. McNamara said: "What's going on, Lee? Are you drunk or something?"
"Why?" I asked, not even realizing anything was wrong.
"Because you keep hitting the wall, that's why."
Vertigo is a problem with equilibrium in the inner ear, and I was suffering a recurrence. They discharged me from the infirmary, but then it happened again. All the tension and pressure made me feel like I had rocks in my head. But somehow I muddled through.
Our highest priority during this period was to maintain the confidence of the consumer. While the hearings were going on, our sales dropped off dramatically. Nobody wanted to buy a car from a company that was about to go belly up. The percentage of consumers who were willing merely to _consider_ a Chrysler product plunged overnight from 30 percent to 13 percent.
There were two schools of thought as to how we should respond to this crisis. By and large, our PR people maintained that silence was the best policy. "Just sit tight," they advised. "It will all work out. The last thing we want to do is call attention to our miserable situation."
But Kenyon & Eckhardt, our ad agency, strongly disagreed. "The situation is critical," they said, "and you've got a choice. You can die quietly, or you can die screaming. We recommend that you die screaming. That way, there's always the chance somebody will hear you."
We took their advice. We asked K&E to put together an ad campaign that would reassure the public about our future. We had to let people know two things—first, that we had absolutely no intention of going out of business, and second, that we were making the kind of cars America really needed.
Instead of our regular advertising, which featured pictures and text describing our new models, we ran a series of editorials expressing our point of view about the loan guarantees as well as Chrysler's long-range plans. Instead of promoting our products, we were promoting the company and its future. We weren't getting our message across through the normal channels—it was time to advertise our cause instead of our cars.
Ron DeLuca of K&E's New York office drew up a series of full-page print ads explaining our position. Before writing each one, he used to come into my office for an hour or so to talk things over. Then I'd edit his copy, and we'd go back and forth until we were both satisfied.
In these ads, which K&E began to refer to as "paid PR," we set the record straight. We exposed some of the more prevalent myths about Chrysler: We were not building gas-guzzlers. We were not asking Washington for a handout. Loan guarantees for Chrysler did not constitute a dangerous precedent.
The ads were unusually straightforward and frank. Ron took an aggressive approach, which I liked very much. We knew all too well what the man on the street was thinking about Chrysler, so we tried to put ourselves in his place and anticipate his questions and doubts. There was no point in ignoring the bad press. Instead we had to meet it head on and replace rumors with the facts.
One of these ads carried a bold headline that spelled out what many consumers were starting to wonder: "Would America be better off without Chrysler?" In the other ads, we asked—and answered—some pretty tough questions:
* Doesn't everyone know Chrysler cars get lousy gas mileage?
* Aren't Chrysler's big cars too big?
* Did Chrysler wait too long to downsize?
* Isn't Chrysler building the wrong kind of cars?
* Doesn't Chrysler have more problems than anyone can solve?
* Is Chrysler management strong enough to turn the company around?
* Has Chrysler done everything it can to help itself?
* Does Chrysler have a future?
These ads were unusual in another way, too. We decided that they should all carry my signature. We wanted to show the public that a new era had begun. After all, a chief executive of a company that's going broke has to reassure people. He's got to say: "I'm here, I'm real, and I'm responsible for this company. And to show that I mean it, I'm signing on the dotted line."
At long last, we would be able to convey that there was some genuine accountability at Chrysler. By putting my signature on these ads, we were inviting the public to write to me with their complaints and their questions. We were announcing that this large, complex company was now being run by a human being who was putting his name and his reputation on the line.
The ad campaign was a major success. I'm pretty sure it played a role in the massive effort to convince Congress to approve the loan guarantees. The great frustration of advertising, of course, is that you never really know what finally makes a difference in the battle for people's minds. But we heard reports of people in the Carter administration and the Congress running from one office to another with these ads in their hands—either furious or delighted, depending on their views.
And there's no question that the ads had a real impact on the public. People would see the front page of the newspaper, which said that we were going broke. Then they'd look inside and find our side of the story.
Meanwhile, on another front, our Washington office had organized a massive dealer lobby. Groups of Chrysler and Dodge dealers were coming to Washington every day. Wendell Larsen, our vice-president of public affairs, would brief them, telling them which congressmen to talk to and what to say.
Car dealers tend to be wealthy (or at least they used to be), and they also tend to be active in their communities, so they have a lot of clout with their representatives. Since most of them are conservative and Republican, their presence had a big impact on the congressmen who were against us on ideological grounds. And many of the dealers had made campaign contributions, which is something a congressman can't always ignore.
When you send a bunch of car dealers into Washington, it's amazing what they can accomplish. We even had a few dealers from other companies, who argued that competition was good for the entire industry and that Chrysler deserved a chance.
In order to make our case, we had to force the congressmen to think of the loan guarantees in real human terms instead of ideology. We delivered to each representative a computer printout of all the suppliers and dealers in his district who did business with us. We outlined exactly what the consequences for that district would be if Chrysler went under. As I recall, there were only 2 districts out of the entire 535 that had no suppliers or Chrysler dealers. This list, which made our problems real, concrete, and local, had a tremendous effect.
Then there was Doug Fraser, who constituted a lobby effort of his own. Doug didn't fall for any crap about a bankruptcy. He knew what would happen to his people if Chrysler failed. And he knew we weren't crying wolf.
Fraser testified brilliantly. He talked vividly about the cost in human lives and suffering if the loan guarantees were not passed. "I don't come here to plead for the Chrysler Corporation," he told the committee. "My concern is the terrible impact that a bankruptcy would have upon the workers and on their communities."
Fraser was a tireless and effective lobbyist who met individually with a number of congressmen and senators. He was also a good friend of Vice President Mondale, and he paid a couple of important visits to the White House.
At one point I went to the White House myself to see the President. Carter didn't get very involved in the Chrysler debate, but he did support our cause. During my visit, he told me how much he and Rosalynn liked my TV commercials. He joked that I was becoming as well known as he was.
Carter delegated the Chrysler problem to the Treasury Department, but he made it clear that he stood behind us. Without the support of the executive branch, the bill would never have passed.
Since leaving office, Carter has come to see me twice. He's proud that Chrysler is thriving. I think he feels as if he fathered the baby. "Of all the things we accomplished in my administration," he told me, "I look back on this as something we really did right." Jimmy Carter had his drawbacks, but his accomplishments have been underrated.
By the time the vote came, we had a lot of backers in Congress. Still, Tip O'Neill's support was crucial. Just before the vote, he stepped down as Speaker and spoke as the representative from Massachusetts. In an impassioned plea for the loan guarantees, he recalled the effect of the Great Depression in Boston, when workers who had lost their jobs had to beg for work shoveling snow. "I have always fought hard to save a hundred jobs," he told his colleagues. "Isn't it a little crazy for us to sit here and argue about this when more than half a million families are out there tonight waiting to hear our verdict?"
Tip used raw emotion to sell his guys in the House. He was one of our leaders in this whole episode. Once you've got the Speaker of the House, you have a lot of clout. When the vote came in, the House had agreed by a two-to-one margin (271 to 136) to help Chrysler get back on its feet.
The Senate vote was a lot closer, 53 to 44, but that's routine in these situations. The bill was passed just before Christmas, and a lot of American families had reason to celebrate. I was exhausted and relieved, but I wasn't wildly optimistic. All too often since coming to Chrysler I had seen a light at the end of the tunnel. And all too often it had turned out to be another train coming at me. I knew that a great many parts of the puzzle had to fall into place before we would ever see a penny of those guaranteed loans.
The legislation called for a restructuring of Chrysler that, according to Treasury Secretary G. William Miller, was to be the most complicated financial transaction in the history of American business. I got tired just thinking about it.
The act created a Loan Guarantee Board with authority to issue up to $1.5 billion in loan guarantees over the next two years, which were to be repaid by the end of 1990. But there were a number of strings attached:
* Our current lenders were required to extend $400 million in new credit and $100 million in concessions on existing loans.
* Foreign lenders were required to extend an additional $150 million in credit.
* We had to raise an additional $300 million through the sale of assets.
* Suppliers had to provide the company with at least $180 million, of which $100 million was in the form of stock purchases.
* State and local governments with Chrysler plants had to provide $250 million.
* We had to issue $50 million in new stock.
* Union members had to come up with $462.2 million in concessions.
* Nonunion employees had to contribute $125 million in pay cuts or freezes.
In addition—and very few people realize this—the government took all of Chrysler's assets as collateral. Everything we owned—cars, real estate, plants, tools, and all the rest—was carried on the books for $6 billion. The government appraisers estimated that the liquidation value of our assets came to $2.5 billion. In a worst-case scenario, the government had first lien. If we went under, they would recover all $1.2 billion of the loans before any other creditors could make claims.
Even if the $2.5 billion estimate was generous, and even if the true value of our assets came to only half of that, the government was still protected. If we had defaulted on our loans, the Loan Guarantee Board could have liquidated our assets and still come out whole. In other words, the government was taking no financial risk at all!
A couple of weeks after the Loan Guarantee Act was passed, the Republicans came into power. Their attitude was: "This is a Carter program. We'll honor the letter of the law, but not one iota beyond that. It's against our ideology. If Chrysler makes it, we'd be embarrassed. And we wouldn't want other companies to get any fancy ideas."
We were lucky that when push came to shove, we had appealed to a Democratic administration that put people ahead of ideology. Democrats usually do. They deal with labor, they deal with people, they deal with jobs. Republicans deal with trickle-down theories of investment.
I realize that I'm stereotyping. I'm the first to admit that when things are going well, when I've made a lot of money, I've always favored the Republicans. But ever since coming to Chrysler, I've leaned toward the Democrats. Overall, I'm for the commonsense party, and when the chips are down, that's usually the Democrats.
There's no question in my mind that if there had been a Republican administration in 1979, Chrysler wouldn't be around. The Republicans wouldn't even have said hello to us. Chrysler would have gone bankrupt, and today they'd be writing books about having protected free enterprise. It's not just Reagan; most Republicans would have said: "Federally guaranteed loans? You must be nuts." Republicans just aren't used to thinking like that.
If our crisis had occurred three years later, when Ford and GM were also in big trouble and International Harvester was going broke, not even the Democrats would have responded. They would have seen that there were fifty other guys lined up right behind us, with no system to handle it all.
So maybe it's a good thing that Chrysler got into trouble a little earlier than it might have with stronger management. If our crisis had come at the same time as Braniff and Pan Am, Washington would have said: "Sorry, boys. The line's already too long."
I'm sure those other companies considered asking for government help. After all, they're not crazy. But they got the message early. What would happen if they came down to ask for a deal like Chrysler? Answer: "Forget it."
As I write these words, it's been four years since the loan guarantees were passed. During that time, we've kept hundreds of thousands of people off the dole. We paid hundreds of millions of dollars in taxes. We preserved competition in the auto industry. We paid back the loans seven years early. We paid large fees to the Loan Guarantee Board. And the government enjoyed a windfall from selling our warrants.
In view of all this, you have to ask a philosophical question. By going to Congress, did we really violate the spirit of free enterprise? Or has our subsequent success actually helped free enterprise in this country? I don't think there's any doubt about the answer. Even some of our opponents from 1979 now concede that the Chrysler loan guarantees were a good idea.
Oh, there are still some diehards such as _The Wall Street Journal_ and Gary Hart—but what the hell! You can't convert them all.
# XX
# EQUALITY OF SACRIFICE
With the passage of the Loan Guarantee Act, we now had a fighting chance to survive. And I do mean "fighting"!
Our mission was the economic equivalent of war. Although no one was getting killed for Chrysler, the economic survival of hundreds of thousands of people depended on whether we could arrange the various concessions that the Loan Guarantee Act required.
I was the general in the war to save Chrysler. But I sure didn't do it alone. What I'm most proud of is the coalition I was able to put together. It shows what cooperation can do for you in hard times.
I began by reducing my own salary to $1.00 a year. Leadership means setting an example. When you find yourself in a position of leadership, people follow your every move. I don't mean they invade your privacy, although there's some of that, too. But when the leader talks, people listen. And when the leader acts, people watch. So you have to be careful about everything you say and everything you do.
I didn't take $1.00 a year to be a martyr. I took it because I had to go into the pits. I took it so that when I went to Doug Fraser, the union president, I could look him in the eye and say: "Here's what I want from you guys as your share," and he couldn't come back to me and ask: "You SOB, what sacrifice have _you_ made?" That's why I did it, for good, cold, pragmatic reasons. I wanted our employees and our suppliers to be thinking: "I can follow a guy who sets that kind of example."
Unfortunately, austerity was a new idea at Chrysler. When I came in, I heard all kinds of horror stories about the extravagance of the previous administration. But I wasn't impressed. After all, I had lived for years with Henry Ford, who thought he owned the company and who was powerful enough to act as if he did. Henry spent enough money to make Lynn Townsend look like a beggar. He made the head of General Motors look like he was on welfare.
Although my reduced salary didn't mean I had to skip any meals, it still made a big statement in Detroit. It showed that we were all in this together. It showed that we could survive only if each of us tightened his belt. It was a dramatic gesture, and word of it got around very quickly.
I learned more about people in three years at Chrysler than in thirty-two years at Ford. I discovered that people accept a lot of pain if everybody's going through the chute together. If everybody is suffering equally, you can move a mountain. But the first time you find someone goofing off or not carrying his share of the load, the whole thing can come unraveled.
I call this equality of sacrifice. When I started to sacrifice, I saw other people do whatever was necessary. And that's how Chrysler pulled through. It wasn't the loans that saved us, although we needed them badly. It was the hundreds of millions of dollars that were given up by everybody involved. It was like a family getting together and saying: "We got a loan from our rich uncle and now we're going to prove that we can pay him back!"
This was cooperation and democracy at their best. I'm not talking about a Bible lesson here. I'm talking about real life. We went through it. It works. It's like magic and it awes you.
But our struggle also had its dark side. To cut expenses, we had to fire a lot of people. It's like a war: we won, but my son didn't come back. There was a lot of agony. People were getting destroyed, taking their kids out of college, drinking, getting divorced. Overall we preserved the company, but only at enormous personal expense for a great many human beings.
Our task was made a little easier by the knowledge that much of America was rooting for us. We were no longer seen as the fat cats asking for welfare. With the congressional hearings behind us, that part of the saga was over. By now, our advertising campaign was beginning to get results. We were the underdog engaged in a heroic struggle, and the public responded accordingly.
Many unknown people wrote to us, saying in a hundred different ways that they were with us, that Henry Ford's loss was Chrysler's gain. The little people said a lot, and they said it well. They understood what we were doing.
Some pretty big people helped us, too. Bob Hope came to see me. He told me that while having a massage he'd seen one of my commercials on television. Now he wanted to do something for us.
I ran into Bill Cosby at dinner one night in Las Vegas. That same night, he called me in my hotel at 1:00 A.M.
I said, "Hey man, you woke me up."
He said: "Hell, we're just getting going. We're up all night. Anyway, I admire what you're doing, and I appreciate how much you're helping the black people. I'd like to do something for you. I make a lot of money and other people are starving." He came to Detroit to do a show for our workers—20,000 of them. Then he got on a plane and left. He never asked for a dime. He never asked for a car. He just wanted to help us out and show his support.
One night Pearl Bailey came up to me at a diabetes function in downtown Detroit. She said she just had to talk to me. She thanked me for trying to preserve jobs and for giving people hope. Instead of doing a concert, she wanted to give a lecture to our workers at the Jefferson Avenue plant.
She made a rousing speech about patriotism and the need to sacrifice. But while she was talking, a couple of hecklers started in: "Easy for you to say, Pearl, you're rich!"
Before we knew it, we almost had a riot on our hands. I had to jump up and bring the meeting to a close. But it was a great gesture, and I really appreciated it.
Frank Sinatra wanted to help, too. He said: "Lee, if you're working for a dollar, I will, too." He did some commercials for us, and during the second year we gave him some stock options. I hope Frank held on to them, because if he did, he made a bundle.
There were a number of these cases. During that period, I got to see the positive side of human beings. I had never really known how people would act when the chips were down. I learned that the majority will rally around. They won't think about greed, even though the media seem to believe that greed is the only motivating force in business. Most people, when called upon, will serve—so long as they're not being singled out to get the short end of the stick.
I also learned that people can act very serenely in a crisis. They accept their fate. They know it's going to be a tough grind, but they grit their teeth and go with it. Watching that happen was the pleasant part—maybe the only pleasant part—of this whole episode.
After I cut my own salary, I started in on the executives. We threw out the stock incentive plan, where we paid half and they paid half. We cut their salaries by up to 10 percent, which had never been done in the auto industry. We cut salaries in all but the lowest levels—we left the secretaries alone. They deserved every cent they made.
The executives were pretty docile about it. They read the papers. They knew very well that the whole ball game could be over at any moment. At such a time, there's no periphery anymore. You see only one thing: the track that leads to survival. Nothing stops you, so you go on adrenaline.
It started with me, but it permeated down through the ranks. For the good of the cause, I could have asked them to jump through the window—and all because of the shared perception that everybody was bleeding equally.
Once I had dealt with the executives, I started in on the unions. Here I had the help of a real pro, Tom Miner, who handles our industrial relations. Today the business world takes union concessions for granted. But back then, we were pioneers.
The union has always had the attitude that the executives are fat cats and the workers get screwed. I said: "Well, now you're looking at a pretty skinny cat, okay? So what do you have to say?"
From that day on, I was their pal. The union loved me. They embraced me. They said: "This guy is going to lead us to the promised land."
I don't mean it was easy. I had to lay it on the line. I talked tough to them. "Hey, boys," I said, "I've got a shotgun at your head. I've got thousands of jobs available at seventeen bucks an hour. I've got none at twenty. So you better come to your senses."
A year later, when things got even worse, I had to go back to them a second time. One bitter winter night at ten o'clock I spoke to the union negotiating committee. It was one of the shortest speeches I've ever given: "You've got until morning to make a decision. If you don't help me out, I'm going to blow your brains out. I'll declare bankruptcy in the morning and you'll all be out of work. You've got eight hours to make up your minds. It's up to you."
That's a hell of a way to negotiate, but sometimes it's what you've got to do. Fraser said it was the worst economic settlement he had ever agreed to. The only thing worse, he added, was the alternative—having no jobs at all.
Our workers made some pretty big concessions. Right away, $1.15 an hour came out of their paychecks. Over the year-and-a-half period of concessions, that amount grew to $2.00 an hour. Over a nineteen-month period, the average working guy at Chrysler gave up close to $10,000.
The union had grown used to my new salary of $1.00 a year, and they ragged me when I didn't do it again the second year. They actually got mad about it. But I didn't see the top guys at Ford or GM taking any salary cuts after the union had agreed to concessions.
As a matter of fact, after GM and the UAW negotiated a contract in which the workers gave up wage increases and benefits that came to $2.5 billion, what did the company do? Roger Smith, the chairman of GM, cut his own salary by all of $1,620 a year! To add insult to injury, on the very day that the union signed the new contract, which included major wage concessions, GM announced a new and bigger bonus plan for its top executives. There's a company that doesn't quite understand equality of sacrifice.
For the first time in many years, the attitude of Chrysler workers began to improve. When the Canadian union went out on strike in 1982, they didn't sabotage the cars or wreck the machinery, which used to be routine. They wanted more money, but they didn't want to do anything to damage the company.
One of the provisions of the loan guarantees was an employee stock ownership plan for our workers. It cost us $40 million a year for four years. But it made good economic sense. If you let workers share in the profits, they're much more motivated to do a good job. (Each worker now has credited to his account about $5,600—a nice nest egg.)
Here, too, the free-enterprise crowd went nuts. And once more I was ready for them. I pointed out that the big pension plans in this country own plenty of stock. They own a large chunk of General Motors and many other major publicly traded companies. So what's wrong with cutting the workers in _while they're working?_
The laissez-faire crowd thinks that this represents the first step to socialism. But I don't see anything wrong with the workers owning a piece of the action. It certainly doesn't interfere with good management. What do I care if the company's stock is owned by a broker's account on Wall Street or by Joe Blow who works on the assembly line? Which one can do more for me? Today, by the way, our workers own about 17 percent of the company.
We also got the union to side with us on absenteeism. There are always a few guys who never come to work but who still want to get paid. Together with the union, we put some teeth into the rules to penalize the chronic offenders.
During this same period, we had to close a number of plants. A lot of people were thrown out of work. It's a very emotional thing for people who have been working in the same plant for twenty or thirty years. In some cases their parents had worked there, too. All of a sudden they find out you're going to lock the doors.
There was plenty of screaming over some of the plant closings. But the union understood very well that we had to take drastic measures. They were able to accept these actions because they knew we were asking for equivalent concessions from our suppliers, our executives, and our banks.
During 1980, I went to every single Chrysler plant in order to speak directly to the workers. At a series of mass meetings, I thanked them for sticking with us during these bad times. I told them that when things got better, we'd try to get them back to parity with Ford and GM workers but that it wouldn't happen overnight. I gave them my pitch, and they hooted and hollered, and some of them applauded and some of them booed.
I also conducted sessions with the plant supervisors. I'd ask if anybody had questions for me. We didn't always agree on the answers, but just having the chance to talk together was a big step forward.
That's communication at the highest level: the chairman talking to the guy on the floor. Everybody hears it and everybody feels part of it. I'd like to do that more often. I did a lot of it at Ford, but then I could afford to—things were running pretty smoothly back at the office.
At Chrysler, however, it's been one crisis after another. You get worn out from it all. And it's an awfully long day shaking hands with hundreds of guys. Inevitably some of the assembly line workers want to come up and hug you, or give you a present, or let you know that they pray for you in church because you saved their job.
During this period a woman named Lillian Zirwas, a maintenance clerk at the Lynch Road plant in Detroit, wrote a piece in the plant newspaper. In effect she told her fellow workers to shape up. She said: "Maybe now you'll have plenty of time to think as you're being laid off of the times you goofed off, or the times you turned an eye on shoddy stuff."
I wrote her a letter telling her how much I liked the piece and invited her to my office. She came in with a cake she had baked. I remember that it had chocolate icing and one of the ingredients was beer. However she made it, it was the best cake I ever ate. My wife wrote to Lillian Zirwas to ask for the recipe.
Of course, not all our workers shared her attitude. It's hard to be happy about a $2.00-an-hour cut. Still, it's not quite accurate to say, as the news media always do, that this put Chrysler workers $2.00 an hour below Ford and GM workers.
That's because, unlike Ford and GM, Chrysler had an unusually large number of retirees. To begin with, we had a work force that was older than average. Then we had to lay off thousands of people. For all the workers who were now at home, the corporation had to pay pensions, health care costs, and life insurance premiums. And it's the active workers who have to produce the money that pays for those expenses.
In normal times, that's not a problem. At least two guys were working for every retiree, and they produced enough to cover his pension and other costs. But by 1980 we were down to the ridiculous and unprecedented ratio of ninety-three workers for every hundred retirees. In other words, we now had more guys sitting at home than coming to work! As a result, every Chrysler worker had on his shoulders the economic burden of supporting himself— _and_ somebody else.
This is one more area where Chrysler's problems reflect what's going on in our society. It's this same phenomenon that's breaking Social Security. People are retiring early, living longer, and there's not a large enough base of workers to support them.
Although our workers took a $2.00-an-hour pay cut, the large number of retirees meant that our labor costs did not go down accordingly. Some of our workers didn't see it this way. Their attitude was: "That's not my problem. I'm not my brother's keeper."
My response was: "Wait a minute. Your union is based on solidarity forever. You put in these pension plans, and now there are a lot of people sitting home, and that's too bad. The industry went to hell. Chrysler was too big, so we cut it down to size. Somebody has to pay those costs. We can't renege on the pension plan."
Even before the union had made any concessions, I invited Doug Fraser to sit on our board of directors. Despite what the press has reported, Fraser's appointment was not part of a package deal with the union.
Now, it's true that the union had been asking for labor representation on the board for many years. But it had become a kind of ritual. I don't think they ever expected to get it. I put Doug Fraser on our board because I knew he could make a special contribution. He's smart, he's politically savvy, and he says what he thinks.
As a board member, Doug found out firsthand what was going on at Chrysler from the perspective of management. He learned how our suppliers contributed and that our turnaround wasn't only due to the workers. He learned that our profit-and-loss statements were real and that profit wasn't a dirty word. He learned and understood so much that some of the workers began to see him as a turncoat, because he told them the truth when we were too weak to take a strike.
He's had an enormous effect. When there's a plant closing, he advises us on how to minimize the dislocation and the suffering that go with it. He's chairman of our public policy committee. He's also on the health care committee, along with me; Joe Califano, former secretary of HEW under Carter; and Bill Milliken, former governor of Michigan. As a foursome we probably know as much about health care as any four guys in the world. The four of us represent labor, management, and federal and state government. Over the years, we were the ones who made the decisions that landed us in the health care mess the country's in today. It took all four groups to screw up the health care system, so it will take the same combination to straighten it out.
Naturally, when I brought Doug Fraser onto our board, the business community went wild. They said: "You can't do that! You're putting the fox into the henhouse. You've lost your mind!"
I said: "Wait a minute. Why is it all right to have bankers on the board when you owe them $100 million, but not a worker? Why is it all right to have suppliers on the board? Isn't that a conflict of interest?"
Until then, no representative of labor had ever sat on the board of a major American corporation. But it's pretty standard in Europe. And in Japan they do it all the time. So what's the problem? It's that the average American CEO is a prisoner of ideology. He wants to be pure. He still believes that labor has to be the natural, mortal enemy of the manager.
That's obsolete thinking. I want labor to understand the inner workings of the company. The old days are gone for good. Some people don't believe it, but they'll find out soon enough. America's economic future depends upon increased cooperation among government, union, and management. Only by working together can we take on the world market.
It wasn't only management types who opposed the Fraser move. Plenty of union guys were against it, too. They were afraid that Fraser's being on the board might compromise their leadership's ability to extract the last drop of blood out of the turnip. All their lives they've had an attitude of get all you can because management will never do anything for the good of the worker unless it's extracted with violence or bloodshed.
For this kind of thinking to change, you need to have reasonable men who can discuss the concept of sharing profits only when we have some to share and wage increases only when we have improved productivity. Maybe that's a concept whose time has not yet come. But it will _have_ to come, because if we continue to slug it out and fight each other for a bigger piece of the pie when all the while that pie is getting smaller, the Japanese will continue to have us for lunch.
When I was at Ford, labor and management saw each other only every three years when it came time to negotiate a new contract. And every three years you'd walk into the room with a chip on your shoulder. You wouldn't know the guy and you'd immediately think: "I don't like him, he's the enemy." It's like meeting at a bridge and trading spies. You hate the other side, even though the exchange is a good thing.
I'm very glad I put Doug Fraser on the board, because he's first-class. I'd put him on any board I was on. He's just that good. He knows how to negotiate. He knows how to compromise. He knows the difference between a good deal and a bad deal. He's so good that I once recommended him to President Reagan as a government negotiator.
If Doug Fraser had served on Lynn Townsend's board, maybe Chrysler wouldn't have bought up the lousiest companies in Europe. Some of those terrible moves could have been stopped by just one bold man asking: "Why are we doing this? Does it really make sense?"
Besides, what have we got to hide from the union? What are we trying to keep from the workers? We need to build better cars for less money. And who else can help us reach that goal if not the head of the union?
Whenever I was taken to task for having Fraser on the board, I gave my standard argument: "Why are you so upset? Either way, you can only gain. If it turns out to be a mistake, you'll know not to try it. You'll be able to talk about it at the country club. You can say: 'Wasn't Iacocca a jerk?'
"But if it does work, then I'll have been the guinea pig, and you'll thank me for leading the way. Some day you may even prosper from it!"
# XXI
# THE BANKS: TRIAL BY FIRE
None of our constituencies found it easy to make concessions. But once they understood how bad the situation was and once they were convinced that other groups were also doing their part, they all went along pretty quickly.
Except the bankers. It took longer to get $655 million in concessions from our four hundred lending institutions than it did to get the loan guarantees of $1.5 billion passed by the entire United States Congress. Compared to dealing with the banks, the congressional hearings were as easy as changing a flat tire on a spring day.
I was disappointed by the attitude of the banks, but I wasn't surprised. During the House and Senate hearings, the bankers had been very negative. Walt Wriston, the head of Citibank, Tom Clausen, president of the Bank of America, and Pete Peterson, head of Lehman Brothers, had all testified against the loan guarantees. Peterson had gone so far as to compare our situation to Vietnam, suggesting that Chrysler might represent an endless quagmire.
I had a couple of very tough meetings with Peter Fitts, who represented Citibank, and Ron Drake from Irving Trust. Fitts and Drake were workout men—specialists in financial restructurings. Their general attitude was that we at Chrysler were dummies who didn't know what we were doing. These guys didn't care about jobs or investments. The only thing that mattered was the return on their money.
Like almost everyone else in the banking world, they wanted us to declare bankruptcy. But I resisted. I did my best to convince them that with equality of sacrifice and with our new management team, Chrysler would be able to make it.
Ron Drake and I had some especially bitter arguments, but then a funny thing happened: today, he's my personal financial adviser at Merrill Lynch. We hated each other in 1980, but we also went through hell together and ended up great friends.
When the Loan Guarantee Act was passed at the end of 1979, Chrysler Corporation and Chrysler Financial, our credit wing, were in debt to over four hundred banks and insurance companies to the tune of $4.75 billion. These loans had accumulated over a period of years, during which our bankers must have been asleep at the wheel. None of them ever seemed to wonder about the health of the company, even though the ominous signs were there for anybody to see.
Chrysler had been a bonanza for the bankers, and nobody had wanted to look a gift horse in the mouth. For over fifty years, Chrysler had borrowed steadily from the banks without missing a single payment.
Chrysler has traditionally been a highly leveraged company, paying generous dividends and borrowing heavily from the banks. That may be good for the banks, but it hasn't always been good for Chrysler. When you're highly leveraged, everything is exaggerated. Good times are better—but bad times are much worse.
It also meant that our credit rating has never been as good as GM's or Ford's. As a result, we've always had to pay a premium on the money we've borrowed. Unlike General Motors, which is big enough and profitable enough to function as its own bank, Chrysler has had to borrow money at the prevailing interest rates. And the banks have been only too happy to oblige.
Through the fat years, the bankers were always right there by our side. But in bad times they backed off in a hurry. As good conservative Republicans, most of the bankers were skeptical of the Loan Guarantee Act. Because most of the bank loans were to Chrysler Financial rather than to Chrysler Corporation itself, the bankers figured that if we declared Chapter 11, they'd still make out pretty well.
But they were in for a big shock. Late in 1979, Jerry Greenwald asked Steve Miller and Ron Trost, a Los Angeles expert on bankruptcy, to prepare a "memo of liquidation." This document made it clear that essentially it didn't matter whether the loans had been made to Chrysler Corporation or Chrysler Financial. In the event of a bankruptcy, _all_ the loans would be tied up for between five and ten years in the courts, and the banks would lose a significant percentage of their investment. And under a quirk in the Michigan law, the interest rates on the outstanding loans would drop to 6 percent a year until the matter was resolved. It didn't take long for the banks to realize that it was in their best interest to grant the concessions that would keep us in business.
Even so, they were far less inclined to compromise than our suppliers and our workers. For one thing, their survival didn't depend on our recovery. For another, the sheer number of banks was overwhelming. When Lockheed received federal loan guarantees in 1971, only twenty-four banks were involved, and all of them were American. Our banks, however, were spread out over most of the fifty states—and all over the world. They ranged from Manufacturers Hanover Trust in New York, where we owed over $200 million, to the Twin City Bank of Little Rock, Arkansas, where we owed a mere $78,000. We owed money to banks in London, Toronto, Ottawa, Frankfurt, Paris, Tokyo—and even Tehran.
Each bank had its own agenda. Manufacturers Hanover, known in the business world as Manny Hanny, had been connected with Chrysler for years. Lynn Townsend had been on their board for nine years, while two of Manny Hanny's chairmen had served on ours. More than once they had helped us through hard times. John McGillicuddy, the current chairman, had established a $455 million revolving credit agreement for Chrysler. In addition, he testified in Congress in favor of the loan guarantees. "I believe that Chrysler Corporation ought to survive," he told the committee. "I am not categorically opposed to government assistance in every case and do not see its sparing use as a threat to the freeenterprise system."
John McGillicuddy was one of our white knights. Manny Hanny was our lead bank, and McGillicuddy pushed his colleagues to accept our package of concessions.
Our other white knight was G. William Miller, secretary of the treasury. He testified before the House committee that Chrysler represented an exceptional case and that the loan guarantees were a good idea. Miller was tough on the banks. He felt they should take their losses and lick their wounds.
But over at Citibank, Walter Wriston was deeply opposed to the guarantees. As the most influential banker in the country, Wriston was our albatross. Citibank was sure we were going bankrupt, and they couldn't wait to get their fifteen cents on the dollar—which is what we had proposed as a settlement. (We were also offering another fifteen cents in preferred stock.) Citibank seems to enjoy its reputation as a hard-nosed outfit. Anytime they could set up a roadblock in our way, they did.
But the conflict between Manny Hanny and Citibank was just the tip of the iceberg. Our lenders included both big-money banks and small-town banks, domestic banks and foreign banks, and even a couple of insurance companies. There were loans to Chrysler Corporation itself, loans to Chrysler Canada, and loans to Chrysler Financial. There were also loans to various foreign subsidiaries and letters of credit against future invoices.
To make matters worse, we had loans outstanding at many different interest rates. There were low-interest, fixed-rate loans at 9 percent. Then there were high-interest, floating-rate loans, which floated with the prime, ranging from 12 percent in January, when we began dealing with the banks, to 20 percent in April, when we formulated an agreement, back to around 11 percent by the time the deal was completed.
There were banks whose lines of credit were fully extended, and others that were only partly drawn down. There were loans that were already six months overdue, such as the one for $5 million from a bank in Spain that was issued in July 1979 and was supposed to have been repaid ninety days later. And there were longer loans, too, including some from insurance companies that didn't come due until 1995.
Naturally, there was a lot of tension and disagreement among the banks about what constituted a fair resolution. Generally speaking, the bankers were in no mood to compromise. Their major conflicts were not with Chrysler but with each other. Everybody had a reason why someone else should bear the brunt of the concessions.
The American banks said: "To hell with the foreign banks." Little did I know that what the big American banks were really worried about were _their_ loans to Mexico, Poland, and Brazil. With all the postponements and defaults on their international loans, the big American banks are now going through the same problems as Chrysler. But unlike us, they have a rich uncle to bail them out—without a lot of the hoopla and publicity.
Not too long ago, when Mexico needed $1 billion to avoid defaulting on loans to New York banks, Paul Volcker of the Fed just wrote them a check over the weekend. That's what I call curb service for the banking fraternity. There were no hearings and no attempt to impose controls. There were no penalties for the banks. And of course the $1 billion came directly from the taxpayers.
The bankers sure didn't like the idea of loan guarantees for Chrysler. But guarantees for them were another matter. They plainly made a lot of mistakes in granting loans to foreign countries, but the International Monetary Fund bailed them out. The banks wanted us to cut executive pay, skip dividends, and all the rest. But I don't see anybody getting tough with them for making bad loans. I'd sure like to be the workout guy who asks Citicorp to start skipping dividends and its officers to take pay cuts!
There's a funny orientation at the Federal Reserve Board—they're all bankers, no businessmen. If a bank goes under for making bad decisions, it gets immediate attention. Two little banks go under in Oklahoma, and you have Paul Volcker yelling about a liquidity crisis and loosening the strings on money. But when Chrysler and International Harvester, two companies with almost a million jobs at stake, are going under, that's good old free enterprise at work.
Not really. That's nothing but a double standard and totally unfair.
Meanwhile, the foreign banks had their own complaints. The Japanese banks said: "Look, when there's a problem in Japan, the home banks cover it and the foreign banks get paid off. This is an American problem—let the American banks deal with it."
The Canadian banks said: "We're not going to let the Americans tell us what to do. We've been pushed around long enough." The Canadian government supported this position. In return for guaranteed government loans, Canada wanted us to provide assurances of a fixed employment level.
The Canadians felt like the youngest kid in the family who gets all the hand-me-downs. We were building our rear-wheel-drive vehicles in Canada—our big van and the New Yorker. At the time it seemed as if these cars were a dying breed.
We ended up with a compromise. Rather than any absolute numbers, we guaranteed the Canadians a percentage of our North American employment, and we agreed on 11 percent. As things turned out, that was an easy promise to keep. Because the United States never did come up with an energy policy, as gas prices dropped these bigger cars took off like rockets. At one point Canadian workers constituted 18 percent of Chrysler's North American employment.
The European banks said: "We're not going along with you. What about Telefunken?" A couple of years earlier, the German government had designed a bailout program for Telefunken, but the American banks had pulled out, leaving the German banks holding the bag. Like the Japanese, the German attitude was: "This is an American problem. Your banks should bear the brunt of it."
When they realized what they were up against, the American banks suddenly got religion. Their position became the same as ours: "No, everybody's in this together. In a bankruptcy, the court is going to treat us all the same." It was beginning to dawn on them that the only way we were going to solve this thing was to ask for fair and equitable contributions from _all_ the banks involved.
Still, there were problems. The smaller banks said: "To hell with New York. Our loans to Chrysler make up a bigger percentage of our assets than the loans from those big New York banks. So let's have everybody's concessions based on the size of the bank."
To induce the banks to make the concessions we needed, we were forced to offer a sweetener: 12 million stock warrants, good until 1990, which could be exercised if the stock ever reached $13 a share. When the Loan Guarantee Board heard about that, they demanded a similar arrangement, on the theory that they too were a lender, with 50 percent more money at risk than the banks. So the government ended up with 14.4 million warrants.
In the end we gave up 26.4 million warrants, representing a major potential dilution of our equity. At the time, we didn't think very much about those warrants. We needed everybody's cooperation, and with our stock as low as $3.50, $13 a share seemed like a distant dream.
It took months to come up with an acceptable plan for the banks. I kicked the whole thing off and went to a few of the early meetings, but the great bulk of the work was handled by Jerry Greenwald and Steve Miller.
The negotiations with the banks were so complicated that Jerry did little else but coordinate the master plan from Highland Park. He set up twenty-two task forces that met every Friday with himself and Steve Miller. Miller, meanwhile, was running all over the place, flying to New York or Washington, with side trips to Ottawa, Paris, London, and dozens of other cities.
Miller's schedule was unbelievable. He spent much of his time in New York, where a typical day would began at six-thirty with a breakfast meeting with one of our lawyers. This would be followed by a series of meetings throughout the day with bankers and their lawyers. At six in the evening he would meet with yet another group of bankers for drinks. At eight, there would be dinner with still others. At ten, he would be back at the hotel trying to prepare for the next day's meetings. Around midnight he would be on the phone to Japan to work out our arrangements with Mitsubishi and the Japanese banks.
Steve worked his tail off, and he also brought a little camaraderie to the task. His attitude to the bankers was: "Hey, this is hard, and I know you've never done anything like it. But neither have we, so let's see if we can't go through these uncharted waters together."
Steve Miller had the perfect personality for the job. He was tough and well-organized, but he also knew when to loosen up. In one meeting where the various banks were all fighting among themselves, he pointed a toy pistol at his head. "If you guys can't agree on this stuff," he said, "I'm going to have to kill myself."
At another of those meetings, the group sent out for sandwiches from a local delicatessen. The response came back immediately: "You guys are from Chrysler? Sorry. We won't deliver unless you pay us in advance!" That's the kind of atmosphere we were living in. Here we were trying to get hundreds of millions of dollars in concessions from the banks, and the local deli wouldn't even carry our corned beef and pastrami sandwiches for half an hour!
At first, Steve had been meeting with the bankers in separate groups. But this method only encouraged their divisiveness. Soon he decided to get everybody together in the same room. That way, each would have to talk to the other and see for themselves how pissed off grown men can really get.
This was a watershed event. It was also the first time that some of the bankers had ever met. Steve made a little speech. "I realize there's no way that my plan is going to strike you as fair," he told the bankers. "I just hope it's equally unfair to everybody. I want you to take the plan home and study it over the weekend. We'll meet again next Tuesday, April 1, and you'll tell me yes or no. But we can't discuss this thing much further. If you don't like the plan, we'd better just forget the whole thing."
Some of the bankers threatened that they wouldn't be back on Tuesday, but they all showed up. As it turned out, the meeting took place at a terrible time in the banking world. The silver market had just gone crazy with the Hunt Brothers. Bache was in big trouble. Interest rates had gone to 20 percent and they looked as if they might soar to 25 percent.
If we couldn't get the bankers to agree at this meeting, it would be all over. And with the nation's economy already shot to hell, it's quite possible that a Chrysler bankruptcy could have started a landslide of economic disasters.
When the whole group had convened for the April 1 meeting, Steve opened with a real shocker: "Gentlemen," he began, "last night Chrysler's board of directors held an emergency meeting. In view of the terrible economy, the declining fortunes of the company, and skyrocketing interest rates—not to mention the lack of support that we've had from our lenders—at nine-thirty this morning we decided to file for bankruptcy."
The room was silent. Greenwald was flabbergasted. He was on the board, of course, but this was the first he had heard of any such meeting. Then Miller added: "I should probably remind you all that today is the first of April."
There was a great sigh of relief. Unfortunately, the Europeans had never heard of April Fool's. They kept staring at the wall, wondering what on earth the date had to do with all of this.
Miller had thought up his little joke about five minutes before the meeting. It was risky, but it worked—it got everybody in the room to focus on the larger picture and to consider the consequences of no agreement. Steve's compromise plan was accepted by all the banks who attended: a total of $660 million in interest deferrals and reductions plus a four-year extension of $4 billion in loans at 5.5 percent.
But the plan could work only if every single bank to whom we owed money agreed to cooperate. Some of these banks, such as Bank Tejarat in Iran, made us pretty nervous. We owed them only $3.6 million, but this was right after the hostage crisis, and the U.S. government had frozen about $8 billion in Iranian deposits. To our great relief, the Iranians agreed to the plan without any problem.
By June, almost every bank had accepted the plan. When we had them all, we could finally get our hands on the first $500 million in guaranteed loans. But we were quickly running out of cash to pay our bills. On June 10, 1980, we had to stop paying our suppliers. Once again, bankruptcy was a real possibility.
The first $500 million in guaranteed loans was only a few days away, but how long would our suppliers stay patient? Even if they didn't force us into immediate bankruptcy, they could always decide to stop shipping, which would have been almost as bad. Because of our very tight inventories, any disruption of parts would be a disaster. Fortunately, as we stood on the edge of the precipice, the suppliers came through.
By this time more than 90 percent of the banks had agreed to go along with our plan. They represented more than 95 percent of the outstanding loans. But we still needed a participation rate of 100 percent. Otherwise, the whole deal was off. Meanwhile, time was quickly running out. Even if every bank agreed to accept the plan, there was still the problem of all the paperwork and the proper signatures.
For example, there was a bank in Alaska that had signed the agreements but had put them in the mail instead of returning them by express courier. The papers were going to arrive too late, so we had to express them another set.
In Minnesota a bank officer had put the agreements in a box next to his desk, planning to sign them the next morning. That night, the cleaning lady picked them up and put them through the shredder.
A bank in Lebanon had signed the documents but couldn't get them out of the Beirut airport during the civil war. We finally got them delivered to the U.S. embassy. Eventually the Loan Guarantee Board accepted the embassy's testimony that the papers were all signed and in order.
In a financial reorganization, the usual practice is that the big banks agree to buy out the little guys at an appropriate discount to make the whole process go more smoothly. But we stood firm that there would be equal treatment for everybody. We knew that if we made any exceptions, it would open the floodgates.
A few of the small bankers honestly believed that extending the loans was just throwing good money after bad. To them it was a matter of taking their losses now rather than down the road.
In May, Steve Miller went on a whirlwind trip to Europe to visit the most stubborn banks over there. His job wasn't made any easier by an article in the _Financial Times_ that said Chrysler had developed a secret plan to pay off the holdouts. As he arrived at each bank, they were all eager to learn the details. They were highly disappointed to find that their only options were to go along with the existing compromise or to send us into bankruptcy.
Back home, the recalcitrants were mostly small rural banks. One of them was threatening to screw up the entire Chrysler deal for a loan of $75,000. Here, too, there were rumors that we were quietly paying off the banks that weren't going along. These rumors encouraged the holdouts, but one by one we got them. As the number of holdouts became smaller, the pressure on each of them became overwhelming. Still, as May stretched into June, I was beginning to wonder just when this agony was finally going to stop.
The most dramatic conflict of all came in Rockford, Illinois, with the American National Bank and Trust Company. David Knapp, the bank president, was convinced that even with federal loan guarantees, Chrysler was about to go broke. He didn't want any part of it. His bank had sued to recover its loan of $650,000, and he was determined to hold out to the bitter end.
Fortunately for us, however, Rockford was also the site of one of our major assembly plants, and many of its residents worked for Chrysler or our suppliers. As soon as they heard about the problem, they started putting pressure on the bank to go along with the general agreement.
When that didn't help, Steve Miller flew down to meet with Knapp. Miller wasn't even sure that Knapp would see him, but if he refused, Steve intended to go to the local newspaper and tell them that Mr. Knapp was going to put five thousand people in Rockford out of work.
The mayor of Rockford set up a meeting with Knapp and Miller at City Hall. Miller gave Knapp a pep talk. He tried to explain that the deal wasn't to everybody's complete satisfaction but that the other banks were going along with it. He said that he just couldn't cut a special deal with any of the banks. Knapp heard him out, but he wouldn't change his mind. His position was: "I'm sorry, but if you take a loan you've got to pay it back."
A few days later the Rockford bank agreed to the plan. David Knapp had received a number of phone calls from companies that depended on Chrysler's survival. He had heard from politicians at every level. Thousands of UAW members had threatened to withdraw their money from his bank. There had even been a bomb threat from somebody in town, which he was sure had come from us.
After the trip to Rockford, Miller went to visit one or two other holdouts. By the end of June we had them all. And that was the end of it.
Or so we thought. Once we had the indicated agreement of all the banks, the only remaining task was to collect all the signed documents and have a closing. Normally, a closing consists of a bunch of lawyers who get together, look over some documents, and declare that the deal is complete.
But Chrysler's case was a bit more complicated. To start with, there were ten thousand individual documents. The printing bill alone for the final agreements came to close to $2 million! Stacked in a pile, the documents would have reached as high as a seven-story building.
Moreover, the documents were scattered in law firms all over New York, and in several other cities, too. Most of them, though, were in the Westvāco Building at 299 Park Avenue in Manhattan, in the law offices of our counsel, Debevoise, Plimpton, Lyons, & Gates.
On Monday evening, June 23, there was a meeting in these offices to get all the papers in order for the next day's closing. We had a large group of lawyers on hand, because if even a single document was missing, the whole deal was off.
At around 7:30 A M., Steve Miller was in the cafeteria on the thirty-third floor of the Westvāco Building when he noticed black clouds of smoke out the window. He assumed that there was a grease fire in the kitchen, but he soon learned that the twentieth floor of the building was burning.
Steve says that he was sorely tempted to ignore the fire, because he didn't want to jeopardize the closing. But a few minutes later the building was evacuated, and everybody who could walked down thirty-three flights to the street.
By the time the group made its way downstairs, Park Avenue was completely blocked off by fire engines. Flames were leaping out of the windows. Steve's first thought was: "This is definitely a message from God. He's casting His vote against the deal. I guess we shouldn't have fooled around with the free-enterprise system."
Our people and the lawyers watched with growing horror as one after another the offices in the building burst into flames, while glass from the big windows went crashing into the street. Fortunately, the fire was being contained on the twentieth floor. All our documents were above the thirtieth floor.
Eventually the fire was under control, and the Chrysler people walked over to a local restaurant to have dinner. While Miller was walking down the street, he ran into Jerry Greenwald, who had just flown into the city to sign the documents. Jerry was on his way to the Westvāco Building when he spotted Steve.
"Boy," said Greenwald. "The traffic here is impossible. There's some kind of fire going on. Could you imagine what would happen if it was our building?"
Steve replied: "It _is_ our building!"
Greenwald was familiar with Miller's sense of humor, so he naturally assumed that Steve was joking. Jerry kept walking until he couldn't go any farther, at which point he realized it wasn't funny.
Finally, at two in the morning, Jerry, Steve, and the lawyers met in the Citicorp Center. They decided that it was essential to retrieve the papers from the smoldering building or the entire deal would be at risk. At two-thirty they were arguing their way through the police lines. A lot of firemen had already been injured in the fire, but our people were allowed in because they insisted that Chrysler's survival depended on removing those documents.
And so twenty guys went up in the elevator. They threw all the documents into cartons and mail carts. An hour later, in the middle of the night, a convoy of lawyers started pushing their mail carts down the middle of Park Avenue, over to the Citicorp Building to the offices of Shearman & Sterling, one of the law firms that represented the banks. They spent the rest of the night putting all the papers together so that the closing could proceed as planned.
The papers were reassembled between nine and noon the next day. Miraculously, nothing had been lost or damaged. At noon a large group of lawyers and bankers marched into a big conference room at Shearman & Sterling for the closing. There were speakerphones with connections to Paris, Detroit, Wall Street, Toronto, and Washington—where the Loan Guarantee Board was standing by.
Bill Matteson, our principal lawyer, called the roll. He went through the long list of banks represented in the room as well as those hooked up on the speakerphones. Are you ready to close, Toronto? Are you ready, Paris? Each group said yes.
At 12:26 P.M. on June 24, the deal was concluded to resounding cheers. We were finally entitled to receive the first installment of our federally backed loans. Later that day, after Salomon Brothers, our financial advisers, took their fee of $13,250,000 off the top, Steve Miller endorsed a check for $486,750,000. He walked over to Manny Hanny and filled out a deposit slip, just like any other depositor.
At long last, the New Chrysler Corporation was in business to stay.
# XXII
# THE K-CAR—AND A CLOSE CALL
During our darkest days, the promise of the K-car was always the light at the end of the tunnel. For a couple of years, the prospect of an American-made, fuel-efficient, front-wheel-drive car was just about all we had to offer. Throughout the congressional hearings, and during the endless negotiations with the banks, our expectations for the K-car were what got us through.
The K-car is a sensational product. It's perfectly okay for me to brag about it, because I arrived at Chrysler too late to play much of a role in its creation.
This is the car that Hal Sperlich had been working on ever since he'd come to Chrysler in 1977. In many ways, it's what Hal and I had always wanted to build at Ford. It's the one we _would_ have done if Henry hadn't been so stubborn about small cars.
The K-car was and is a comfortable, front-wheel-drive vehicle that ran well on only four cylinders. It offered twenty-five miles per gallon in city driving and forty-one on the highway. These figures were impressive in their own right. But even more important, they were slightly better than GM's X-car, which had been launched a year and a half earlier. Detroit had come out with small cars before, but the K-car was the first one roomy enough to accommodate a family of six while still light enough to deliver super fuel economy.
Sperlich's great triumph was that the car was strong and well stanced. It was solid. It wasn't flimsy-looking, like some of the other compacts on the market. Like the Mustang, the K-car was small and stylish. The difference was that the K-car could run on a very small engine.
In our ad campaign we announced that the K-car was an American alternative. To drive that point home, many of the ads were done in red, white, and blue. We also pointed out that the K-car was roomy enough to hold "six Americans"—a little shot at our Japanese competitors. We even had to install six seat belts in each car, which added slightly to our cost.
But our master stroke of marketing was to use the term "K-car" instead of the real names, Aries (for the Dodge line) and Reliant (for Chrysler). I'd love to take credit for that decision, but this was just one of those happy accidents that happens on its own. With all that we had been through, we were certainly overdue for a lucky break.
When a new car is in the early stages of development, the stylists usually assign it a code name for internal use. At Ford, we always used the names of animals. Chrysler and GM use letters of the alphabet. Later the marketing team goes through a list of possible names and researches them in detail.
At Chrysler, the K-car was the last train in the station. If we failed here, it was all over. With that awareness, we began talking about the car at a very early stage in its development, long before we had settled on the actual names. Without our planning it, the letter K seemed to stick in the public mind.
Naturally, once the public picked up on the "K-car" theme, we stuck with it in our advertising by announcing that "the K-cars are coming." We even decided upon a special promotion with a major retailer, which we called "K-car comes to K-Mart." Before long, the "K" designation had grown so popular that the real names, Reliant and Aries, had become more like subtitles. In 1983, when we finally removed the letter K from the back of the cars, our advertising agency was convinced it was a big mistake.
The Aries and Reliant are definitely the right cars for the times. They provide great fuel economy and a comfortable ride, and they look pretty good, too. That isn't just my judgment, by the way. _Motor Trend Magazine_ named the Aries and Reliant as cars of the year for 1981, an award we had won three years earlier for the Omni and Horizon.
"These are the cars we need," wrote the magazine. "Surely these must be indicators of quality, signs of times that have come. But more than this, they reveal that maybe for the first time an American automaker has calculated the demeanor of the general car-buying public. With the Aries and Reliant, Chrysler will be able to serve up a substantially better car that will last longer in the face of heavy rock salt _and_ traditional buyer neglect."
And Jim Dunne, automotive editor of _Popular Science_ , observed: "If Chrysler could have designed a car that was right for today's market just three weeks ago instead of three and a half years ago, they still would have designed this car."
Today the K-car serves as the foundation for almost everything we do. Virtually all our other cars have been derived from its platform, including the LeBaron, Chrysler E Class, Dodge 600, the New Yorker, and to a lesser degree our sports cars, Dodge Daytona and Chrysler Laser.
Because we've done so much off the K platform, we've taken a lot of heat from the press—especially _The Wall Street Journal_. The way they describe it, you'd think we had invented some new way to cheat the customer!
Now, it's true that once upon a time, the ideal in Detroit was to create a completely new car for every price range. But these days, a totally new model requires an investment of about $1 billion. These days, "new" cars are an illusion. Each "new" car is invariably a mixture of new and previous parts. The new parts may include the sheet metal, the transmission, or the chassis. But nobody, not even GM, can afford to make a new car from scratch anymore.
Building a new car off the platform of another model has been going on in Detroit for fifty years. The Japanese have done it from the start. GM has been masterful at doing it, and many parts of the Chevrolet have found their way into Buicks and Cadillacs. And at Ford, as we've already seen, the Mustang was a restyled Falcon.
The smart guys use interchangeable parts to get their costs down. That's not only permissible, it's also essential. These days, to do a new car from scratch when you're unsure of the volume is a sure formula for bankruptcy.
At the same time, there _is_ such a thing as going too far in that direction. GM learned this the hard way on two different occasions. In 1977, GM found themselves short of Oldsmobile V-8 engines, so they began to install comparable Chevrolet V-8's in some of their Oldsmobiles, Pontiacs, and Buicks.
Unfortunately, they forgot to tell their customers about the switch. Some of them got so angry that they filed lawsuits. When it was all over, the engine switch had cost GM more than $30 million.
GM had a similar problem with the Cadillac Cimarron. The Cimarron was rushed into production when some of the marketing guys at Cadillac noticed that the median age of Cadillac buyers was somewhere between seventy and "deceased."
But the new model was little more than a fancied-up Chevrolet Cavalier. Even Pete Estes, a former GM president, complained that the Cimarron looked too much like a Chevrolet. Leather seats and automatic headlight dimmers were not enough to distinguish it from the basic J-car. The consumers sensed that something was wrong, and the Cimarron bombed in the marketplace.
Even with the perfect product, you can make mistakes. Eventually the K-car saved us. But its first year on the market coincided with some of the worst problems we ever had.
To our great distress, the K-car got off to a poor start. In October 1980, when we introduced the Aries and Reliant, they fizzled. We had some unexpected problems with our new robotic welders in the factories, which led to production snags. For a proper launch, we needed thirty-five thousand cars in the showrooms on Introduction Day. Instead, there were only ten thousand.
Worse, we had sticker-shocked the consumers right off their feet. At the time, we were involved in a tough price war with GM's X-car, our primary domestic competitor. Their basic Citation Hatchback went for $6,270, so we'd priced the basic K-car at $5,880.
The only way we could underprice GM and still survive was to make it up on options. And so we built a lot of cars with air conditioning, automatic transmissions, velour upholstery, and electric windows, which added a couple of thousand dollars to the price.
We should have paid more attention to our research. We had advance information that customers would be more interested in the basic models, which sold for around $6,000. But we were in a crisis mentality. As a result, we sent out too many cars whose total price was between $8,000 and $9,000.
It was a costly mistake. We should have waited until the K-car had gained some initial acceptance and _then_ introduced the options. We had no business reaching for the wealthier customers. These weren't the people who were going to buy the K-car in the first place.
The good news is that we identified the problem very early and were able to correct it. We knew that the customers were coming into the showrooms, so the interest was certainly there. But we also knew that most of them were leaving without placing an order. When we interviewed these people on their way out the door, they all told us the same thing: "I thought this car was supposed to be a good buy. Then I looked at the sticker price." As soon as possible, we started producing more basic models. Before long, sales picked up.
But by December we had run into another problem. The prime rate had now zoomed up to 18.5 percent. Two months earlier, when the K-cars were first introduced, interest rates had been 5 percent lower. If they had _stayed_ at 13.5 percent, we could have sold a lot of cars. But in those days, interest rates were changing almost daily. And cars as well as houses were going unsold.
I was furious with the Fed's mercurial behavior on interest rates, but there was nothing I could do to change it. I could, however, respond to the situation. And I did.
To fight the specter of high interest rates, we came up with a floating rebate plan. We would grant a refund to any customer who bought a car on credit—based on the difference between 13 percent and the prevailing interest rate when the car was purchased.
When I announced the new plan, I said: "The Lord helps those who help themselves." He must have been listening, even though Paul Volcker wasn't, because our gamble paid off. Before long, Ford and GM were offering rebates of their own.
By early 1981, sales had picked up considerably. Despite the awkward beginning, the K-cars finished the year with more than 20 percent of the compact-car market. And they've been selling well ever since. While some people were still writing us off, we sold a million Aries and Reliants, which gave us the cash to start developing other new models.
But that came later. Because our K-cars got off to such a slow start, we began 1981 in very bad shape. Although we had fought so hard all year to keep Chrysler's bad news off the front pages, we soon had to go back to Washington to draw down another $400 million in guarantees.
When it came to actually borrowing that money, the Loan Guarantee Board had put a number of roadblocks in our way. For example, we couldn't get the loans all at once, but only in installments. The first two installments were pretty close together in 1980.
But the third drawdown, a year later, was a complete disaster from the perspective of public relations. Most people just didn't understand what was going on. They saw the story on television and they thought: "Here we go again. Those guys just got a billion and a half dollars. Why are they going back for more?"
I should never have agreed to borrow the money in three installments. For each drawdown, we had to face up to the bad headlines. It was terrible. I don't think the Loan Guarantee Board would have let us borrow the entire sum all at once, but instead of three installments, we could probably have arranged for two installments of $600 million each.
Each time we went back for more money, our sales dropped off. The public was under the impression that Chrysler was a bottomless pit. Plenty of people who were considering our products changed their minds and bought cars from our competitors. It's impossible to know for sure, but my guess is that about one third of the $1.2 billion that we actually received in guaranteed loans was wasted through lost sales as a result of all the bad publicity. Even so, I don't know any other way we could have survived.
To qualify for the final $400 million of our loan, we had to arrange for yet another round of concessions. We asked the banks for an additional $600 million through the conversion of debt into preferred stock. We asked labor for a freeze on cost-of-living adjustments. We asked our suppliers for more time to pay and a 5 percent price reduction during the first quarter of 1981. And G. William Miller, secretary of the treasury, asked the banks to forgive half of our remaining debt. Once again, the alternative was bankruptcy.
This time, the banks forgave a total of $1.1 billion worth of debt in exchange for preferred stock in the company. Preferred stock normally pays a dividend, but in our case there wouldn't be any until we had paid off the guaranteed loans. The bankers didn't take our stock offer too seriously. But the optimists among them knew that if Chrysler ever came back from the grave, they'd eventually recover a good part of their money.
Throughout 1981, our survival was never more than a week-by-week proposition. Even with the K-car, our losses were still staggering—$478.5 million for the year. To make matters worse, the Loan Guarantee Board was putting some additional strictures on us that did little to lift our morale.
One of their rules was that we had to pay them an administrative fee of $1 million every month. That really ticked me off, because our January payment alone covered their annual expenses, so the next $11 million was pure profit for the Treasury. Hell, if I could have had a deal like that for Chrysler, I wouldn't have needed the loan guarantees in the first place!
Under the terms of the act, the government was required to charge us an annual fee of .5 percent of the total amount to administer the loans. But William Miller had the authority to raise the fee to 1 percent if he believed the loans were at risk. He did—and 1 percent of $1.2 billion comes to $12 million a year. We had no negotiating leverage on that one, no opportunity to say: "That's too much, we don't like it." That extra $6 million could have gone for something more productive to help ensure our long-term future.
My second quarrel with the board was the ridiculous amount of paperwork with which they burdened us. One good comprehensive report a month would have given them all the information they needed. Instead, they asked us for a continuing mountain of documents, and it was a pain to keep up with it all.
To make matters worse, they didn't even _read_ the stuff. If they had any questions, they'd just pick up the phone and call. I can understand that early on in the whole process the Loan Guarantee Board must have been nervous and that it was important to them to make sure that everybody knew what was going on. But as we gradually became healthier, there was no mechanism to change the rules.
Then we ran into a problem that could only have come from the fertile mind of a real bureaucrat. The board ordered us to sell our Gulfstream jet. To the little minds in Washington, the Chrysler jet was a symbol of the profligate spending of a big corporation. Never mind that the government had a hundred private jets—all at taxpayers' expense—to help them conduct _their_ business. Nobody blinks when you spend $100 million for new robots, but when you send one of your top guys around to the factories to teach the workers how to use those new robots, that's OK—but only if he flies commercial.
So what if he has to get from Highland Park, Michigan, to Rockford, Illinois, or Kokomo, Indiana. Some of our plants can't be reached very easily by commercial aircraft. And if I'm paying a guy two hundred grand a year, I don't want him spending his time in airports.
Private planes save a lot of wear and tear on our employees. People outside the business world often have the impression that most executives goof off. Not the ones I know. They work twelve and fourteen hours a day, and their time is valuable.
The corporate jet is not a perk. It's a necessity. Believe me, it would be a lot nicer to fly first class in a commercial airplane with a friendly stewardess serving us drinks. But the company jet is a great time-saver—and a stress-saver as well.
To be fair, not everything that the Loan Guarantee Board asked us to do was trivial or unduly meddlesome. Among their more reasonable demands was that we look actively for a merger partner. When I first came to Chrysler with Global Motors on my mind, I assumed that any conceivable merger would involve a foreign company such as Mitsubishi or Volkswagen. But after one look at our balance sheet, nobody would even talk to me.
In 1981, as the roof was caving in, it seemed a merger might be the only way out. They say that necessity is the mother of invention. Well, when the tide turned against us once more, we got as inventive as we could. We came up with a last-ditch plan, an idea that sounded preposterous on the surface but that actually made a lot of sense. Because we had the K-car and they had no real equivalent, we proposed a merger between Chrysler and Ford.
There were a thousand obstacles to such a plan, but the first thing that came to everyone's mind was the personality question. "Let's say it all works," said our bankers. "But Henry's still around and so are you—how could you two make a go of it?"
"Listen," I replied, "here's what I'll do. Henry has already announced that he's stepping aside. I'm willing to do the same. I'd like to stick around for twelve months to help put this deal together. After it's done, I'll walk away. This thing is obviously bigger than both of us."
The other major problem was that this kind of merger would normally be a violation of the antitrust laws. So I checked with Pete Rodino of Watergate fame and with some of the other guys on the Judiciary Committee. They thought that because we were failing, the rules could be waived. I also called Bob Strauss, a great lawyer and major figure in the Democratic party. He too thought that we might be able to pull it off.
Once the antitrust problem was out of the way—at least in theory—we could focus on the positive. The previous year, 1980, had been a disaster for us: we ended up losing $1.7 billion. But 1980 had been no picnic at Ford, either. Their losses were almost as bad as ours—over $1.5 billion. Far more important was that their market share was plunging. Back in 1978, it had been as high as 28 percent. Three years later, it had dropped as low as 15 percent.
I asked Tom Denomine of our staff to draw up some plans. Within a few weeks Tom put together a proposal that made beautiful sense.
Under its terms, Ford would physically take over Chrysler. Because they were so much larger as well as healthier, Ford had to be the surviving company. Chrysler and Dodge would continue to operate, but as a third and fourth division at Ford, alongside the Ford and Lincoln-Mercury Divisions.
Tom and I saw great benefits for both companies in a merger. Their strengths were our weaknesses—and vice versa. Both of us had spent many years at Ford before coming over to Chrysler, so we understood the problems and the needs of each side.
If the merger went through, the benefits to Chrysler would be obvious—so obvious, in fact, that they could be summed up in a single world. Survival.
But what was in it for Ford? A great deal. At the time, Ford was very strong in Europe, where they were spending a disproportionate amount of money. But in America they were dying in the marketplace. After the second oil crisis, they were being badly hit by the imports. Aside from the Escort/Lynx subcompact—Ford's "world car" and their equivalent of our Omni/Horizon—they didn't have any small front-wheel-drive cars.
Moreover, Ford was about to embark on a massive investment of billions of dollars in order to produce the Tempo and Topaz, only to duplicate the kind of roomy, front-wheel-drive product that already existed at Chrysler in the K-car. If we merged, we could begin selling a version of their Escort to replace our own Omni/Horizon, and they could begin selling a version of our new Aries and Reliant. Under the terms of our plan, Ford would provide a larger, front-wheel-drive car, originally planned for 1987, and most of the larger models as well as the trucks. We would supply the 1984 minivan.
For Ford, a merger with Chrysler represented the fastest, easiest way to get back to their original position of being a strong number two. With a stroke of the pen, they would surpass GM in truck sales and also be number one in the Canadian and Mexican car markets. Domestically, a merger would mean that Ford's market share would jump straight up from 17 percent to 27 percent.
If a merger with Chrysler went through, Ford would have been at 75 percent of GM's strength in U.S. car sales. Then we would have seen a real horse race. Alfred Sloan would have turned over in his grave, because the new company would have four divisions against GM's five. It would have been a fantastic thing to have these two great companies going at it head to head. It would have been great for America. And the bankers and the lawyers would have loved it, because it would have been the biggest deal in the history of American industry.
On the other hand, if Chrysler simply folded, our research showed that Ford's share would rise only minimally. In that scenario, the great bulk of our business would be picked up by GM and especially by the imports.
We showed the plan to some of the top bankers in New York, and they flipped. "Made in heaven," they said. "The products fit. The dealer organizations fit. Everything works."
We had drawn up hypothetical balance sheets, and they looked terrific. We had an operating plan. We were in a position to add $1 billion in profit to the combination. There was strength in those numbers.
Salomon Brothers, our investment bankers, thought the plan was pretty good. Jim Wolfensohn, who handled the Chrysler account, agreed to approach Goldman Sachs, who represented Ford. Using financial data from Chrysler plus whatever they could dig up on Ford, Salomon Brothers fleshed out the idea and put together a point-by-point guide as to why the merger made sense for both parties and how it could best be brought about.
Goldman Sachs showed some interest in the proposal, and they passed it along to the top people at Ford. At this stage the plan was absolutely secret. Because this was a once-in-a-lifetime opportunity, I went to see Bill Ford and I pitched it to him. But aside from that meeting, we had taken great pains to conceal it from the world. Everything had been done behind the scenes, hush-hush, without any leaks to the media.
Suddenly the whole thing came tumbling down. Philip Caldwell, chairman of Ford, blew the whistle. He preempted the whole discussion by making a statement to the press. In effect, what he said was: Chrysler has proposed a merger with us, but we'd never be that stupid.
Ford put out that statement to rag us a little. But at no point did they give the proposal a thorough analysis. Caldwell simply announced that the board had voted unanimously not to open any negotiations with Chrysler. Later one of the Ford board members told me that they got about a two-minute look at the plan. They had responded in twenty-four hours; it would have taken them twenty-four _days_ to study that proposal properly. In a single day all they could do was declare it was a bad idea and go along with management.
The way I see it, Ford's management was opposed because they knew that we had already taken most of their good guys, and they figured that if the deal went through, they might be left out in the cold. I imagine that Henry, who was supposedly retired, also retched at the idea. So they outlined only the worst-case scenario. I think they missed a great opportunity.
I responded with a statement of my own that such a merger would have been good for the country and that America needed a real competitor to General Motors. It was a shame, because I had already gotten the right people in Washington to start nodding. They'd said that if we could get Ford to agree, they'd do their best to make sure it could fly. But the plan got blown out of the water by Ford without a fair test.
If we could somehow have put this deal together, the only ones going crazy trying to stop it would have been General Motors. Their attitude would have been: "We already did that in the 1920s. Nobody should be allowed to do it again. A Chrysler-Ford cartel? No way! That would make things too hot for us."
If the merger had gone through, the American automobile industry would have been permanently changed. The morning after the merger, there would have been no duplication between Chrysler and Ford. We'd be saving three or four billion dollars in investments. Purchasing would be easier in a larger company. And fixed costs would be cut drastically because, like GM, we'd have a lot of interchangeable parts.
The timing was right. Perhaps it still is. But I don't think the Justice Department would allow it now. They'd yell and scream because it's a perfect horizontal integration of two giants in an oligopoly that has only three players. It would get knocked down in the Justice Department on antitrust grounds. But with the GM-Toyota deal and Washington's new philosophy on mergers, who knows?
A merger would still make sense, even though Chrysler is now healthy. GM has five divisions, but Ford and Chrysler have only two each. That's a recipe for losing your shirt on fixed costs.
The way things are going, by the year 2000 there will be only two fighters in the ring anyway: GM and Japan, Inc. A merger between Ford and Chrysler is probably the single most dramatic action that could be taken to strengthen the American automotive industry vis-à-vis the Japanese.
Of course, it all depends on your perspective. Over at Ford they still believe the industry will bounce back to what it was in the good old days and that Ford will become a contender once more. But they'll always be caught in the middle, with the Japanese underpricing them on the low end and GM owning most of the high-price and luxury business. Ford is the meat in the sandwich, gradually being eaten up.
Even without a merger with Ford, I had hoped that we would be on solid footing by the end of 1981. What I hadn't counted on were continuing high interest rates and a terrible economy. On November 1, we reached yet another crisis point: we were down to our _last one million dollars_!
At Chrysler we generally spend about $50 million _a day._ To be down to our last $1 million was absurd. It was like having a buck and a half in your checking account. In the car business, $1 million is like the spare change you keep in your top drawer.
At this point any one of the big suppliers could have knocked us off. You've got to realize that our accounts payable to suppliers was running about $800 million a month. The only way out was to ask all of our suppliers for more time. But that's harder than it sounds. If we went to them and said, "Hey, we're going to be a little slow in paying you," it could have started a chain reaction. Confidence is what keeps the company and its suppliers glued together. If that starts to come undone, the suppliers begin to act in their own interest. They get nervous, and their fear can easily lead to disaster.
A couple of small suppliers actually did stop shipping. We were forced to shut down our Jefferson Avenue plant for a couple of days. But we managed to work out deals with them to extend credit terms from twenty to twenty-two or twenty-three days, and in some cases as much as thirty. Goodyear Tire and National Steel made deals with us on the side. Chuck Pilliod and Pete Love, I will remember you forever—you kept the faith!
I also worried a lot about meeting our payrolls, but we never missed a single one. We always paid our people on time. Amazingly, we never missed paying a supplier, although we did stretch things out and pay slowly at times—but only by prior agreement. There were times when I said: "God, we need to ship a thousand more cars to get this much cash or we can't meet a twenty-eight-million-dollar payment on Thursday, or a fifty-million-dollar payroll on Friday." Day by day, it was that close, and oh, the numbers were so big.
We had to be magicians. We had to know which ones we could delay payment on, whose calls we had to take. When you scramble, you scramble like a son of a bitch.
These days, of course, they see our cash in the bank and they give us sixty days. Now we can get credit without even asking for it!
It's the old Catch-22. Want a loan? Show us that you don't need it, and then we'll give it to you. If you're rich, if there's money in the bank, there's always plenty of credit. But if you don't have the cash, then you can't get any.
My father had taught me this fact of life thirty years earlier, but I guess I wasn't listening. I sure saw the light in November of 1981!
## _It Only Hurts When I Laugh_
Of all the forms of reporting, there is nothing more concise and cutting than the newspaper cartoon. During the Chrysler crisis, hundreds appeared. A caricature and a caption captured the news in a hurry. The chronology over the four years shows our changing fortunes. Here are some of the best—or worst—depending on your point of view.
_Summer 1979_
_Winter 1979_
_Winter 1981_
_Winter 1981_
_Spring 1982_
_Summer 1982_
_Winter 1983_
_Spring 1983_
_Spring 1983_
# XXIII
# PUBLIC MAN, PUBLIC OFFICE
By the middle of 1983, when the company was solidly on its feet again, there were stories floating around that I was running for President. I guess the rumors started because of all the TV commercials I did for Chrysler. Many people now think I'm an actor. But that's ridiculous. Everybody knows that being an actor doesn't qualify you to be President!
During the congressional debate, the ads we ran to explain our position were all signed by me. The campaign was highly effective, and when it was over, our ad agency decided to take the idea of my accountability one step further by featuring my face in television commercials.
This wasn't the first time that idea had come up. Prior to K&E's arrival on the scene, Young & Rubicam had also urged me to appear on TV. I was against it, and I turned for advice to my old friend Leo-Arthur Kelmenson, the president of Kenyon & Eckhardt.
Leo shared my skepticism. "Lee," he said, "if I were you, I wouldn't do it. The timing's wrong." Kelmenson stressed that the only valid reason for my appearing in our ads was to strengthen Chrysler's credibility. But at that point, he said, I was still too new on the job, and the company was too weak. Credibility is something you can earn only over time. And if you haven't earned it, you can't use it.
When Kenyon & Eckhardt asked me to go on television, they made a better case. A year had passed and a lot had happened. During the congressional hearings, I had become a nationally known figure. The Chrysler story was constantly in the news, and the advertising people were eager to turn this liability into an asset.
At our strategy meetings in Highland Park, the agency made a strong presentation: "Everybody thinks Chrysler's going bankrupt. Somebody has to tell them you're not. The most believable guy to do that would be you. First, you're well known. And second, the viewers know very well that after you make the commercial, you have to go back to the business of making the cars you just touted. By appearing in these ads, you're putting your money where your mouth is."
In retrospect, I have to admit they were right. It's clear that my appearing in the television ads was an essential part of Chrysler's recovery.
But when the idea was first suggested, I was totally negative. Signing the print ads was one thing. That was like writing a series of open letters to the American public. But television ads were a completely different kettle of fish. Among other problems, I didn't see how I had the time to do them. There's a very good reason why commercials are the best thing on television—they're made with far more care and creativity than almost anything else on the tube.
But all that care and creativity are enormously time-consuming to produce. Making a commercial is the most tedious thing in the world. It's like watching the grass grow. I like to move fast, but shooting a single sixty-second spot can easily take up eight or ten hours. Every day I spent in front of the television cameras would mean that much less time to work at the car business. You just can't be an actor and a CEO on the same day.
I was also convinced that any corporate chairman who appears in his company's ads has got to be on an ego trip. Whenever I've seen a CEO pushing his own company, it's left a bad taste in my mouth. I had spent thirty years in marketing, and there were certain broad standards you just didn't violate. One of them goes something like this:
When a client proves refractory
Show a picture of his factory.
If the boss still moans and sighs,
Make his logo twice the size.
But only in the direst cases
Ever show the clients' faces.
Naturally, I was concerned that my appearing in television commercials would be seen by the public as a final act of desperation that would cause the entire enterprise to backfire.
For years, celebrities had been pitching products on TV. At Chrysler, we had used Joe Garagiola and Ricardo Montalban. Then we added John Houseman and Frank Sinatra. But until recently, only a handful of national business leaders have starred in their companies' advertising—and the three most notable are all named Frank: Frank Borman of Eastern Airlines, Frank Sellinger of Schlitz—and of course Frank Perdue, the chicken king.
Besides credibility, there's another reason to feature the boss in the ad, although it's not a very good one. If the ad fails, it's _his_ ass on the line. You can always blame it on the chairman's enormous ego. After all, the public routinely assumes that it was his idea—even when it wasn't.
Some months earlier, the people at K&E had asked me to allow one of their people to come to our meetings with a hand-held movie camera to prepare a film record of our recovery. They shot some footage of me addressing a group of dealers, and as an experiment, they used a few seconds of it at the end of one of our commercials.
They liked what they saw, and they asked me to make a couple of commercials on my own. While I understood their reasoning, I still didn't like the idea. But one day I was on a plane with John Morrissey, the agency head in Detroit, and he put it to me flatly: "We have to tell the public that we're a new company, different from the old Chrysler bunch. The best way to get that message across is to feature the new boss. I don't think there's any other answer except for you to do it." So I agreed to give it a shot.
There was only one aspect of all of this that appealed to me. Unlike some of the spokesmen we had used in the past, I work cheap. Once I did 108 takes in about ten hours, and all I got for it was a corned beef sandwich and a cup of coffee!
At first I delivered only tag lines—brief announcements at the end of commercials, such as: "I'm not asking you to buy one of our cars on faith. I'm asking you to compare." Or: "If you buy a car without considering Chrysler, that'll be too bad—for both of us."
Later we got bolder and developed a more aggressive approach, including: "You can go with Chrysler, or you can go with someone else—and take your chances," and the now-famous line in which I pointed my finger at the camera and said: "If you can find a better car—buy it." That one was my own, by the way, which may explain why I could deliver it with such conviction.
"If you can find a better car—buy it" has already been parodied in a hundred different ways. It must have been effective, since I'm always getting letters telling me: "I did what you said. I shopped around and I couldn't find a better car."
But of course, others said: "I followed your advice. I _found_ a better car, and it sure as hell wasn't yours!" But that's part of the risk—and part of the fun. My phrase became part of the jargon. I tried to ignore the hundreds of innovative suggestions that played on this same theme, like a big billboard in Dallas that announced: "If you can find a better Bourbon, drink it," or a letter that said: "If you can find a better lemon, suck it!"
The more commercials I made, the more active I became in deciding exactly what I would say. Of course, whenever the chairman comes up with a good line, it makes things a little awkward for the agency. They start to wonder: "Gee, if that line is so good, why didn't _we_ think of it?"
In a later commercial, which has also become famous, I started out by saying: "There was a time when 'Made in America' meant something. It meant you made the best. Unfortunately, a lot of Americans don't believe that anymore." At that point I wanted to add the following line: "And for good reason. We probably deserved that reputation, because we shipped a lot of crap out of Detroit in our day."
When they heard that, even in the cleaned-up version, the agency went bananas. They said: "This isn't the place to make confessions. If you say that, the guy sitting in front of the tube whose 1975 Volaré has rusted through is going to write in for a thousand-dollar adjustment." So we compromised. I added the words "And maybe with good reason"—and we left it at that.
At the time, these ads were pretty unusual. But given our situation, we needed something dramatic. Due to circumstances beyond our control, Chrysler already had an identity all its own. We were already perceived as being very different from the rest of the American auto industry.
In marketing terms, the choice we faced was simple—either we could try to join the crowd and become one of the boys, or we could accept our separate identity and try to make it work to our advantage. By featuring the chairman in our ads, we chose the second course.
In the television ads, as in the print ads that preceded them, we decided to deal directly with the public's reservations and doubts. It was no secret that American consumers had a low opinion of American cars. Most people believed that German and Japanese cars were inherently better than anything Detroit was turning out.
We let them know right off the bat that this was no longer the case. And we backed up our claim with an offer of $50 to any customer who compared one of our cars with anyone else's—even if they ended up buying from the competition.
At the same time, we were careful not to be _too_ bold. We wanted to project a spirit of confidence but not arrogance. Given the perception of Chrysler products, we didn't want to claim directly that Chrysler made the best cars—although that's what we believed.
Instead, we wanted the customer to come to that decision on his own. And so we maintained that anyone who was looking for a new car ought to at least _consider_ one of ours. We believed that the quality of our cars would be apparent to anyone who checked them out. If we could only get enough customers into the showrooms, our sales would increase accordingly. And that's what happened.
But I can't stay on as a pitchman forever. I get tired of it, and so does the public. In a disposable society like ours, there are no real heroes. Nobody lasts very long. Every week _People_ magazine serves us up a new bunch of celebrities. Within a few months most of them have disappeared.
So I don't want to wear out my welcome. I'm in people's living rooms fairly often, and I want to stop before they say: "Oh, no, here comes that man again."
Ever since I started making commercials, I've been trying to stop. But K&E has always found ways to keep me in the picture. I found out only recently that they had even worked up a secret plan for a Lee Iacocca Muppet to join Miss Piggy, Kermit, and the rest of them. Without telling me, they tested the idea before some audiences around the country. The audiences thought the commercials were fun but too cute. Thank God for that.
The crisis at Chrysler has been over for a couple of years now, and I want to convey that in the commercials. When I disappear from television, I hope people will say: "We're not hearing from that guy anymore because he's on his feet again. He came to us when he was sick, and now he's healthy." Otherwise there's the danger of crying wolf.
There's another problem with the commercials: they've wrecked my privacy. In a one-industry town like Detroit, I've been a celebrity for years. But now, because of the commercials, I can't even walk down the street in New York. I walk a block, and there are five double-takes, six people stopping me, and seven drivers yelling out my name. It was fun for about a week. After that, it's a pain in the ass.
A couple of years ago I was watching a TV show in Detroit. The host was interviewing a local columnist, and he said: "I want to throw out some names, and I'd like you to tell me what they mean in this town."
The first name was "Iacocca."
Right away, the guy answered: "Fame."
"Fame?" asked the host. "What do you mean? Is he powerful?"
"Oh, no," said the columnist. "He doesn't have any power. He's just famous—famous for his TV commercials."
I nodded and thought: "I agree." It's like somebody said a few years back: in our society, a celebrity is a person who's famous for being well known.
Fame is fleeting. To me, what it means most of all is that loss of privacy. Don't get me wrong—there are times when it can be very pleasant. I remember being on an elevator at the Waldorf in New York when a woman got on and pointed to me: "Iacocca," she said, "we're so proud of you. Keep doing what you're doing. You're a real American." Then she shook my hand and got off.
One of our board members turned to me and said: "Doesn't that make you feel good inside?" You're damn right it does.
A few minutes later, I was out on the street and a little old lady came up to me. "I know who you are," she said. "I come from Puerto Rico. I've only been here a few years, but I think you're doing a very good thing for this country. You're so strong and so American." There's an element of pent-up patriotism to many of these encounters, probably because of the "made in America" commercial, or just because America roots for the underdog.
But fame has other sides, too. Whenever I'm trying to have dinner in a restaurant, every five minutes some guy comes over to talk about his '67 Mustang or his Dodge Dart that's still running—or not running!
Believe this or not, I'm really a very private person. That was pretty hard for even me to remember when a couple of years ago I was asked to be grand marshal of the Columbus Day parade in New York. It was a great honor, but it also made me pretty nervous, being exposed like that in front of a million people and waving like I was Douglas MacArthur or someone coming home from the wars.
I certainly like being recognized for what I've done, but I'm always being reminded that my fame has little to do with my accomplishments. Am I famous for the Mustang? For guiding Ford through the most profitable years in its history? For having turned around Chrysler? It's a hell of a note, but I have a feeling I'm going to be remembered only for my TV commercials. Oh, that cursed tube!
Twenty-five years ago, I ran across an astounding number. I learned that in American homes, television sets were on an average of 42.7 hours per week! From that day forward, I have been awed by the power of television. I started committing millions of dollars to the purchase of TV commercials. At one point at Ford, I got carried away and bought 100 percent of all NFL games. At a half a million dollars a minute, that would be impossible today.
I knew then how powerful TV was, but I hadn't yet experienced it personally. As a result of my Chrysler commercials, I've now heard from just about everybody. A dozen optometrists zeroed in on my eyeglasses and concluded the frames were made in France. They didn't think this appropriate for a guy who was delivering a made-in-America commercial. Then there were three oral surgeons who wrote me about my loose dentures. I was offended and wrote back that my teeth were all mine—and in great shape. They were disturbed that my teeth never showed, even when I smiled, but they said the cure was simple. They had what they called "an aesthetic procedure" to buck my teeth out or cut my lips back! Now I'll do anything to sell cars, but that is going a little too far.
If my mail is any indication, I also seem to have popularized blue shirts with white collars. By the way, even though I've never smoked a cigar during a TV commerical, I've been seen a number of times on television with a cigar in hand. And that is a no-no, believe me! The press insists I smoke somewhere between 12 and 100 cigars a day. Pure fiction. Three cigars is a big day for me.
It's those damn commercials that started all the stories that I was running for President. I got patriotic and said, "Let's make America mean something again," and people identified with it. I really had no idea that the commercials would be seen in this light.
The presidential rumors got a major boost in June of 1982 with a front-page story in _The Wall Street Journal_ that began: "Lee Iacocca, it is whispered around Detroit, has a hankering for public office. Not just any public office, but one grand enough to satisfy a man with an ego as big as all outdoors. Lee Iacocca, the chairman of Chrysler Corp., it is said, yearns to be the president of all the people. If a Hollywood star can, why not a Detroit car salesman?"
The logic was somewhat less than compelling. Iacocca gives a lot of speeches. He does those TV commercials. He's involved with the Statue of Liberty. He's a colorful figure in an industry of faceless men. He obviously has a big ego. Therefore, he's running for President.
Nevertheless, the story resulted in a tremendous amount of attention. Lots of articles, lots of mail. How did it start? My best hunch is that a few of the Detroit journalists got together over drinks one day and cooked it up as a gag. When they first asked me if I'd like to be President, I didn't know how to answer, so I kidded with them and said: "Yeah, I'd like to be President, but only if I were appointed and only for one year." I didn't even say one term, because it makes you too old. I got old enough during my first term at Chrysler.
Amanda Bennett's article appeared in the _Journal_ 's semihumorous column in the middle of the front page. Amanda had just done a piece on the last whorehouse in Michigan, and this one ran in the same spot. That pretty well describes what I thought of the article.
A few months later, there was a story in _Time_ about possible presidential candidates in 1984, and again my name was mentioned. The magazine said I could run for President because I have "an expressive face." Another example of persuasive political logic.
It's a funny thing about that phrase. Back in 1962, _Time_ threw a big reception in Detroit, and Henry Luce, the founder, was there. I was invited because I was an up-and-coming young Ford vice-president, although this was a couple of years before the Mustang came out.
At one point in the evening I was introduced to Mr. Luce. He looked at me and said: "An expressive face." A few minutes later one of his guys said to me: "Someday he'll put you on the cover. He likes expressive faces." And I'll be damned if the ghost of Henry Luce didn't use that same phrase to describe me twenty years later. It hit me like a ton of bricks. Is that really how we choose our leaders?
People end up in the White House for all kinds of reasons. I once asked Jimmy Carter why he ran for President, and he said: "As governor of Georgia I had visits from some of the other people running for President, and they didn't seem very smart." I know the feeling.
But while I might enjoy being President, it's strictly a fantasy because I couldn't imagine running for office. These guys are programmed like robots sixteen hours a day—lunches, dinners, the banquet circuit, shaking hands, going to the gates of the factories—it's endless. If you run for President, you've got to be enthusiastic. To endure all that drudgery, you've got to want it really badly.
I've already shaken millions of hands. Over the past forty years I've gone to more meetings and conventions than I can possibly remember. I've held so many cocktail glasses that my right hand is permanently bent. I feel like I've seen every factory in the world.
I've now made something like a hundred speeches just in the ballroom of the Waldorf-Astoria. By now, the staff there knows the Chrysler story as well as I do. During one of my recent speeches, I noticed some of the waiters lip-synching my text as I spoke. Later one of them came up and asked me for a loan guarantee of $200 until payday!
But in all seriousness, I'm exhausted. I've grown old during my years at Chrysler. If I were ten years younger—then maybe I could see myself going into politics. Back then, I was full of piss and vinegar. But the firing at Ford and the long crisis at Chrysler and especially the loss of my dear wife have taken a lot out of me.
I also don't have the temperament for politics. I watched McNamara, and if he couldn't cut it and really help this country, I couldn't possibly do it, because he's more disciplined than I am. Besides, I'm far too impatient. I'm candid to a fault, not a diplomat. I can't exactly imagine myself waiting eight years to see if we could get an energy bill passed.
I'm too outspoken to be a good politician. If a guy's giving me a lot of baloney, I tell him to buzz off because he's wrong. Somehow I don't think the presidency works that way.
But I do think that our national leadership consists of too many lawyers and not enough people from business. I'd like to see a system where we brought in twenty top managers to run the business side of the country and maybe even paid them $1 million a year, tax-free. That would be a real incentive, and then we'd see a lot more talented people interested in public life.
A couple of years ago, a high-powered group of political types from Michigan tried to get me to run for governor. Why? Because being a governor is the best springboard to the presidency. They said: "You've saved Chrysler, and now it's doing very nicely. What about Michigan? It's got all the same problems and it's your home state now."
I had a good answer for them. "Look," I said, "if I'm ever going to run for governor, find me a nice cash-rich state like Arizona. Maybe then I'll consider it. But no more going with anybody without a little money in the bank. Once is enough!"
Ever since that _Wall Street Journal_ story appeared in 1982, I've had to spend a lot of time denying that I'm running for President. But it's a no-win situation, because even the _real_ candidates tell you that they're not running until they finally decide to go public with their ambitions. So a lot of people don't believe me. "If he's not running," they ask, "then why is he writing a book? Why is he involved with the Statue of Liberty unless he's planning to wrap himself in the flag?"
When nobody bought my denials, I decided to have some fun. Whenever I was asked if I intended to run for President, I would say: "Let me get those rumors out of the way. I find them unjustified and unsettling. Besides, they stir up a lot of unrest in my campaign staff."
For the most part, there was nothing I could do to put an end to the speculation. If you talk only about cars, people say you're parochial. If you talk about national and world issues, they say you're running for office.
Finally, at the end of 1983, I signed a three-year contract with Chrysler. And that, more than anything else, put an end to the talk of my alleged political ambitions.
Although I was never a candidate, I learned a lot from all the presidential talk. Shortly after the whole business began, I was having a conversation with a guy in advertising. He said something interesting: "I've decided why everybody talks about you as a presidential candidate. It's very simple. They don't believe anybody anymore. You talk to them and you make them believe that you stand for something and then you pursue it. You don't bullshit them, and the American public has been bullshitted too often."
Another thing that I apparently represent to people is that I'm a good manager. I can cut costs and make money and manage a large institution, and if there's anything I'm sure of, it's that. I know how to control a budget, and I've had experience in turning around a failing company. Americans must be looking for a leader who can balance the budget as well as restore a sense of purpose to the country.
I get a lot of mail about running for President. It's made me aware that there's a real vacuum out there. People are hungry for somebody to tell them the truth—that America isn't bad, it's great—or at least that it can be made great again if we just get back on track. They write to me because I'm on TV, because I make speeches, and because Chrysler is back on its feet. A guy will write in longhand: "Why don't you turn this country around? Why are you wasting your time selling cars?"
People are hungry to be led. I don't believe for a moment that we live in an antihero society. It's just that since Eisenhower, we haven't found ourselves a leader we can depend on. Kennedy got killed. Johnson dragged us into a war. Nixon disgraced us. Ford was an appointed, interim leader. Carter, for all his virtues, turned out wrong for his time. Reagan lives in the past.
Eventually we'll find somebody who can be a real leader. I'm deeply honored that a lot of people think it could have been me. That, in itself, gives me all the satisfaction I'll ever need.
# XXIV
# A BITTERSWEET VICTORY
In 1982, when the smoke of battle finally cleared, good things began to happen.
Only three years earlier, the Chrysler Corporation had to sell 2.3 million cars and trucks just to break even. Unfortunately, we were only selling around 1 million. With a little quick math, you can understand how that doesn't add up.
But now, through the combined effort of a lot of different people, we had reduced our break-even point all the way down to 1.1 million units. Before long we were actually adding people to our payroll and signing up new dealers.
In other words, we were poised for a major upswing. Unfortunately, the economy wasn't.
But late in 1982, as the economy began to heat up, so did car sales. Finally! When the year was over, we actually showed a modest profit.
My first instinct was to call a press conference to bury all the adjectives that had been used to describe us during our long crisis. Attention, reporters. Effective immediately, Chrysler is no longer "cash-starved," or "struggling," or "financially troubled." If you insist, you may continue to call us "the nation's number three automaker." But those other phrases are now banished forever!
The following year, 1983, we made an honest operating profit of $925 million—the best by far in Chrysler's history.
We had come a long way since the loan guarantee hearings, when we had made so many promises. We promised to modernize our plants and convert them to the latest technology. We promised to convert our entire fleet of cars to front-wheel-drive technology. We promised to be the leaders in fuel economy. We promised to maintain employment for half a million workers. And we promised to offer exciting products.
Within three years we had made good on every one of those vows.
By the spring of 1983, we were actually in a position to make a new stock offering. Originally we had planned to sell 12.5 million shares, but there was so much demand for our stock that we ended up issuing more than twice that number.
The buyers were lined up and waiting. Our entire offering of 26 million shares was sold out within the first hour. With a combined market value of $432 million, this was the third-largest equity offering in American history.
Now, whenever you issue more equity, you naturally dilute the value of each outstanding share. But a funny thing happened on this one. At the time of the offering, our stock was selling at $16 5/8. Within a few weeks, there was so much demand for Chrysler stock that the price zoomed all the way up to $25—and then shortly thereafter to $35. If that's the effect of dilution, I'm all for it.
Not long after the stock sale, we paid off $400 million—or one third—of our guaranteed loans. This represented the most expensive of the three drawdowns, as the interest on those loans was a whopping 15.9 percent.
A few weeks later we made a momentous decision—to pay back the _entire_ loan right away, seven full years before it came due. Not everybody at Chrysler thought this was a wise move. After all, you have to be pretty sure of the next couple of years if you're going to give up that much cash.
But by now I was confident of our future. Besides, I was determined to get the government off our backs as soon as possible.
I announced the loan payback at the National Press Club. The date was July 13, 1983—and, by an eerie coincidence, exactly five years to the day since Henry Ford had fired me.
"This is the day that makes the last three miserable years all seem worthwhile," I said. "We at Chrysler borrow money the old-fashioned way. We pay it back."
I was having a good time. "The people in Washington have a lot of experience in handing out money," I said in my speech, "but not much in getting it back. So maybe the surgeon general should be standing by in case anyone faints when we hand over the check."
Actually, the government couldn't even accept the check that day. Because of red tape it took them over a month to figure out how to do it. It seems no one had ever paid them back that way before.
At a ceremony in New York I presented our bankers with the largest check I had ever seen: for $813,487,500. I also collected a bushel of apples for my trouble. During the congressional hearings, Mayor Koch of New York had bet me a bushel of apples that the city would repay its federally guaranteed loans before we would. But when we cleaned up our balance sheet, New York City still had an outstanding balance of more than $1 billion.
Now that we were out of danger, it was time to think about having fun again.
Ever since Detroit stopped making convertibles almost ten years ago, I really missed them. The very last domestic convertible was the Cadillac Eldorado, which was produced until 1976. The last Chrysler convertible was the Barracuda in 1971.
A lot of people are under the impression that convertibles were suddenly outlawed by the government. That's not really true, although things were certainly moving in that direction. In Washington, the regulators did make a push to ban the convertible—or at least to make serious changes in its structure. By that time, we already had more than enough regulatory headaches. Nobody was looking for still more problems, so convertibles were phased out.
What really killed the convertible was air conditioning and stereo. Neither one makes much sense if you're driving around without a roof.
In 1982, as we began to get healthy again, I decided to bring back the convertible. As an experiment, I had one built by hand from a Chrysler LeBaron. I drove it over the summer, and I felt like the Pied Piper. People in Mercedes and Cadillacs started running me off the road and pulling me over like a cop. "What are you driving?" they all wanted to know. "Who built it? Where can I get one?"
When they recognized my now-familiar face behind the wheel, they would sign up for one right on the spot. I drove to my local shopping center one day, and a big crowd gathered around me and my convertible. You would have thought I was giving away $10 bills! It didn't take a genius to see that this car was creating a great deal of excitement.
Back at the office, we decided to skip the research. Our attitude was: "Let's just build it. We won't make any money, but it'll be great publicity. If we're lucky, we'll break even."
But as soon as word got out that we were bringing out a LeBaron convertible, people all over the country started putting down deposits. One of them was Brooke Shields, and we delivered the very first convertible to her as a special promotion. By then it was clear that we'd be selling quite a few of these babies. Turned out, we sold 23,000 the first year instead of the three thousand we had planned.
Before long, GM and Ford were bringing out convertibles of their own. In other words, little old Chrysler was now leading the way instead of bringing up the rear.
The convertible was done mostly for fun—and for publicity. But in 1984 we brought out a new product that was both fun _and_ very profitable—the T115 minivan.
The minivan is an entirely new vehicle for people who want something bigger than a conventional station wagon but smaller than a van. The minivan holds seven passengers. It has front-wheel drive. It gets thirty miles a gallon. And best of all, it fits into a conventional garage.
Whenever I speak to students in our nation's business schools, somebody always asks me how we managed to bring out the minivan so quickly after our prolonged crisis. "How could you as a businessman put seven hundred million dollars on the line three years in advance while you were going broke?"
It's a good question. But really, I had no choice. I knew we couldn't eat the seed corn. There would be no point to our struggle if there was nothing to sell when we were back on our feet again.
And only half-kiddingly I used to say: "Look, I'm already in hock up to my eyeballs. So what's another seven hundred million among friends?"
The minivan was actually born over at Ford. Shortly after the first OPEC crisis, while Hal Sperlich and I were working on the Fiesta, we designed a project we called the Mini-Max. We had in mind a small front-wheel-drive van that was compact on the outside and roomy on the inside. We built a prototype and we fell in love with it.
Then we spent $500,000 to research it. And in the process we learned three things. First, the step-up height had to be low enough to appeal to women, who mostly wore skirts in those days. Second, we had to make the car low enough to fit into a garage. Third, there had to be a "nose" with an engine up front to provide a couple of feet of crush space in case of an accident.
If we took care of these things, the research shouted, we were looking at a market of eight hundred thousand a year—and that was in 1974! Naturally, I went to see the king right away.
"Forget it," said Henry. "I don't want to experiment."
"Experiment?" I said. "The Mustang was an experiment. The Mark III was an experiment. This car is another winner."
But Henry wouldn't buy it.
In my book, if you're not number one, then you've _got_ to innovate. If you're Ford, you've got to beat GM to the punch. You've got to find market niches that they haven't even thought of. You can't go head to head with them—they're just too big. You've got to outflank them.
So instead of doing the minivan in 1978 at Ford, Hal and I did it in 1984 at Chrysler. And now it's _Ford's_ customers we're stealing.
This time, by the way, the research is even more convincing. As I write these words in the middle of 1984, the new minivan is completely sold out.
Moreover, Ford and GM are falling over each other to bring out their own versions. I guess imitation really is the sincerest form of flattery.
Even before the minivan came out, _Connoisseur_ magazine selected it as one of the most beautiful cars ever designed. _Fortune_ called it one of the ten most innovative products of the year. And the car-buff magazines featured it on their covers months before it went on sale.
Not since we unveiled the Mustang in 1964 have I been this excited about a new product—and this confident of success. I still remember the first time I drove the minivan at our proving grounds. They couldn't get me off the track. I just kept going around and around. I loved what the engineers had done to the handling and the ride. This car was really fun to drive.
Record profits, paying back the loan, the minivan—these were all part of our triumph.
But our success had a dark side as well. When we finally held the victory parade, a lot of our soldiers were missing. We won the war, but not without a great many casualties. A lot of people—blue-collar, white-collar, and dealers—who had been with us in 1979 were no longer around to enjoy the fruits of victory.
There was also the matter of the 14.4 million warrants we had issued to the Loan Board in June 1980, just before we received our first $500 million in guaranteed loans.
These warrants entitled the bearer to purchase 14.4 million shares of Chrysler stock at $13. When we issued them as a "sweetener," our stock was in the neighborhood of $5.00. At the time, $13 a share seemed a long way off.
But now, with our stock price hovering around $30, the government was sitting on a windfall. Moreover, they could exercise the warrants any time until 1990, when the loans were officially due.
These warrants were a sword hanging over our head. At any point over the next seven years, the government—or anyone else who owned the warrants—could demand that we issue an extra 14.4 million shares of Chrysler stock at bargain-basement prices.
As we saw it, we were already paying far too much for our government-guaranteed loans. We had borrowed $1.2 billion for ten years, but we were paying it back in three. During those three years, we had shelled out $404 million in interest, $33 million in administrative fees to the federal government, and another $67 million to the lawyers and investment bankers.
Depending on the price of the stock, the warrants could be worth as much as $300 million. Combined with the interest and the fees, this would give the government and the lenders the equivalent of 24 percent a year. When you consider that the government's money was never at risk in the first place—they had a lien on everything we owned, which was worth far more than $1.2 billion—that kind of profit was almost indecent.
But more important, of all the constituencies that had helped us in our recovery, not one was in a position to reap a windfall from our success. We had sacrificed equally when we were in trouble—so we should share equally in the rewards. If the government made a killing on the Chrysler warrants, what kind of example would that set for the workers and suppliers—and the dealers who had worked so hard?
So we quietly asked the government to surrender the warrants to us at little or no cost.
What a mistake! There was a huge uproar over our request. "Chutzpah," said _The Wall Street Journal_ with a snort. "There's just no other word for Chrysler's request." This time, however, the _Journal_ wasn't alone. Everybody thought we were being greedy. From a public-relations viewpoint, it was a disaster. One minute we were heroes for paying back our loan seven years early. The next thing we knew, we were bums. It was a painful experience.
We quickly retreated from our position. As a compromise, we offered the loan board $120 million for the warrants. No way. Then we raised the offer to $187 million. Nothing.
Finally, on July 13, the very same day we were paying off the loans, we offered $250 million for the warrants.
"No dice," said the Loan Board. "We're selling them to the highest bidder."
And that they did. Don Regan, a former stockbroker, reverted to type. He insisted on an auction—and, of course, lots of fees for the Wall Street crowd. But it was to be expected. From the beginning he was against the loan guarantees for ideological reasons. In three full years he never once convened a meeting of the Loan Board and never made a single move to help us.
The Reagan people, led by Don Regan, were always saying: "Whatever the Carter administration promised you is what you're going to get. We won't lift a finger to change it one way or the other. Whether it hurts you or helps you, we don't care."
As we started to recover, I said: "Embrace me, embrace me. Take some credit for our success. If nothing else, it's good politics." But Donald Regan and most of the administration said: "Ideologically we were opposed to the bailout and we still are. We don't believe in results." To the bitter end, they maintained that the government loans for Chrysler had set a bad precedent.
The issue got so hot that I went to see President Reagan twice. He said that as a matter of equity I had a strong case. On a trip I made with him on Air Force One to St. Louis he told Jim Baker to look into it.
He looked into it, all right. All he did was buck it back to Don Regan, who kept me twisting slowly in the wind. I don't know what happened in the White House, but in the end Regan prevailed.
Even now, I can't believe it. Where I come from, if I as a CEO tell someone to do something and I never get an answer back, I fire him. It's incredible that this guy Regan could sit out this guy Reagan.
In the end we were forced into bidding against our own $250 million offer and ended up buying back the warrants for over $311 million. At the time, I was furious. In fact, I still am. Why should the government be playing the stock market with our warrants? I had offered $250 million, which was a generous payment. But that wasn't enough. Their attitude was, "Screw Chrysler. Let's get every cent we can."
One congressman said: "What an opportunity! Let's take that $311 million and use it to retrain unemployed auto workers. The money came from Chrysler, so let's put it back in the auto business. Let's help the guys who lost their jobs when Chrysler had to cut back." But the government wasn't interested.
I proposed another plan. "Since you didn't expect this windfall," I said to the government, "why don't you take the money, leverage it ten to one, and use that $3 billion to help our industry become competitive with Japan?"
But the government decided to put the money back into the general fund. I'm afraid that our $311 million didn't make much of a dent in the federal deficit. But every little bit helps!
The entire episode with the warrants left a bad taste in my mouth. But what really made the Chrysler victory a mixed blessing for me is that it coincided with the greatest personal sadness of my life.
All through my career at Ford and later at Chrysler, my wife, Mary, was my greatest fan and cheerleader. We were very close, and she was always by my side.
But Mary had diabetes, a condition that led to many other complications. Both of our daughters, for example, had to be born by Caesarean section. Mary also suffered through three miscarriages.
Above all, a person with diabetes has to avoid stress. Unfortunately, with the path I had chosen to follow, this was virtually impossible.
Mary had her first heart attack in 1978, just after I was fired from Ford. She had been ailing for some time, but the trauma of that event made her condition even worse.
She had a second coronary in January of 1980. She was in Florida at the time, while I was in a Washington restaurant with all of our lobbyists. President Carter had just signed the Loan Guarantee Act, and we were celebrating our victory. In the middle of our dinner, I got a call from Florida saying that Mary had suffered another heart attack.
Two years later, in the spring of 1982, she had a stroke. On each of these occasions when her health failed her, it was following a period of great stress at Ford or at Chrysler.
Anyone who suffers from diabetes or who lives with a diabetic will recognize the symptoms. Mary was a very brittle diabetic. Her pancreas worked only part of the time. She controlled her diet very well, but her insulin injections, which she gave herself twice a day, were another story. Insulin shock, usually in the middle of the night, was very common. There would be orange juice with sugar, the stiffening of the body, the ice-cold sweats, and sometimes the paramedics struggling in the bedroom and the sudden trip to the hospital.
When I had to travel, which was often, I would call Mary two or three times a day. It got so that I was able to tell her insulin level just by the sound of her voice. On nights when I wasn't home, we would always have someone at the house with her. There was always the ever-lurking danger of shock or coma.
To the everlasting credit of my daughters, they not only accepted their mother's illness but ministered to her needs like a couple of little saints.
In the spring of 1983, Mary got very sick. Her tired heart just gave out. On May 15, she died. She was only fifty-seven and still very beautiful.
I'll always regret that she didn't live to see the loan payback only two months later, which would have made her so happy. Still, she knew we were going to make it. "The cars are really getting better," she told me before she died. "Not like the junk you were bringing home a couple of years ago."
Her last few years were not easy. Mary never understood how I could put up with Henry Ford. After the 1975 investigation, she wanted me to go public—sue him, if necessary. But even though she disagreed with my decision to stay on, she respected it and continued to support me.
During my final two years at Ford, I protected Mary and the girls from most of what was happening at the office. When I was fired, I felt worse for them than I did for myself. After all, they didn't really know how bad things had become.
After the firing, Mary was really a tower of strength. She knew I wanted to stay in the auto business, and she encouraged me to go to Chrysler—if that was what I wanted. "The Lord makes everything turn out for the best," she said. "Maybe being fired from Ford is the best thing that ever happened to you."
But after the first few months at Chrysler, our world started to fall apart again. Gasoline is the blood of the car industry, and interest rates are the oxygen. In 1979, we had both the Iran crisis and rising interest rates. If those two events had happened a year earlier, I would never have gone to Chrysler.
I didn't want to give up, but maybe events had outrun our ability to cope with them. At one point, Mary urged me to leave. "I love you and know you can do anything you set your mind to," she said. "But this mountain is straight up. There's no disgrace in walking away from an impossible task."
"I know that," I said, "but it's gonna get better." Little did I know that things would get much worse before they would finally begin to improve.
Like me, Mary was crushed by the way old friends deserted us after I was fired at Ford. But she didn't let it break her. She had always been a straightforward, gutsy person—and she stayed that way.
One day, shortly after I had joined Chrysler, she read in the paper that the daughter of some former close friends of ours was getting married. We were both very fond of the girl.
"I'm going to her wedding," Mary told me.
"You can't," I replied. "You're _persona non grata_ and you haven't been invited."
"That's what you think!" said Mary. "I can certainly go to the ceremony. I like this kid and I want to see her get married. If her parents don't want anything to do with us because you've been fired, that's their problem."
She also went to the Ford annual meeting after I was canned. "I've been going for years," she said. "Why shouldn't I go now? Remember, after the Ford family, we're the biggest stockholders."
Mary was at her best when things got rough. In adversity she took charge. Once when we were visiting our good friend Bill Winn, he had a heart attack. While I panicked, she had the firemen there with a Pulmotor and a heart surgeon standing by with a heart catheter—all within twenty minutes.
Another time a close friend, Anne Klotz, called her to complain of severe head pains. Mary drove to her house, found her unconscious on the floor, called for the ambulance, got to the hospital, and stayed with her right through emergency brain surgery.
Nothing fazed her. She could be at the scene of an accident with somebody's head cut off, and her reaction would be: "What do I do next?" She just moved with dispatch, and as a result, two people owe their lives to her. When our daughter Kathi was ten years old, the brakes on her bicycle locked. She flew over the handlebars and landed on her head. Years before, my doctor had told me that the sure way of knowing if someone had suffered a concussion was that the pupils of the eyes dilated and filled the whole eye, one black mass. I took one look at Kathi's pupils—they were huge and black. I promptly proceeded to faint. Mary, meanwhile, picked her up, sped to emergency, had her in a hospital bed in half an hour, came home, made my favorite soup, had _me_ in bed in half an hour, and never said a word. She was the essence of grace under pressure.
If you talked to friends about Mary today, they'd say: "Oh, God, that's what I remember about her—her strength under tough conditions. Her feistiness."
Mary cared deeply about diabetes research, and she herself was a volunteer for other diabetics. She accepted her condition with great courage and accepted death with equanimity. "You think I have it bad?" she used to say. "You should have seen the people who were with me in the hospital."
She believed in educating people about diabetes, and together we set up the Mary Iacocca fellowship at the Joslin Diabetes Center in Boston. Mary would explain that diabetes was the nation's third leading cause of death, behind heart disease and cancer. But because the word "diabetes" rarely appears on the death certificate, the public underestimates the severity of the problem. When she died, I made sure that her death certificate told the truth: complications from diabetes.
We had a lot of good times together, but Mary never got wrapped up in the corporate life. She didn't try to keep up with the Joneses. For both of us, the family was supreme. As for the responsibilities of the corporate wife, she did what was necessary and she did it with a smile. But her values—and mine—were home and hearth.
We took a lot of trips together, especially to Hawaii, which was her favorite place. But when we were in town, we spent our evenings and weekends at home, together with the kids.
Playing golf with the guys from the office has never been my idea of fun. Besides, I think that whole aspect of corporate life has been overrated. I'm not saying that you have to be a recluse. But in the end, what counts is performance. Your job takes up enough time without having to shortchange your family.
The four of us used to take lot of motor trips, especially when the kids were young. That's when we really got close as a family. No matter what else I did in those years, I know that two sevenths of my whole life—weekends, and a lot of evenings—was devoted to Mary and the kids.
Some people think that the higher up you are in the corporation, the more you have to neglect your family. Not at all! Actually, it's the guys at the top who have the freedom and the flexibility to spend enough time with their wives and kids.
Still, I've seen a lot of executives who neglect their families, and it always makes me sad. After a young guy dropped dead at his desk, McNamara, then president of Ford, sent out a memo that said: "I want everybody to be out of the office by 9:00 P.M." The mere fact that he had to issue such an order tells you that something was screwed up.
You can't let a corporation turn into a labor camp. Hard work is essential. But there's also a time for rest and relaxation, for going to see your kid in the school play or at a swim meet. And if you don't do those things while the kids are young, there's no way to make it up later on.
One evening two weeks before her death, Mary called me in Toronto to tell me how proud she was of me. We had just announced our first-quarter earnings. Yet during those last few difficult years, I never once told her how proud I was of _her._
Mary sustained me, and she gave everything she had to Kathi and Lia. Yes, I've had a wonderful and successful career. But next to my family, it really hasn't mattered at all.
# STRAIGHT TALK
# XXV
# HOW TO SAVE LIVES ON THE ROAD
On the whole, we Americans are good drivers. And compared to drivers in other countries, we're terrific. Although far too many people are killed each year on roads and highways, our traffic-death rate of 3.15 per 100 million vehicle miles is the lowest in the world.
I don't pretend to be an expert on driving. But I do know a few things about cars. And I want to explain why seat belts—and not air bags—are the key to reducing traffic fatalities in the United States.
For years I've been promoting a very unpopular cause: mandatory seat-belt use. In 1972, as president of Ford, I took it upon myself to write to each of the fifty governors, letting them know that our company endorsed mandatory seat-belt use and urging them to support this life-saving cause.
Twelve years later, as I'm writing these words, not one state in our entire country has yet passed such a law. Eventually we'll come to our senses. But it's taking us far too long.
The opposition to mandatory seat-belt use comes from several directions. But here, as with so many issues, the chief argument is ideological. The idea of mandating safety just goes against the grain of some people. There are many who feel it is just another example of government intervention in their civil rights.
This is especially true in the Reagan administration. Unfortunately, their old-fashioned, laissez-faire view of economics extends to safety as well.
It's hard to believe, but even in this day and age there are still a lot of people who believe that telling a guy he's got to keep from killing himself (or his neighbor) just isn't the American way. In the name of ideology, they're willing to let thousands of people die and tens of thousands more be injured. As far as I'm concerned, those people are living in the nineteenth century.
But every time I come out with a statement in favor of mandatory seat-belt use, I can count on getting a big pile of negative mail from people complaining that I'm interfering with their right to go out and kill themselves if they choose.
But am I really? You have to have a license to drive, don't you? You have to stop at a red light, don't you? You have to wear a helmet in some states if you're on a motorcycle, don't you?
Are these laws examples of undue government interference? Or are they necessary rules in a civilized society? We'd have carnage at every corner if we didn't have some running rules.
And what about some state laws that say certain people can't drive unless they're wearing their glasses? I'm one of those people. If a cop pulls me over in Pennsylvania and I'm not wearing my glasses, I get a ticket. I think it's time we added another line to the driver's license, which reads: "Not valid without a seat belt."
I'm sorry, but I can't find anything in the Constitution that tells me driving is an inherent right. That's because it's not. Driving a car is a _privilege._ And like all privileges, it comes with certain responsibilities.
Would a law mandating seat-belt use constitute undue government intervention? Of course not. When it comes to government intervention, some people think you have to be either fish or fowl—completely for it or completely against.
But as with anything else, you have to look at the circumstances. There are areas of life where the government has to act to protect society. Only in America do we allow the ideologues to prevail over the demands of safety.
What these purists seem to forget is that the damage done by not using seat belts raises our taxes, increases our insurance rates, and harms us and our loved ones. And if that's not an intrusion on my freedom, I don't know what is.
But I don't want to get into a philosophical argument about seat belts, because that's the ideologue's game. We have to consider what's practical, what works in the real world.
The plain truth is that if you're wearing a combined shoulder- and lap-belt system, it's almost impossible to be killed under thirty miles per hour. Among other reasons, seat belts can prevent you from being knocked unconscious in a crash, which can happen even at relatively slow speeds.
What really gets me is that even the opponents of seat belts concede that they save lives. In case anybody still needs proof of that, a famous study by the University of North Carolina surveyed traffic accidents and determined that seat belts reduced serious injuries by up to 50 percent and fatal injuries by as much as 75 percent. And in the late 1960s, a study in Sweden examined almost twenty-nine _thousand_ accidents among seat-belt users and found that not a single one had resulted in death.
The National Highway Traffic Safety Administration (NHTSA) estimates that fatalities would drop _by at least 50 percent overnight_ if everybody used seat belts. But at the present time, only about one person in eight buckles up.
People are always telling me that mandatory seat-belt use is an impossible dream. But I don't think most people actively oppose seat belts. They just don't bother to wear them. Surveys have shown that consumers aren't against the _idea_ of seat belts. It's just that most people find them inconvenient, intrusive, and a nuisance. Which they are.
These complaints aren't new, either. In 1956, when Ford offered seat belts as an option for the first time, about 2 percent of our customers ordered them. The indifference shown by the other 98 percent cost us a lot of money.
And you should have heard the reasons people gave for not wanting them. Some people complained that the belts clashed with the color of the interior. And I'll never forget one letter that said: "They're very bulky and uncomfortable to sit on!"
Let's deal with the other arguments, too, although they're no more compelling. I've heard people say that they don't want to be belted in case their car catches fire in an accident and they can't escape. Now, it's true that something like that _could_ happen. But in actual fact, fires are the cause of only one tenth of one percent of traffic fatalities.
Besides, even if you _are_ caught in a fire, it's just as easy to release your seat belt as it is to open your door. And nobody has yet suggested that we drive around with our doors open.
Another argument against mandatory seat-belt use is that you might be "thrown clear" in a crash rather than trapped inside the car. Here, too, there's a grain of truth. After all, occasionally a passenger really _is_ thrown clear in an accident.
But it doesn't happen very often. Actually, your chances of being killed are _twenty-five times higher_ if you're thrown out of the vehicle than if you remain inside and let the car protect you.
Yet another argument is that seat belts are really necessary only for highway driving. But what many people don't realize is that 80 percent of all accidents and serious injuries occur in urban areas, at speeds of less than forty miles per hour.
We've come a long way since the days when seat belts were used only in airplanes. They were developed during the early days of aviation, when one of the biggest challenges of flying was simply to remain safely in the cockpit. By around 1930, federal regulations required seat belts to be worn on all passenger planes.
Today, while commercial aircraft are far more advanced and safer than they used to be, the law still mandates that you can't fly on a plane without buckling up for takeoff and landing. That's because seat belts are even more effective on the ground than in the air. If you violate that law, the airline has the right to throw you off the flight.
Originally, seat belts in cars were used only for racing. When both Ford and Chrysler offered seat belts in their 1956 models, there were few takers. A mere eight years later, in 1964, seat belts became standard equipment on all passenger cars.
I've been on a seat-belt campaign for almost thirty years. It began back in 1955, when I was part of the marketing group at Ford that decided to offer safety devices on our 1956 models. The safety package we put together seems very primitive by today's standards, but at the time it was revolutionary. In addition to seat belts, it included safety door latches, sun visors, a deep-dish steering wheel, and crash padding on the dashboard. In our ad campaign for the 1956 models, we stressed that Ford cars were safe cars.
At the time, promoting safety in cars was a revolutionary act in Detroit—so much so that some of the top guys at GM apparently called Henry Ford and told him to stop it. In their view, our safety campaign was bad for the industry, because it conjured up images of vulnerability and even death—hardly the stuff of successful marketing. Robert McNamara, whose values were markedly different from those of his fellow auto executives at Ford and elsewhere, had decided on the safety campaign. He almost lost his job because of it.
While we were selling safety, Chevrolet, our chief competitor, was promoting jazzy wheels and high-powered V-8 engines. Chevrolet clobbered us that year. By the next year, we had switched our strategy to "hot" cars with fast acceleration. Instead of safety, we marketed performance and racing, with far greater success.
Ever since the 1956 campaign, I've been quoted as having said that "safety doesn't sell," as though I were offering an excuse for not making safer cars. But that's a severe distortion of what I said and certainly of what I believe. After the failure of our campaign to promote safety features, I said something like: "Look, fellas, I guess safety didn't sell, even though we did our damndest to sell it!"
And we did. We spent millions of dollars and gave it everything we had, but the public didn't even stir. We developed the hardware, we advertised, promoted, and demonstrated it, and we couldn't give the stuff away. We had customers saying things like: "Sure, I'll take the car, but you'll have to take out those seat belts or I'm not interested."
When I first came to Detroit in 1956, I was a safety nut. I still am. But I learned the hard way that safety is a pretty poor marketing device, which is why the government has to get involved.
In this respect, at least, the cynics were right: if you stress safety, the customer starts to think about having an accident, which is the last thing in the world he wants to consider. He instinctively says: "Forget it. I'll never be in an accident. My neighbor might, but not me."
Although that particular campaign did not work out, I'm still proud that I was involved in the pioneering of safety devices back in 1956, when, for all I know, Ralph Nader was scooting around on a bicycle.
Despite the failure of our safety campaign in 1956, Ford continued to offer seat belts as an option each year, even when our competitors took them out because the public wasn't responding. I remember that a lot of people thought we were crazy: "Seat belts, like an airplane? But we're driving, not flying!"
But I also remember sitting in breakfast meetings where safety researchers would show us color slides of car accidents, so that we could understand exactly what happened in a crash. It was pretty horrible stuff, and I had to leave the room once with nausea. But it was also a good education. It made me realize that by far the most effective safety factor is the seat belt—provided you wear it.
Sometimes you have to scare people into getting the point. In 1982, I had lunch with the editors of _The New York Times._ I talked a lot about seat belts, and I gave some graphic illustrations as to how important they were in preventing serious injuries and deaths.
A few days later I got a letter from Seymour Topping, the managing editor. Until our lunch together, he had been a dedicated ignorer of seat belts. But after hearing my frightening stories, he decided to buckle up.
Later that week, as he was driving home in a storm, the car in front of him skidded and blocked his lane. He braked sharply to avoid an accident, but because of the rain, his car swerved and smashed into a containment wall. Thanks to his seat belt, he walked away unharmed. Today he's a believer.
You can be a great driver, but you still should be wearing a seat belt. Nobody thinks they'll be in an accident. But 50 percent of all accidents are caused by drunk drivers. And when _they_ hit _you_ , you're in big trouble if you're not protected.
About ten years ago, I realized that we weren't going to have laws mandating seat-belt use in the near future. So I came up with a plan that would force drivers and passengers to buckle up. With the help of the engineers at Ford, I developed a device called Interlock, whereby the car's ignition would not operate until the driver and front seat passenger had fastened their belts. American Motors joined us in supporting Interlock, but GM and Chrysler opposed it.
After some heated controversy, the National Highway Traffic Safety Administration mandated in 1973 that all new cars had to be equipped with Interlock. But the law was a failure. The public hated Interlock and soon found ways to get around it. Many people kept their seat belts buckled—but without wearing them. And since almost any weight in the front passenger's seat could cut off the ignition, even a heavy bag of groceries could cause problems if it weren't belted up.
The popular uprising against Interlock was so great that the House of Representatives, led by Congressman Louis Wyman, a Republican from New Hampshire, soon dismantled it. In response to public pressure, Congress took about twenty minutes to outlaw Interlock. They replaced it with an eight-second buzzer that would remind passengers to buckle up.
Interlock had its problems. But I still think that it could have been perfected and that it would have saved lives. When it was thrown out by Congress, I came up with another plan: a special light on your car that would show green when you're wearing your seat belt and red when you're not. Whenever your light showed red, you would be fined. I had in mind something similar to a radar gun, where the police don't even have to stop the offending car: they just send the driver a ticket in the mail. But in the wake of Interlock, nobody was interested.
When it comes to safety, people don't always look out for their own interests. Because so many lives are at stake here, the only solution is to have seat-belt-use legislation.
Evidently I'm not the only guy in the world who thinks this way. More than thirty countries, and five of Canada's ten provinces, already have laws on the books. In Ontario, just a few minutes from where I work, auto fatalities have dropped by 17 percent since their seat-belt-use law was passed. In France, after they enacted a similar law, the death rate in traffic accidents dropped by 25 percent.
In some places, the penalty for noncompliance is a fine. In others, you lose your insurance, and in a few cases—both. But the United States has yet to put through such legislation. The federal government generally maintains that it's up to the states, but the states have not acted. How many more people will have to die before we get smart about seat belts?
Some states now have a mandatory seat-belt-use law for children. It's time that we protected their parents as well. Nothing would be more tragic than to do only half the job—and to create a bunch of orphans in the process.
Now, I've always thought that as the home of the automobile, Michigan ought to take the lead on this issue. Whenever the question of mandatory seat-belt-use comes up before the legislature in Lansing, I either testify or publicly support it.
There are those who believe that air bags are the answer. I disagree. I've been speaking out against them since they were first developed almost twenty years ago. I have the feeling that when I die—and assuming that I go to heaven—St. Peter is going to meet me at the gate to talk to me about air bags.
Air bags were developed in the 1960s by a group of engineers at Eaton Corporation, an automotive supply company in Cleveland. In 1969, the National Highway Traffic Safety Administration decided that air bags were the best way to increase highway safety, and NHTSA began a campaign of promoting their mandatory installation in all American cars.
That same year, Congress passed a law authorizing the secretary of transportation to mandate auto safety devices. Air bags were finally mandated in 1972, but the ruling was soon reversed by a federal court. The Ford administration dropped air bags, but the Carter people revived them. In 1977, NHTSA ordered the automakers to install "passive restraint devices"—which is generally taken to mean air bags—by 1982. The question of air bags has been tied up in the courts and in Congress ever since.
The air bag itself is made of nylon coated with neoprene, which is folded inside the hub of the steering wheel and under the glove compartment—along with about a hundred grams of sodium azide. In case of an accident, special sensors are activated that cause the sodium azide to ignite immediately and to release enough nitrogen to fill the bag. When the system works, the air bag acts as a gigantic balloon, which cushions the impact of the blow.
Air bags sound like the ideal solution, but there are problems—big problems—that their proponents usually don't discuss. For one thing, although air bags are supposed to be a form of "passive restraint"—which means the consumer doesn't have to take any action at all to activate them—they are effective _only if they're used together with seat belts._ Without seat belts, the air bag works only in head-on collisions. By themselves, air bags are of no help at all in over 50 percent of accidents or on "second" hits.
Most people are still under the mistaken impression that air bags will eliminate the need to wear seat belts. I'm afraid that we in Detroit have not been very successful in explaining this point.
Air bags can also be dangerous. There's always the possibility that the bag will not inflate when it should, or that it _will_ inflate when it shouldn't. Bags _can_ go off inadvertently, and when this happens, they can lead to injury and even death. A bag blowing up at the wrong time can throw back the driver and lead to an accident. Even in relatively innocuous cases, an air bag blowing up prematurely can be very expensive to fix. Besides, sodium azide isn't the kind of chemical I want to be riding around with.
Whether an air bag fails to work at the proper time or whether it works prematurely, the whole business is a paradise for product liability lawyers. Because many people see air bags as a panacea, they won't hesitate to sue the manufacturers when—as would undoubtedly happen—people get killed and maimed even in cars equipped with air bags.
To be fair, the technology is now at the point where air bags are highly reliable. Let's say they'll work in 99.99 percent of cases. If all cars were equipped with air bags, and if, as now, there were 150 million cars on the road, that means that .01 percent of the air bags would not be reliable. And _that_ means that about fifteen thousand times a year—which comes to about forty times a day—somebody's air bag would malfunction. If only 1 percent of those people sued, that would still be a pretty expensive proposition.
Air bags are one of those areas where the solution may actually be worse than the problem. After all, they're a pretty powerful piece of technology. Once when I was in Europe I picked up an English newspaper and was amazed to see a headline that read: "Yank Suggests Air Bags for Capital Punishment." I figured this was a gag, but apparently the proposal was made seriously. The guy who thought it up was a retired safety engineer in Michigan, and he was proposing that air bags would offer a humane alternative to the electric chair and to other forms of capital punishment.
In his application to the U.S. Patent Office, the inventor stated that by inflating an air bag directly under a condemned person's head, the force of twelve thousand pounds can instantly snap the guy's neck far more effectively than the hangman's noose, and so quickly as to preclude any pain whatsoever. I'm not sure I'd want one of those gizmos in _my_ car.
Air bags are not the answer. And in fact, since the proposed legislation never actually specifies "air bags" but only "passive restraints," the legislation could be satisfied by passive belts—a kind of lap-and-shoulder belt that fastens automatically when the car doors are closed. These were developed by Volkswagen: you climb in underneath the shoulder harness, and the belt is fastened automatically. Belts that grab you whether you like it or not now come as optional equipment in the Rabbit.
Air bags have been offered only once by an American car manufacturer. In 1974, GM invested $80 million in an air-bag program and tooled up to produce three hundred thousand units. They were offered as options on certain Cadillacs, Buicks, and Oldsmobiles from 1974 through 1976. But only ten thousand customers ordered them, which means that each air bag ended up costing the company $8,000. As one GM official said at the time, "We would have been better off selling the bags and giving away the cars."
I suspect that ten years after this book is published, the government will still be debating air bags. When the crusaders get on their high horses, it's impossible to stop them. Air bags have been a red herring from the start. Barring unforeseen developments, the argument will probably continue for a long time.
But it's not air bags that we need. What we need are laws mandating seat-belt-use. The sooner we get them, the more lives we'll save.
Until we have those laws, please do yourself and your loved ones a favor. Buckle up!
# XXVI
# THE HIGH COST OF LABOR
As someone who comes from a family of hardworking immigrants, I'm a strong believer in the dignity of labor. As far as I'm concerned, working people should be well paid for their time and effort. I'm certainly not a socialist, but I am in favor of sharing the wealth—so long as the company is making money.
Back in 1914 the first Henry Ford decided to pay his workers $5.00 a day and created a middle class in the process. He had the right idea, for unless the working people of this country are making a good living, we'll be wishing away our middle class. The cement in our whole democracy today is the worker who makes $15 an hour. He's the guy who will buy a house and a car and a refrigerator. He's the oil in the engine.
The mass media tend to focus on the very rich and the very poor, but it's the middle class that gives us stability and keeps the economy rolling. As long as a guy is making enough money to meet his mortgage payments, eat fairly well, drive a car, send his kid to college, and go out with his wife once a week for dinner and a show, he's satisfied. And if the middle class is content, we'll never have a civil war or a revolution.
America is different from Europe. Here auto workers are as capitalistic as management. And no wonder. When it comes to hourly workers, the UAW members are the elite of the world. And when money talks, ideology walks.
But high wages are not the real problem between management and the UAW. The real problem lies in all the fringe benefits.
As long as Detroit was making money, it was always easy for us to accept union demands and recoup them later in the form of price increases. The alternative was to take a strike and risk ruining the company.
The executives at GM, Ford, and Chrysler have never been overly interested in long-range planning. They've been too concerned about expediency, improving the profits for the next quarter—and earning a good bonus.
They? I should be saying "we." After all, I was one of the boys. I was part of that system. Gradually, little by little, we gave in to virtually every union demand. We were making so much money that we didn't think twice. We were rarely willing to take a strike, and so we never stood on principle.
I sat there in the midst of it all and I said: "Discretion is the better part of valor. Give them what they want. Because if they strike, we'll lose hundreds of millions of dollars, we'll lose our bonuses, and I'll personally lose half a million dollars in cash."
Our motivation was greed. The instinct was always to settle quickly, to go for the bottom line. In this regard, our critics were right—we were always thinking of the next quarter.
"What's another dollar an hour?" we reasoned. "Let future generations worry about it. We won't be around then."
But the future has arrived, and some of us are still around. Today we're all paying the price for our complacency.
Looking back, I see three key areas where management gave in and now we're getting killed: unlimited cost-of-living allowance; "thirty-and-out"; and cradle-to-grave medical benefits.
The first of these is the cost-of-living allowance. COLA is the engine that fuels runaway inflation. The two million workers who got it originally were in the auto industry. Today millions of American workers in industry and government are protected by COLA.
As much as I'd like to blame the unions for COLA, it really wasn't their idea. COLA was actually the invention of management, not labor. In 1946, Charlie Wilson, president of General Motors, proposed a cost-of-living allowance to deal with the temporary inflation that occurred when the government lifted price controls.
Inflation soon came down, but the unions got scared. In the 1948 settlement, GM came up with COLA, an escalator clause that provided for wage allowances based on changes in the cost of living as measured by the Consumer Price Index.
As with all new contract settlements, Ford and Chrysler soon followed with similar plans. For a few years, we managed to have a ceiling on COLA. But before too long, the auto workers struck and the ceiling came off. That's when COLA became insidious. Under the guise of fighting inflation, COLA actually _creates_ it.
COLA feeds on itself; the more you try to keep up with raising prices, the more inflation you create. But like every other benefit, once COLA was introduced, it was impossible to eradicate or even to modify it. It's a rolling snowball.
During the 1950s and 1960s, it was never much of a problem. These were boom years. American industry enjoyed huge markets. Western Europe and Japan were ravaged by the war and took years to recover. All through the 1950s and 1960s, our inflation rate was low—around 2 percent a year. Meanwhile, our national productivity was high—rising by an annual rate of around 3 percent. That meant COLA was not really inflationary, because raises could always be paid out of the growth in productivity.
But in recent years, it's been the opposite: inflation has soared while productivity has dwindled. Unless we can reverse both these trends, COLA will become an even bigger problem than it already is.
When COLA was first introduced, it was a major contract gain. But over the years it's gradually turned into a ritual. By contrast, increases in productivity used to be a ritual. Now they're history. Is it any wonder, then, that labor costs are getting out of hand?
Today COLA has found its way into Social Security, Medicare, the armed forces, and plans for government workers. We taught them all dirty habits. The problems these groups suffer from today emanate from the uncapped cost of COLA.
In contrast to COLA, "thirty and out" was the union's idea—and a bad one, too. Walter Reuther, the founder of the UAW, made it the lead negotiating item with GM just before he died in 1970. Together with the demand for unlimited COLA, it was the basis for the big strike against GM that fall.
"Thirty and out" stipulates that after a guy has worked for thirty years, he has the right to retire early, whatever his age, and leave with a full pension—60 percent of his salary—just as if he were already sixty-five.
"Thirty and out" _sounds_ good, and it was conceived for the purpose of creating jobs for the younger group coming into the work force, but it's the kind of program that makes America less and less competitive. Why? We get a good, hardworking guy at eighteen, train him for years, and at forty-eight he goes home for good. Not only do we lose a skilled worker, but we also have to pay his pension for the rest of his life—which on average will be for another thirty years!
According to the rules, this "retired" guy is not allowed to work. If he does work, he loses his pension. But if he's forty-eight, he's not going to stay home for long. Typically, he becomes a cabdriver or picks up odd jobs and works for cash. As a high union official once admitted to me: "They don't stop working. They just change jobs. The rules say the guy can't work, but who's going to check up on him?"
As a result, some of the best electricians who once worked for me at Ford and Chrysler are now driving cabs. And the irony of it all is that if I want to hire new guys to be electricians, I have to train a bunch of cabdrivers who don't know the first thing about the auto business. It's crazy! The country has been stood on its head in a headlong rush into mediocrity.
"Thirty and out" makes me furious. It's a crime to retire a guy just because he's worked thirty years. At fifty he's just hitting his stride. By then he has a wealth of experience and a variety of skills. Instead of using those skills, he's out driving a cab or sitting home twiddling his thumbs.
I'm not arguing with the idea of a good pension. But we can no longer afford to give pensions to guys who are fifty or fifty-five. I'd like to modify the "thirty and out" rule to one where the guy could still take early retirement with a full pension if he's worked for thirty years—as long as he's reached the age of sixty or higher.
Otherwise, we're paying the guys who should be helping us take on the Japanese $800 a month _not_ to come to work. Does that really make any sense?
The third major abuse in the system has been the medical benefits. When I came to Chrysler, I saw that Blue Cross/Blue Shield had already become our largest supplier. They were actually billing us more than our suppliers of steel and rubber! Chrysler, Ford, and GM are now paying $3 billion a year just for hospital, surgical, medical, and dental insurance (H-S-M-D), plus all pharmaceutical bills. At Chrysler, that comes to $600 million or about $600 per car. All told, that adds up to over $1 million a day!
Like every other benefit that management provides to labor, the medical plans began modestly. But over the years, we've gone from paying no medical bills to the point where the company now pays for everything you can think of: dermatology, psychiatry, orthodontics—even eyeglasses.
To make matters worse, there's no deductible for doctor's fees or hospital costs. There is a small one for prescription medicines: the guy has to pay the first $3.00 himself. That's my great claim to fame. The deductible used to be $2.00, and I got it up to $3.00. Twenty-five years of negotiating and that was my only clear-cut victory.
The real nut of the problem is there's no buyer/seller relationship left in the delivery of medical goods and services. The attitude is always to let Uncle Sam or Uncle Lee pick up the tab. "So what if you're charging me too much for the tests or the surgery— _I'm not paying for it."_
Like Medicaid, this system leads to incredible abuse. I recently found four podiatrists who were each making $400,000 a year just from the families of Chrysler workers. How the hell can a podiatrist see that many patients? They must be treating these people one toe at a time! I also found that in a single year we paid for two hundred forty thousand blood tests. That's a lot of blood to check at a time when we had only sixty thousand employees.
Health care costs us $600 for every car and truck we manufacture. For some of our smaller cars, that comes out to as much as 7 percent of the sticker price. In 1982, for example, we paid $373 million in health insurance premiums for employees, retirees, and their dependents. In addition, we also paid $20 million in Medicare taxes. And finally, we estimate that about $200 million of our payments to suppliers went to cover _their_ employees' health insurance premiums.
Every time we strike a deal with the union, we have to give similar benefits to our white-collar people, from the chairman on down.
A couple of years ago Mary was in the hospital for two weeks. The total bill came to around $20,000. Guess how much they asked me to pay? A grand total of $12! (And that was for the TV set.) Chrysler got a bill for $19,988. The fact that I wasn't even asked to pay the first $1,000 is a scandal. But that's the way the system works.
We've worked hard to get some of these abuses out of the system, but we still have a long way to go. One reasonable solution to the problem might be for the government to tax employees on the contributions we make for their health insurance premiums. That way, people would think twice before going for extra tests. As the system works now, the doctors and the hospitals are killing us.
Those are the three big areas where we gave in too quickly to union demands. But there was almost a fourth—the four-day week. This is something the union has been talking about for years, although they never call it by its right name, which is five days of pay for four days of work.
Whenever this one comes up, I always think back to World War II: France was on a four-day week, and Germany was on a six-day week. Remember who got creamed?
The union is much too smart to talk openly about a four-day week. They know full well that the public would never accept it. Leonard Woodcock, then-president of the UAW, once said to me: "Lee, I'll have a four-day week and you won't even know it's happening." His roundabout plan was to petition for so many days off that the union would soon have the equivalent of a four-day week.
That's the origin of that brilliant invention called paid personal holidays, where each worker gets a certain number of days off a year just for the hell of it. In 1976 the union won twelve paid personal holidays—five in the second year of their contract, and seven in the third. For a while, even a guy's _birthday_ was a paid holiday. But that one was a big headache, so the union agreed to change it. These days, we celebrate everybody's birthday at the same time—usually by counting the last Sunday before Christmas as a workday.
All of these plans—unlimited COLA; "thirty and out"; unlimited medical benefits; and paid personal holidays—violate common sense. No matter how sophisticated something like paid personal holidays sounds, there's no logical way you can pay a guy just to stay home.
If we're going to survive, it's absolutely essential that labor and management figure out a new and more practical method of working together. The kind of joint effort that saved Chrysler will have to become standard operating procedure.
I know it won't be easy. For one thing, workers have long memories. Some of the violent confrontations with the auto companies earlier in this century are still not forgotten. It hasn't been _that_ long since the National Guard was called to Flint in 1937 to quell the rebellious GM workers and their union organizers.
In addition, workers and management represent different social classes, which is always a source of tension. The worker on the assembly line is resentful of the managers who, he imagines, drink coffee all day and don't really work very hard.
The seniority system is another factor that leads to union militancy. The younger guys are always the first to be laid off in hard times. In the UAW, unemployed workers have the right to vote on contracts for six months after their unemployment benefits expire. After that, they have to fill out forms every month if they want to keep their voting rights. Most workers just don't bother.
So whenever there's a referendum on a new contract or a proposed concession, the workers who vote are the guys with the most seniority. Older workers can afford to be militant, because they're protected from losing their jobs unless the whole place shuts down. But what about the younger worker who's temporarily out of a job? He's willing to make concessions in order to get his job back, but usually he has no say in the matter.
The union was established to protect the rights of the workers, who were mistreated and underpaid. And it's been more than successful. But today it represents an elite group that is well paid and highly protected. In a way, the UAW has made it harder for a young, unskilled worker to get himself a job in the auto industry. In many cases the union has priced him right out of the market.
How did this sad state of affairs come to pass? It began when the auto industry was golden.
Even when I left Ford in 1978, we had just finished our three most profitable years _ever._ Until then, with a few exceptions, the history of the Big Three was a series of variations on a single theme: success.
This was especially true in the aftermath of World War II. Back then, cars were almost as important as food, and the ability to produce them was like a license to print money. GM was—and still is, for that matter—more like a country than a corporation. Ford was the third largest industrial corporation in America. Even Chrysler, the smallest of the Big Three, was until recently the tenth largest manufacturing corporation in the world.
It took two very different groups to produce this great success. On one side was management, led by a group of highly paid executives. Today management is dominated by M.B.A.'s. But it wasn't always that way. For most of its history, the car industry was led by a group of rugged individualists—arrogant, high-powered, and rich.
On the other side were the unions. The United Auto Workers, which really came into its own after World War II, was in its own way as powerful as management. The UAW has always been a monopoly—it alone has supplied the labor force that has kept the entire industry going.
The United Auto Workers began in the 1930s as part of the Congress of Industrial Organizations (the CIO), which broke away from the American Federation of Labor in 1935. Before that, the AFL had tried repeatedly to unionize the auto industry, but to no avail. Finally, after major and often violent battles with each of the major automakers, the UAW established itself as a force to be reckoned with.
I was too young to have known Walter Reuther, the union's founder and its president from 1946 to 1970. He died in a plane crash around the time I got to be president of Ford. But I do know that he was pretty enlightened. His attitude could be summed up very simply: labor's task is to carve up the pie as advantageously as possible. And the bigger the pie, the more money in it for the workers.
According to the old-timers in Detroit, Reuther would actually sit down at the negotiating sessions and draw a picture of a pie. "It's the job of management to bake this pie," he'd announce. Then he'd point to the various segments of the pie and explain—as if he were talking to schoolchildren: "This much goes for raw materials, this much for overhead and rent, this much for executive salaries, and this much for labor. We're here today, gentlemen, because we're not entirely satisfied with the way this pie has been divided. We want to cut it up just a little bit differently."
Walter Reuther's speeches became something of a joke around town because he'd say exactly the same thing at every session. It was like a record. Some of the reporters used to write up their stories in advance and they never guessed wrong.
Because Reuther cared about profits and productivity and because he understood that the fate of labor was inherently linked to the fate of the company, he gained the respect of management as well as workers. In fact, I sometimes like to remind the present union leadership of his attitude. Although Reuther founded the UAW, they don't invoke his name very much these days. And for good reason. The union is still clamoring for a bigger serving, but the pie is getting smaller.
Reuther never fought automation. He never opposed industrial progress, even when the short-term interests of labor seemed to be threatened. From the very start, he supported the installation of robots. "Never fight the new machinery," he would tell his people, "because it's the way to get more productive. And if the companies get more productive and earn bigger profits, we'll be in a better position to negotiate."
With this attitude, management and labor prospered together. And both groups have made more money in Detroit than their counterparts anywhere else in the world.
For all my complaints about the UAW, I have to admit that Reuther's enlightened outlook put his union far ahead of other unions, such as the railroad workers or the printers, with all their feather bedding and make-work. When the diesel locomotive was developed, for example, the railroads no longer needed a fireman to shovel coal into the engine. But the union insisted that the fireman had to stay on, even though his job was now obsolete.
Walter Reuther could be tough and even unreasonable. Still, he was a real visionary. Journalist Murray Kempton once said that Reuther was the only man he ever met who could reminisce about the future.
In 1948, under Reuther's leadership, management and the union developed a pattern of multiyear contract negotiations. Before that there had been annual bargaining sessions, a situation that was bound to create an unstable working environment. The 1948 labor agreement ran for two years instead of one. It was followed in 1950 by a five-year contract. Eventually the union settled into a series of three-year contracts with each of the Big Three.
In some industries, such as rubber or steel, companies have banded together at times and done industrywide collective bargaining. But the auto workers have always negotiated separately with General Motors, Ford, and Chrysler. Every three years, the union would choose a pattern company, and—often after a strike or at least the _threat_ of a strike—they'd work out an agreement with that company that became the model for the others.
Pattern bargaining made life easier for everybody. One advantage was that no company could undercut the competition on wages. On the other hand, pattern bargaining helped make management complacent when it came to dealing with the unions. After all, if the same labor agreement was in force for all four auto companies (American Motors was part of this arrangement), there was less incentive for management to cut a better deal during the negotiations.
I was involved in a number of labor talks during the 1970s when I was president of Ford. Throughout those years, I always felt that the companies were at a real disadvantage in dealing with the union. It had us over a barrel, because included in the union's arsenal was the ultimate weapon: the right to strike. And the mere threat of a work stoppage was the most frightening thing we could imagine.
Everybody in Detroit has a clear memory of the 1970 strike against General Motors, which lasted sixty-seven days in the United States and ninety-five days in Canada. It was a disaster for labor and management alike. The four hundred thousand workers who were idled lost $760 million in wages. The union's strike fund was quickly depleted, and the workers had to live off their savings.
GM had an equally rough time of it. Their income in 1970 fell by 64 percent from the previous year. As a result of the strike, GM failed to produce at least 1.5 million cars and trucks that were scheduled for production, which would have resulted in more than $5 billion in sales. I remember thinking that any union with the power to bring GM to its knees must be pretty strong.
Back in 1950, Chrysler had sustained a 104-day strike. It was then that Ford overtook Chrysler, so in a way the effects of that strike are still being felt today. We at Ford had our share of strikes, too, during which time our losses ran to around $100 million a week. At that rate, pretty soon you're talking about real money.
Because the strikes were so devastating, the leaders of the industry would do almost anything to avoid one. In those days, we could afford to be generous. Because we had a lock on the market, we could continually spend more money on labor and simply pass the additional costs along to the customer in the form of price increases.
A lockout would have been the answer, a kind of strike in reverse, where management closes down the plants. It would have been expensive, of course, but we might have had a final bloodletting. It's just possible that we could have changed the pattern between union and management before it was too late.
But there's never been a lockout in the auto industry. When I was at Ford, I urged that solution. But GM was always in favor of acquiescing to union demands, because for them money wasn't a problem. Chrysler wanted to give in, too, for the opposite reason—as the marginal player, they would be the first to go broke in the event of a prolonged strike.
Before each negotiating session, when the heads of the Big Three used to meet to plan our strategy, the possibility of a lockout would always come up. We used to go through the motions, but we were always too divided among ourselves to take any joint action. Ford, GM, and Chrysler could not agree on anything all year long—there was no reason to think they'd make an exception for something as important as this. The union had absolutely nothing to fear.
# XXVII
# THE JAPANESE CHALLENGE
Shortly after I joined Chrysler, I flew over to Japan for a series of meetings with the top people at Mitsubishi Motors. Back in 1971, Chrysler had purchased 15 percent of Mitsubishi and arranged to import some of their excellent small cars under the Dodge and Chrysler names. We've been partners ever since.
The talks were held in the shrine city of Kyoto. During one of the breaks, I went out for a walk with Dr. Tornio Kubo, the dynamic chairman of Mitsubishi. As we strolled through the private shrines and temple gardens of the city, I asked my new friend why his company had built its giant engine plant in this peaceful and rural environment.
Kubo laughed and replied: "Actually, our Kyoto factory started out as Japan's major aircraft plant. This is where we built our bombers during the war."
"But why here," I asked, "in the middle of all this beauty?"
"That's why," he replied. "You see, before the war, your President and Mrs. Roosevelt came here on a vacation. They fell in love with this city. And when the war began, Mr. Roosevelt gave orders that Kyoto was not to be bombed. As soon as our military intelligence learned of this order, we decided to build our aircraft plant in a place whose safety was already guaranteed."
When I heard this story, I just shook my head. "I guess all's fair in love and war," I said.
Kubo nodded in agreement. "What would you have done?" he said. "We in Japan look out for our self-interest. What I don't understand is why your country doesn't always do the same."
I don't understand it either. Right now, we're in the midst of another major war with Japan. This time it's not a shooting war, and I guess we should be thankful for that. The current conflict is a trade war. But because our government refuses to see this war for what it really is, we're well on the road to defeat.
Make no mistake: our economic struggle with the Japanese is critical to our future. We're up against a formidable competitor, and all things being equal, we'd be lucky to stay even with them.
But all things are not equal. The field where this game is being played is not level. Instead, it's strongly tilted in favor of Japan. As a result, we're playing with one hand tied behind our back. No wonder we're losing the war!
To begin with, Japanese industry is not playing by itself. It's backed to the hilt in its close relationship to the Japanese government in the form of MITI, the Ministry of International Trade and Industry. MITI's job is to determine the industries that are critical to Japan's future and to help out in their research and development.
To the American observer, MITI might sound like a meddlesome collection of low-level bureaucrats. It's not. In Japan, government service attracts many of the best and the brightest young people. When you also consider that the ministries of trade, economics, and finance are the most prestigious areas within government, you get some idea of the kind of talent that MITI draws. MITI has made some classic mistakes, but its overall impact on Japanese industry has been incredible.
When Japan started to rebuild after the war, its government targeted autos, steel, chemicals, shipbuilding, and machinery manufacturing as critical industries. In other words, Japan's economic destiny was not left up to the free play of laissez-faire economics. Now, Japan is not Russia, which has a totally planned economy. Far from it. But Japan does have a system of goals and priorities that allows government and industry to work together to achieve their national objectives.
As a result, Japan's auto industry has been wrapped in a cocoon of protection: government loans, accelerated depreciation, R&D assistance, protection from imports, and a prohibition against foreign investment. Because of this concerted effort, Japan's auto production has gone from a hundred thousand vehicles back in the mid-1950s to eleven million today.
But regardless of how the Japanese manufacturers were helped, they also deserve our respect and admiration. They've shown themselves to be prudent planners and engineers. They didn't sit back behind the barriers and grow fat.
Instead, management, shareholders, the government, bankers, suppliers, and workers all pulled together. They designed products that were world class, using state-of-the-art technology. They built fuel-efficient cars, motivated by a national energy policy of high gasoline taxes for a scarce resource. No wonder the Japanese were prepared for the Arab-Israeli war of 1973 and the Shah's hasty departure in 1980.
Another Japanese advantage is that their taxes are the lowest of any industrial country in the world. And one reason they can afford such low taxes is that they don't spend very much on defense. Ever since the end of World War II, we've taken care of that burden for them. After they surrendered, we said to them, "Listen, you guys, stop making arms. You can see where that got you. Don't worry, we'll defend your country for you. We want you to start making some nice, peaceful things for a change—like cars. We'll even show you how. The people in Detroit will give you a hand!"
And we did. In the process, we gave birth to a monster. Today he's about thirty-five years old, fully grown, with big muscles. He's running amok through the American car market, and he's going to continue doing so unless we put a stop to it.
But how do you compete with a country that is spending only $80 annually per citizen on defense when we're spending more than ten times as much? While we're busy protecting _both_ countries, the Japanese are free to spend _their_ money on research and development.
Still another major advantage for the Japanese is the artificial weakness of the yen. Their currency manipulation is enough to bring you to your knees. Their banks and their industry have conspired to keep the yen weak so that the price of their exported goods can remain attractive to Western markets.
Unfortunately, the manipulation of the yen is very difficult to prove. Whenever I complain about it in Washington, the government asks me for evidence. Everybody wants to know exactly how Japan is going about it.
I haven't the slightest idea. And I don't have an embassy in Tokyo or London or Zurich to help me with the answers. The U.S. Treasury has 126,000 employees. Let _them_ figure it out!
All I know is that if it walks like a duck and quacks like a duck, the chances are pretty good that it _is_ a duck. And when our prime rate goes from 10 percent up to 22 percent and back down to 10 percent—and during all those fluctuations the yen stays locked in at 240 to the dollar—you know that something is rotten in Tokyo.
At a minimum, the yen is undervalued by 15 percent. That may not sound like much, but it works out to a cost advantage of over $1,000 on a new Toyota. How the hell are we in Detroit supposed to compete with something like that?
Whenever this subject comes up, the Japanese always say it's not the yen that's too weak but the dollar that's too strong. There's certainly some truth to that charge, and our recent fiscal policies haven't helped. The Reagan administration has to accept some of the blame, because its policy of tight money and high interest rates has made our dollar too attractive to foreign capital.
One of my biggest fears is that in ten years we'll have an incredibly efficient operation at Chrysler, with an increased profit margin of $1,000 per car. And then suddenly the yen will take a big swing and wipe out that advantage we worked so hard to create.
We can't go on like this. It's time for our government to call the kid in after class and ask him to explain his behavior. His excuses aren't convincing any longer, and his actions are disrupting our economy. We should give the Japanese ninety days to tell us why the yen is undervalued—and what they intend to do about it.
Finally, there's the problem of free trade. Or perhaps I should say the _myth_ of free trade. As far as I can tell, free trade has been practiced only four times in all of history. One is in textbooks. The three real-world practitioners were the Dutch, briefly; the English at the beginning of the Industrial Revolution; and the United States after World War II.
The English could do it two hundred years ago because they had no real competition. As soon as other industrial economies developed, England abandoned free trade.
Similarly, the United States once had the world to itself. Over the years our dominance has eroded, but in our heads, we're still trapped in 1947.
Free trade is fine—as long as everyone is playing by the same rules. But Japan has its own rules, so we're constantly at a disadvantage.
Here's how it works. When a Japanese car is put on a boat for the United States, the Japanese government rebates about $800 to the manufacturer. That's a commodity tax rebate, and it's perfectly legal under the General Agreement on Tariffs and Trade (GATT). In other words, a housewife in Tokyo pays more for a Toyota than she would in San Francisco.
How should we respond? Well, in Europe they routinely slap on a border tax to offset the rebate that the Japanese provide for their exports.
Is that free trade? Of course not. Is it sensible? You bet!
Take a Toyota that sells for $8,000 in Japan. As soon as it arrives in San Francisco, the price drops to $7,200. But if that same Toyota goes to Frankfurt, its price goes up to $9,000. If it goes to Paris, it sells for $10,500. Because we see ourselves as the last bastion of free enterprise, we're being played for suckers.
Now, how can we give the imports 25 percent of a twelve-million-car market and then plead with them not to take 35 percent. It's unheard-of in the annals of history that we would offer up our labor-producing goods and then tell the Japanese: "Take anything you want. Let us worry about the social consequences."
Until some equilibrium is reached in our national trade deficit, we should limit the Japanese share of our domestic auto market by saying: "You guys can have 15 percent—and that's it."
Europe is a lot older than we are and a lot more experienced. If free trade is so important, then why are they setting limits on their imports?
Italy says two thousand Japanese cars a year is the most they'll tolerate. France says the limit is 3 percent. And what about Germany, that great free-trader? They don't like such strict limits. But when the Japanese share reached 11 percent in Germany, what did they do over there? They said: "Ten percent and no more." England did the same.
Unfortunately, our government finds this course of action difficult to imagine. Many of our leaders seem to think that we're still the only producers around and we have to be magnanimous. But forty years have passed since World War II, and it's time to acknowledge that the situation has changed.
Meanwhile, do the Japanese play fair with imported goods from America? Not on your life! Recently, some of our trade representatives met with the Japanese to discuss these inequities. Our people wanted to talk about beef and citrus products, which are protected in Japan, and about opening up new markets for our exports there.
But the Japanese said none of this was negotiable. Without cracking a smile, they said they'd be willing to take the tariff off tomato puree. Mind you, not tomatos—just tomato puree. Terrific! That should cut our $30 billion trade deficit with Japan by over a thousand bucks.
Meanwhile, Japan restricts the sale of American pharmaceuticals. They bar our telecommunications equipment and our fiber optics. They've created a web of almost five hundred government-protected cartels that practice two-tiered pricing and closed bidding on contracts. The Japanese marketplace is protected by a festival of crazy performance requirements and bureaucratic red tape that make it all but impossible to sell many kinds of American goods there.
For example, their system of product reclassification is an absolute sham. Take potato chips, which the Japanese really like. Potato chips were initially classified as a processed food, carrying a 16 percent tariff. But when an American manufácturer threatened to make significant inroads into the Japanese market, guess what happened? Potato chips were suddenly redesignated as "confectionery," and a 35 percent duty was slapped on.
My favorite example is cigarettes. They allow our cigarettes to be sold in Japan—but in only 8 percent of the tobacco shops. Moreover, there's a duty of fifty cents a pack. Does that sound like free trade?
Until 1981, American cigarette manufacturers were not allowed to advertise in Japan—except in English. Maybe, to even the score, we ought to force Datsun and Toyota to advertise here only in Japanese. Can you imagine the screams of anguish if we did that? I wonder how you say "Oh, what a feeling" in Japanese?
When people ask me whether I'm in favor of free trade or protectionism, my response is: None of the above. I'm opposed to protectionism. I'm also opposed to local content legislation. But the United States is just about the only industrial country left in the world that doesn't have an enlightened, modern-day trade policy. We're the only country in the world that comes close to practicing free trade—and we're getting clobbered.
That's why I take a middle road that I call _fair_ trade. Fair trade involves some selective—and temporary—restraints against the one country in the world that is running such a lopsided negative trade balance with us.
Let's look at what is really going on here. We ship them wheat, corn, soybeans, coal, and timber. And what do they ship us? Cars, trucks, motorcycles, oil well equipment, and electronics.
Question: What do you call a country that exports raw materials and imports finished goods?
Answer: A colony.
Now, is _that_ the kind of relationship we want to have with Japan? We were in a similar situation once before, and we ended up throwing a lot of tea into Boston Harbor!
But this time we're just sitting by and watching the Japanese take aim at one industry after another.
They've already taken electronics. They've taken sporting goods. They've taken copiers. They've taken cameras. They've taken a quarter of the automobile industry.
Along the way, they've taken a quarter of the steel industry, too. The Japanese have a clever way of smuggling their steel into the United States. They paint it, put it on four wheels, and call it a car.
While the Japanese are shipping us Toyotas, they're really exporting something more important than cars. They're sending us unemployment. Their subsidies are aimed at maintaining full employment in Japan, and the policy is working. Their unemployment is 2.7 percent. Ours is three to four times as high.
What's next? It's no secret, because they've been kind enough to tell us: airplanes and computers.
Now, I don't want to give anyone the wrong impression about my attitude toward the Japanese. Yes, I'm angry about the tilted playing field. And I'm angry that we're sitting passively while all this is going on. But Japan is really doing nothing wrong. As Kubo said, they're simply dealing in their own self-interest. It's up to us to start dealing in _ours._
Because I speak out on these inequities while many of my colleagues in the auto industry are silent, people get the impression that I'm anti-Japanese. There's even a story going around the country these days about a third-grade history class where the teacher is giving a little quiz:
"Now, class," says the teacher, "who said, 'I only regret that I have but one life to give for my country'?"
A little Japanese girl in the first row stands up and replies: "Nathan Hale, 1776."
"Excellent," says the teacher. "Now, who said, 'Give me liberty or give me death'?"
The little Japanese girl stands up again. "Patrick Henry, 1775."
"Good work!" says the teacher. "Boys and girls, I think it's wonderful that Kiko over here knows the answers. But the rest of you should be ashamed of yourselves. Remember, you're American and she's Japanese."
Just then, a boy at the back of the room mutters, "Ah, screw the Japanese."
"All right," snaps the teacher, "who said that?"
Whereupon a voice calls out: "Lee Iacocca, 1982!"
It's a cute story, but in reality I'm a great admirer of the Japanese. Why? Because they know where they've come from, they know where they're at, and they know where they're going. And most important, they have a national strategy to get them there.
They also know how to make good cars. During the 1970s, their cars were actually better than ours. That's not true any longer, but many Americans still believe it.
How did Japan's cars get so good? It starts with the workers. To begin with, labor costs over there are much lower than ours. Japanese workers earn about 60 percent of what their American counterparts take home. They don't have automatic cost-of-living increases tied to the Consumer Price Index, as American workers do. And they don't have the same array of company-paid medical benefits that cost the consumer several hundred dollars a car.
Japan's workers are also more productive than ours. I don't mean that they're _better_ , merely that they operate by a different set of rules.
There are really only two job classifications in Japan: skilled and unskilled. Depending on what needs to be done on a given day, a worker may perform a variety of jobs. If the floor is dirty, he'll pick up a broom and sweep it without worrying about whether that's part of his job definition. Naturally, this sense of responsibility leads to much greater efficiency.
Such a system would be unthinkable in Detroit, where every worker has a specific set of duties. Next to the simplicity and common sense of the Japanese factory, our own system of union rules and regulations looks pretty ridiculous. The UAW now has about 150 job classifications. Whereas the attitude of the Japanese worker is, "How can I help?," the attitude of his American counterpart is, all too often, "That's not my job."
Japanese labor unions work very closely with management. Each side understands that its fate is bound up in the other guy's success. The relationship between labor and management is one of cooperation and mutual respect. That's a far cry from the antagonism and mutual suspicion that has long been the tradition in our country.
The Japanese worker is highly disciplined. If something's crooked, he'll straighten it. If there's a problem on the assembly line, he'll stop the line until it's fixed.
These guys have a lot of pride. They see their work as a mission. You don't hear stories in Japan about workers showing up with a hangover. There's no industrial sabotage and no visible worker alienation.
In fact, I once read that some Japanese companies had to fine their supervisors because so many of them insisted on working on holidays as well as on their days off. Could you imagine that happening in Michigan or Ohio?
Japanese management, too, operates by a set of assumptions that might seem strange to us but that contribute to their overall success. The typical Japanese auto executive doesn't earn anything close to what his counterparts are making in Detroit. Nor does he receive any stock options or deferred compensation.
At some point in his career, he may have worked on a production line. American managers would probably be shocked to learn that the chief executive officer of Mitsui was once the head of his company's labor union. Unlike his counterparts in Detroit, the Japanese executive lives in the same world as the workers rather than in a completely rarefied environment.
What it all boils down to is that in Japan, government, labor, and industry are all working on the same side. In our country, industry and labor are traditional adversaries. And despite what the public may believe, private industry and government don't work together, either.
Here again, I blame the ideologues who seem to think that _any_ government involvement in the national economy somehow undermines our free-market system. Certainly there can be such a thing as too much intervention. But as we continue to fall behind Japan, it's become increasingly clear that there's also such a thing as too little.
We have to take action. We must replace free trade with fair trade. If Japan—or any other nation—protects its markets, we should be doing the same. If they encourage local industry, we should respond in kind. And if they play tricky games with their currency, we should take steps to equalize the exchange rate.
I don't know when we're going to wake up, but I hope it's soon. Otherwise, within a few years our economic arsenal is going to consist of little more than drive-in banks, hamburger joints, and videogame arcades.
Is that really where we want America to be by the end of the twentieth century?
# XXVIII
# MAKING AMERICA GREAT AGAIN
These days, _everybody's_ talking about the national deficit. But because we almost lost Chrysler a few years ago, I had the dubious honor of starting to worry about this problem a little earlier than most people. We were being killed by high interest rates, and it was clear that as long as the government was using up more than 50 percent of the nation's credit, interest rates could never come down very much.
So back in the summer of 1982, I wrote a piece for _Newsweek_ where I proposed a simple way of cutting the national deficit in half. At the time, the deficit was only— _only!_ —$120 billion. My plan involved cutting $30 billion from government spending while raising another $30 billion in revenues.
I had already learned firsthand that Chrysler was alive only because of the combined efforts of management, labor, the banks, the suppliers, and the government. And so I wondered: why couldn't the principle of "equality of sacrifice" be applied to the federal deficit as well?
My plan was simple. First I would cut 5 percent a year out of the defense budget. That would come to $15 billion, and it could be done without affecting a single hardware program.
Then we'd call in the Democrats and say to them: "Okay, boys, I want you to match this $15 billion cut with an equal cut in the social programs you've put in over the past forty years."
Then comes the hard part. Once we've cut $30 billion in spending, we match it dollar for dollar on the revenue side. First, we raise $15 billion with a surtax on imported oil, designed to help OPEC keep their oil prices at $34 a barrel. Then we add a fifteen-cent tax to gas at the pump, which raises another $15 billion.
Even with these new taxes, American gas and oil would still be cheaper than anywhere else outside the Arab world. And in addition to all that revenue, we'd finally be creating an energy policy. The next time OPEC struck, we'd be ready for them.
Taken together, these "four 15s" would cut the deficit by $60 billion a year. The beauty of this program is that it spreads the sacrifice equally among all our people—Republicans and Democrats, business as well as labor.
When I came up with this plan, I went to every CEO I knew on Wall Street and asked them: "What would happen if the President went on TV and announced that he was cutting the federal deficit in half?" They all agreed that this announcement would trigger the biggest investment binge in our history. It would restore our credibility as a country. It would prove that we knew what we were doing.
Needless to say, we didn't do it. But it's not as if nobody was listening. Thousands of _Newsweek_ readers wrote to tell me they liked my plan. I even got a call from the White House asking me to come and see the President.
When I walked into the Oval Office, President Reagan greeted me with the _Newsweek_ article in his hand. "Lee," he said, "I like what you've written here. And I'm worried about the size of the deficit, too. But Richard Wirthlin, my pollster, tells me that a gas tax is the most unpopular thing I could do."
"Wait a minute," I thought. "Are we running this country by the polls? Is that what leadership is all about?"
The President wanted to talk about the defense budget. "We spent too little under Carter," he told me. "We've got to spend a lot more for our national security. You don't understand the whole picture."
"That's true," I replied. "I don't understand it all. And I don't want to be presumptuous. But the defense budget is now more than $300 billion. I'm a businessman. Believe me, I can cut 5 percent out of _anything_ and you'll never know I did it. In fact, I've been doing that all my life."
Well, we didn't cut the deficit in August 1982. And now it's grown to over $200 billion. As I write these words in the spring of 1984, we're still wringing our hands about what to do.
Unfortunately, the budget deficit is only the tip of the iceberg. If anyone doubts that we've lost some of our economic greatness, let's consider the following questions:
Why does the country that produced Walter Chrysler, Alfred Sloan, and the original Henry Ford have so much trouble making and selling cars competitively?
Why does the country of Andrew Carnegie have so much trouble competing in steel?
Why does the country of Thomas Edison have to import most of its phonographs, radios, television sets, Videorecorders, and other forms of consumer electronics?
Why does the country of John D. Rockefeller have oil problems?
Why does the country of Eli Whitney have to import so many of its machine tools?
Why does the country of Robert Fulton and the Wright brothers face such heavy competition in transportation equipment?
What became of the industrial machine that was once the envy and the hope of the rest of the world?
How, in less than forty years, did we manage to dismantle the "arsenal of democracy" and wind up with an economy that is flabby in so many critical areas?
Our loss of leadership did not come about overnight. The gradual erosion of our strength and power began in those halcyon years following World War II. But in no period of our history has America showed more vulnerability than in this past decade.
First, we woke up one morning and discovered that something called OPEC had the power to bring America to its knees. Like Pavlov, who rang a bell to achieve his desired results, OPEC rang its bell and we responded. And now, more than ten years later, we still have no real program to respond to this monumental economic danger.
Second, in the name of free trade, we're sitting by and watching Japan systematically capture our industrial and technological base. By combining the skills and efficiencies of their culture with a whole host of unfair economic advantages, Japan appears capable of looting our markets with impunity.
In Washington this is known as laissez-faire economics, and they love it. In Tokyo they call it _Veni, Vidi, Vici_ economics, and believe me, they love it even more. The Japanese have come, they've seen, and they are conquering. And our dependence on Japan will continue to grow until we establish some practical limits to their enjoyment of our markets.
Third, the Soviet Union has caught us in overall nuclear capability. America no longer has a decisive military edge. We've now defined a program to regain that edge, but its dominance of the national agenda has been so total that I'm beginning to wonder what all these new weapons are going to _protect._ Without a strong, vital industrial infrastructure, we're a nation bristling with missiles that surround a land of empty factories, unemployed workers, and decaying cities. Where is the wisdom in this policy?
Finally, at some point in our recent past America lost sight of its true source of power and greatness. From a nation whose strength has always flowed from investments in the production and consumption of goods, we have somehow turned into a nation enamored with investing in paper.
And so our biggest companies are pouring huge sums of money into buying up the stock of other companies. Where is all this capital ending up? In new factories? In new production equipment? In product innovation?
Some of it is, but not very much. Most of that money is ending up in banks and other financial institutions who are turning around and lending it out to countries such as Poland, Mexico, and Argentina. That doesn't help America much. But at least when these countries went broke and the banks cried wolf, they accomplished what Chrysler, International Harvester, and the housing industry could never have done: they persuaded the Federal Reserve to back off of tight money.
Each month, some new type of financial instrument is created for the express purpose of absorbing consumer purchasing power and enriching the brokerage houses. Looking back on this period of deep-discount this and zero-coupon that, I can't help but think that never before in history has so much capital produced so little of lasting value.
Right now, our biggest industrial employers are in autos, steel, electronics, aircraft, and textiles. If we want to save millions of jobs, we've got to preserve these industries. They're the ones that create markets for the service sector as well as for high technology. They're also critical to our national interest. Can we really maintain the backbone of our defense system without strong steel, machine tool, and auto industries?
Without a strong industrial base, we can kiss our national security good-bye. We can also bid farewell to the majority of our high value-added jobs. Take away America's $10 to $15-an-hour industrial jobs and you undercut our whole economy. Oops—there goes the middle class!
So we've got to make some basic decisions. Unless we act soon, we're going to lose both steel and autos to Japan by the year 2000. And worst of all, we will have given them up without a fight.
Some people seem to think that this defeat is inevitable. They believe we should even hasten along the process by abandoning our industrial base and concentrating instead on high technology.
Now, I don't for a moment dispute the importance of high technology in America's industrial future. But high tech alone won't save us. It's important to our economy precisely because so many other segments of American industry are its customers.
Especially the auto industry. We're the ones who use all the robots. We've got more computer-aided design and manufacturing facilities than anyone. We're using computers to get better fuel economy, to clean up emissions, and to get precision and quality in the way we build our cars.
Not many people know that IBM's three biggest customers (excluding defense) are GM, Ford, and Chrysler. There can't be a Silicon Valley without a Detroit. If somebody is producing silicon chips, somebody else has to _use_ them. And we do. There's now at least one computer on board every car we build. Some of our more exotic models have as many as five!
You can't sell your silicon chips in a brown paper bag down at the hardware store. They've got to have a use. And America's basic industries are the users. Close us down and you close down your market. Close down autos and you close down steel and rubber—and then you've lost about one of every seven jobs in this country.
Where would that leave us? We'd have a country of people who serve hamburgers to each other and silicon chips to the rest of the world.
Don't get me wrong: high technology is critical to our economic future. But as important as it is, high tech will never employ the number of people that our basic industries do today. That's a lesson we should have learned from the demise of the textile industry. Between 1957 and 1975, 674,000 textile workers were laid off in New England. But despite that region's booming high-tech industries, only 18,000 of those workers—about 3 percent—found work in the computer industry.
Nearly five times as many ended up in lower-wage retail trade and service jobs. In other words, if you lost your job in a textile mill in Massachusetts, you were five times as likely to end up working at K-Mart or McDonald's than at Digital Equipment or Wang. You just can't take a forty-year-old pipefitter from Detroit or Pittsburgh or Newark, put a white coat on him, and expect him to program computers in Silicon Valley.
So the answer isn't to promote high technology at the expense of our basic industries. The answer is to promote _both_ of them together. There's room for all of us in the cornucopia, but we need a concerted national effort to make it happen.
In other words, our country needs a rational industrial policy.
These days, "industrial policy" is a loaded term. It's like yelling "fire!" in a crowded theater. A lot of people panic whenever they hear the phrase.
Don't they want America to be strong and healthy? Sure they do. But they want it to happen without any planning. They want America to be great _by accident._
The ideologues argue that industrial policy would mark the end of the free-enterprise system as we know it. Well, our wonderful free-enterprise system now includes a $200 billion deficit, a spending program that's out of control, and a trade deficit of $100 billion. The plain truth is that the marketplace isn't always efficient. We live in a complex world. Every now and then the pump has to be primed.
Unlike some people who talk about industrial policy, I don't mean that the government should be picking winners and losers. The government has proved again and again that it's not smart enough to do that.
And I don't want the government interfering in the operations of my company—or any other company, for that matter. Believe me, the existing regulations are bad enough.
As I see it, industrial policy means restructuring and revitalizing our so-called sunset industries—the older industries that are in trouble. Government must become more active in helping American industry meet the challenge of foreign competition and a changing world.
Almost everyone admires the Japanese, with their clear vision of the future; the cooperation among their government, banks, and labor; and the way they lead from their strengths. But whenever somebody suggests that _we_ ought to follow their lead, the image suddenly shifts to the Soviets and their five-year plans.
But government planning doesn't have to mean socialism. All it means is having a game plan, an objective. It means coordinating all the pieces of economic policy instead of setting it piecemeal, in dark rooms, by people who have only their own vested interests at heart.
Is planning un-American? We do a great deal of planning at Chrysler. So does every other successful corporation. Football teams plan. Universities plan. Unions plan. Banks plan. Governments all over the world plan—except for ours.
We're not going to make progress until we give up the ridiculous idea that any planning on a national level represents an attack on the capitalist system. Because of this fear, we're the only advanced country in the world without an industrial policy.
Actually, that's not entirely true. America already _has_ an industrial policy, and it's a bad one. Nobody who's familiar with Washington can claim that the government would somehow violate free enterprise if it helped American industry. Washington is Subsidy City! And each subsidy adds up to an industrial policy.
Let's start with federal loan guarantees. (I'm an expert in this area.) Chrysler wasn't the first. Before we came along, there were $409 billion in guaranteed loans. Now the figure is up to $500 billion and still climbing. That's industrial policy.
Then there's defense. Eisenhower warned us about this one when he talked about the military-industrial complex. That complex has us spending over $300 billion a year. It's the only protected industry we have left in this country. It's the only industry where, by law, the Japanese are not allowed to compete.
That's why when we at Chrysler sold our tank division to General Dynamics, a lot of people asked: "Why don't you sell the car business and keep the tanks? The tanks are making you $60 million a year guaranteed and protected!"
Then there's NASA and the space program. That's industrial policy, too. The moon shot is what sent our computer industry into high gear.
Or what about the International Monetary Fund? It bails out foreign countries that have borrowed beyond their means and can't keep up the payments. Not long ago Paul Volcker gave Mexico another $1 billion to keep its credit intact and to relieve some big U.S. banks that lent them the money in the first place. Volcker made his loan overnight, without a hearing. But in order to get $1.2 billion to save Chrysler—an American company—we had to tie up Congress for weeks. What kind of industrial policy is that?
In the past, the U.S. government has made loans to Poland at 8 percent while we ask Polish Americans to buy houses at 14 percent. If the Democrats can't make hay out of that, they _deserve_ to lose.
And what about tax policy? The auto industry in the aggregate pays 50 percent of its income in taxes. The banking industry pays only 2 percent. That's another form of industrial policy.
So we _do_ have an industrial policy—or more accurately, _hundreds_ of industrial policies. The only problem is that they're all over the lot and do little if anything for our basic industries.
Is industrial policy some kind of radical new idea? Not at all. We had an industrial policy in America even before we had a nation. Back in 1643, Massachusetts granted a new smelting company exclusive iron-producing privileges for twenty-one years to encourage this developing industry.
More recently, in the nineteenth century, our industrial policy included extensive government support for our railroads, the Erie Canal, and even our universities.
In the twentieth century, we've seen government support for our highways, for synthetic rubber, modern jet travel, the moon shot, integrated-circuit industries, high technology, and much more.
Over the past few decades we've had a phenomenally successful industrial policy—in agriculture. Three percent of our population not only feeds the rest of us—they feed much of the rest of the world to boot. Now, _that's_ productivity!
How did that happen? Well, there's more going on here than good climate, rich soil, and hardworking farmers. We had all those things fifty years ago, and all we got were dust bowls and disasters.
The difference lies in a wide range of government-sponsored projects. There are federal research grants; county agents to educate people; state experimental farms; rural electrification and irrigation projects such as the TVA; crop insurance; export credits; price supports; acreage controls; and now Payment in Kind—which pays farmers _not_ to grow certain crops. That program alone now comes to over $20 billion a year.
With all of that government help (or, some would say, interference) we've created a miracle. Our agricultural industrial policy has made us the envy of the world.
Now, if we've got an agricultural-industrial policy and a military-industrial policy, why the hell can't we have an _industrial-_ industrial policy?
I guess my attitude toward an industrial policy is the same as Abraham Lincoln's when somebody told him that Ulysses S. Grant got drunk a lot. Lincoln said: "Find out what kind of whiskey he drinks and send it to my other generals."
Here's my six-point program that could form the basis for a new industrial policy.
First, we should provide for energy independence by 1990 by taxing foreign energy, both at the port and at the pump, in order to restore the conservation ethic and rekindle investments in alternate sources of energy. We must not be lulled by the current depressed demand. OPEC will always act in its own interest, and that interest will always be served best by high prices and tight supplies. The American people are willing to pay a price for energy independence. They know it can't be achieved without a sacrifice.
Second, we should provide for specific limits to Japan's market share for certain critical industries. We should declare a state of economic emergency for those industries and unilaterally set aside the restrictive GATT provisions during this period. We don't have to apologize for taking this commonsense approach to trade with Japan. At this point in our history, we can't afford a trading partner who insists on the right to sell but who refuses to buy.
Third, as a nation, we've got to face reality on the costs and funding mechanisms for federal entitlement programs. They're studying this to death in Washington because it's a political hot potato. But the answer has always been right in front of our noses: we can't continue to pay out more than we take in, and that will mean some very painful adjustments.
Fourth, America needs more engineers, scientists, and technicians. On a per-capita basis, Japan graduates about four times as many engineers as we do. (But we graduate fifteen times as many lawyers!) Special education grants and loans should be provided for high-technology fields of study. The Soviets and the Japanese are both dedicated to building up their technological competence—and we are not keeping up.
Fifth, we need new incentives to increase research and development efforts in the private sector and to accelerate factory modernization and productivity in critical industries. One approach is to offer investment tax credits for R&D and twelve-month depreciation write-offs for productivity-related investments.
Finally, we need to establish a long-term program for rebuilding America's arteries of commerce—our roadways, bridges, railroads, and water systems. Our infrastructure, which is vital to any strengthening and expansion of our industrial power, is deteriorating at an alarming rate. Something must be done. Such a program could be partially funded by the OPEC energy tax. It would also provide a major buffer from the future employment dislocation that will inevitably result from productivity gains and industrial automation.
To put all these programs into practice, we should set up a Critical Industries Commission—a forum where government, labor, and management could get together to find a way out of the mess we're in. We have to learn how to talk to each other before we can take joint action.
This tripartite coalition would recommend specific measures to strengthen our vital industries and to restore and enhance their competitiveness in international markets.
Let me make clear that I am _not_ proposing a welfare system for every company that gets into trouble. _We need a program that kicks in only when troubled American companies have agreed to equality of sacrifice among management, labor, suppliers, and financial backers._ It worked for Chrysler, and it can work for the rest of America.
When an industry or a company comes looking for help, as I did five years ago in Washington, the commission should ask on behalf of the taxpayers, who are going to take the risk, "What's in it for us?" What's in it for the people? In other words, "What are management and labor bringing to the party?"
I've lived through this, and it's simple. It's management agreeing to do something _before_ the government does _anything_ —such as loan guarantees, or import restraints, or investment tax credits, or R&D help. Management might have to agree to plow back its earnings into job-creating investments—in _this_ country. It might have to agree to profit sharing with its employees. It might even have to agree to keeping a lid on prices.
As for the unions, they would have to come out of the dark ages. They'd have to agree to changes in the many work rules that hamper productivity—such as having 114 job classifications in assembly plants where about 6 would do fine. They might even have to agree to restraints on the runaway medical costs that are now built into our system.
If neither management nor labor is going to make sacrifices, then the meeting's over. You can't expect to get government help if you're not willing to get your own house in order. In other words, there's no free lunch. Whoever applies for assistance will have to understand that there are strings attached.
If all of this sounds a little like a Marshall Plan for America, that's exactly what it is. If America could rebuild Western Europe after World War II, if we could create the International Monetary Fund and a dozen international development banks to help rebuild the world, we ought to be able to rebuild our own country today. If the World Bank—which is a profit-making institution—can successfully help out underdeveloped countries, why couldn't a new national development bank do as well in helping out troubled American industries?
Maybe what we need is an _American_ Monetary Fund. What's so terrible about a $5 billion national development bank to get our basic industries competitive again?
Early in 1984, the Kissinger Commission requested $8 billion for the economic development of Central America. Now, I always thought that Central America meant places like Michigan, Ohio, and Indiana. (Shows you how simple-minded I am!) What about _our_ Central America? How can we spend $8 billion to strengthen the economies of other countries while neglecting ailing industries in our own backyard?
Some people say that an industrial policy is nothing more than lemon socialism. If it is, I'll take a crateful—because unless we act fast, our industrial heartland is going to turn into an industrial wasteland.
Any realistic industrial policy for America will have to include a monetary and fiscal policy.
We can't have a stable, healthy economy with high interest rates—or with interest rates that fluctuate every ten minutes. High interest rates are man-made disasters. And what man makes, man can unmake.
I look back on October 6, 1979, as a day of infamy in this country. That's when Paul Volcker and the Federal Reserve Board let the prime rate float. That's when the monetarists said, "The only way to break inflation is by controlling the supply of money—and to hell with interest rates."
As we all learned the hard way, that decision unleashed a tidal wave of economic destruction. There's got to be a better way to control inflation than to break it on the backs of the workers in the auto and housing industries. When future historians look back on our way of curing inflation and all the pain the cure caused, they'll probably compare it to bloodletting in the Middle Ages!
Detroit got hit first. We suffered the longest car-sales depression in fifty years. The housing industry came next. After that, almost everybody else in the country got hit.
Before the prime rate came unglued, interest rates had gone as high as 12 percent only once in our entire history, and that was during the Civil War. But now, once they hit 12 percent, they kept on going. At one point they reached as high as 22 percent. That's legalized usury. Some states have laws that kick in at 25 percent, suggesting criminal intent. The Mafia calls it vigorish.
But as tough as 20 percent interest rates are, what's even worse is the yo-yo effect. From October 6, 1979, to October 1982, rates went up (or down) eighty-six times, which comes out to once every 13.8 days. How can you plan anything on that?
When interest rates are high, consumers divert a lot of money into short-term securities. But making money on money isn't productive. It doesn't create any jobs. And those of us who _do_ create jobs, who invest in productivity and want to expand and are willing to pay our fair share of taxes, end up downstream waiting for a few measly drops of credit to get through so we can put a few more people back to work.
High interest rates encourage the big boys to play their new game of making money on money. When money is expensive, investment in research and development is risky. When rates are high, it's cheaper to buy a company than to build one.
Of the ten largest corporate mergers in U.S. history, nine have taken place during the Reagan administration. One of the biggest involved U.S. Steel. While protected by trigger prices (which cost us $100 more per car to buy American steel), U.S. Steel paid $4.3 billion to buy Marathon Oil. Most of that money was borrowed. It should have been used to buy modern basic oxygen furnaces and continuous casters to compete with the Japanese.
When the steel workers saw what was going on, they were so mad they demanded that any wage concessions they made be plowed back into the steel business. It's almost unbelievable that American management should have to be lectured to by the workers on just how our system works.
Or what about DuPont buying Conoco for $7.5 billion, and in the process tripling its debt to $4 billion? It costs DuPont $600 million a year in interest just to service that debt. Wouldn't we all be better off if DuPont used that money to develop the kind of new and inventive products that made them world-famous?
And what about Bendix, United Technologies, and Martin Marietta borrowing $5.6 billion to fund their corporate cannibalism—without creating a single new job in the process? That three-ring circus ended only when Allied threw a tent over it all and put a stop to the whole thing.
Think of this: in the decade between 1972 and 1982, the total number of employees in America's five hundred largest industrial companies actually declined. All the new jobs—well over ten million—came from two other sources. One was small business. The other, I'm sorry to say, was government—which may be the only real growth industry left.
Why don't we pass a law that says when you borrow money to buy somebody else and cannibalize him, the interest payments on those loans are not deductible? That would get the excesses out of the system pretty fast.
Right now, if you want to buy up a competitor, generally you can't. That would violate the antitrust laws. But if you want to buy a company that does something else entirely, that's okay.
Where's the sense in that? Why should a guy who's been in the steel business suddenly become an oil man? It's a completely different world. It will take him years to learn about it. And most important, it's not productive.
If we lowered interest rates and ended this merger madness, we could get the money changers out of the temple of the national economy. We could get back to doing business the American way, by reinvesting and competing instead of buying each other up. And by creating more jobs so more people could participate in our economic growth. Welfare costs for local, state, and federal governments would come down. Capital would begin to accumulate. Plants would expand again.
As everyone knows, the way to lower interest rates is to make big cuts in the federal deficit. It's time somebody took away the government's charge card. Today Washington uses more than half of all the available credit (54 percent to be exact) to finance the national debt.
Despite all of President Reagan's campaign promises, the national debt is out of control. Back in 1835, the federal debt was a mere $38,000. In 1981, it broke $100 billion for the first time in history. Today it's about $200 billion. And, over the next five years it's expected to total over $1 _trillion_!
We picked up a deficit that big once before—during the period from 1776 through 1981. Think of it. It took us 206 years, with eight wars, two major depressions, a dozen recessions, two space programs, the opening of the West, and the terms of thirty-nine presidents to do that. Now we're going to duplicate that record in just five years while we're at peace—and during a so-called economic recovery.
To put it another way, there are sixty-one million families in this country and we're going to put all of them in hock for $3,000 a year _without their permission._ It's like Uncle Sam is using your credit card without asking. As a result, we're mortgaging the futures of our kids and our grandchildren. Since most of them can't vote yet, they've given us their proxy. And we're not using it very well. In my book, the boys in Washington—all of them—get an F on the budget.
We have to attack the budget deficit and our other economic problems before they completely overwhelm us. Of course, to solve big problems you have to be willing to do unpopular things. As a child of the Great Depression, I've always been a great fan of F.D.R. He did a lot for this country, even though the ideologues were fighting him every step of the way. He melted the pot. He included the excluded. He had the audacity to take people off the street corners where they were selling apples and put them to work.
Above all, he was pragmatic. When he was confronted by big problems, he _did_ something—and that always takes more courage than doing nothing. Roosevelt did not attack the problems of the Depression with charts and graphs, with Laffer curves, or with Harvard Business School theories. He took concrete action. He was always willing to try something new. And if that didn't work, he was willing to try something else.
We need a little more of that spirit in Washington today. Our problems are huge and they're complicated. But there _are_ solutions. They aren't always easy, and they aren't always comfortable. But they do exist.
The great issues facing us today are not Republican issues or Democratic issues. The political parties can debate the means, but both parties must embrace the end objective, which is to make America great again.
Can we succeed in this undertaking? Someone once said that in great undertakings there is glory even in failure. So we must try, and if we do, I believe that we'll make it.
We are, after all, a resourceful people in a nation that has been blessed with abundance. With direction, leadership, and the support of the American people, we can't miss. I'm convinced that this country can once again be that bright and shining symbol of power and freedom—challenged by none and envied by all.
# EPILOGUE
# THE GREAT LADY
When President Reagan asked me to serve as chairman of the Statue of Liberty-Ellis Island Centennial Commission, I was up to my ears at Chrysler. But I accepted anyway. People asked me: "Why did you take this on? Don't you have enough to do?"
But this was a labor of love for my mother and father, who used to tell me about Ellis Island. My parents were greenhorns. They didn't know the language. They didn't know what to do when they came here. They were poor, and they had nothing. The island was part of my being—not the place itself, but what it stood for and how tough an experience it was.
But my getting involved in the restoration of these two great symbols is more than just a memorial to my parents. I, too, can identify with their experience. And now that I'm involved, I've found that almost every other American I meet feels the same way.
Those seventeen million people who passed through the gates of Ellis Island had a lot of babies. They gave America a hundred million descendants, which means that close to half of our country has its roots there.
And roots are what this country is yearning for. People are aching to return to basic values. Hard work, the dignity of labor, the fight for what's right—these are the things the Statue of Liberty and Ellis Island stand for.
Except for the American Indians, we're all immigrants or the children of immigrants. So it's important that we go beyond the stereotypes we've lived with. The Italians brought more to this country than pizza and spaghetti. The Jews brought more than bagels. The Germans brought more than knockwurst and beer. All the ethnic groups brought their culture, their music, their literature. They melted into the American pot—but somehow they also managed to keep their cultures intact as each rubbed off on the other.
Our parents came here and were part of the industrial revolution that changed the face of the world. Now there's a new high-tech revolution and everyone's scared out of their wits. When you're in a mode of change, as we're in right now, the great fear is that a lot of people are going to get hurt—and that one of those people might just turn out to be you. That's why so many people are worried. They're asking themselves: "Will we be as good as our parents in coping with these new changes, or will we be left out in the cold?" And our kids are beginning to ask: "Do we have to lower our expectations and our standard of living?"
Well, I want to say to them: It doesn't have to be that way. If our grandparents could overcome, maybe you can, too. You may never have thought about it, but they went through hell. They gave up a lot. They wanted your life to be better than theirs.
When the chips were down, my mother found nothing wrong with working in the silk mills so I could have lunch money for school. She did what she had to do. When I got to Chrysler I found a royal mess, but I did what I had to do.
Think about it. The last fifty years can give you a vision for the next fifty. What the last fifty taught us was the difference between right and wrong, that only hard work succeeds, that there are no free lunches, that you've got to be productive. Those are the values that made this country great.
And those are the values that the Statue of Liberty represents. The Statue of Liberty is just that—a beautiful symbol of what it means to be free. The reality is Ellis Island. Freedom is just the ticket of admission, but if you want to survive and prosper, there's a price to pay.
I've had a terrific career, and this is the country that gave me the chance to do it. I seized the opportunity, but I was no ninety-day wonder. It took me almost forty years of hard work.
People say to me: "You're a roaring success. How did you do it?" I go back to what my parents taught me. Apply yourself. Get all the education you can, but then, by God, _do_ something! Don't just stand there, make something happen. It isn't easy, but if you keep your nose to the grindstone and work at it, it's amazing how in a free society you can become as great as you want to be. And, of course, also be grateful for whatever blessings God bestows on you.
Since most of my life has been selling—selling products, or ideas, or values—I guess it would be out of character to close this book without asking for the order. So here goes:
Please help me in the restoration of Ellis Island and the Statue of Liberty. Send your tax-deductible contribution to: Statue of Liberty-Ellis Island Foundation, Box 1986, New York, NY 10018. Don't let the flame in the Statue go out!
Remember, if nothing else, Christopher Columbus, my father, and I will be forever grateful.
# About the Author
Lee Iacocca is the former president of Ford Motor Company and chairman of the Chrysler Corporation. Now retired, he devotes his time to the Iacocca Foundation, which raises money for diabetes research. He lives in Los Angeles, California, and enjoys spending time with this two daughters and seven grandchildren.
Just married: my Parents, Nicola and Antoinette Iacocca in 1923.
Barely nine months old.
In pre-Depression finery, 1926.
With my sister, Delma, in 1927.
Learning to drive, 1929.
With my father, 1934.
High jinks at Lehigh, 1942 ( _second from left_ ).
Big man on campus: Princeton, 1945.
My first paycheck from Ford—after taxes!
Mary, 1948.
With Henny Youngman ( _center_ ) and Murray Kester ( _right_ ), 1953.
Egg on my face for selling safety in '56.
New Ford president Robert McNamara ( _left_ ) with Henry Ford II in 1960.
With Charlie Beacham in Phoenix, 1961.
Father of the Mustang.
While New York City slept, a 1966 Mustang was flying high on top of the Empire State Building.
Presenting the first 1974 Mustang to Mr. Honda at his home in Tokyo.
President of Ford, 1974.
1975; the beginning of the end. AP/WIDE WORLD
A collector's item: the car that made it, but I didn't, 1979.
The day after.
How's that for timing?
The savior: Chrysler's first K-Car, 1980.
Would you buy a used car from this man? My first commercial, 1981.
With Detroit's Mayor Coleman Young and comedian Bill Cosby.
Life's little rewards.
I'll drink to that! The payback: August 15, 1983.
With Jerry Greenwald ( _center_ ) and Hal Sperlich ( _right_ ).
With the President in St. Louis, 1983.
And if drafted, I shall not run.
The success car of the 80s.
With Kathi, 1964.
The family, 1973.
December 10, 1970: my parents and Mary celebrating my election to the presidency of Ford.
In costume for my 50th birthday.
Kathi (right) and Lia, 1981.
Our surprise 25th wedding anniversary party.
The Three Musketeers: with my friends Bill Fugazy ( _left_ ) and Vic Damone.
|
{
"redpajama_set_name": "RedPajamaBook"
}
| 9,351
|
\section{Introduction}
The memristor~\cite{14} is a novel electronic component of interest because it possesses an implicit memory: this has led to the suggestion that it will be useful next-generation computer memory~\cite{15} and of use in mimicking how the brain works.
The memristor was first defined as a device that directly related charge, $q$ to magnetic flux $\varphi$, and thus is the fourth fundamental circuit element (after the resistor, inductor and capacitor) and the first non-linear one~\cite{14}. From Chua's seminal paper in 1971~\cite{14}, it was theorised that the memristor would give a pinched hysteresis I-V curve (a Lissajous curve) which crosses at the origin. Memristive systems were then defined as a memristor with a second state variable~\cite{84}. Once memristors were knowingly fabricated~\cite{15} and ReRAM explained via memristor theory~\cite{119}, the focus on how to test if a device was a memristor changed. The requirement that the memristor cross at the origin (as opposed to being merely pinched at the origin) was relaxed~\cite{8,276} with suggestions that it might not be necessary condition to define a memristor~\cite{291} and that real devices can posses a `nanobattery'~\cite{292}. The frequency test was expanded: 2 of the 3 fingerprints suggested to define the memristor~\cite{276} are to do with frequency behaviour. These are that above some critical frequency, $\omega^{*}$, the hysteresis
lobe area should decrease monotonically and the pinched hysteresis loop should shrink to zero when the frequency tends to infinity~\cite{276}. Chua suggested that researchers should plot $q$ and $\varphi$ to prove that they have a memristor, however, due to the difficulty in understanding which magnetic flux was relevant~\cite{F1} and the fact that it's more standard to plot voltage-current curves, few people currently do. However, Chua then suggested that to prove if a device was a memristor, the frequency effect should be tested for -- this idea has gained acceptance amongst memristor experimentalists.
\begin{figure}
\centerline{\subfigure[PEO-PANI 3-terminal memristive system]{\includegraphics[width=1.65in]{PEO-PANI.jpg}
\label{fig_first_case}}
\hfil
\subfigure[TiO$_2$ sol-gel memristors]{\includegraphics[width=1.65in]{TiO2.jpg}
\label{fig_second_case}}}
\caption{Devices Tested.}
\label{fig:Devices}
\end{figure}
The frequency effect has been derived from memristor theory, however the physics of the effect is not well-understood and have not been related to the memristor material properties. The memristor is commonly thought to be an a.c. component, however we have been experimentally investigating the d.c. response of the memristor~\cite{SpcJ}, which is the route of the short-term memory of the memristor. In this short paper, we shall show how the hysteresis is related to the d.c. response of the memristor (its short-term memory), discuss how the material properties of the device give rise to this effect and finally demonstrate the effect using experimental data from real devices.
The data presented in this paper come from two different types of memristors, see figure~\ref{fig:Devices}: the flexible TiO$_2$ sol-gel memristors described~\cite{260} and the plastic electronic PEO-PANI memristors~\cite{12,23,51} (technically a memristive system~\cite{84} under strict definitions). Note that, the TiO$_2$ sol-gel memristors appear similar to a non-faradic capacitor~\cite{293} over this range, but that standard seemingly `pinched' (the devices actually approach zero but do not cross at zero due to either lag in the ionic current, presence of a nanobattery arising from the electrochemistry~\cite{292}) memristor curve is observed over larger ranges~\cite{260}.
\section{Methodology}
The dynamics of the two memristors are different, so have been measured with different values. In both cases, the voltage waveform was a triangular waveform with $x$ measurement steps, $\Delta t$, at each voltage step $\Delta v$, an example $V-t$ waveform is shown for PEO-PANI in figure~\ref{fig:Vt}. The PEO-PANI memristors were measured on a Keithley programmable multimeter, the total number of measurement steps, $N$ was $N=432$, $x = 12$, $\Delta t=20s$, $\Delta V$=0.1V, with a maximum voltage $\pm 0.9V$. The TiO$_2$ memristors were measured using a Keithley 2400 sourcemeter, N=1600, $\Delta t=0.01s$, $x=10$, $\Delta V=0.0375$, with a maximum of $\pm V 1.5V$. The Keithley was used in auto-zero mode for maximum accuracy, which adds a 0.6s padding time during which the sourcemeter auto-zeroed before taking the reading and the time step was then applied after that. The machine was operated such that the current range was set so there was no extra time searching for the correct current range (which can happen in some set-ups).
\section{Mathematical Description of the System}
\begin{figure}
\centering
\includegraphics[width=3.2in]{2780711CV-t.png}
\caption{Voltage waveform used for PEO-PANI measurements.}
\label{fig:Vt}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=3.2in]{191211D4aaCU.png}
\caption{d.c. response of the memristor. The device was subjected to a voltage step from 0V to +0.5V after 4 time-steps, $\Delta t=0.05s$ in this measurement.}
\label{fig:DC}
\end{figure}
For each voltage step, $\Delta v$, the voltage is first changed at $t=0$, then the current response is measured at $i_1$, (which would be at $t=0$ if the auto-zero time were turned off), then further measurements made an integer number of time-steps after at $i_2$, $i_3$ ... $i_x$ where $x$ is the number of measurement points at each voltage step. As the size of $\Delta v \rightarrow \delta v$, the current response tends to the continuum (a.c.).
The d.c. response of the memristor (for the TiO$_2$ sol-gel device) is shown in figure~\ref{fig:DC} and has been discussed at length in~\cite{SpcJ}. The measured current is the response to a voltage step and the features are: $i_{\mathrm{max}}$, the maximum size of the peak; $\tau_{\infty}$, the time after which the current is at its equilibrium value (i.e. the value at $t=\infty$ if nothing else changes); the set of measurements we make which is $\{ i(\Delta t) \}$; and the continuous time ($t$) decay dynamics given by $I(t)$. We have shown that $i(\Delta t)$ can be fit by a memristor model~\cite{254}, but in this work we assume that we do not know the form of $I(t)$. The d.c. response of the memristor, can also be described as its short-term memory, and $\tau$ is the persistence time of that memory.
\begin{figure}
\centering
\includegraphics[width=3.2in]{280711BReDrawn.png}
\caption{PEO-PANI Memristor No. 1. Key:- Red dashes: $i(t_1)$; Green dots: $i(t_6)$; blue dot-dashes: $i(t_{12})$}
\label{fig:PP_1}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=3.2in]{2780711CReDrawn.png}
\caption{PEO-PANI Memristor No. 2 Key:- Red dashes: $i(t_1)$; Green dots: $i(t_6)$; blue dot-dashes: $i(t_{12})$}
\label{fig:PP_2}
\end{figure}
\section{Experimental data}
Figures~\ref{fig:PP_1} and ~\ref{fig:PP_2} show the response of two different PEO-PANI devices. The first ($t=1$), middle ($t=6$) and last ($t=12$) measurement points at each voltage have been joined together with red, green and blue lines. At each voltage step, as time passes, the hysteresis associated with it decreases (although it seems to shift in the positive lobe of PEO-PANI memristor 1, rather than decrease). An $I-t$ slice through this I-V curve at V=+0.6 is shown in figure~\ref{fig:PP_Slice}: these dynamics are consistent with those seen under steady state voltage experiments with these devices.
\begin{figure}
\centering
\includegraphics[width=3.2in]{2780711CV0p6Slice.png}
\caption{`Decay' dynamics at $\pm$0.6V on the PEO-PANI memristor No. 2. Blue: response to +0.6V, Red: response to -0.6V. Similar decay curves are seen in all PEO-PANI devices measured.}
\label{fig:PP_Slice}
\end{figure}
Figure~\ref{fig:TiO2} shows the response for a flexible TiO$_2$ device that exhibits open loop behaviour. The dynamics are faster than PEO-PANI, but the behaviour is qualitatively the same: as dwell time at each voltage increases the magnitude of the current decreases, leading to a shrinking hysteresis.
\begin{figure}
\centering
\includegraphics[width=3.2in]{D4zRedrawn.png}
\caption{TiO$_2$ sol-gel memristor I-V curves. Key:- Red dashes: $i(t_1)$; Green dots: $i(t_4)$; blue dot-dashes: $i(t_10)$}
\label{fig:TiO2}
\end{figure}
\section{Discussion}
These data are for step $V-t$ waveforms (the experimental reason for this is that it is impossible to source slow enough alternating voltage waveforms), but if we move from the descretized time measurement domain to a continuous time domain, we can investigate the frequency response.
For our set of, for example, 12 measurement points, we have the following data points for $i$: $\{ i(\Delta t), i(2 \Delta t), ... i(12\Delta t) \}$. By drawing a line between points with the same value of $x$ (where $x$ is the measurement point) we get the following set of frequencies: $\{ \omega \} = \{ (x N \Delta t)^{-1} \}$, where $x = 1,2... 12$. In the PEO-PANI example, these frequencies are given by: $\{ \omega \} = \{ 1, \frac{1}{2}, \frac{1}{3}, \frac{1}{4} ... \frac{1}{12} \} $, in units of $\frac{1}{N \Delta t}$; which is actually a set of slower (larger) frequencies. So, by plotting the lines between adjacent measurements with the same $x$ value, we are actually approximating different frequency responses. And, we see from the data that as the frequency gets larger the hysteresis, $H$, decreases.
The frequency response calculated in this way is approximate however, because we are actually getting a measure of the state of the memristor (or the amount of short-term memory it has) after that time, we are not including the response to a changing voltage. Specifically, at voltage step $n$ measurement step $x$ we get the response to the voltage input at $t=0$ (which was $x$ time-steps before). For an actual measurement of the corresponding frequency we would have the response to both the voltage input at $t=0$ and the voltage input at that measurement step ($x$) and that frequency. Thus we need to know the effect of a changing voltage on this memory and there are two ways to do this. The first is to actually measure the memristor at several different frequencies, which we have done (not shown here for space reasons) and which shows that slower frequencies tend to decrease the hysteresis as expected. The second is to take account of the interaction between a voltage input and the memristor's short-term memory, which we know from previous work~\cite{P0c} means that the response is smaller than it would be if there was no memory, this effect does not change the qualitative results shown here, and so, acknowledging these facts, we can still proceed to see what further information these plots can give us.
As $\Delta t \rightarrow \delta t$ (i.e. we go from descretized time to continuous time), $v(\Delta t)$ becomes a triangular waveform and $\{ i(\Delta t \}$ becomes $I(t)$ and spikes are smoothed into a curve, similar to those drawn by joining points with the same value of $x$ and $\{ \omega \}$ becomes a continuum. Thre result that the hysteresis decreases as the frequency gets larger, becomes $\omega \rightarrow \infty, H \rightarrow 0$, which is the third fingerprint of the memristor. The observations that this effect exists with a descretized waveform, that the points have similar dynamics to those seen in $I-t$ plots and match results for different frequency tests illustrates that the short-term memory (d.c. response) of the memristor is relevant for understanding the frequency effect.
\subsection{What is the Single Valued Function?}
The third fingerprint of the memristor is that the `pinched hysteresis loop should shrink to a single-valued function when the frequency tends to infinity'~\cite{276}, what is this single valued function? At slow frequencies, the memory of the memristor is lost at each `time-step' and the measured current is that of $i(\tau_{\infty})$. As $\omega \rightarrow \infty$, $\{ i \Delta t \} \rightarrow \{i(\tau_{\infty},v_1), i(\tau_{\infty},v_2), ... i(\tau_{\infty},v_N) \}$, and because $i(\tau_{\infty},v_k) =i(\tau_{\infty},v_l)$, if $v_k=v_l$ there is no hysteresis. This is because the different current values seen at $v_k$ and $v_l$ (if say $v_k$ is +0.6V on the first quadrant of the $V-t$ plot and $v_l$ is +0.6V on the second, i.e. after the device has been taken to $V_{\mathrm{max}}$ and back) are entirely a result of the memory in the system which is stored as the short-term memory and essentially different actions applied to the device move the current response up and down the $I-t$ curve shown in figure~\ref{fig:DC}. Thus, moving from descretized time to continuous time as before, we get $\omega \rightarrow \infty, H \rightarrow 0,$ and $I(t) \leftarrow \{ i \Delta t \} \rightarrow \{i(\tau_{\infty},v_1), i(\tau_{\infty},v_2), ... i(\tau_{\infty},v_N) \}$, or the memory-less response, which is a straight-line in $I-V$ space corresponding to an ideal ohmic resistor with resistance of the equilibrated resistor, $M(\tau_{\infty})$.
\subsection{What is the Maximal Value of the Hysteresis?}
From examination of the $I-t$ plot we can answer the question of what happens in the short-time limit. At the shortest time we can measure (around 0.05s in the memristor devices using the current set-up) we see the maximum spike current, $i_{\mathrm{max}}$, and if we measure at the corresponding frequency, we will see the largest value of the hysteresis. We postulate that there is a resonant frequency, $\omega_0$, where we will get the largest hysteresis, and this corresponds to the systems being as close to the peak of $i_{\mathrm{max}}$ in d.c. space as possible. Below this frequency, we see the hysteresis decreasing with frequency (as shown here experimentally). If this $\omega_0$ is the same as the critical frequency $\omega^{*}$, then this would match the limits of the second fingerprint of the memristor. There are reasons to believe that $\omega_0$ is not close to 0 and that the hysteresis decreases above it as well as below it, specifically, in that it takes time for the memory property of the system
to respond.
\subsection{Material Causes of the Frequency Effect}
Memristance arises due to the slower response time of the memory-carrying ions/vacancies than the conducting electrons to a voltage change. Thus memristance can be described as a two level system involving the interaction of two (or more) charge carrying particles with different mobilities. For TiO$_2$ memristors we believe that the timescale of memristance is related to the ion mobility of oxygen vacancies (a point of view also held by others~\cite{15}). The oxygen ions take time to respond to a voltage change, due to their mass. Thus, if an applied frequency is so fast that the period is less than the time taken for the oxygen ions to change direction, no appreciable change in resistance will be seen and the hysteresis will shrink to 0. The maximal value of the hysteresis would thus be seen when the frequency was able to move the oxygen ions the furthest over a period. Straight-line resistor-like $I-V$ responses have been recorded by us when the frequency is too fast for the system (not shown in this short paper). For PEO-PANI memristors a similar argument holds, but the memory carrying ions are positive ions, not oxygen vacancies.
\section{Conclusion}
This type of I-V curve offers information about the dynamics of the system and demonstrates the frequency effect, by virtue of being a single graph from a single experiment and we suggest including this type of plot in memristor papers generally. We highlight that the d.c. response of the memristor gives information about its short-term memory and it is the interaction of this memory with the frequency of measurement (which is related to the frequency of the $V-t$ curve in the continuum case) which causes the frequency effect. Finally, we suggest (and discuss elsewhere~\cite{F1}) that this frequency effect arises different timescales for ions and electrons.
\bibliographystyle{IEEEtran.bst}
\maketitle
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 7,846
|
Georges Rubel
Born in Paris in 1945. High school education. Bachelor of Philosophy. Pupil of Jacques Moreau, known as Le Maréchal, who brought him, from 1963 to 1965, the first notions of the art of the painter and the engraver. From 1972, he attended the evening classes for adults of the City of Paris, more particularly the studio of master engraver Jean Delpech.
From 1974 to date, he has participated in a number of collective exhibitions, both in France and abroad.
In the collection of the National Library and the State; by the Fine Arts Museum in San Francisco. Many private collections.
Featured in numerous catalogs and publications, including "Visionary Art", by Michel Random, 1979 and 1991; "From Bonnard to Baselitz: ten years of enrichment of the Cabinet des estampes, 1978-1988", National Library, Paris, 1992.
Associate artist of the Young Contemporary Engraving (JGC) since 1980.
Born in Paris in 1945. High school education. Bachelor of Philosophy. Pupil of Jacques Moreau, known as Le Maréchal, who brought him, from 1963 to 1965, the first notions of the art of the painter and the engraver. From 1972, he attended the
Partie de Campagne Ancienne et Moderne
Other Surrealist Artists
view movement
Paul Wunderlich
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 3,320
|
\section{Introduction.}
As the top quark is very heavy, it
decays even before it can hadronize, predominantly into a
$W$-boson and a quark, with the branching fraction of $t\to Wb$ close to 1,
which means that the decay at the leading order is
almost exclusively governed by the $Wtb$ coupling.
Due to the almost immediate decay, the information about the top quark
spin and couplings is passed to
its decay products without being obscured by the hadronization process
and it can be best gained from the analysis of differential cross sections,
in particular from the angular distribution of the lepton from the $W$-boson
decay \cite{Jezabek}.
Therefore the top quark production processes are ideal for tests of
extensions of the standard model (SM)
that lead to modifications of the pure left-handed $Wtb$ coupling of SM.
This issue has been already extensively addressed in literature, see, e.g.,
\cite{kane}, \cite{Wtb}, \cite{GHR}, \cite{CK1}, \cite{tt6fwtb}.
In \cite{GHR}, a decoupling theorem was proven,
which states that the angular distribution of the secondary lepton resulting
from a decay of the top quark produced in $e^+e^-\to t\bar t$ receives no
contribution from the anomalous $Wtb$ coupling
in the narrow width approximation (NWA). The theorem turned out to
remain correct also in a more complicated case of the off
shell top quark pair production in $e^+e^-$
annihilation and decay in 6 fermion final states including
the non-double resonance background contributions, which was checked
by direct computation in \cite{tt6fwtb}.
It was also shown \cite{afbKK} that the anomalous
$Wtb$ coupling cannot explain discrepancies between the forward-backward
asymmetry (FBA) in the top quark pair production in high energy
proton-antiproton collisions observed by the CDF \cite{afbCDF}
and D0 \cite{afbD0} experiments at Tevatron and the SM expectations
\cite{afbSM}.
The FBA in \cite{afbKK} was computed taking into account leading order
cross sections of all the sub-processes of
quark-antiquark annihilation, which dominate the top
quark pair production at the Tevatron, of the form
$q\bar{q} \;\rightarrow\; b q\bar{q}'\;\bar{b} l\bar{\nu}_l$,
with $u\bar u$ and $d\bar d$ in the initial state and a single charged lepton
in the final state.
In spite of the fact that off resonance contributions to such reactions
are changed in the presence
of the anomalous $Wtb$ coupling, as it substantially alters the
total top quark decay width, the rapidity distributions
of the final state lepton remain almost unchanged. This can be considered
as another example of the decoupling theorem
of \cite{GHR} that remains
valid in the off shell top quark pair production and decay
in quark-antiquark annihilation.
In the proton-proton collisions at the LHC, the top quarks are produced
dominantly in pairs through
the underlying gluon-gluon fusion or the quark-antiquark annihilation processes
\begin{eqnarray}
\label{ggtt}
gg \; \rightarrow \; t \bar{t}, \qquad q\bar{q}\; \rightarrow \; t \bar{t}.
\end{eqnarray}
The single top production processes, as, e.g., $qb\to q't$,
$q\bar{q}'\to t\bar{b}$, or $qg\to q't\bar{b}$,
have much smaller cross sections.
Each of the top quarks of (\ref{ggtt})
decays into a $b$-quark and a $W$-boson,
and the $W$-bosons decay into a fermion-antifermion pair each which leads to
reactions with 6 fermions in the final state.
The top quark pair production events are best identified if
one of the $W$ bosons decays leptonically and the other hadronically that
corresponds to reactions of the form
\begin{eqnarray}
\label{pp6f}
pp \;\rightarrow\; b q\bar{q}'\;\bar{b} l\bar{\nu}_l.
\end{eqnarray}
This means that one should selects events
with an isolated electron or muon with large
transverse momentum, a missing transverse momentum from the undetected
neutrino and four or more jets.
For the sake of clarity, in the present work, we will concentrate on one
specific channel of (\ref{pp6f}):
\begin{eqnarray}
\label{ppbbudmn}
pp \;\rightarrow\; b u\bar{d}\;\bar{b} \mu^-\bar{\nu}_{\mu}
\end{eqnarray}
and address the question to which extent the anomalous $Wtb$ coupling
affects different distributions
of the final state $\mu^-$. In other words, we would
like to check if the decoupling theorem of \cite{GHR}
holds also for the top quark pair
production in proton-proton collisions at the LHC.
We will also illustrate the role of the off-resonance background
contributions in (\ref{ppbbudmn}) by comparing
the distributions computed with the full set of leading order Feynman
diagrams with those computed with the $t\bar t$ production
diagrams only.
\section{An anomalous $Wtb$ coupling at the LHC}
The underlying hard scattering processes of (\ref{ppbbudmn}) that contribute
most to its cross section are the following:
\begin{eqnarray}
\label{ggbbudmn}
gg &\rightarrow& b u\bar{d}\;\bar{b} \mu^-\bar{\nu}_{\mu},\\
\label{uubbudmn}
u\bar u &\rightarrow& b u\bar{d}\;\bar{b} \mu^-\bar{\nu}_{\mu},\\
\label{ddbbudmn}
d\bar d &\rightarrow& b u\bar{d}\;\bar{b} \mu^-\bar{\nu}_{\mu}.
\end{eqnarray}
In the leading order, neglecting light fermion masses,
$m_u=m_d=m_{\mu}=0$, and the Cabibbo-Kobayashi-Maskawa mixing between quarks,
there are 421 Feynman diagrams of the gluon-gluon fusion process
(\ref{ggbbudmn}) and 718 diagrams of each of
the quark-antiquark annihilation processes (\ref{uubbudmn}) and
(\ref{ddbbudmn}).
Some examples of the diagrams of processes (\ref{ggbbudmn}) and (\ref{uubbudmn})
are shown in Figs.~\ref{diags_gg} and \ref{diags_uu}. There are 3
double resonance $t\bar t$ production signal diagrams of the gluon-gluon
fusion processes (\ref{ggbbudmn}): two of them are depicted
in Figs.~\ref{diags_gg}a and \ref{diags_gg}b and
the third is obtained by interchanging the gluon lines in Fig.~\ref{diags_gg}b.
At the same time the quark-antiquark annihilation process
(\ref{uubbudmn}) receives contributions from 6
$t\bar t$ production signal diagrams: 3 of them are depicted in
Figs.~\ref{diags_uu}a and \ref{diags_uu}b and the other 3 are obtained
by interchanging the $u$-quark lines in each diagram of Figs.~\ref{diags_uu}a
and \ref{diags_uu}b. The Feynman diagrams of process (\ref{ddbbudmn}) are
obtained from those of process (\ref{uubbudmn}) just by replacing the initial
state $u$-quarks with $d$-quarks. Note that if the top quarks were assumed
to be produced
on-shell, which corresponds to the NWA for the top quarks, then the number
of the signal diagrams for each
of the processes (\ref{ggbbudmn}), (\ref{uubbudmn}) and (\ref{ddbbudmn})
would be equal 3.
Thus, in the NWA, not only does one neglect a plethora of background
contributions represented by the diagrams in Figs.~\ref{diags_gg}e,
\ref{diags_gg}f and \ref{diags_uu}d, but
also part of the double resonance signal diagrams and the diagrams with two
or one top quark propagators, as those
depicted in Figs.~\ref{diags_gg}c, \ref{diags_gg}d and \ref{diags_uu}c.
Let us note that the $Wtb$ coupling that is indicated by a blob enters
twice both in the $t\bar t$ production signal diagrams of
Figs.~\ref{diags_gg}a, \ref{diags_gg}b, ~\ref{diags_uu}a, \ref{diags_uu}b
and in the non double resonance diagrams of Figs.~\ref{diags_gg}c,
\ref{diags_gg}d and \ref{diags_uu}c.
\begin{figure}[htb]
\centerline{
\epsfig{file=diags_gg.eps, width=120mm, height=50mm}}
\caption{Examples of the leading order Feynman diagrams of process
(\ref{ggbbudmn}). Blobs indicate the $Wtb$ coupling.}
\label{diags_gg}
\end{figure}
\begin{figure}[htb]
\centerline{
\epsfig{file=diags_uu.eps, width=120mm, height=25mm}}
\caption{Examples of the leading order Feynman diagrams of process
(\ref{uubbudmn}). Blobs indicate the $Wtb$ coupling.}
\label{diags_uu}
\end{figure}
The effective Lagrangian of the
$Wtb$ interaction containing operators of dimension up to five
considered in the present work has the following form \cite{kane}:
\begin{eqnarray}
\label{lagr}
L_{Wtb}&=&\frac{g}{\sqrt{2}}\,V_{tb}\left[W^-_{\mu}\bar{b}\,\gamma^{\mu}
\left(f_1^L P_L +f_1^R P_R\right)t\right.\nonumber\\
&&\qquad\qquad\qquad
\left.-\frac{1}{m_W}\partial_{\nu}W^-_{\mu}\bar{b}\,\sigma^{\mu\nu}
\left(f_2^L P_L +f_2^R P_R\right)t\right]\nonumber\\
&+&\frac{g}{\sqrt{2}}\,V_{tb}^*\left[W^+_{\mu}\bar{t}\,\gamma^{\mu}
\left(\bar{f}_1^L P_L +\bar{f}_1^R P_R\right)b\right.\nonumber\\
&&\qquad\qquad\qquad \left.
-\frac{1}{m_W}\partial_{\nu}W^+_{\mu}\bar{t}\,\sigma^{\mu\nu}
\left(\bar{f}_2^L P_L +\bar{f}_2^R P_R\right)b\right],
\end{eqnarray}
where form factors $f_{i}^{L}$, $f_{i}^{R}$, $\bar{f}_{i}^{L}$ and
$\bar{f}_{i}^{R}$, $i=1,2$ can be complex in general and
the remaining notation is obvious. See \cite{afbKK} for details
and the corresponding Feynman rules.
The lowest order SM Lagrangian of $Wtb$ interaction is reproduced
for $f_{1}^{L}=\bar{f}_{1}^{L}=1$ and all the other form factors equal 0.
CP conservation leads to the following relationships between
the form factors of (\ref{lagr}):
\begin{equation}
\label{rel}
\left.\bar{f}_1^{R}\right.^*=f_1^R,
\quad \left.\bar{f}_1^{L}\right.^*=f_1^L, \qquad \qquad
\left.\bar{f}_2^R\right.^*=f_2^L, \quad \left.\bar{f}_2^L\right.^*=f_2^R.
\end{equation}
First direct limits on the form factors of (\ref{lagr}) were
obtained by the CDF Collaboration by investigating two form
factors at a time while assuming the other two at their SM values
\cite{wtbCDF}. The limits
have been improved recently by the D0 Collaboration \cite{wtbD0}
and they read:
\begin{eqnarray}
\label{limits_2dim}
\left|V_{tb}f_{1}^R\right|^2 < 0.93, \qquad
\left|V_{tb}f_{2}^R\right|^2 < 0.13, \qquad
\left|V_{tb}f_{2}^L\right|^2 < 0.06.
\end{eqnarray}
More stringent are one-dimensional limits at 95\% C.L. \cite{wtbD0}:
\begin{eqnarray}
\label{limits_1dim}
\left|V_{tb}f_{1}^R\right|^2 < 0.50, \qquad
\left|V_{tb}f_{2}^R\right|^2 < 0.11, \qquad
\left|V_{tb}f_{2}^L\right|^2 < 0.05.
\end{eqnarray}
Limits derived from ATLAS \cite{wtbATLAS} and CMS \cite{wtbCMS} measurements
of $W$-boson helicity fractions using a program TOPFIT \cite{wtbAguilar}
with one non-zero coupling at a time
and $V_{tb}= 1$ read:
\begin{eqnarray}
\label{limitsLHC}
{\rm Re}f_{1}^R\in [-0.20,0.23], \quad
{\rm Re}f_{2}^R\in [-0.08,0.04],\quad
{\rm Re}f_{2}^L\in [-0.14,0.11].
\end{eqnarray}
Limits (\ref{limitsLHC}) are weaker if two couplings are varied
at a time \cite{wtbCMS}. Amazingly enough, the right-handed vector form factor
$f_{1}^R$ is least constraint in (\ref{limits_2dim})--(\ref{limitsLHC}), but
if CP is conserved then it
is indirectly constrained from the CLEO data on
$b\rightarrow s\gamma$ \cite{cleo} and from other rare $B$
decays \cite{fajfer}.
\section{Results}
Lagrangian (\ref{lagr}) was implemented
into {\tt carlomat} \cite{carlomat}, a general purpose program for the Monte
Carlo (MC) computation of lowest order cross sections.
A new version of the program \cite{carlomat2} was already used
to make predictions for the FBA in top
quark production at the Tevatron \cite{afbKK}.
In this section, a sample of results is presented that illustrate an influence
of the tensor form factors of Lagrangian (\ref{lagr})
on the distributions of the secondary $\mu^-$
in top quark pair production at the $pp$ collisions at the LHC energies
through reaction (\ref{ppbbudmn}). As in \cite{afbKK}, we put
$V_{tb}=1$ and assume form factors $f_{i}^{L}$, $f_{i}^{R}$, $\bar{f}_{i}^{L}$ and
$\bar{f}_{i}^{R}$, $i=1,2$, of Lagrangian (\ref{lagr}) to be real.
Moreover, the vector form factors are fixed at their SM values of
$f_{1}^{L}=\bar{f}_{1}^{L}=1$, $f_{1}^{R}=\bar{f}_{1}^{R}=0$ and
only the tensor form factors $f_{2}^{L,R}$, $\bar{f}_{2}^{L,R}$ are changed by
assigning them two values: 0 or 0.2 in different, CP-even or CP-odd,
combinations. A value of 0.2 that exceeds limits
(\ref{limits_2dim})--(\ref{limitsLHC}) is
chosen just for the sake of illustration of the anomalous coupling effects
that for smaller values of the form factors would have been hardly
visible in the plots. However, an interested user can easily obtain
predictions for any other choice of the form factors with the
publicly available program \cite{carlomat2}.
The physical input parameters that are
used in the computation are the same as in \cite{afbKK}. In order to avoid
on-shell poles the following complex mass parameters:
\begin{equation}
\label{m2}
m_b^2 \rightarrow M_b^2=m_b^2-im_b\Gamma_b, \;\;\; b=Z, W, h,\quad
m_t\rightarrow M_t=\sqrt{m_t^2-im_t\Gamma_t}
\end{equation}
are used instead of masses in propagators of unstable particles,
both in the $s$- and $t$-channel.
The particle widths in (\ref{m2}) are assumed to be constant and the square
root with positive real part is chosen, see \cite{carlomat} for details.
The computation is performed in the complex mass scheme, where the electroweak
(EW) couplings are parametrized in terms
the complex EW mixing parameter $\sin^2\theta_W=1-{M_W^2}/{M_Z^2}$
which preserves the lowest order Ward identities \cite{Racoon} and minimizes
the unitarity violation effects at high energies.
The width of the top quark has substantial influence on the cross
section of reaction (\ref{ppbbudmn}). Therefore, it is calculated
in the leading order for every specific choice of the form factors
with effective Lagrangian (\ref{lagr}) that, due to the fact that branching
fractions of the decays $t\to bW^+$ and $\bar t\to \bar{b}W^-$ are close to 1,
practically determines it.
It should be stressed that for CP-odd choices of the form factors the widths
$\Gamma_t$ of $t$ and $\Gamma_{\bar t}$ of $\bar t$ differ from each other.
Thus, the both widths are calculated and the following rule is applied
to put the width in the $s$-channel top quark propagator:
$\Gamma_t$ is used if the propagator goes into $bW^+$ and
$\Gamma_{\bar t}$ is used if the propagator goes into $\bar{b}W^-$. The rule does
not work for the propagators in $t$-channel, but the actual value
of the top quark width does not play much of a role there.
If the prescription is applied then the $t\bar t$ production signal
contribution to the cross section of (\ref{ppbbudmn}) in the NWA takes the
following form
\begin{eqnarray}
&&\left.\sigma(pp\to t^*\bar t^* \rightarrow b u\bar{d}\;\bar{b} \mu^-\bar{\nu}_{\mu})
\right|_{\rm NWA}\nonumber\\
&&\qquad\qquad\qquad
\approx\sigma(pp\to t\bar t)\; \frac{\Gamma_{t\to bW^+}}{\Gamma_t}\;
\frac{\Gamma_{W^+\to u\bar{d}}}{\Gamma_{W}}\;
\frac{\Gamma_{\bar t\to \bar{b}W^-}}{\Gamma_{\bar t}}\;
\frac{\Gamma_{W^-\to \mu^-\bar{\nu}_{\mu}}}{\Gamma_{W}}\nonumber\\
&&\qquad\qquad\qquad
\approx\sigma(pp\to t\bar t)\;
\frac{\Gamma_{W^+\to u\bar{d}}}{\Gamma_{W}}\;
\frac{\Gamma_{W^-\to \mu^-\bar{\nu}_{\mu}}}{\Gamma_{W}}\nonumber
\end{eqnarray}
and unitarity is preserved. The unitarity argument can be also used to justify
the prescription for the $s$-channel top quark propagator in the off resonance
background Feynman diagrams which, as will be illustrated later, contribute
very little to the cross section.
However, a field theoretical
justification of the effective prescription proposed would actually
require calculation of higher order corrections to partonic
processes (\ref{ggbbudmn})--(\ref{ddbbudmn})
with nonrenormalizable Lagrangian (\ref{lagr}). This formidable and delicate
task is beyond the scope of this work.
The cross section of reaction (\ref{ppbbudmn})
is calculated by folding CTEQ6L parton distribution
functions (PDFs) \cite{CTEQ} with the cross sections of underlying
hard scattering processes
(\ref{ggbbudmn}), (\ref{uubbudmn}) and (\ref{ddbbudmn}), with the cross
sections of the quark-antiquark annihilation processes being symmetrized
with respect to the interchange of the initial state quark and antiquark.
The factorization scale is assumed to be equal
$Q = \sqrt{m_t^2+\sum_jp_{Tj}^2}$.
The $t\bar{t}$ production events are identified with the following
acceptance cuts on the transverse momenta $p_T$, pseudorapidities $\eta$,
missing transverse energy $/\!\!\!\!E^T$ and separation
$\Delta R_{ik}=\sqrt{\left(\eta_i-\eta_k\right)^2
+\left(\varphi_i-\varphi_k\right)^2}$ in the
pseudorapidity--azimuthal angle $(\varphi)$ plane between
the objects $i$ and $k$:
$$p_{Tl} > 30\;{\rm GeV}/c, \qquad p_{Tj} > 30\;{\rm GeV}/c, \qquad
\left|\eta_l\right| < 2.1, \qquad \left|\eta_j\right| < 2.4,$$
\begin{eqnarray}
\label{cuts}
/\!\!\!\!E^T > 20\;{\rm GeV},\qquad
\Delta R_{lj,jj} > 0.4.
\end{eqnarray}
The subscripts $l$ and $j$ in (\ref{cuts}) stand for {\em lepton}
and {\em jet}, a direction of the latter is identified with the
direction of the corresponding quark. Cuts (\ref{cuts}) are rather restrictive
which means that only slightly more than 1\%
of the MC events generated by {\tt carlomat} pass them.
Effects of the anomalous $Wtb$ coupling must be considered relative to the
corresponding SM result. Therefore, in Figs.~\ref{figptl}--\ref{figcthstar}
the differential cross sections of (\ref{ppbbudmn}) calculated with
different choices of the tensor form factors of Lagrangian (\ref{lagr})
and the vector form factors set to their SM values, i.e.
$f_{1}^{L}=\bar{f}_{1}^{L}=1$ and $f_{1}^{R}=\bar{f}_{1}^{R}=0$, are each time
plotted together with the corresponding SM cross section.
The actual values of the tensor form factors used are always specified in a
plot.
The absolute size of the cross sections should be treated with great care,
as it to large degree depends on the choice of PDFs
or factorization scale. To diminish the dependence on the latter higher order
QCD corrections should be taken into account. It should be also realized that
the form factors get contributions from the EW loop corrections
that, however, should be much smaller than the value of 0.2 used in the plots.
The relative size of the modification is on the other hand independent of
the choice of PDFs which has been checked explicitly by repeating the
calculations with MSTW PDFs \cite{MSTW}.
Figs.~\ref{figptl}--\ref{figcthstar} show the results for a few distributions
of the final state $\mu^-$
of reaction (\ref{ppbbudmn}) at two different $pp$ collision energies
of 8~TeV and 14~TeV. In each of the figures, the SM cross
section is plotted with grey boxes and the cross sections
in the presence of different CP-even (two upper rows)
and CP-odd (two lower rows) choices of the tensor form factors of
Lagrangian (\ref{lagr}) are plotted with solid lines.
The transverse momentum and rapidity distributions of the
$\mu^-$ are shown in Figs.~\ref{figptl} and \ref{figrapl}.
The distributions in $\cos\theta_{l{\rm b}}$, where $\theta_{l{\rm b}}$
is the angle between the momentum of $\mu^-$ in the $pp$ centre of mass frame
and the beam, are plotted in Fig.~\ref{figctlb}.
Finally, the distributions in $\cos\theta^*$, where $\theta^*$ is
the angle between the momentum of $\mu^-$ and the reversed momentum
of the $b$-quark, both boosted to the rest frame of the $W$-boson,
are plotted in Fig.~\ref{figcthstar}.
Distributions in $\cos\theta^*$ are usually used in order to determine
the helicity fractions of the $W$-boson produced in top quark decays, see,
e.g., \cite{wtbATLAS}, \cite{wtbCMS}.
Changes in the distributions are rather moderate, at most of the order of
several per cent, both for the CP-even and CP-odd combinations
of the tensor form factors.
This observation can be regarded as another example of
the decoupling theorem of \cite{GHR} that was originally
proven in the NWA, but now seems to work also for
the off shell top quark pair production and decay in proton-proton collisions
at the LHC energies.
Although all the cross sections increase by about a factor 4
if the energy of $pp$ collisions is increased from
$\sqrt{s}=8$~TeV to $\sqrt{s}=14$~TeV, the relative changes caused
by the tensor form factors are fairly independent of the $pp$ collision energy,
as can be seen by comparing plots on the left- and right-hand sides of
Figs.~\ref{figptl}--\ref{figcthstar}.
Let us note that shapes of the distributions remain practically
unchanged by the non zero form factors, both in the CP-even
and CP-odd case, except for the distribution in $\cos\theta^*$ of
Fig.~\ref{figcthstar}.
The distributions of $\mu^-$ of reaction (\ref{ppbbudmn}) at $\sqrt{s}=14$~TeV
in the same variables as in Figs.~\ref{figptl}--\ref{figcthstar}
computed with the full set of leading order
Feynman diagrams, plotted with the shaded boxes, and with
the $t\bar t$ production signal diagrams, plotted with the dashed
lines, are compared in Fig.~\ref{figsva}.
The comparison demonstrates very
little effect of the off resonance background contributions
in the presence of acceptance cuts (\ref{cuts}).
The results for other combinations of the tensor form factors, which are
not shown, look very similarly.
\begin{figure}[htb]
\vspace{100pt}
\begin{center}
\setlength{\unitlength}{1mm}
\begin{picture}(35,35)(0,0)
\special{psfile=ptl8.2002.ps angle=0 hscale=50 vscale=45
hoffset=-60 voffset=-100}
\end{picture}
\hfill
\begin{picture}(35,35)(0,0)
\special{psfile=ptl14.2002.ps angle=0
hscale=50 vscale=45 hoffset=-130 voffset=-100}
\end{picture}\\[1.cm]
\begin{picture}(35,35)(0,0)
\special{psfile=ptl8.0220.ps angle=0 hscale=50 vscale=45
hoffset=-60 voffset=-100}
\end{picture}
\hfill
\begin{picture}(35,35)(0,0)
\special{psfile=ptl14.0220.ps angle=0 hscale=50 vscale=45
hoffset=-130 voffset=-100}
\end{picture}\\[1.cm]
\begin{picture}(35,35)(0,0)
\special{psfile=ptl8.2000.ps angle=0 hscale=50 vscale=45
hoffset=-60 voffset=-100}
\end{picture}
\hfill
\begin{picture}(35,35)(0,0)
\special{psfile=ptl14.2000.ps angle=0
hscale=50 vscale=45 hoffset=-130 voffset=-100}
\end{picture}\\[1.cm]
\begin{picture}(35,35)(0,0)
\special{psfile=ptl8.0002.ps angle=0 hscale=50 vscale=45
hoffset=-60 voffset=-100}
\end{picture}
\hfill
\begin{picture}(35,35)(0,0)
\special{psfile=ptl14.0002.ps angle=0 hscale=50 vscale=45
hoffset=-130 voffset=-100}
\end{picture}
\end{center}
\vspace*{-2.cm}
\caption{Distributions in $p_T$ of the final state $\mu^-$ of reaction
(\ref{ppbbudmn}) in $pp$ collisions at $\sqrt{s}=8$~TeV (left) and
$\sqrt{s}=14$~TeV
(right) for CP-even (two upper rows) and CP-odd (two lower rows)
choices of the tensor form factors of (\ref{lagr}).
}
\label{figptl}
\end{figure}
\begin{figure}[htb]
\vspace{100pt}
\begin{center}
\setlength{\unitlength}{1mm}
\begin{picture}(35,35)(0,0)
\special{psfile=rapl8.2002.ps angle=0 hscale=50 vscale=45
hoffset=-60 voffset=-100}
\end{picture}
\hfill
\begin{picture}(35,35)(0,0)
\special{psfile=rapl14.2002.ps angle=0
hscale=50 vscale=45 hoffset=-130 voffset=-100}
\end{picture}\\[1.cm]
\begin{picture}(35,35)(0,0)
\special{psfile=rapl8.0220.ps angle=0 hscale=50 vscale=45
hoffset=-60 voffset=-100}
\end{picture}
\hfill
\begin{picture}(35,35)(0,0)
\special{psfile=rapl14.0220.ps angle=0 hscale=50 vscale=45
hoffset=-130 voffset=-100}
\end{picture}\\[1.cm]
\begin{picture}(35,35)(0,0)
\special{psfile=rapl8.2000.ps angle=0 hscale=50 vscale=45
hoffset=-60 voffset=-100}
\end{picture}
\hfill
\begin{picture}(35,35)(0,0)
\special{psfile=rapl14.2000.ps angle=0
hscale=50 vscale=45 hoffset=-130 voffset=-100}
\end{picture}\\[1.cm]
\begin{picture}(35,35)(0,0)
\special{psfile=rapl8.0002.ps angle=0 hscale=50 vscale=45
hoffset=-60 voffset=-100}
\end{picture}
\hfill
\begin{picture}(35,35)(0,0)
\special{psfile=rapl14.0002.ps angle=0 hscale=50 vscale=45
hoffset=-130 voffset=-100}
\end{picture}
\end{center}
\vspace*{-2.cm}
\caption{Distributions in rapidity of the final state $\mu^-$ of reaction
(\ref{ppbbudmn}) in $pp$ collisions at $\sqrt{s}=8$~TeV (left) and
$\sqrt{s}=14$~TeV
(right) for CP-even (two upper rows) and CP-odd (two lower rows)
choices of the tensor form factors of (\ref{lagr}).}
\label{figrapl}
\end{figure}
\begin{figure}[htb]
\vspace{100pt}
\begin{center}
\setlength{\unitlength}{1mm}
\begin{picture}(35,35)(0,0)
\special{psfile=ctlb8.2002.ps angle=0 hscale=50 vscale=45
hoffset=-60 voffset=-100}
\end{picture}
\hfill
\begin{picture}(35,35)(0,0)
\special{psfile=ctlb14.2002.ps angle=0
hscale=50 vscale=45 hoffset=-130 voffset=-100}
\end{picture}\\[1.cm]
\begin{picture}(35,35)(0,0)
\special{psfile=ctlb8.0220.ps angle=0 hscale=50 vscale=45
hoffset=-60 voffset=-100}
\end{picture}
\hfill
\begin{picture}(35,35)(0,0)
\special{psfile=ctlb14.0220.ps angle=0 hscale=50 vscale=45
hoffset=-130 voffset=-100}
\end{picture}\\[1.cm]
\begin{picture}(35,35)(0,0)
\special{psfile=ctlb8.2000.ps angle=0 hscale=50 vscale=45
hoffset=-60 voffset=-100}
\end{picture}
\hfill
\begin{picture}(35,35)(0,0)
\special{psfile=ctlb14.2000.ps angle=0
hscale=50 vscale=45 hoffset=-130 voffset=-100}
\end{picture}\\[1.cm]
\begin{picture}(35,35)(0,0)
\special{psfile=ctlb8.0002.ps angle=0 hscale=50 vscale=45
hoffset=-60 voffset=-100}
\end{picture}
\hfill
\begin{picture}(35,35)(0,0)
\special{psfile=ctlb14.0002.ps angle=0 hscale=50 vscale=45
hoffset=-130 voffset=-100}
\end{picture}
\end{center}
\vspace*{-2.cm}
\caption{Distributions in $\cos\theta_{l{\rm b}}$, with $\theta_{l{\rm b}}$ being
an angle between the momenta of the final state $\mu^-$ of reaction
(\ref{ppbbudmn}) and the beam,
in $pp$ collisions at $\sqrt{s}=8$~TeV (left) and $\sqrt{s}=14$~TeV
(right) for CP-even (two upper rows) and CP-odd (two lower rows)
choices of the tensor form factors of (\ref{lagr}).}
\label{figctlb}
\end{figure}
\begin{figure}[htb]
\vspace{100pt}
\begin{center}
\setlength{\unitlength}{1mm}
\begin{picture}(35,35)(0,0)
\special{psfile=cthstar8.2002.ps angle=0 hscale=50 vscale=45
hoffset=-60 voffset=-100}
\end{picture}
\hfill
\begin{picture}(35,35)(0,0)
\special{psfile=cthstar14.2002.ps angle=0
hscale=50 vscale=45 hoffset=-130 voffset=-100}
\end{picture}\\[1.cm]
\begin{picture}(35,35)(0,0)
\special{psfile=cthstar8.0220.ps angle=0 hscale=50 vscale=45
hoffset=-60 voffset=-100}
\end{picture}
\hfill
\begin{picture}(35,35)(0,0)
\special{psfile=cthstar14.0220.ps angle=0 hscale=50 vscale=45
hoffset=-130 voffset=-100}
\end{picture}\\[1.cm]
\begin{picture}(35,35)(0,0)
\special{psfile=cthstar8.2000.ps angle=0 hscale=50 vscale=45
hoffset=-60 voffset=-100}
\end{picture}
\hfill
\begin{picture}(35,35)(0,0)
\special{psfile=cthstar14.2000.ps angle=0
hscale=50 vscale=45 hoffset=-130 voffset=-100}
\end{picture}\\[1.cm]
\begin{picture}(35,35)(0,0)
\special{psfile=cthstar8.0002.ps angle=0 hscale=50 vscale=45
hoffset=-60 voffset=-100}
\end{picture}
\hfill
\begin{picture}(35,35)(0,0)
\special{psfile=cthstar14.0002.ps angle=0 hscale=50 vscale=45
hoffset=-130 voffset=-100}
\end{picture}
\end{center}
\vspace*{-2.cm}
\caption{Distributions in $\cos\theta^*$, where $\theta^*$ is an
angle between the momentum of $\mu^-$ and the reversed momentum of
$\bar b$-quark of (\ref{ppbbudmn}), both boosted to the $W$-boson rest frame,
in $pp$ collisions at $\sqrt{s}=8$~TeV (left) and $\sqrt{s}=14$~TeV
(right) for CP-even (two upper rows) and CP-odd (two lower rows)
choices of the tensor form factors of (\ref{lagr}).}
\label{figcthstar}
\end{figure}
\begin{figure}[htb]
\vspace{100pt}
\begin{center}
\setlength{\unitlength}{1mm}
\begin{picture}(35,35)(0,0)
\special{psfile=ptl14.sva.sm.ps angle=0 hscale=50 vscale=45
hoffset=-60 voffset=-100}
\end{picture}
\hfill
\begin{picture}(35,35)(0,0)
\special{psfile=ptl14.sva.2002.ps angle=0
hscale=50 vscale=45 hoffset=-130 voffset=-100}
\end{picture}\\[1.cm]
\begin{picture}(35,35)(0,0)
\special{psfile=rapl14.sva.sm.ps angle=0 hscale=50 vscale=45
hoffset=-60 voffset=-100}
\end{picture}
\hfill
\begin{picture}(35,35)(0,0)
\special{psfile=rapl14.sva.2002.ps angle=0 hscale=50 vscale=45
hoffset=-130 voffset=-100}
\end{picture}\\[1.cm]
\begin{picture}(35,35)(0,0)
\special{psfile=ctlb14.sva.sm.ps angle=0 hscale=50 vscale=45
hoffset=-60 voffset=-100}
\end{picture}
\hfill
\begin{picture}(35,35)(0,0)
\special{psfile=ctlb14.sva.2002.ps angle=0
hscale=50 vscale=45 hoffset=-130 voffset=-100}
\end{picture}\\[1.cm]
\begin{picture}(35,35)(0,0)
\special{psfile=cthstar14.sva.sm.ps angle=0 hscale=50 vscale=45
hoffset=-60 voffset=-100}
\end{picture}
\hfill
\begin{picture}(35,35)(0,0)
\special{psfile=cthstar14.sva.2002.ps angle=0 hscale=50 vscale=45
hoffset=-130 voffset=-100}
\end{picture}
\end{center}
\vspace*{-2.cm}
\caption{Distributions of $\mu^-$ of (\ref{ppbbudmn}) at $\sqrt{s}=14$~TeV
in the same variables as in Figs.~\ref{figptl}--\ref{figcthstar}.
The distributions computed with the full set of leading order
Feynman diagrams are plotted with the shaded boxes and those computed with
the $t\bar t$ production signal diagrams only are plotted with the dashed
lines.}
\label{figsva}
\end{figure}
\section{Summary}
A new version of {\tt carlomat} \cite{carlomat2}, a general purpose program
for the MC computation of lowest order cross sections,
has been used to compute the transverse momentum, rapidity and
two angular distributions of the final state $\mu^-$ of reaction
(\ref{ppbbudmn}) in the presence
of the anomalous $Wtb$ coupling with operators of dimension up to
five. The considered CP-even and CP-odd combinations of the tensor
form factors have
rather small effect on the distributions which actually could be expected, as
the top quarks are produced unpolarized.
At the same time, the shapes of the presented distributions remain practically
unchanged, except for the distribution
in $\cos\theta^*$, where $\theta^*$ is the angle between the momentum
of $\mu^-$ and the reversed momentum of the $b$-quark, both
boosted to the rest frame of $W$-boson. It is just the change in shape
of the $\cos\theta^*$ distribution that potentially gives the best prospects
for improving limits on the tensor form factors in future measurements
at the LHC.
It has been also shown that the off resonance background contributions
have rather little impact on the distributions independently of
whether the anomalous tensor form factors are present or not.
{\bf Acknowledgements:}
This project was supported in part with financial resources
of the Polish National Science Centre (NCN) under grant decision
number DEC-2011/03/B/ST6/01615 and by the Research Executive
Agency (REA) of the European Union under the Grant Agreement number
PITN-GA-2010-264564 (LHCPhenoNet).
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 6,358
|
Q: Class not found Laravel5 Class Book was not found. I have read the documentation that everything should work with namespaces , i have tried many different combinations but nothing works. help pls.
this is my code from routes.php
Route::get('/', function ()
{
$book= new Book;
$book->write='Mark Twain';
$book->title='the adventures of ton saywer';
$book->description='A nover about a young boy';
$book->published=date('y-m-d');
$book->save();
return $book->id;
return View::make('hello');
});
and this is my code from Book.php
<?php
namespace App;
use Illuminate\Database\Eloquent\Model;
class Book extends Model
{
//
}
A: Try this code for creating new Book object
$book= new App\Book;
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 518
|
Muscles dorsiflexing the ankle
Peroneus tertius
Tibialis anterior is a long fusiform muscle situated on the front of the leg lateral to the anterior border of the tibia. It is covered by strong fascia and gains its upper attachment from the deep surface of this fascia, the upper two-thirds of the lateral surface of the tibia and the adjoining part of the interosseus membrane. The muscle becomes tendinous in its lower third, passing downwards and medially over the distal end of the tibia. The tendon continues through both the superior and inferior extensor retinaculae to insert into the medial side of the medial cuneiform and base of the first metatarsal, the insertion reaching the under surface of both bones to blend with that of peroneus longus.
Nerve supply
This muscle is supplied by the deep peroneal nerve, root value L4, 5. The skin covering the muscle is also supplied by roots L4, 5.
Tibialis anterior is a dorsiflexor of the foot at the ankle joint. When working with tibialis posterior it acts as an invertor of the foot, in which the sole of the foot is turned to face medially.
Functional activity
As with other muscles in the leg, tibialis anterior is concerned with balancing the body on the foot. It works with the surrounding muscles to maintain body balance during activities of the upper part of the body which change the distribution of weight.
Not only is tibialis anterior responsible for dorsiflexing the foot as the lower limb is carried forward during the swing-through phase of walking, so preventing the toes catching the ground, it also controls the placement of the foot on the ground following initial ground contact by the heel. On close observation, especially in slow motion, it will be seen that the heel does not strike the ground and remain immobile at the initiation of the stance phase, but glides on to the surface and acts as the first braking force of the lower limb's forward movement. Overactivity of tibialis anterior accounts for the wear patterns seen on the posterolateral aspect of the heel, due to the frictional forces between the shoe and the ground. The rest of the foot is then gradually lowered to the ground in a controlled manner taking up the undulations of the surface concerned. The landing of the foot on the ground is similar to the landing of an aeroplane; the main wheels touch down first applying the initial braking force followed by a controlled lowering of the front of the craft as the speed decreases.
Tibialis anterior in association with the other dorsiflexors, therefore, plays an important part in the lowering of the forefoot to the ground in walking or running and will be put under stress in extended activity particularly over rough terrain. The anterior calf muscles are enclosed in particularly tight fascia which allows very little expansion of the tissues. The result is a compression of the muscle during activity and a dragging on the attachments of the surrounding fascia, particularly where it attaches to the bone. This leads to a painful condition of this area commonly called "shin splints".
Paralysis of tibialis anterior causes footdrop because the remaining dorsiflexors are not strong enough to raise the toes and so prevent them dragging along the ground. The patient may overcome this by flexing the knee more than normal during walking or by fitting a "toe-raise" orthosis to patients or their shoe.
Both the muscle belly and tendon can be seen and felt when the foot is dorsiflexed against resistance, the tendon being the most medial at the ankle joint.
Extensor digitorum longus is again situated on the anterior aspect of the leg, being lateral to tibialis anterior, and overlying extensor hallucis longus. It has a linear origin from the upper-two thirds of the anterior surface of the fibula, the deep fascia and the upper part of the interosseus membrane with its upper fibres reaching across the lateral condyle of the tibia in conjunction with those of peroneus longus. It is a pennate muscle with the tendon appearing on the medial side; the muscle fibres pass downwards and medially to reach it. The tendon passes over the front of the ankle joint deep to the superior extensor retinaculum and then through the loop of inferior extensor retinaculum accompanied by peroneus tertius. At the level of the inferior extensor retinaculum or immediately distal, it gives rise to four tendons which run to the lateral four toes. The four separate tendons are enclosed in a common synovial sheath at the level of the inferior extensor retinaculum. On the dorsal surface of the proximal phalanx, each tendon forms a triangular membranous expansion, known as the extensor hood (dorsal digital expansion). Each hood is joined on its medial side by the tendon of the lumbrical and on the lateral side for the second to fourth toes by the tendon of extensor digitorum brevis. The interossei of the foot do not have an attachment to the extensor hood.
As the hood passes forwards over the proximal phalanx it divides into three parts before reaching the dorsum of the proximal interphalangeal joint. The central portion attaches to the base of the middle phalanx, while the two outer portions unite before inserting on to the base of the distal phalanx. An attachment of the extensor hood to the dorsal aspect of the proximal phalanx has also been described.
This muscle is supplied by the deep peroneal nerve, root value L5, S1. The skin covering the muscle is supplied by root L5.
As its name implies, extensor digitorum longs is an extensor of the lateral four toes at the metatarsophalangeal joints, and also assists in extension at the interphalangeal joints. However it is unable to perform the latter action unaided, which is primarily performed by the lumbricals. If the lumbricals are paralysed, extensor digitorum longus produces hyperextension of the metatarsophalangeal joint, while the interphalangeal joints become flexed. As the muscle passes across the front of the ankle joint, it also aids in dorsiflexion of the foot.
During walking and running extensor digitorum longus draws the toes upwards after they have been flexed prior to toe-off, and keeps them clear of the ground until the heel and foot make contact with the ground again. Unfortunately, the lateral four toes in most individuals tend to be flexed at the proximal interphalangeal joint and extended at the distal interphalangeal joint. Consequently extensor digitorum longus will lift the toes in this adapted position.
The muscle belly is easily palpated on the anterolateral aspect of the leg. From the head of the fibula on the lateral side of the leg, just below the knee joint, run the fingers downwards and medially for about 2cm. When raising the toes off the floor, the muscle can be felt contracting. Now place the fingers over the front of the ankle joint; the tendon can be identified standing out clearly, being lateral to those of tibialis anterior and extensor hallucis longus. From here the tendon can now either be traced upwards, under the superior part of the extensor retinaculum to join the muscle belly, or downwards where it breaks up into four individual tendons running towards each of the lateral four toes. Each tendon stands clear of the metatarsophalangeal joint as it passes towards the dorsum of the toe.
Extensor hallucis longus is situated deep to and between tibialis anterior and extensor digitorum longus on the front of the leg. Arising from the middle half of the anterior surface of the fibula and the adjacent interosseus membrane, the muscle fibres pass downwards and medially to the tendon which forms on its anterior surface. In this respect it is a unipennate muscle. The tendon passes under the superior extensor retinaculum, through the upper part of the inferior extensor retinaculum in a separate compartment enclosed in its own synovial sheath, and then deep to the lower band of the inferior extensor retinaculum on its way towards the base of the great toe. Generally, the tendon does not form a fully developed extensor hood but passes to attach to the base of the distal phalanx on its dorsal surface. Tendinous slips may be given off to the dorsal aspect of the base of the proximal phalanx and the first metatarsal.
Extensor hallucis longus is supplied by the deep peroneal nerve, root value L5, S1. The skin covering this area is supplied by roots L4, 5.
As its name implies, extensor hallucis longus will extend all of the joints of the great toe, but mainly the metatarsophalangeal joint. It is also a powerful dorsiflexor of the foot at the ankle joint.
In running, the great toe is the last part of the foot to leave the ground and therefore the final thrust will come from the long flexors of the toes. After this, the toe must be brought back into the extended position at the same time as the foot is dorsiflexed and slightly inverted, ready for the heel to be placed on the ground for the next weightbearing phase. By extending the great toe and dorsiflexing the foot, clearance of the surface is also achieved. It should be noted that the great toe does not have a lumbrical muscle or interossei associated with it. Consequently, extension of the interphalangeal joint depends entirely on extensor hallucis longus. Paralysis of the muscle will result in flexion of the joint and buckling of the toe during the last phase of gait, due to the unopposed action of the flexor muscles.
If the great toe is extended, the tendon of the muscle is clearly visible as it crosses the first metatarsophalangeal joint to its insertion into the base of the distal phalanx. Trace the fingers up the tendon; it can be felt and seen crossing the anterior aspect of the ankle joint lateral to the tendon of tibialis anterior. From here the tendon can be felt passing upwards and laterally before passing deep to the surrounding muscles. Continue to move the fingers upwards for another 12cm and allow them pass a little laterally; when the great toe is rhythmically extended and flexed, the muscle can just be felt contracting under the fingers.
Peroneus tertius is situated on the lower lateral aspect of the leg and appears to have been part of extensor digitorum longus. It arises from the front of the lower quarter of the fibula in continuation with the attachment of extensor digitorum longus (with no gap between them), and from the intermuscular septum and adjoining fascia. Its fibres pass downwards and laterally into a tendon which passes deep to the superior and through the inferior extensor retinacula to insert into the medial and dorsal aspect of the base of the fifth metatarsal.
Peroneus tertius is supplied by the deep peroneal nerve, root value L5, S1. The area of skin covering the muscle is also supplied by roots L5, S1.
The muscle acts as a weak evertor and dorsiflexor of the foot at the ankle joint.
It is difficult to assess the importance of this small muscle as its actions appear to be covered by other muscles which have a much better mechanical leverage. Indeed in some subjects it is absent. It does, however, pass over the anterior talofibular ligament of the ankle joint, and it is well-known that this is very often damaged in inversion injuries. It is therefore well placed to help prevent too much inversion during sports activities, for example, and may be responsible for keeping down the number of injuries. Unfortunately, the muscle is often torn and may be completely ruptured during violent inversion, which is the cause of considerable pain and swelling. It is possible that with the attainment of bidepalism, peroneus tertius is assuming a more important role because eversion of the foot is a peculiarly human characteristic.
Peroneus tertius is very difficult to palpate. However, it can be felt by drawing the fingers downwards from the anterior part of the lateral malleolus into the small hollow found there. The tendon can be felt crossing the lateral part of the hollow to its insertion into the medial side of the base of the fifth metatarsal. Take care not to confuse the tendon of peroneus tertius with that of peroneus brevis, which lies lateral to this point as it passes forwards to insert into the tubercle on the lateral side of the fifth metatarsal.
Unknown је рекао...
Nice post.Jhansi Orthopaedic Hospital is renowed name for its best fracture healing hospital in Jhansi at affordable price.For any query visit website.
13.2.16. 12:50
Top 10 Own Goals HD
Top 10 header goals!
Muscles inverting the foot
Muscles plantarflexing the ankle joint
The worst ever own goal in football history!!!
Muscles medially rotating the tibia at the knee joint
Muscles laterally rotating the tibia at the knee j...
Football Funny Moments - Of All Time!
Muscles extending the knee joint
Muscles flexing the knee joint
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 761
|
Altmann, Peter
Sustained innovativeness and human resource management2011Ingår i: Research on Technology, Innovation and Marketing Management 2009-2011: Introducing the Research Area of Innovation Science / [ed] Sven-Åke Hörte, Halmstad: Högskolan i Halmstad , 2011, s. 21-35Kapitel i bok, del av antologi (Övrigt vetenskapligt)
Innovation is paramount to success. Over time firms must maintain their ability to innovate in order to maintain their competitive edge. In this paper we explore the role human resource management has in nurturing and enhancing the innovative capability of the firm. To explore HRM activities, functions and processes that enhance or impede innovativeness we conducted a literature review. Following this review, 10 propositions have been made that link HRM to both incremental and radical innovativeness respectively. Our results include suggestions for empirical studies to validate our propositions as well as some managerial implications.
Andersson, Svante
Differences in managerial behavior between small international and non-international firms2011Ingår i: Journal of International Entrepreneurship, ISSN 1570-7385, E-ISSN 1573-7349, Vol. 9, nr 3, s. 233-258Artikel i tidskrift (Refereegranskat)
The main question raised in this article is whether there are any differences between the work activities of managers in small firms primarily operating on an international market and those managing firms doing business on a domestic market. If so, what are these differences, and what do they tell us about the internationalization of small firms? The comparative method used here is based on multiple approaches including interviews, diary studies, and direct observations. The conclusions indicate that managers in small international firms are more proactive in their networking behavior, delegate operative activities and devote more time to planned strategic activities connected with their international expansion than managers in other small firms.
Exploring differences in the work of owner-managers in small international and non-international firms2009Konferensbidrag (Refereegranskat)
The main question raised in this article is whether there are any differences between the work activities of managers in small firms primarily operating on an international market and those managing firms doing business on a domestic market. If so, what are these differences, and what do they tell us about the internationalization of small firms? The comparative method used here is based on direct observation and analysis of about 2400 activities. The conclusions indicate that managers in small international firms are more proactive, delegate operative activities and devote more time to planned strategic activities connected with their international expansion than managers in other small firms.
Exploring managerial behavior in small international firms2008Ingår i: Journal of Small Business and Enterprise Development, ISSN 1462-6004, E-ISSN 1758-7840, Vol. 15, nr 1, s. 31-50Artikel i tidskrift (Refereegranskat)
Purpose: The purpose of this paper is to discuss the research on internationalization in small firms and research on managerial behavior, and it aims to develop new research questions that can enhance the understanding of the interface between these two areas.
Design/methodology/approach: A literature review of internationalization of small firms is carried out. It is concluded that understanding of managerial behavior in small international firms is in need of improvement. Therefore, the literature on managerial behavior is described, scrutinized and deployed in the context of small firms' internationalization.
Findings: No previous research has combined the research on small-business internationalization and managerial behavior. Hypotheses that can be empirically tested and new research questions that can yield a better understanding of the internationalization processes in small firms are developed.
Research limitations/implications: The hypotheses developed in this study have not yet been tested empirically. Further research is suggested to confirm and elaborate these propositions.
Practical implications: As the propositions in this study are not tested their practical implications are limited at present. However, earlier research has shown that there is a link between managerial behavior and firm behavior. Managers may be inspired by the study to reflect upon this link and adjust their behavior in ways that can improve their firms' international development.
Originality/value: In this paper the research on internationalization in small firms is merged with the research on managerial behavior. By adding knowledge from the latter research tradition, the understanding of small-firm internationalization should be advanced through raising novel issues and applying new methodological tools.
What do managers in small international firms really do?2006Ingår i: McGill Conference on International Entrepreneurship, 2006Konferensbidrag (Refereegranskat)
Managerial behavior and small firm's internationalization2005Ingår i: McGill Conference on international entrepreneurship, 2005Konferensbidrag (Refereegranskat)
Brundin, Ethel
Jönköping International Business School.
The behavioral complexity of small firm entrepreneurs and the relation to firm performance: A framework2007Ingår i: Proceedings of the 4th International AGSE Entrepreneurship Research Exchange / [ed] L. Murray Gillin, 2007Konferensbidrag (Övrigt vetenskapligt)
Collaborative approaches to management learning in small firms2003Ingår i: Journal of Workplace Learning, ISSN 1366-5626, E-ISSN 1758-7859, Vol. 15, nr 5, s. 203-216Artikel i tidskrift (Refereegranskat)
The purpose of this paper is to describe how learning in collaborative approaches – in this paper labeled "collaborative approaches to management learning" (CAML) – can support the learning situation of small firm owner-managers. Drawing on a socio-cognitive learning framework, the context of the small firm and its consequences for management learning are framed and discussed. Drawing on four episodes of management learning in CAML, it is suggested that CAML establishes a new context in which old truths can be questioned and new insights can be created. In CAML the owner-managers are offered a position on the periphery of practice of the other managers and other network visitors, where trust among the network participants provides the foundation for admitting and openly facing lack of knowledge on different issues, something that is prohibited within their enterprises, due to the lack of peers and expected omniscience of the owner-manager.
Managerial work and learning in small firms2005Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
This thesis deals with how managerial work sets the agenda for managerial learning in small firms. Although studies of learning in organizations are numerous, research on managerial learning in the small-firm context is limited. In particular, our knowledge of managerial learning suffers from an insufficient understanding of what top managers in small firms do. The primary purpose of this thesis is to describe how the work of small-firm managers sets the agenda for managerial learning, and how their learning can be supported. Additionally, the thesis explores the use of so-called "Action Technologies" in supporting managerial learning in small firms.Drawing on an observational study of six owner-managers in small (17-43 employees) manufacturing firms, and a synthesis of earlier studies, this thesis shows that three features of managerial work shape managerial learning in small firms: The small firm's top manager (i) operates in context with specific structural conditions that affect his/her behavior, (ii) have certain cognitive predispositions guiding his/her behavior, and (iii) have certain behavioral preferences directing his/her behavior.The main argument in this thesis is that managerial learning in small firms is made difficult due to features that make it hard to come to a point where learning (in terms of reflection and conceptualization) is given time and resources, as the manager has trouble in finding time for learning, and as learning risks to become low-priority. Learning is also difficult due to barriers related to the learning process: the work of the manager fosters a superficial learning orientation, makes it difficult to probe deeply into and to develop complicated understandings of issues at hand, and makes peer-learning rarely possible.Drawing on an action research project of managerial learning in four networks of small-firm owner-managers, the thesis also explores, in a concrete manner, how managerial learning might be supported in a way that circumvents the deficient situation for managerial learning in this kind of firm. More specifically, it seems that Action Technologies by their design constitute a learning context that supports the learning of the small-firm top manager by dissolving the barriers to learning identified above.
Managerial work in small firms: summarising what we know and sketching a research agenda2006Ingår i: International Journal of Entrepreneurial Behaviour & Research, ISSN 1355-2554, E-ISSN 1758-6534, Vol. 12, nr 5, s. 272-288Artikel i tidskrift (Refereegranskat)
Purpose: The purpose of this article is to describe the basic characteristics and qualities of managerial work in small firms.
Design/methodology/approach: The article draws on a summary and synthesis of five studies from the "managerial-work research tradition" that investigates the behaviour of top managers in small firms by means of direct observation. Studies are evaluated by using research on managers' jobs in general, and some needs as well as guidelines for future research on entrepreneurial and managerial work in small firms are suggested.
Findings: Managerial work in small firms is described by discussing: how managers divide their time between different activities; managerial interaction and communication, and the elements of managerial work in small firms. Three limitations of existing studies are identified: they are difficult to compare; they adopt a simplistic conception of the constituents of managers' jobs, and more specifically of the relation between the managing actor and the context in which he/she works; and they fail to recognise to the value of inductive analysis.
Research limitations/implications: Future studies of managerial work in small firms have much to gain by considering the development that has been taking place within general management theory and in the study of managers' jobs. This article contributes a first step towards bringing research on managers' jobs into the small-business research community.
Originality/value: The paper initiates a better understanding of the basics of managerial work in small firms, which has not previously been elaborated upon and is an important step in exploring the dynamics of small business management.
Organising small-firm growth2011Ingår i: Research on Technology, Innovation and Marketing Management 2009‐2011: Introducing the Research Area of Innovation Science / [ed] Sven-Åke Hörte, Halmstad: Högskolan i Halmstad , 2011, s. 117-133Kapitel i bok, del av antologi (Övrigt vetenskapligt)
This paper summarises the results some major undertakings to explain small‐firm growth. This is achieved through an in‐depth reading of three Swedish doctoral theses written by Tomas Brytting (1991), Frederic Delmar (1996) and Johan Wiklund (1998), and a number ofrecently published articles that have addressed this issue. The purpose of this paper is todescribe what we know about "organising for small‐firm growth" on a firm level. The main result of the paper is a description of what is known about organising for small‐firm growth in accordance with four dimensions: i) the strategy of the growing firm, ii) the entrepreneur/manager in the growing firm, iii) the resources and the capabilities of the growing firm and iv) the consequences of small‐firm growth, i.e. what organisational growth brings to a small firm. The paper also includes a discussion of the limitations of the reviewed research and suggestions for future research.
Agostini, Alessandro
Einsights Pte. Ltd., Singapore, Singapore.
The Business Model Innovation Map: A Framework for Analyzing Business Model Innovation2015Ingår i: IAMOT 2015: 24th International Association For Management Of Technology Conference Proceedings: Technology, Innovation and Management for Sustainable Growth / [ed] Leon Pretorius & George Alex Thopil, Hatfield: University of Pretoria & Media Chef CC , 2015, s. 2192-2207Konferensbidrag (Refereegranskat)
Business model innovation has received substantial attention by both practitioners and researchers during the last fifteen years. While many companies have good processes and a shared sense of how to innovate technology, they are less capable when it comes to how they should innovate business models. This lack of practical skills is mirrored by the shortage of scholarly understanding, in which business model innovation as a phenomenon is poorly explained in comparison to e.g. product or process innovations.
Although previous research has contributed greatly to the advancements of business model innovation, our conceptual understanding of business model innovation is still rather confused. Behind this study, lies two related assumptions; (i) not all business model innovations are the same, and, (ii) different types of business model innovation will challenge firms in different ways. To this background, the purpose of this study is to develop a framework that will allow for a conceptual differentiation between different types of business model innovation.
The paper draws on previous studies in the field of technology and innovation management and develops a framework – "The Business Model Innovation Map" – that distinguishes between different types of business model innovation according to their degree of novelty. The framework is illustrated by several real-life examples of business model innovation.
The paper adds to our understanding of innovation management as it allows for a better understanding of business model innovation as a distinct type of innovation. More specifically, it helps differentiating transformative business model innovations from mere incremental ones, and, as such, it presents a novel approach to categorize different types of business model innovation. The framework can serve as a basis for future in-depth empirical investigations of different types of business model innovation that can help firms to better understand how to manage such innovations. Copyright © 2015 by Halmstad University and Einsights Pte. Ltd.
Frishammar, Johan
Luleå University of Technology, Luleå, Sweden.
From Preliminary Ideas to Corroborated Product Definitions: Managing the Front End of New Product Development2012Ingår i: California Management Review, ISSN 0008-1256, E-ISSN 2162-8564, Vol. 54, nr 4, s. 20-43Artikel i tidskrift (Refereegranskat)
Front-end activities largely influence the outcomes of new product development processes, because it is here that firms create new ideas, give them direction, and set them in motion. We show that the front end can be understood as comprising three core activities: idea/concept development, idea/concept alignment, and idea/concept legitimization, which allow firms to create corroborated product definitions. The paper provides important implications for managers interested in front-end management, and devote specific attention to the differences between incremental and radical front end development and to the front end in the light of increasingly open innovation processes.
14. Florén, Henrik
Research Note: What is the 'fuzzy front end', why is it important, and how can it be managed?2013Ingår i: Managing Innovation: Integrating Technological, Market and Organisational Change / [ed] Joe Tidd & John Bessant, Chichester: John Wiley & Sons, 2013, 5, s. 418-420Kapitel i bok, del av antologi (Övrigt vetenskapligt)
Lee, Carmen
Ericsson, Magnus
Luleå tekniska universitet, Luleå, Sweden.
Gustafsson, Stefan
Höganäs AB, Höganäs, Sweden.
A framework for raw materials management in process industries2013Konferensbidrag (Refereegranskat)
Firms in the process industries manipulate materials properties to produce upgraded raw materials for applications and products upstream in a supply chain. About 25% of the most research intensive firms in the world belong to the process industries, so proper management of raw materials is a key concern for many firms. This article explores the concept of "raw materials management". By studying the current world leader in powder metallurgy, the Höganäs Corporation, the article describes the external and internal factors impacting how raw materials are managed, and how raw material issues affect different aspects of firm performance. Managerial implications are presented elaborating three key-areas that firms should deal with when developing a strategic approach to raw materials management.
Löf, Anton
RMG Consulting, Stockholm, Sweden.
Raw Materials Management in Iron and Steelmaking Firms2019Ingår i: Mineral Economics, ISSN 2191-2203, E-ISSN 2191-2211, Vol. 32, nr 1, s. 39-47Artikel i tidskrift (Refereegranskat)
This paper adds new knowledge on how raw materials should be managed in iron and steelmaking firms. While previous research has contributed significantly to how firms should deal with functional challenges related to raw materials, the understanding of Raw Materials Management from a holistic perspective is largely lacking, and extant research does not provide qualified advice to firms on this matter. This study provides such knowledge by drawing on insights from Höganäs AB, a world leader in ferrous powder metallurgy, and their efforts to identify key aspects and principles of raw materials management. Our elaboration of a more holistic view on raw materials management builds on two elements. First, we depict five external uncertainties and three internal conditions that impact firm-level raw materials management. Second, we present six critical capabilities that underpin proficient firm-level raw materials management. The paper concludes with a discussion of implications for both firms aiming to increase their raw materials proficiency and to future investigations into this important area. © The Author(s) 2018
Parida, Vinit
Wincent, Joakim
Luleå University of Technology, Luleå, Sweden & Hanken School of Economics, Helsinki, Finland.
Critical success factors in early new product development: a review and a conceptual model2018Ingår i: The International Entrepreneurship and Management Journal, ISSN 1554-7191, E-ISSN 1555-1938, Vol. 14, nr 2, s. 411-427Artikel i tidskrift (Refereegranskat)
The literature on the front end in the New Product Development (NPD) literature is fragmented with respect to the identification and analysis of the factors that are critical to successful product development. The article has a two-fold purpose. First, it describes, analyses, and synthesizes those factors through a literature review of the research on the front end in NPD. Second, it conceptualizes a framework that features two types of success factors: foundational success factors (common to all the firm's projects) and project-specific success factors (appropriate for the firm's individual projects). The article makes recommendations for the management of this important phase of product development, discusses limitations of relevant previous research, and offers suggestions for future research. The article makes a theoretical contribution with its analysis and synthesis of the reasons for success in front-end activities and a practical contribution with its conceptual framework that can be used as an analytical tool by firms and their product managers. © 2017 The Author(s)
Gabrielsson, Jonas
Survival through Business Model Innovation: A Longitudinal Case Study from the Process Industries2013Konferensbidrag (Refereegranskat)
Itis widely acknowledged that the design and quality of the business model is amain building block in what constitute a successful company. In this paper, weapproach the critical question of how firms can successfully renew theirbusiness models over time. The aim is to identify the main sequences of eventsthat precede business model innovation and which trigger evolutionary changesin how a firm develops and capture value. Theoretically, we approach businessmodel innovation as an evolutionary phenomenon by emphasizing the dynamic andpath dependent aspects of strategic change processes. Empirically, we employ ahistorical case study where we make an in-depth analysis of a firm in theprocess industry that has managed to innovate its business model several timessince its inception. In all, the study identifies five main sequences of eventsrelated to customer value proposition, strategic investments, corporateidentity, corporate structure, and value networks.
It is widely acknowledged that the design and quality of the business model is a main building block in what constitute a successful company. In this paper, we approach the critical question of how firms can successfully renew their business models over time. The aim is to identify the main sequences of events that precede business model innovation and which trigger evolutionary changes in how a firm develops and capture value. Theoretically, we approach business model innovation as an evolutionary phenomenon by emphasizing the dynamic and path dependent aspects of strategic change processes. Empirically, we employ a historical case study where we make an in-depth analysis of a firm in the process industry that has managed to innovate its business model several times since its inception. In all, the study identifies five main sequences of events related to customer value proposition, strategic investments, corporate identity, corporate structure, and value networks.
Hörte, Sven-Åke
Management av eco-innovationer2011Rapport (Övrigt vetenskapligt)
The Business Model and Supply Strategy: What is the Connection between them?2013Ingår i: Proceeding of 20th International Annual EurOMA Conference, Dublin, Ireland, 2013Konferensbidrag (Refereegranskat)
An assumption of this paper is that investments in business model development are only beneficial when firms understand how to deal with both customer and supplier interdependencies. We argue that an inadequate understanding of how to align supply strategy and business model design has hampered knowledge development within business model research.
We review the literatures on business models and supply strategy to identify the conceptual intersection between these interrelated areas. We synthesize the fields of supply strategy and business model research to provide to an improved understanding of firms should incorporate a supply perspective in business model design.
Högskolan i Halmstad, Akademin för ekonomi, teknik och naturvetenskap, Centrum för innovations-, entreprenörskaps- och lärandeforskning (CIEL). Halmstad Univ, Sch Business Engn & Sci, Halmstad, Sweden..
Fischer, Sebastian
Sanofi Aventis Deutschland GmbH, Frankfurt, Germany.
Entrepreneurial orientation and human resource management: effects from HRM practices2016Ingår i: Journal of Organizational Effectiveness, ISSN 2051-6614, E-ISSN 2051-6622, Vol. 3, nr 2, s. 164-180Artikel i tidskrift (Refereegranskat)
The purpose of this paper is to explore the relationship between HRM practices and entrepreneurial orientation (EO) in large established firms. More specifically, the purpose is to add to the understanding of the influence of HRM practices on EO.
Design/methodology/approach
An e-mail survey was distributed to a sample of Swedish and German manufacturing firms in high-tech and medium high-tech manufacturing industries, and firms in knowledge-intensive services sectors, with more than 250 employees. In total, 810 surveys were distributed, with a response rate of 12.7 per cent. Findings - The results show that an emphasis on entrepreneurial aspects leads to an increased EO only in the case of training and development. A conclusion therefore is that it seems difficult to recruit personnel or to use appraisal and rewards as to create EO on a firm level.
Practical implications
The study indicates that firms aiming to increase their EO should make sure to emphasize entrepreneurial aspects during staff training and development activities. Originality/value - This empirical study paves the way towards a better understanding of the link between HRM practices and EO. The results should be of interest for both HR professionals and researchers interested in understanding this important relationship.
Schuler, Randall S.
Rutgers University, Piscataway, NJ, USA.
Bondarouk, Tanya
University of Twente, Enschede, Netherlands.
Ruël, Huub
Windesheim University of Applied Sciences, Zwolle, Netherlands.
HRM and innovation: themes, contingencies and directions for future research2014Ingår i: European Journal of International Management, ISSN 1751-6757, E-ISSN 1751-6765, Vol. 8, nr 5, s. 570-577Artikel i tidskrift (Refereegranskat)
The purposes of this special issue were to connect Human Resource Management (HRM) research and innovation research and to contribute towards a better understanding of how HRM can be deployed to support organisations in their innovation efforts. In this commentary, we review the results from the five articles in this special issue in general and offer suggestions for future research from these five contributions. We do this by pinpointing a number of themes, contingencies, measurement challenges and ideas on working with other research areas that might be useful in future research on the relationship between HRM and innovation.
A Review of the Literature on Learning and SMEs2002Ingår i: The SEAANZ Conference, 22nd-24th September 2002, Adelaide, Australia, 2002Konferensbidrag (Övrigt vetenskapligt)
Key learning themes in the small-business literature2003Ingår i: Small Enterprise Research: The Journal of SEAANZ, ISSN 1321-5906, Vol. 11, nr 1, s. 56-70Artikel i tidskrift (Refereegranskat)
This article presents a review of the literature on learning in small businesses. The sources for the review are two major databases on management research: Social Science Citation Index (SSCI) and ABI/INFORM (ABI). In all, about 500 abstracts published between 1973 and 2002 have been classified. The review shows that research still is built on primary empirical research and that there are no obvious core groups of researchers publishing in the field. Our review does, however, identify a general trend pointing towards an increasing interest in research on learning in small businesses. Further, it is shown that key learning themes discussed during the last 30 years related to small businesses are: education and training (of both management and employees), strategic planning and IT/Software support. During the last decade, the interest in inter-organizational learning (networks and clusters) has increased dramatically. The review indicates that research on small businesses and learning is multidisciplinary and in an early stage of its growth. An in extenso analysis, of all articles in the five most prominent journals found in the review, shows few signs of coherent bodies of knowledge on which the literature draws. Many of the articles (37%) give no accounts of explicit theory. This is the case particularly in the early publications. The review does not reveal any 'original' theory generated by the small-business research community. Instead theories are extracted from other academic disciplines, mainly from the field of economics but also from other social sciences such as sociology and psychology and from engineering. The review shows that empirical studies of learning in small businesses are rare. This means that our understanding of learning processes in this kind of organisations is limited. Research is necessary to increase our knowledge of learning in different levels but also from different perspectives in small firms. The 'small-firm effect' on learning needs to be further explored.
Managerial behavior in slow and fast growing small firms2009Rapport (Övrigt vetenskapligt)
The objective of the paper is to fill a gap in our understanding of what makes certain small firms grow while others do not by exploring the relation between managerial behavior and small firm growth. This has been done by direct observation of the owner‐managers in twelve small manufacturing firms (six slow‐growing and six fast‐growing). Methodologically the project draws on the extensive research that has been conducted within the area of mana‐ gerial work. We have used the method of structured observation as developed by Henry Mintzberg as the primary tool for data collection. Data consists of approximately 330 hours of observation and about 2460 activities have been observed and classified according to their primary purpose.The framework used to analyze the data comes from established conceptualizations of "ma‐ nagerial behavior". More specifically, the two groups of managers have been compared in terms of; how the managers' allocate their time; with whom they interact; with whom do they communicate; and the roles they shoulder in their firms.What is both striking and surprising in the empirical material is that there are only minor dif‐ ferences between the groups of growing and slow‐growing firms. These differences, however, all point in the same direction and confirm one suspicion following our observations of the two groups which is that the hectic and turbulent work situation characterizing the situation of the slow‐growing managers were not present in the growing firms. There might not seem to be such a big difference between the two groups, but trivial questions consumes much of the time for managers in slow‐growing firms which isn't the case for managers in fast‐ growing firms. This gives the managers in fast‐growing firms more time to focus on other work than the daily operations and problems of the firm, which consumes much of the man‐ agers time in slow‐growing firms
Managerial behaviour in small firms: Does it matter what managers do?2012Ingår i: The work of managers: Towards a practice theory of management / [ed] Stefan Tengblad, Oxford: Oxford University Press, 2012, s. 245-263Kapitel i bok, del av antologi (Refereegranskat)
This chapter examines why some small firms grow and others do not. The focus is on the relationship between managerial behaviour and small firm growth in fast- and slow-growing firms. Using Sune Carlson's and Henry Mintzberg's methodology, twelve top managers are observed - six from fast-growing firms and six from slow-growing firms. The results indicate there are no significant differences in the two manager groups as far as their roles, 'proactiveness', networking behaviour, or managerial formality is concerned. It is suggested that there is a generic aspect that is common to the management at both fast- and slow-growing firms. Much of a small firm manager's work, regardless of the pace of company growth, involves this generic, non-managerial behaviour (acting as a specialist or a substitute operator). Small firm managers should not overstate the importance of acting only 'managerially'. © Oxford University Press, 2013.
Managerial Work and Growth in Small Firms2007Ingår i: The 20th SEAANZ Conference, 23rd- 26th September, 2007, Auckland, New Zealand, 2007Konferensbidrag (Övrigt vetenskapligt)
Managerial Work in Small Firms: Testing the Robustness in Mintzberg's propositions2006Ingår i: CPDR on Innovation and Product Development / [ed] Sven-Åke Hörte, Halmstad: Halmstad University , 2006, s. 123-140Kapitel i bok, del av antologi (Övrigt vetenskapligt)
On learning in University Driven Networks: Prerequisites for the learning process in networks of SME-managers and researchers2000Rapport (Övrigt vetenskapligt)
Högskolan i Halmstad, Akademin för ekonomi, teknik och naturvetenskap, Centrum för innovations-, entreprenörskaps- och lärandeforskning (CIEL). Department for Project Management and FENIX Research Program, Chalmers University of Technology, Gothenburg, Sweden & Stockholm School of Economics, Stockholm, Sweden.
The emergent prerequisites of managerial learning in small firm networks2004Ingår i: Leadership & Organization Development Journal, ISSN 0143-7739, E-ISSN 1472-5347, Vol. 25, nr 3/4, s. 292-307Artikel i tidskrift (Refereegranskat)
Descriptive studies have shown that co-operation in networks produces better possibilities for higher-level learning than small firms can organise on their own. Previous studies of learning in networks, however, have not considered how the prerequisites for higher-level learning develop over time in networks. This paper reports on a seven-year participant observational study of two different network constellations. A conclusion from the study is that the learning in networks of small-firm owner/managers is based on trust and has emergent prerequisites. These prerequisites are reciprocity between learning actors, the learning actors' receptive and confronting capacity, and the transparency of the dialogue in the networks. Over time these prerequisites develop and create better opportunities for higher-level learning.
What do owner-managers in small firms really do?: Differences in managerial behavior in small and large organizations2004Ingår i: Small Enterprise Research: The Journal of SEAANZ, ISSN 1321-5906, Vol. 12, nr 1, s. 57-70Artikel i tidskrift (Refereegranskat)
The research presented is a replication of Mintzberg's on managerial work. The article focuses on owner-managers in small manufacturing firms in an initial attempt to reveal the nature of the work undertaken by this type of managers. The purpose is to describe what they do and to compare their behaviour with that of managers in large and intermediate organizations as described by Mintzberg and Kurke & Aldrich. Our study compliments an earlier small-scale study on managerial behavior in small firms and includes sufficient data to test Mintzberg's propositions on managerial work. Empirically this paper draws on an observational study that deployed the method of structured observation. The daily activities of the small-firm owner-managers in our study are characterized by, among other things, informality and constant interruption as the process by which their work is organized. This differs partly from the results found in the studies of managers' work in larger organizations, where formal and planned activities serve more often as the procedure through which the managers design their work. Of Mintzberg's seven propositions, we found support for four, although with some hesitation. This calls into question the asserted generality of several such propositions. Our study indicates that there seem to be certain myths about what small-firm owner-managers really do, myths that need to be considered in future research.
What do owner-managers of small firms really do?2003Ingår i: The 48th ICSB World Conference, June 15-18, 2003, Belfast, Northern Ireland, 2003Konferensbidrag (Övrigt vetenskapligt)
What do owner-managers of small firms really do? : Replicating Choran, Mintzberg, and Kurke and Aldrich2003Ingår i: The 16th SEAANZ Conference, 28 September – 1 October, 2003, Ballarat, Australia, 2003Konferensbidrag (Övrigt vetenskapligt)
Research Note: What is the "fuzzy front end", why is it important, and how can it be managed?2009Ingår i: Managing Innovation: Integrating Technological, Market and Organisational Change / [ed] Joe Tidd, John Bessant & Keith Pavitt, Hoboken: John Wiley & Sons, 2009, 4, s. 341-343Kapitel i bok, del av antologi (Övrigt vetenskapligt)
Center for Management of Innovation and Technology in Process Industry (Promote), Luleå University of Technology, Sweden.
Where New Product Development Begins: Success Factors, Contingencies and Balancing Acts in the Fuzzy Front End2008Ingår i: Proceedings of the 17th International Conference on Management of Technology, IAMOT 2008, 2008, s. 47-Konferensbidrag (Övrigt vetenskapligt)
In light of the increasing attention to predevelopment activities in new product development, this paper reviews the literature on the "fuzzy front end" (FFE). By means of an extensive literature study, we identify, describe and analyze 17 important success factors for organizing and managing the FFE. Our findings first highlight which success factors firms need to excel in when managing and organizing the FFE. Second, the findings show that focusing these factors is not sufficient as such, as interdependencies among factors call for a broader approach. Therefore, relationships among factors and not just the factors per se need to be taken into account. Third, the paper identifies key contingencies requiring adjustment of the FFE process at the firm level. Furthermore, the paper draws attention to several "balancing acts" which impose on firms a trade-off among important variables, where maximizing one dimension may imply the minimizing on another. The paper ends with additional post-hoc analysis of the literature, followed by implications for the scholarly literature as well as management practice.
Center for Management of Innovation and Technology in Process Industry, Luleå University of Technology, Sweden.
Joakim, Wincent
Division of Entrepreneurship, Luleå University of Technology, Sweden.
Patterns of Uncertainty and Equivocality during Predevelopment: Findings from Process‐Based Firms2009Ingår i: Proceedings of the 18th International Conference on Management of Technology, 2009, s. 14-Konferensbidrag (Övrigt vetenskapligt)
Previous literature suggests that innovation managers should prioritize uncertainty reduction in early phases of innovation projects. When uncertainty is high, the general prediction is negative consequences in the form of time‐delays, waste of resources, unclear team vision and, ultimately, concept failure. There are strong reasons to believe, however, that simultaneous management of equivocality is equally important, but this concept has largely been neglected in previous research. By means of a case‐study relying upon exploratory interviews addressing unique observations of 58 innovation projects, we notice that the perhaps most significant challenge for being successful or not is not the initial levels of uncertainty. Rather, it is managerial attempts to actively fight for reducing uncertainty but also addressing the equivocality dimension in the pre‐development stages of the innovation process. We observe reduced patterns of uncertainty and equivocality in successful product innovation and process innovation projects in pre‐development stages. This was not the case for unsuccessful projects. Similarly, we find significantly lower levels of equivocality for successful projects, which is a contribution to prior research suggesting that uncertainty is the major concern during predevelopment. Moreover, our results show that perceived patterns of uncertainty and equivocality differ between product innovation and process innovation projects in different sub‐phases of pre‐development. Key results are summarized as propositions which not only provide guidance for future research, but also provide direct managerial implications on how to address uncertainty and equivocality in different sub‐phases of predevelopment.
Luleå University of Technology.
Beyond Managing Uncertainty: Insights from Studying Equivocality in the Fuzzy Front-End of Product and Process Innovation Projects2011Ingår i: IEEE transactions on engineering management, ISSN 0018-9391, E-ISSN 1558-0040, Vol. 58, nr 3, s. 551-563Artikel i tidskrift (Refereegranskat)
Previous research has shown uncertainty reduction to be critical in the fuzzy front end of the innovation process, but little attention has been given to the equally important concept of equivocality, although it is a defining characteristic of many front-end projects. To address this research gap, this paper report the resultsfrom a longitudinal, multiple case study of four large companiesoriented to both product and process innovation. First, our results show that both uncertainty and equivocality is more effectively reduced in successful front-end projects than in unsuccessful ones. Second, the negative consequences of equivocality appear more critical to front-end performance than the consequences following uncertainty. Third, our results show that uncertainty and equivocality are reduced sequentially in successful projects and simultaneously in unsuccessful projects. Finally, uncertainty and equivocality takes longer time to reduce in process innovation projects than in product innovation projects, which is a consequence of the systemic nature of process innovation. Altogether, these findings provide strong implications for managing front-end projects more proficiently.
Holmén, Magnus
Types and Nature of Business Model Innovation Processes2017Konferensbidrag (Refereegranskat)
The paper explores the population of business model innovation processes of incumbent rms Thus, the paper identi es and describes different types of business model innovation processes and set out to characterize their relations We suggest that there are (at least) seven types of business model innovation processes: i) No process, (ii) "lazy approach", (iii) tools approach, (iv) (unintentional) trial and error or "business model innovation happens", (v) (intentional) experimental approach, (vi) trigger-oriented approach, and (vii) planned (sequential) approach By depicting business model innovation processes as involving (a) cognitive operations, (b) eld activities, and (c) creation of artefacts, the seven identi ed types of business model innovation processes are characterized and related Type (i) and (ii) have rarely been dealt with in the literature, despite their commonality Type (iii) has recently become much used, sometimes being a managerial toy, sometimes as a crucial mechanisms or stage gate for business creation and is often a critical part of the other approaches The paper concludes by suggesting a typology of business model innovation processes, based on the identi cation of three dimensions: intentional vs unintentional, ad hoc vs systematic and event- vs process- oriented
Gullbrand, Jeanette
Barth, Henrik
Additive manufacturing and industrial transformation: evidence from the literature2019Konferensbidrag (Refereegranskat)
Chibba, Aron
Department of Business Administration and Management, Luleå University of Technology, Sweden.
Product Development in SMEs: A literature review2008Ingår i: International Journal of Technology Intelligence and Planning (IJTIP), ISSN 1740-2832, E-ISSN 1740-2840, E-ISSN 1740-2840, Vol. 4, nr 3, s. 299-325Artikel i tidskrift (Refereegranskat)
Product Development (PD) in Small and medium-sized Firms (SMEs) is a long-neglected research area, and little cumulative work has been conducted previously. The purpose of this paper is to provide a first overview of the area of PD in SMEs. In doing so, we draw upon a sample of 149 peer-reviewed research papers selected from an initial sample of 5694 papers. The review provides tentative answers to issues such as the analytical and methodological approaches of the papers, which topics or areas of research have been focused on by previous scholars, and what kinds of topics that are well covered.
42. Rundquist, Jonas
Sustained innovativeness in growing firms using Human Resource Management2011Konferensbidrag (Övrigt vetenskapligt)
Human Resource Management and Innovation Strategy Formulation and Implementation2012Konferensbidrag (Övrigt vetenskapligt)
Using Strategic Human Resource Management to Balance Exploration and Exploitation in Fast Growing Firms2011Konferensbidrag (Övrigt vetenskapligt)
Ludwigshafen Rhine University, Ludwigshafen am Rhein, Germany.
Entrepreneurial orientation and Human Resource Management: Effects from HRM practices2013Konferensbidrag (Refereegranskat)
From previous research it can be concluded that entrepreneurial orientation, as it for instanceinvolves organizational learning shaped by creativity, individual commitment and teamwork, can beinfluenced by human resource management practices. This paper aims to further explore the relationship between HRM practices andentrepreneurial orientation in large established firms. More specifically, our purpose is to add indepthknowledge of the influence of HRM practices on entrepreneurial orientation. Usinga a survey, data from a sample of Swedish and German manufacturing firms in high‐ and medium high‐techmanufacturing industries, and firms in knowledge‐intensive services sectors was analyzed. The results suggest that it is only in the case of training & development including entrepreneurial aspects actually lead to increased entrepreneurial orientation.
Windesheim University of Applied Sciences, Zwolle, The Netherlands.
Human resource management and firm innovativeness in a European context: advancing our understanding of the relationship (Introduction to the thematic issue)2014Ingår i: European Journal of International Management, ISSN 1751-6757, E-ISSN 1751-6765, Vol. 8, nr 5, s. 465-471Artikel i tidskrift (Refereegranskat)
This paper introduces the papers included in the thematic issue on Human Resource Management (HRM) and firm innovativeness in a European context. Furthermore it presents the results of a literature review on human resource management and firm innovativeness. The literature shows that the positive relationship between HRM and firm innovativeness has been confirmed. However, the explanation for how this relationship works is not equivocal/unified. Empirical studies have investigated the role of strategic HRM, specific HRM systems and HRM practices. For strategic HRM, the empirical support is still limited, while for HRM systems considerable work confirms the positive influence of commitment-based HRM. For HRM practices, in particular training, working in teams, and internal labour flexibility, including job rotation, the literature provides empirical evidence and indications that they are positively related to firm innovativeness. Copyright © 2014 Inderscience Enterprises Ltd.
Högskolan i Halmstad, Sektionen för hälsa och samhälle (HOS), Centrum för samhällsanalys (CESAM), Centrum för studier av politik, kommunikation och medier (CPKM).
Järpe, Eric
Högskolan i Halmstad, Sektionen för Informationsvetenskap, Data– och Elektroteknik (IDE), Halmstad Embedded and Intelligent Systems Research (EIS).
Evolution of Green Innovation in Sweden: Models, Management, Policies2011Ingår i: Evolution of Green Innovation in Sweden: Models, Management, Policies, 2011Konferensbidrag (Övrigt vetenskapligt)
Quantitative analysis of the evolution of innovations at national systems level is not alwayspossible due to the lack of reliable, comprehensive and adequate data sets. Therefore, managerialpractice among organizations as well as policy decision making are often myopic anduninformed about actual dynamics.In the Swedish case, there are promising data sets, even if the adequacy of existing variabledefinitions needs to be explored and debated. Official data collected by the central statisticsauthority SCB (Statistics Sweden) includes several potentially relevant variables on all privateand public organizations in Sweden and their employees. These data are compiled into timeseries for a number of years which allows for longitudinal analysis. Data can also be mergedwith other data sets on the environmental goods and services sector and energy consumption dataand therefore allow for a detailed "demographic" or "population ecology" analysis ofenvironmentally oriented or friendly innovation since at least 2003. Halmstad University hasrecently gained full access to these data.In this paper, these databases are described in some detail. Problems of definitions andmeasurement are particularly discussed, and some initial descriptive statistics are presented.Further, the paper advocates the use of models inspired by population ecology and demographyin analyzing existing data. In particular it is suggested that interactive diffusion models mayenhance the understanding of the evolution of green innovations and their dynamics. It is alsosuggested that multi-level regression analysis is applicable in estimating the power of factors thatbring progress to the "greening" of the Swedish innovation system.Together, such models are potentially useful in forecasting the development of innovationsystems. The models can also be used in generating, testing by simulating and thus evaluatingapproaches to management of innovation and innovation policy implementation. A dynamicunderstanding of the "greening" of the innovation system is a critical asset in the development oftools to be used for continuous improvements in both policy making and the management ofinnovation in organizations.
The Greening of the Swedish Innovation System: Exploring Official Registry Data2011Konferensbidrag (Övrigt vetenskapligt)
Most countries aim to transform towards becoming greener societies. In parallel, many companies struggle with the question of how to build more sustainable operations while at the same time sustaining or developing their competitive advantage. Research has, up until today, however, largely failed to provide solid explanations for how to achieve these aims, from which policy and managerial decision-making can deduced. One reason for this failure is that quantitative analysis of "green" innovation at national systems level is not always possible due to the lack of reliable, comprehensive and adequate data sets. In the Swedish case, there are promising data sets, even if one always can debate the adequacy of existing variable definitions. Official data collected by Statistics Sweden (SCB) includes several interesting variables on all private and public organizations in Sweden and all employees, compiled into time series for a number of years. These can be merged with other data sets on the environmental goods and services sector and energy consumption data and therefore allow for a detailed "demographic" or "population ecology" analysis of environmentally oriented or friendly innovation since at least 2003. In this paper, these databases are described in some detail. Problems of definitions and measurement are particularly discussed. Initial explorations describe the shift from fossil to non-fossil energy sources in the Swedish innovation system. Further, we also suggest some models inspired by demography and population ecology and also multi-level models. In particular it is suggested that diffusion models could be applied, including models in which diffusion processes interact in micro-level systems. It is suggested to apply multi-level regression analysis in order to estimate the power of factors affecting the "greening" of Swedish innovation system.
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 4,918
|
Board.prototype.generateBoard = function() {
for(var i = 0; i < this.size; i++) {
for(var j = 0; j < this.size; j++) {
$('.main-board').append("<div class='cell' id='r_"+i+"-c_"+j+"'></div>")
}
}
}
function Board(size) {
size = typeof size == 'undefined' ? 50 : size
this.size = size;
}
Board.prototype.displayScore = function (score) {
$('.score').text("Eugene's score: " + score);
}
Board.prototype.activateCell = function(r,c){
$("div#r_" + r + "-" + "c_" + c ).addClass("active");
};
Board.prototype.disActivateCell = function(r,c){
$("div#r_" + r + "-" + "c_" + c ).removeClass("active");
};
Board.prototype.activateApple = function(r,c){
$("div#r_" + r + "-" + "c_" + c ).addClass("apple");
};
Board.prototype.disActivateApple = function(r,c){
$("div#r_" + r + "-" + "c_" + c ).removeClass("apple");
$("div#r_" + r + "-" + "c_" + c ).removeClass("head");
};
Board.prototype.isSnake = function(r, c){
return $("div#r_" + r + "-" + "c_" + c ).hasClass('active');
};
Board.prototype.renderSnakeCoords = function (snakeArray) {
for (var i = 0; i < snakeArray.length-1; i++)
{
var rowCell = snakeArray[i][0];
var colCell = snakeArray[i][1];
this.activateCell(rowCell, colCell);
}
};
Board.prototype.renderSnakeHead = function (snakeArray)
{
var headRow = snakeArray[snakeArray.length-1][0];
var headCol = snakeArray[snakeArray.length-1][1];
this.activateHeadCell(headRow,headCol);
}
Board.prototype.activateHeadCell = function(r,c){
$("div#r_" + r + "-" + "c_" + c ).addClass("head");
};
Board.prototype.disActivateHeadCell = function (r,c){
$("div#r_" + r + "-" + "c_" + c ).removeClass("head");
}
//
// isActivecell(); - determines whether cell should be active (contains part of snake)
// activateCell(); - changes attribute of cell to display active state (snake)
// activateAllCells();
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 2,673
|
\section{Introduction}
The next machine after the LHC will be a linear electron positron collider at the TeV scale. This machine will allow high precision measurements to extend the scientific results of the LHC. Currently the most advanced proposal is the International Linear Collider (ILC) with a centre-of-mass energy of up to 500 GeV. An alternative at higher center-of-mass energies than the ILC is the Compact Linear Collider (CLIC).
The e$^+$/e$^-$ collisions will lead to multi-jet final states. Their reconstruction will be based on so-called particle flow algorithms (PFA)~\cite{brvi02, thomson2009particle}. The goal is to reconstruct every single particle of the final state which requires the combination of information from each sub-detector. Particularly a perfect association of the signals in the tracking systems with those in the calorimeters is required. Charged particles are measured with the tracking system, while neutral particles can only be measured in the calorimeters. The particle flow technique requires a specific detector design. A limiting factor of the particle flow, called confusion, is due to overlapping showers. To separate the particles, calorimeters need to be of high granularity. They have to be very compact since they will be embedded within the magnetic coil of the detectors.
The CALICE collaboration~\cite{calice} designs and studies electromagnetic and hadronic calorimeters for experiments at the ILC. All detectors are developed with a common approach to obtain ultra granular calorimeters optimised to particle flow algorithm. The prototypes are tested in combined beam tests in order to study several technologies and the association of electromagnetic and hadronic calorimeters. These beam tests allow for developing reconstruction algorithms and for the validation of simulations.
\section{Silicon tungsten electromagnetic calorimeter}
The silicon tungsten electromagnetic calorimeter (ECAL) is built following particle flow algorithm requirements and based on a sampling design. The physics prototype of the ECAL, used in this study, is composed of 30 layers of silicon as active material, alternated with tungsten as absorber material. Tungsten has a short radiation length and a small Moli\`ere radius which gives compact showers and allows for the efficient separation of close particles. The silicon allows for a thin and easily segmented readout detection system suited for high granularity. The silicon wafers are segmented in 1 $\times$ 1 cm$^2$ pads. Each wafer consists of a square of 6 $\times$ 6 pixels and each layer is a matrix of 3 $\times$ 3 wafers resulting in an active zone of 18 $\times$ 18 cm$^2$ giving a total of around 10000 readout channels. As shown on Figure~\ref{fig:ecalSlab}, the printed circuit boards (PCB) are mounted two by two in an elementary detection unit called slab. The silicon wafers are located on each side of a H-shaped tungsten supporting structure. These slabs are shielded by aluminum foils and inserted in the a carbon fiber composite mechanical structure. Three different longitudinal samplings were used, finer in the first ten layers (1.4 mm plates of tungsten), 2.8 mm plates in the ten intermediate layers, and 4.2 mm in the last ten layers~\cite{repond2008design}.
\begin{figure}[h]
{\centering
\subfloat{\includegraphics[width=0.4\textwidth]{ecalSlab}}
\subfloat{\includegraphics[width=0.4\textwidth]{fig_ecal}}
\caption{\sl Pictures of the ECAL prototype. The top figure shows the structure of a single detector slab while the bottom figure shows an overview of the whole prototype.}
\label{fig:ecalSlab}
}
\end{figure}
During the years 2005-2011, the calorimeter was tested with various beams: electrons, positrons, muons, pions and protons in the momentum range between 1 and 180 GeV/c. Beam campaigns were conducted at DESY, CERN and FNAL. The main goal of these beam tests was to demonstrate the principle of highly granular calorimeters. Using data collected with electron beams at energies from 6~GeV to 45~GeV, the linearity and resolution of this calorimeter to electrons were estimated~\cite{adloff2009response}. The linearity is better than 1\% while the relative energy resolution is estimated to be $\sigma_E/E = (16.53\pm0.14(\mathrm{stat})\pm0.4(\mathrm{syst}) )/\sqrt{E({\mathrm{GeV}})} \oplus (1.07\pm0.07(\mathrm{stat})\pm0.1(\mathrm{syst}))$~(\%). To compare the test beam data with the simulation, the detector has been simulated within the Geant4-based MOKKA simulation framework~\cite{mokka}~\cite{agostinelli2003geant4}.
In addition to standard beam test analysis (calibration, noise and stability), the high granularity allow to study hadronic interactions in the detector and to validate hadronic model implementations in Geant4 simulations. As hadronic interactions are poorly understood, the high granularity of the calorimeter offers unprecedented information to study hadronic interactions. Several model combinations called physics lists are proposed in Geant4. Our studies allow for a detailed testing of these simulations. A study of interactions of pions in the physics prototype has been published in~\cite{calice2010} for energies between 8\,GeV and 80\,GeV. The work presented in this article concentrates rather on energy range 2\,GeV - 10\,GeV.
\section{Results}
The high granularity permits detailed view into hadronic showers. In order to exploit the imaging of hadronic showers, we have to develop new analysis methods like particle tracking or interaction vertex localisation in the calorimeter.
The high granularity of the calorimeter allows the tracking of particles as they pass through the detector and the use of imaging processing techniques. For instance, the Hough transform technique has been tested to find tracks in the calorimeter~\cite{fehr2010}. This technique has been applied to reconstruct a muon track near to a 30 GeV electromagnetic shower. The Figure~\ref{fig:dist} shows the reconstruction efficiency as a function of the distance between the track and the shower axis. The efficiency reaches 100\% for distance of 25~mm. This separation efficiency is essential for particle flow algorithm, especially to separate charged and neutral particles which are not detected by trackers.
\begin{figure}[h]
{\centering
\includegraphics[width=0.47\textwidth]{distance}
\caption{\sl Efficiency of MIP detection as a function of distance from electron shower}
\label{fig:dist}}
\end{figure}
\begin{figure}[h]
{\centering
\subfloat{\includegraphics[width=0.45\textwidth]{PLevt}}
\subfloat{\includegraphics[width=0.45\textwidth]{FBevt}}
\caption{\sl Examples of hadronic interactions in the ECAL. "FireBall" event on the top and "PointLike" event on the bottom.}
\label{fig:evt}}
\end{figure}
\begin{figure}[h]
{\centering
\subfloat{\includegraphics[width=0.43\textwidth]{FracInt}}
\subfloat{\includegraphics[width=0.43\textwidth]{FracNonInt}}
\caption{\sl Frequency of event types and comparison with several physics lists as function of energies from 2~GeV to 10~GeV. The top figure shows the rates of interactive classes while bottom figure shows the rates of non-interactive classes.}
\label{fig:frac}}
\end{figure}
Figure~\ref{fig:evt} illustrates the potential of the high granularity. We distinguish two different and recognizable topologies. Events can be classified as a function of their topologies into 4 classes. MIP and elastic scattering are considered as non interactive events. The two distributions presented in Figure~\ref{fig:evt} show the two types of interacting events called ``Pointlike'' (top) and ``Fireball'' (bottom)~\cite{philippe_thesis}~\cite{doublet2011}.
In Figure~\ref{fig:frac}, we compare the relative frequency of each event class between data and some Geant4 physics lists. The frequency of ``Fireball'' events in the data is about 55\% over the whole energy range. After delta-rays correction, the frequency of ``Pointlike'' events is about 4\% at small energies and tend towards zero at higher energies. The frequency of both classes for inelastic events is well reproduced by all physics lists which confirms that the total inelastic cross sections are well implemented into the physics lists. Cross sections of non-interacting events are also well modeled by Geant4~\cite{philippe_thesis}~\cite{doublet2011}.
\subsection{Transverse profiles}
The shower radius is defined by:
\begin{equation*}
\displaystyle \mathrm{R}_{\mathrm{E}} = \sqrt{\sigma_{\mathrm{E,x}}^2+\sigma_{\mathrm{E,y}}^2}
\end{equation*}
where:
\begin{equation*}
\displaystyle \sigma_{\mathrm{E,x}}^2 = \frac{ \displaystyle \sum_{\mathrm{hits}}x_{\mathrm{hit}}^{2}E_{\mathrm{hit}} }{\displaystyle \sum_{\mathrm{hits}}E_{\mathrm{hit}}} - \left( \frac{\displaystyle \sum_{ \mathrm{hits}}x_{\mathrm{hit}}E_{\mathrm{hit}}}{\displaystyle \sum_{ \mathrm{hits}}E_{\mathrm{hit}}} \right)^{2}
\end{equation*}
and the same for y. The transversal profile is an important observable affects the overlap of shower thus the confusion.
For the calculation of the observables, only hits in the interaction layer and all subsequent layers are taken into account. In order to define in the same way a measure of the radius of non interacting events, i.e. interactions where no interaction point could be found, the width R$_{E}$ is calculated by summing over all hits in the ECAL~\cite{philippe_thesis}~\cite{doublet2011}.
The left part of Figure~\ref{fig:traprof} shows the comparison of the transverse profile between data and simulation at energies from 2~GeV up to 10~GeV. In this plot we use the QGSP\_BERT physic list. We distinguish 2 maxima at 5~mm and 20~mm. Up to 6~GeV, data are well reproduced by the simulation except for radius larger than 35~mm. At 8~GeV the simulation overestimate the data in the transition region between the two peaks. The situation is comparable at 10\,GeV
\begin{figure}[ht]
\begin{center}
\includegraphics[width=0.47\textwidth]{traprof.jpg}
\includegraphics[width=0.49\textwidth]{evclass.png}
\caption{\sl \underline{Left:} Lateral distributions of the hadronic shower energy at energies from 2 GeV to 10 GeV. For each distribution: the top view features the comparison between test beam data in red and the simulation with QGSP\_BERT in black. The bottom view shows the ratio of test beam data over simulation. \underline{Right:} Lateral distributions of the hadronic shower for each event classes at 8 GeV. For each distribution: the top view features the comparison between test beam data in red and the simulation with QGSP\_BERT in black. The bottom view shows the ratio of test beam data over simulation.
}
\label{fig:traprof}
\end{center}
\end{figure}
In the right part of Figure~\ref{fig:traprof}, the contribution of each event type is separated for 8 GeV events. We see that the first maximum in Figure~\ref{fig:traprof} left is created by MIP events and the second one by ``Fireball'' events. The maxima of ``Pointlike'' and ''Scattered'' events are located in the transition region. The four event types show the same disagreement~\cite{philippe_thesis}~\cite{doublet2011}.
\subsection{Longitudinal profiles}
\begin{figure}[h]
{\centering
\subfloat{\includegraphics[width=0.4\textwidth]{LongProf_2GeV_QGSP_BIC_Total}}
\subfloat{\includegraphics[width=0.4\textwidth]{LongProf_2GeV_QGSP_BERT_Pointlike}}
\caption{\sl Total longitudinal profiles for the two interacting event types: comparison between test beam
data in red and simulation in black at 2~GeV. For simulated events, we separated the contributions of the secondary particles. The blue lines are the contributions from electrons and positrons. The green lines are the contributions from protons. The red lines are the contributions of pions. Other particles are in violet. The top figure shows the comparison between test beam data and the QGSP\_BIC physic list for "Fireball" events while the bottom figure shows the comparison between test beam data and the QGSP\_BERT physic list for "Pointlike" events.}
\label{fig:prof}}
\end{figure}
The longitudinal profile is given as a function of pseudolayers in order to account for the different sampling fractions in the ECAL. In the first module, pseudolayers are equivalent to real layers. In the second module, each layer is subdivided in two pseudolayers and in the third module, layers are subdivided into three pseudolayers. The energy is linearly interpolated between the pseudolayers. In case of interacting events, the longitudinal shower profile starts from the interaction layer. In case of non-interacting events, the longitudinal profile is calculated from the first detector layer~\cite{philippe_thesis}~\cite{doublet2011}.
In Figure~\ref{fig:prof}, the test beam data are shown in red and the simulation in black. For simulated events, we separated the contributions of the secondary particles. The blue lines are the contributions from electrons and positrons. The green lines are the contributions from protons. The red lines are the contributions of pions. Other particles are in purple. For "Fireball" events, none of the models give a satisfactory description of the data. For instance, the top distribution shows significant disagreement between data and the QGSP\_BIC model. In the bottom part of Figure~\ref{fig:prof}, we present longitudinal profile of "Pointlike" events and the comparison with QGSP\_BERT model. This class of events is better reproduce by the Bertini model~\cite{philippe_thesis}~\cite{doublet2011}.
\section{Conclusion and outlook}
This study investigates in depth the interactions of pions in an energy range between 2 and 10\,GeV. It demonstrates the outstanding potential of the CALICE silicon tungsten electromagnetic calorimeter to resolve details of hadronic cascades. The data obtained in test beams are compared with different physics lists provided by Geant4. Visible differences between models appear at this level of detail. The study on shower decomposition is the first step toward the use of sophisticated algorithms which may be developed in collaboration with experts from applied mathematics. To succeed the physics prototype, a technological prototype is in development which will feature a four times higher granularity.~\cite{techprot}
\section{Acknowledgments}
Thanks to Thibault Frisson who has written the major part of these proceedings. The text is based on the PhD thesis of Philippe Doublet.
\bibliographystyle{unsrt_tibo}
\begin{footnotesize}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 7,847
|
Farroupilha Park (Parque Farroupilha in Portuguese), also known as Parque da Redenção, is a major urban park in the city of Porto Alegre, the state capital of Rio Grande do Sul, in Brazil.
The park was designed by French architect Alfred Agache and founded on September 19, 1935.
Near to the Centro Histórico (Historic Centre), Farroupilha Park is located within a polygon formed by José Bonifácio, João Pessoa, Luiz Englert, Setembrina and Osvaldo Aranha Avenues.
History
The site where the park is located was formerly called Várzea do Portão, a large flooded lowlands close to the old gate to Porto Alegre. On February 23, 1807, the City Council requested the Governor of the Province, Paulo José da Silva Gama, to donate the land to be used as public area, as well as a focus area for herds of cattle brought for local supply. However, its measurement would only be effectively carried out between 1820 and 1825.
After its donation to the city, it suffered several attempts of alteration of its primary goals, which have always been hindered by the government. During the Ragamuffin War the Várzea was outside the city's fortifications, and after the end of the conflict an inspection found several irregularities, such as fences advancing their territory and built a mansion at its center, all was immediately demolished. In the years that followed, government and private individuals tried to split the ground to give it other uses, always finding opposition. In 1870, the Lowland received its first official name, changing its name to Campo do Bonfim, in view of the construction of Capela do Bonfim (Lord Jesus Chapel of the Good End, Chapel Bonfim) on its northern boundary. There were also subsequent threats to the integrity of the area, all frustrated, and in 1872 the President of the Province authorized the construction of a military base in its southeastern limit, being the source of the current Colégio Militar de Porto Alegre (Military School of Porto Alegre).
The site was also used as a drying area for leather, a meeting place for carts and as a deposit of the municipal waste until mid-1890, in spite of contrary opinions Hygiene of the Board of the Province. In 1884 the street had its name changed to Campos da Redenção (Fields of Redemption), celebrating the early abolition of slavery in the city.
In 1927, the actual landscaping of the Campos da Redenção began, with the implementation of the Jardim Paulo Gama garden to the north and the banning of the parade of carts and herds in 1928. In 1935 for the centenary celebrations of the Revolução Farroupilha (Ragamuffin War), the entire southern part of the field was drained, flushed and urbanized, following the designs of French architect Alfred Agache. This year its name was changed to its current name Parque Farroupilha.
Activities and Landmarks
Araujo Viana Auditorium
Auditorium for concerts, performances and meetings. Designed by architects Moacir Moojen e Carlos Fayet, was inaugurated in March 1964, making it an important space for cultural events.
Brique da Redenção
Every Sunday from 9:00 am the Porto Alegrenses have their favorite outing in Brique da Redenção.
There are dozens of stalls selling crafts, Arts, Souvenirs, Food and Antiques, all along the Avenida Jose Bonifacio.
The Park is full of people walking, talking and taking their mate, especially on sunny mornings.
A must for candidates at election time and movements of all types and organizations.
Feira Ecológica and Feira de Artesanato
Every Saturday, two fairs exhibit their products on Avenida José Bonifácio. First, we have the Eco-Fair, with several stalls of organic fruits and vegetables at a very good price. Seconds, with the have the Arts and Crafts Fairs, with 60 exhibitors selling their products.
Recanto da Ilha
The dock in the little lake inside the park, was located where now stands the Cafeteria. Recently, in 2001, the pier was transferred to the other side, where there is the Belvedere, in the middle of the lake on an island, which is reached through a beautiful bridge.
There are paddle boats that are rented from the wharf at the box office, in March/2004 they were renovated and have buoys and life jackets now, there are boats for 2, 3 and 4 people, some in the shape of swans.
Monumento ao Expedicionário
Inaugurated on June 16, 1957, the Monument to the Expeditionary, made of granite with a double Arc de Triomphe, with 12.50 m in height, is home to the Pira da Pátria, an important point of the celebrations of the Independence of Brazil, September 7, and the Ragamuffin War, on September 20.
After World War II the Brazilian Expeditionary Force members who had fought against the Axis on the Italian front returned to Brazil, and the country multiplied in tribute to the GIs and their deeds. Porto Alegre was no exception, especially as many gaucho soldiers and officers had participated in the war.
So in 1946 there was a competition for projects and models of a "Arc de Triomphe" to honor the BEF and its soldiers.
Espelho D'Água
Located in the Avenue of the States, the water surface suggests tranquility and peace to visitors who can see reflected in its surface the image of blue sky, the trees bloom and the birds singing in the park.
Recantos Oriental and Europeu
Located on the right of Avenue of the States, the Recanto Oriental is a space for meditation. Formed around a dragon-shaped lake, it has small semi-arc-shaped bridges, a sculpture in the shape of the Fuji-Yama volcano, and a Pagoda where a sculpture of the Buddha is located. Recanto Europeu, in turn, can be found next to Araujo Viana Auditorium, a small space that simulates in a simple way a European garden, with a French Fountain and the Roman Pergola. There are also two other gardens, Recantos Solar e Alpino of lesser notoriety in the park.
References
External links
A Redenção
Parks in Porto Alegre
World's fair sites in South America
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 5,924
|
\subsection{Interference Avoidance}
To avoid the interference from a WiFi transmitter, a straightforward solution is to move the backscattered signal to another channel that does not overlap with the channel where the excitation WiFi signal is sent. We achieve this by toggling its RF transistor at a higher speed~\cite{zhang2016hitchhike}, \eg, $20$ MHz. Then, the backscattered signal will be moved to a channel that is $20$ MHz away from the channel where the excitation WiFi signal stays. Configuring the receiver to work on the channel of the backscattered signal will address the interference from the excitation signal.
To avoid the interference from multiple tags that concurrently backscatter signals, the above idea can be extended to assign different available WiFi channels to each of the tags by toggling their RF transistors to different speeds. In this way, the tags can be distinguished by their allocated WiFi channels. Each channel corresponds to a particular tag. To receive packets from all tags, the receiver in our system needs to be capable of sweeping all WiFi channels except the channel of the excitation signal. We achieve this by implementing a frequency band sweeping protocol~\cite{vasisht2016decimeter} in the iwlwifi driver of Intel 5300 NIC. Since the number of non-overlapped WiFi bands is limited, Rover can only simultaneously localize a limited number of tags. To maximize the ability of simultaneous localization, it is vital to choose the channel of the excitation signal.
Suppose a tag uses a frequency $f_b$ square wave signal to control the on-off frequency of the RF switch. $f_c$ is the carrier center frequency of the 802.11n excitation signal. Let $\omega_b = 2\pi f_b$, $\omega_c = 2\pi f_c$, and $\alpha_{\text{base}}(t)$ denotes a baseband waveform. The square wave can be formulated as $S_{\text{tag}} = \frac{4}{\pi}\sum_{n=1}^{\infty}\frac{\sin\left[(2n-1)\omega_b t\right]}{2n-1}$. Hence, the backscattered signal $\beta(t)$ can be written as,
\begin{equation}
\beta(t) = \alpha_{\text{base}}(t)e^{j\omega_c t}S_{\text{tag}}(t).
\end{equation}
Let $F_{\text{base}}(\omega)$ and $F(\omega)$ be the Fourier transform of $\alpha_{\text{base}}(t)$ and $\beta(t)$ respectively. We have
\begin{equation}
\begin{aligned}
F(\omega) = & \sum_{n=1}^{\infty}\frac{2j}{\pi (2n-1)}\left( F_{\text{base}} \left( \omega - \omega_c + (2n-1)\omega_b \right) - \right. \\
& \left. F_{\text{base}} \left( \omega - \omega_c - (2n-1)\omega_b \right) \right).
\end{aligned}
\end{equation}
This indicates that the frequency-shifted backscattered signal can be received at two bands, $f_c \pm f_b$, causing sideband interference to other channels.
Based on this, Rover chooses the most side channels in the band, \ie, channel $165$ or $36$, to transmit the the excitation signal in order to avoid the sideband interference.
\subsection{AoA Estimation}
\begin{figure}[t!]
\centering
\includegraphics[width=3in]{circular_array3.eps}
\caption{A uniform circular array that consists of three antennas in our system: The signal with AoA $\theta$ travels an additional distance of $d\cos\left(\theta + \frac{\pi}{3}\right)$ to the third antenna and $d\cos(\theta)$ to the second array in the array compared to the first antenna.}
\label{fig:background_b}
\end{figure}
So far, we have addressed the interference problem. A WiFi receiver can receive the backscatter packets from tags. In this section, we describe how Rover estimates the AoAs of backscatter tags to the receiver, which is amounted on a robot, leveraging the CSI of received packets. The AoA estimation technique for low-power backscatter tags was first proposed in~\cite{kotaru2017localizing}. Here we extend it to work with a circular antenna array with uniform spacing $d$ that can measure AoAs in $[0, 360]$ degrees as shown in Fig.~\ref{fig:background_b}.
Localizing backscatter tags involves two physical paths, transmitter-to-tag path and tag-to-receiver path, as shown in Fig.~\ref{fig:paths}. Thus, the received CSI depends on the locations of backscattered tags and the access point (AP). We combine $j$\spth path on the transmitter-to-tag link with $i$\spth path on the tag-to-receiver link to form a virtual path between the excitation source (AP) and the receiver at the robot. The virtual path has a ToF of $\widehat{\tau}_k = \tau_j + \tau_i^*$ where $\tau_i^*$ ($\tau_j$) denotes the ToF of the signal along a path on the tag-to-receiver (transmitter-to-tag) link, the AoA of the virtual path $\widehat{\theta}_k = \theta_i^*$ where $\theta_i^*$ is the AoA of $i$\spth path on the tag-to-receiver link, and the corresponding complex attenuation of $\widehat{\gamma}_k = \gamma_j \gamma_i^*$ where $\gamma_i^*$ and $\gamma_j$ denote the complex attenuation along $i$\spth path on the tag-to-receiver link and $j$\spth path on the transmitter-to-tag link, respectively. The overall signal obtained at the three antennas for $n$\spth subcarrier can be written as
\begin{equation}
\begin{aligned}
H_{n, m} & = \sum_{k=1}^{L_{\text{tx}} L_{\text{tag}} }\widehat{\gamma}_k e^{-j2\pi\left(\widehat{\tau}_k(n-1)f_\delta + (m-1)d \cos\widehat{\theta}_k/\lambda\right)}, m = 1, 2 \\
H_{n, 3} & = \sum_{k=1}^{L_{\text{tx}} L_{\text{tag}} }\widehat{\gamma}_k e^{-j2\pi\left(\widehat{\tau}_k(n-1)f_\delta + d \cos\left(\widehat{\theta}_k+\frac{\pi}{3}\right)/\lambda\right)},
\end{aligned}
\end{equation}
where $L_{\text{tag}}$ is the number of paths on the tag-to-receiver link, $L_{\text{tx}}$ is the number of paths on the transmitter-to-tag link, $f_\delta$ is the frequency gap between two consecutive subcarriers. This overall signal is reported as CSI corresponding to the particular subcarrier and antenna.
\begin{figure}[t!]
\centering
\includegraphics[width=3in]{paths3.eps}
\caption{The received signal traverses two physical paths where $\tau_j$ denotes the time of flight (ToF) of $j$\spth path on the transmitter-to-tag link and $\tau^*_i$ denotes the traversing time of $i$\spth path on the tag-to-receiver link.}
\label{fig:paths}
\end{figure}
The signal model is a standard form to apply a joint AoA-ToF estimation technique~\cite{kotaru2015spotfi}. The insight of this technique is that multiple subcarriers of an OFDM signal encode ToF information. By smoothing the subcarriers represented in the CSI matrix, it allows a super-resolution AoA estimation with a small antenna array, \eg, a three-antenna array available for Intel 5300 NIC, jointly estimating AoAs and ToFs\footnote{This ToF cannot correctly infer the traveling distance of a propagation path due to its poor distance resolution from the narrowband signal.} of all paths. The AoA of the path with the smallest ToF is the is the direct-path AoA of a tag to the receiver.
Unfortunately, the obtained AoA can be corrupted by the heading direction of the robot. The robot has three degrees of freedom, including 2D position and the heading direction. It can rotate and change its heading direction while moving, \eg, turning at a corner of the room. Thus, the onboard antenna array will be turning with the robot together. The system can no longer use the measured AoA to localize the robot via triangulation because the AoA not only encodes the geometric constraint of translations but also manifests the rotation (refer to Fig.~\ref{fig:principle} for details). Therefore, we need to correct the rotation from the measured AoA and recover the angle that only relates to the translation.
Fig.~\ref{fig:aoa_correction} shows the workflow of AoA correction. Basically, we leverage the IMU to estimate the robot's heading direction in angle $\phi$, assuming that the initial heading direction is angle $0\degree$. The gyroscope in IMU provides raw measurements of angular velocity. However, it is well-known that simply integrating them to obtain the heading will result in error accumulation. We correct the heading by using a magnetometer onboard that provides a reference direction represented by the magnetic field strength. Note that in indoor venues, the reference direction is not the earth's North due to the magnetic interference from surrounding electronic devices. Nevertheless, the reference direction is stable in few hours so that it is eligible to correct the drift during the trajectory. Since the rotation estimation is non-linear, we employ the extended Kalman filter (EKF) to determine the heading by fusing the measurements from gyroscope and magnetometer~\cite{sabatini2006quaternion}. Finally, we correct the AoA by subtracting the heading angle $\phi$ from the obtained AoA $\theta$.
At this stage, we obtain the corrected direct-path AoAs of multiple tags to the receiver. Next, we fuse them with the IMU measurements to localize the tags and the robot simultaneously.
\begin{figure}[t!]
\centering
\includegraphics[width=3.5in]{aoa_correction.eps}
\caption{The workflow of AoA correction. We first use the extended Kalman filter to fuse the magnetic field strength with the angular velocity to correct the drift of gyroscope. Then we can trivially correct the AoA.}
\label{fig:aoa_correction}
\end{figure}
\subsection{AoA-IMU Localization System}
The angle (AoA) can be used to determine a target's location via triangulation. Recall that conventional localization systems usually require a few landmarks with known locations to localize the target. The essence of this requirement is defining the metric scale of environments, \ie, the unit (meter, millimeter, etc.) in measuring distances between objects, to fix the size of triangles.
In Rover, since the location of both the tags and the robot are unknown, the AoA we obtained cannot yield locations with the metric scale of environments. Nevertheless, with the aid of the onboard IMU and the mobility of a robot, we can localize both the connected tags and the robot in that the IMU provides accelerations in unit $m/s^2$, defining the metric scale. With the translations and the AoAs of incident signals at different positions, it forms a fixed triangle. We take one tag as an example illustrated in Fig.~\ref{fig:principle}. As a robot moves, the IMU measures translation $\Delta d$ and the antenna array measures AoAs $\theta_1$ and $\theta_2$ referring to the tag at different positions, one can determine the relative positions of the robot and the tag through triangulation. Note that the measured AoA has to be corrected from the rotation $\phi$ so as to obtain the correct geometric constraint between the tag and the robot.
Obtaining the translation by integrating the accelerations from the IMU is straightforward but suffers from temporal accumulated errors due to the inherent noise~\cite{he2017pervasive}, causing large localization errors once the result severely distorts the triangle in Fig.~\ref{fig:principle}. To address this issue, we develop an AoA-IMU SLAM approach that optimizes the locations of the robot and backscatters subject to measurement constraints with respect to WiFi AoAs and the IMU odometry.
Roughly speaking, the central idea of SLAM is to obtain a maximum likelihood estimate of both robot positions and environment features (backscatter tags in our system) given observations (AoAs) from the antenna array. Solutions to the SLAM problem can be either filtering-based or graph-based approaches. While filtering-based approaches are considered to be more efficient in computation~\cite{lu2019collaborative}, we choose graph-based approaches that can achieve better performance via repetitively linearizing past robot states and multi-view constraints~\cite{lin2018autonomous}.
\begin{figure}[hp]
\centering
\includegraphics[width=3.2in]{veri_loc4.eps}
\caption{Localization principle: triangulation with the robot's motions. The AP sends WiFi packets to excite the backscatter tag. The receiver on the robot measures the AoAs of the tag to the robot from backscatter signals and the onboard IMU measures translation $\Delta d$ to provide the metric scale of environments. $\hat{(\cdot)}$ denotes the measured AoA and $\phi$ is the rotation of the robot since the previous state.}
\label{fig:principle}
\end{figure}
In addition, solving the SLAM problem is a batch process that incorporates multiple observations to produce accurate results. However, it can become unacceptably slow as the size of the environment grows. This delays the location estimates of the robot so that the robot loses its own navigation capability, being unable to move along the desired trajectory. To let our system run in real-time, we employ an incremental update method to speed up the computation. We formulate a sliding window based model that only keeps a limited amount of AoAs and corresponding robot hidden {\em states}, \eg, the positions of the robot at different timestamps in the workspace, to bound the computation complexity.
\subsection{System Overview}
\label{subsec:overview}
\begin{figure*}[t!]
\centering
\includegraphics[width=6in]{slam_overview.eps}
\caption{The overview of the SLAM-based system.}
\label{fig:slam}
\end{figure*}
Upon the introduction of the AoA-IMU localization principle, we give an overview of our system as shown in Fig.~\ref{fig:slam}. Basically, Rover uses two sensors: the Intel 5300 WiFi NIC as an exteroceptive sensor that observes the AoAs with respect to backscatter tags and the IMU as an interoceptive sensor that observes the dynamics of the robot. The sensor data are buffered in a sliding window array for bounding the computation complexity. Then the SLAM-based system model takes the data to solve out the locations of the tags as well as the robot.
Intuitively, the AoA observed by the NIC imposes a geometrical constraint that imply the relative locations of the robot and the connected tags. Note that only the corrected AoA (refer to Fig.~\ref{fig:aoa_correction}) manifests the constraint. To localize the tags, we need to move the robot and capture the dynamics of the robot by IMU. The IMU provides the odometry constraint that indicates the locations of the robot by integrating angular rates and accelerations. Although it is well known that such an integration suffers from a temporal drift, the drift can be corrected by combining the AoA constraint (refer to Section~\ref{subsec:formulation}).
To limit the states and observations in the sliding window, we need to marginalize the data in the window when new observations come. A vanilla option of data marginalization is first-in-first-out (FIFO) that marginalizes out the oldest state and its corresponding measurements. This however cannot handle degenerate motions, \eg, being stationary or moving at a constant velocity. Specifically, if a robot stays at a position for a moment, the measurements keep updating and rendering the sliding window so that the data in the window are all related to the same position. This cannot correctly recover the metric scale by triangulation because the translation $\Delta d$ (Fig.~\ref{fig:principle}) almost diminishes. If a robot moves at a constant velocity, the translation cannot be correctly measured by the IMU due to zero acceleration. Therefore, we propose a flexible marginalization scheme to properly manage the data in the sliding window (refer to Section~\ref{subsec:marginalization}).
\subsection{Sliding Window Formulation}
\label{subsec:formulation}
Table~\ref{table:notation} describes the mathematical notation used in the SLAM algorithm, listed in the order they appear in the text.
\begin{table*}[h]
\centering
\caption{Mathematical notation.}
\label{table:notation}
\begin{tabular}{{c}l*{1}{c}}
Symbol & Description \\
\hline
$\hat{(\cdot)}$ & the quantity that can be measured by sensors, \ie, antenna array and IMU \\
$\bm{\mu}_i$ & the hidden state at discrete timestamp $i$ \\
$\mathbf{o}_{i}^j$ & the geometric observation from the AoA of backscatter $j$ at timestamp $i$ \\
$\mathbf{b}_j$ & the position of backscatter $j$ \\
$\mathbf{u}_{i+1}^i$ & the relative translation between two robot states $\bm{\mu}_i$ and $\bm{\mu}_{i+1}$ \\
$\bm{\mathcal{S}}$ & the state vector in the sliding window\\
$\mathcal{A}$ & the set of AoA measurements between all tags and the robot in the window \\
$\mathcal{I}$ & the set of all inertial measurements in the window \\
$\mathbf{Q}_{i}^{j}$ & the information matrix of the AoA constraint \\
$\mathbf{\Omega}_{i}^j$ & the AoA covariance matrix \\
$\theta$ & the corrected AoA \\
$\mathbf{r}_i^j$ & the direction vector referred to $i$\spth tag at timestamp $j$ \\
$d_i^j$ & the distance between the robot and $i$\spth tag at timestamp $j$ \\
$\mathbf{n}_i^j$ & the measurement noise \\
$\mathbf{P}_{k+1}^{k}$ & the information matrix of the odometry constraint \\
$\bm{\Lambda}_{k+1}^k$ & the IMU covariance matrix \\
$\mathbf{a}_t$ & the acceleration at current time $t$ \\
$\bm{\omega}_t$ & the angular rate at current time $t$ \\
$\mathbf{R}_t^k$ & the incremental rotation matrix from time $k$ to current time $t$ \\
$\mathbf{V}_{k+1}^k$ & the robot's relative velocity between timestamp $k$ and $k+1$ \\
$\mathbf{T}_{k+1}^k$ & the robot's relative translation between timestamp $k$ and $k+1$ \\
$\bm{\nu}_{k}$ & the velocity at timestamp $k$ \\
$\textbf{g}$ & the earth's vertical gravity \\
$\Delta t$ & the time interval between two consecutive measurements \\
\hline
\end{tabular}
\end{table*}
With the AoAs and IMU measurements, we can fuse them to solve the SLAM problem. In this topic, there exists many sensor fusion methods, \eg, EKF, particle filter. However, they usually requires a good initialization, which is very hard to obtain by AoAs due to the lack of metric scale information. Moreover, although filter-based approaches are very efficient in computation as they only estimate the current robot state and the map, the main drawback is that fixing the linearization points early may lead to suboptimal results. Therefore, we employ a graph-based SLAM framework in that 1) it achieves better performance via repetitively linearizing past robot states~\cite{lin2018autonomous}; 2) it is insensitive to the initialization because the multi-view constraint can help recover the initial state.
Fig.~\ref{fig:estimator} shows the graph representation of our SLAM formulation. Let $\bm{\mu}_i$ denote the hidden state at discrete timestamp $i$. At each timestamp, the robot observes a set of AoAs from multiple backscatters. $\mathbf{o}_{i}^j$ is the geometric observation from the AoA of backscatter $j$ at timestamp $i$ and $\mathbf{b}_j$ denotes the position of backscatter $j$. The relative translation between two robot states $\bm{\mu}_i$ and $\bm{\mu}_{i+1}$ is captured by an odometry edge $\mathbf{u}_{i+1}^i$, which can be obtained by IMU preintegration techniques~\cite{forster2015rss}.
We define the state vector in the sliding window that merges the hidden variables of robot and backscatter together,
\begin{equation}
\bm{\mathcal{S}} = [\bm{\mu}_0, \bm{\mu}_1, \dotsc, \bm{\mu}_{n-1}, \mathbf{b}_0, \mathbf{b}_1, \dotsc, \mathbf{b}_{m-1}]^\top,
\label{eqn:state}
\end{equation}
\noindent where the initial position $\bm{\mu}_0 = [0, 0, 0]$. All these variables refer to the world frame, which is related to the real world where the gravity is vertical. $n$ is the number of robot's state in the sliding window, $m$ denotes the number of observed backscatter tags, and $\mathbf{b}_i$ is the position of tag $i$ in the world frame. At this stage, we have constructed the graph from the AoA observations and the IMU odometry. Next step we seek to find the configuration of the positions of the robot and tags that best satisfies the constraints, \ie, the edges of the graph.
Since our system only involves translations, parameters in $\bm{\mathcal{S}}$ are in Euclidean space. We can formulate the problem as a linear problem and the optimal state sequence $\bm{\mathcal{S}}^*$ in the sliding window can be estimated by solving:
\begin{equation}
\bm{\mathcal{S}}^* = \argmin_{\bm{\mathcal{S}}} \Big\{\overbrace{\mathbf{A}(\bm{\mathcal{S}})}^\text{AoA constraint} + \overbrace{\mathbf{D}(\bm{\mathcal{S}})}^\text{odometry constraint} \Big\},
\label{eqn:cost}
\end{equation}
where
\begin{equation}
\begin{aligned}
\mathbf{A}(\bm{\mathcal{S}}) &= \sum_{(i, j)\in\mathcal{A}}\left\|\hat{\mathbf{o}}_{i}^{j} - \mathbf{Q}_{i}^{j}\bm{\mathcal{S}}\right\|^2_{\bm{\Omega}_{i}^j} \\
\mathbf{D}(\bm{\mathcal{S}}) & = \sum_{k\in\mathcal{I}}\left\|\hat{\mathbf{u}}_{k+1}^{k} - \mathbf{P}_{k+1}^{k}\bm{\mathcal{S}}\right\|^2_{\bm{\Lambda}_{k+1}^k}.
\end{aligned}
\label{eqn:cost_specific}
\end{equation}
\noindent $\mathcal{A}$ denotes the set of AoA measurements between all tags and the robot in the window. $\mathcal{I}$ denotes the set of all inertial measurements in the window. The constraints are the sum of the Mahalanobis norm of their measurement errors. Specifically, the AoA constraint is
\begin{equation}
\left\|\hat{\mathbf{o}}_{i}^{j} - \mathbf{Q}_{i}^{j}\bm{\mathcal{S}}\right\|^2_{\bm{\Omega}_{i}^j} = \left(\hat{\mathbf{o}}_{i}^{j} - \mathbf{Q}_{i}^{j}\bm{\mathcal{S}}\right)^\top \left(\bm{\Omega}_i^j\right)^{-1} \left(\hat{\mathbf{o}}_{i}^{j} - \mathbf{Q}_{i}^{j}\bm{\mathcal{S}}\right),
\end{equation}
and the odometry constraint is
\begin{equation}
\begin{aligned}
& \left\|\hat{\mathbf{u}}_{k+1}^{k} - \mathbf{P}_{k+1}^{k}\bm{\mathcal{S}}\right\|^2_{\bm{\Lambda}_{k+1}^k} = \\ & \left(\hat{\mathbf{u}}_{k+1}^{k} - \mathbf{P}_{k+1}^{k}\bm{\mathcal{S}}\right)^\top \left(\bm{\Lambda}_{k+1}^k\right)^{-1} \left(\hat{\mathbf{u}}_{k+1}^{k} - \mathbf{P}_{k+1}^{k}\bm{\mathcal{S}}\right).
\end{aligned}
\end{equation}
To solve this system, the terms of the AoA constraint $\left\{\hat{\mathbf{o}}_{i}^{j}, \mathbf{Q}_{i}^{j}, \mathbf{\Omega}_{i}^j\right\}$ and the odometry constraint $\left\{\hat{\mathbf{u}}_{k+1}^{k}, \mathbf{P}_{k+1}^{k}, \bm{\Lambda}_{k+1}^k\right\}$ need to be defined.
{\bf AoA constraint}. The direction vector $\mathbf{r}_{i}^{j}$ referred to the observed $i$\spth tag at timestamp $j$ can be defined by the AoA $\theta$ as $\mathbf{r}_{i}^{j} = [\cos(\theta), \sin(\theta), 0]^{\top}$. With an unknown distance $d_i^j$, a simple geometric relationship can be expressed as
\begin{equation}
d_i^{j}\mathbf{r}_{i}^{j} = \mathbf{R}_{0}^{j}\left(\mathbf{b}_{i} - \bm{\mu}_{j}\right),
\label{eqn:similar_equation}
\end{equation}
\noindent where $\mathbf{b}_{i}$ is the $i$\spth tag's position and $\bm{\mu}_j$ is the robot position at timestamp $j$. Since $\mathbf{r}_{i}^{j}$ should have the same direction as the vector $\mathbf{b}_{i} - \bm{\mu}_{j}$ if there is no measurement noise. The expected observation can be expressed by a cross product operation,
\begin{equation}
\hat{\mathbf{o}}_i^{j} = \hat{\mathbf{0}} = \left(\mathbf{R}_{j}^{0}\mathbf{r}_{i}^{j}\right) \times \left(\mathbf{b}_{i} - \bm{\mu}_{j}\right) = \mathbf{Q}_i^{j}\bm{\mathcal{S}} + \mathbf{n}_i^{j},
\label{eqn:wifi_measurement_model}
\end{equation}
\noindent where $\mathbf{n}_i^{j}$ denotes the noise, assuming that it follows a Gaussian distribution. The AoA covariance $\bm{\Omega}_i^j$ can be pre-measured by statistical methods and updated along the optimization process. Initially, the distance $d_{i}^{j}$ is given by a reasonable guess. Then it will be refined automatically along the sliding window optimization as the positions of the robot and tags are updated. Therefore, the initial guess is insensitive in our system.
Note that we consider the AoA in 2D case for the ease of representation. Our system can be trivially extended to work in 3D case. The circular antenna array we use is capable of measuring azimuth $\theta$ angle and elevation angle $\psi$ for 3D AoA representation. The direction vector becomes $\mathbf{r} = \left[ \cos\theta \sin\psi,\; \sin\theta \sin\psi, \; \cos\psi \right]$. However, we can no longer employ the joint AoA-ToF estimation technique~\cite{kotaru2015spotfi} to obtain the 3D AoA as the joint parameter searching process of this technique will increase the computation complexity exponentially due to the additional parameter, \ie, $\psi$. To reduce the complexity, we employ an additional parameter search instead of the joint search. This is an approximate solution of~\cite{kotaru2015spotfi} that slightly sacrifices the accuracy to significantly save the computation cost. Its computation complexity remains the same as the 2D case. It may occasionally miss the optimal parameter configuration but the overall performance is very close to the optimal solution as proved by~\cite{xie2019md}. Since the 3D extension is incremental to our contribution, we omit the details in this paper.
{\bf Odometry constraint}. Typically, the data rate of IMU is higher than AoA rate. Given two consecutive timestamps $[k, k+1]$ at which the AoAs from multiple tags are received, there have been multiple buffered inertial measurements, which include acceleration $\mathbf{a}_t \in \mathbb{R}^{3}$ and angular rate $\bm{\omega}_t \in \mathbb{R}^{3}$. We can preintegrate them to obtain an overall odometry representation between $\bm{\mu}_k$ and $\bm{\mu}_{k+1}$ as follows:
\begin{equation}
\begin{aligned}
\mathbf{V}_{k+1}^{k} &= \sum_{t\in[k, k+1]}\mathbf{R}_t^{k}\mathbf{a}_t \Delta t \\
\mathbf{T}_{k+1}^{k} &= \sum_{t\in[k, k+1]}\left[\mathbf{V}_{k+1}^{k}\Delta t + \mathbf{R}_t^{k}\mathbf{a}_t\Delta t^2\right],
\end{aligned}
\label{eqn:preimu}
\end{equation}
\noindent where $\mathbf{R}_t^{k} = \sum_{i \in [k, t]}\left[\mathbf{R}_i^{k}\lfloor\bm{\omega}_t\times\rfloor \Delta t\right]$, $\mathbf{R}_t^{k} \in \text{SO}(3)$. $\lfloor\bm{\omega}_t\times\rfloor$ is the skew-symmetric matrix from $\bm{\omega}_t$, $\Delta t$ the time interval between two consecutive measurements. $\mathbf{R}_t^{k}$ denotes the incremental rotation from time $k$ to current time $t$, which is available through short-term integration of gyroscope measurements. Then, we can write the propagation model of positions as
\begin{equation}
\bm{\mu}_{k+1} = \bm{\mu}_{k} + \mathbf{R}_{k}^0\bm{\nu}_{k}\Delta t - \mathbf{R}_{k}^{0}\textbf{g}\Delta t^2/2 + \mathbf{R}_{k}^0\mathbf{T}_{k+1}^{k},
\label{eqn:linear_update}
\end{equation}
\noindent where $\mathbf{T}_{k+1}^{k}$ can be obtained by Eqn.~\eqref{eqn:preimu}. $\textbf{g} = [0, 0, 9.8]^\top$ is the vertical gravity. Since the robot only moves in a room (assuming a horizontal plane), it is safe to obtain the accelerations that account for motions by directly subtracting the gravity. $\bm{\nu}_k$ denotes the velocity at timestamp $k$. It can be propagated as
\begin{equation}
\bm{\nu}_{k+1} = \mathbf{R}_{k}^{k+1}\bm{\nu}_{k} - \mathbf{R}_{k}^{k+1}\textbf{g}\Delta t + \mathbf{R}_{k}^{k+1}\mathbf{V}_{k+1}^{k},
\label{eqn:velocity_update}
\end{equation}
where $\mathbf{V}_{k+1}^{k}$ is obtained from Eqn.~\eqref{eqn:preimu}. $\mathbf{R}_{k}^{0}$ is the change in rotation since the initial state. We can see that the update equation for the quantity $\bm{\mu}_{k}$ and $\bm{\nu}_{k+1}$ will be linear in Eqn.~\eqref{eqn:linear_update} and Eqn.~\eqref{eqn:velocity_update} if rotation $\mathbf{R}_{k}^{0}$ are provided. This rotation can be obtained by solving a linear system that incorporate the short-term integration of gyroscope measurements. For brevity, we omit the details and refer to the broad literature discussing these ideas~\cite{shen2016initialization}.
Accordingly, Eqn.~\eqref{eqn:linear_update} can be rewritten as a linear function of the state $\bm{\mathcal{S}}$:
\begin{equation}
\begin{aligned}
\hat{\mathbf{u}}_{k+1}^{k} = \hat{\mathbf{T}}_{k+1}^{k}
& = \mathbf{R}_{0}^{k}\left(\bm{\mu}_{k+1} - \bm{\mu}_{k}\right) - \bm{\nu}_{k}\Delta t + \textbf{g}\frac{\Delta t^2}{2} \\
&= \mathbf{P}_{k+1}^{k}\bm{\mathcal{S}} + \mathbf{n}_{k+1}^{k},
\end{aligned}
\label{eqn:imumodel}
\end{equation}
\noindent where $\bm{\nu}_k$ can be updated by Eqn.~\eqref{eqn:velocity_update}, $\mathbf{n}_{k+1}^{k}$ denotes the additive measurement noise. Typically, we assume the additive noise follows a Gaussian distribution. Then the covariance $\bm{\Lambda}_{k+1}^{k}$ can be calculated using the pre-integration technique proposed in~\cite{lupton2012visual}.
At this point, all constraints in Eqn.~\eqref{eqn:cost_specific} are explicitly defined. The information matrices and state vectors in the sliding window can be stacked to construct a large array of linear equations so that the positions of the robot and the tags in the window can be solved altogether.
\begin{figure}[t!]
\centering
\includegraphics[width=3in]{estimator4.eps}
\caption{Graph representation for sliding window AoA-SLAM. $\bm{\mu}$ is the hidden state of robot position; $\mathbf{b}$ denotes the hidden state of backscatter position; $\mathbf{o}$ denotes the AoA observation; $\mathbf{u}$ is the odometry captured by IMU. The sliding window represented by the blue dashed box contains four states and their observed AoAs.}
\label{fig:estimator}
\end{figure}
However, the robot may undergo some degenerated motions in practical, causing the data marginalization problem as mentioned in Section~\ref{subsec:overview}. We next elaborate on our novel marginalization scheme.
\subsection{Flexible Marginalization}
\label{subsec:marginalization}
The FIFO marginalization scheme works fine when the robot is moving with non-zero acceleration. However, this scheme fails when the robot performs degenerate motions (zero acceleration), \eg, being stationary or moving in a constant velocity. In these cases, the IMU odometry, \ie, the translations between AoAs, cannot be correctly measured, failing to recover the metric scale. Unfortunately, zero acceleration motion is unavoidable in practice for a mobile robot and it must be handled properly.
When being stationary, the FIFO scheme results in that all measurements in the sliding window come from the same position. The translation between two AoAs is unobservable so that we cannot recover the metric scale. Intuitively, the last-in-first-out (LIFO) sliding window scheme can preserve the scale observability. In this case, we only update the position of the robot because LIFO scheme does not keep new AoAs.
When moving at a constant velocity, the translations between AoAs cannot be correctly measured, making the metric scale still unobservable. For example, if the robot first undergoes generic motions with sufficient accelerations ($\bm{\mu}_0, \bm{\mu}_1, \dotsc, \bm{\mu}_{l-1}$) and then enters a constant velocity motion ($\bm{\mu}_l, \bm{\mu}_{l+1}, \dotsc, \bm{\mu}_{l+n-1}$), the scale can only be observed when the states correspond to generic motions are included in the sliding window. However, this will inevitably increase the computation complexity so that the limited computation source of the robot cannot ensure the real-time property. A promising solution is to provide an initial estimate of $\bm{\mu}_l$, then we can propagate the scale from $\bm{\mu}_{l-1}$ to $\bm{\mu}_l$. This can be done by proper marginalization of $\bm{\mu}_{l-1}$ as it is removed from the sliding window at step $l+n$.
Based on the above discussion, we propose a flexible marginalization scheme to address the issue of degenerated motions. Consider a full state vector $\bm{\mathcal{S}} = \left[ \bm{\mu}_0, \dotsc, \bm{\mu}_{n-1} | b_\mathcal{L}\right]$ where $b_\mathcal{L}$ denotes the set of all observed backscatters in the sliding window. We add a state with a new AoA observation $\bm{\mu}_n$ to the sliding window if any of the following three criteria are satisfied:
\begin{itemize}
\item The time between two AoAs $\Delta t$ is larger than $\delta$.
\item The observed backscatter tags change in the new state.
\item The newest AoA observation significantly differs from the second newest observation in the sliding window.
\end{itemize}
The first criterion aims to bound the error in the integrated result of IMU measurements between two AoAs. Through some tests, we empirically set $\delta$ to be $500$ ms. The second criterion indicates that the system observes new tags that are needed to be localized. The third criterion aims to ensure that the translation of the robot with respect to the observed AoAs is significant.
To quantify the difference of AoA observations, we define the {\em similarity} between two AoA observations. At each timestamp, an AoA observation is a set of AoAs from multiple backscatters. For the AoA $\theta_i^j$ of $i$\spth backscatter observed at timestamp $j$, we have its direction vector $\mathbf{r}_i^j = [\cos(\theta_i^j), \sin(\theta_i^j)]^\top$. Then we define the AoA observation at timestamp $j$ as
\begin{equation}
\mathbf{O}^j = [\mathbf{r}_1^j, \mathbf{r}_2^j, \dotsc, \mathbf{r}_{m}^j], \quad \mathbf{O}^j \in \mathbb{R}^{2\times m},
\end{equation}
where $m$ is the number of observed backscatters at time $j$. For any timestamp $k > j$ that the observed backscatters remain unchanged, the similarity can be defined as
\begin{equation}
\mathcal{M}_{jk} = 1 - \frac{1}{m}\sum_{i = 1}^m \left( \mathbf{O}^j(i)^\top \cdot \mathbf{O}^k(i) \right),
\end{equation}
where $\mathbf{O}^j(i)$ denotes $i$\spth column of $\mathbf{O}^j$. The similarity $\mathcal{M} \in [0, 2]$. The smaller $\mathcal{M}$ the more similar AoA observations. Through experiments, we empirically set a threshold $\varepsilon$. When the similarity of the most recent two AoA observations is larger than $\varepsilon$, it satisfies the third criterion.
The pseudo code is shown in Algorithm~\ref{alg:marginalization}. The algorithm requires that all newly added AoAs $b_{\mathcal{L}^{+}}$ to have at least two observations to succeed in recovering the scale via triangulation (Line 1). Then we set a variable $f = \text{LIFO}/\text{FIFO}$ to indicate whether the system marginalizes out the second newest state $\bm{\mu}_{n-1}$ or the oldest one $\bm{\mu}_0$. The value of $f$ is determined based on whether the new state observed a new tag or the similarity $\mathcal{M}_{n-1}^n$ between two most recent AoA observations (Lines 5--9 and Lines 14--18).
\begin{figure}[t!]
\centering
\includegraphics[width=3in]{marginalization.eps}
\setlength{\belowcaptionskip}{-16pt}
\caption{An illustration of the flexible marginalization. If the second latest state has a similar AoA observation to the latest one, we will simply marginalize it and all its corresponding AoA measurements. However, pre-integrated odometry measurements are kept and the pre-integration process is continued towards the next state. Otherwise, we will keep it in the window and marginalize the oldest state and its corresponding AoA and odometry measurements. The information of marginalized states is turned into a prior.}
\label{fig:marginalization}
\end{figure}
To marginalize a chosen state, we first construct a new prior based on all measurements related to the removed state (Lines 3 and 11). We then remove the state, the corresponding AoA observation, and the backscatter tags $b_{\mathcal{L}^{-}}$ that are first observed by it (Lines 4 and 12). The new prior can be expressed as
\iffalse
\begin{equation}
\begin{aligned}
\bm{\Gamma}_{p}^{+} = \bm{\Gamma}_{p} & + \sum\limits_{(i, j)\in \mathcal{A}^{-}} \left(\mathbf{Q}_i^j\right)^\top \left(\bm{\Omega}_i^j\right)^{-1} \mathbf{Q}_i^j \\
& + \sum\limits_{k\in \mathcal{I}^{-}} \left(\mathbf{P}_{k+1}^k\right)^\top \left(\bm{\Lambda}_{k+1}^k\right)^{-1} \mathbf{P}_{k+1}^k,
\end{aligned}
\label{eqn:prior}
\end{equation}
\fi
\begin{equation}
\begin{aligned}
\bm{\Gamma}_{p}^{+} & = \bm{\Gamma}_{p} + \\
& \sum\limits_{(i, j)\in \mathcal{A}^{-}} \left(\mathbf{Q}_i^j\right)^\top \left(\bm{\Omega}_i^j\right)^{-1} \mathbf{Q}_i^j + \sum\limits_{k\in \mathcal{I}^{-}} \left(\mathbf{P}_{k+1}^k\right)^\top \left(\bm{\Lambda}_{k+1}^k\right)^{-1} \mathbf{P}_{k+1}^k,
\end{aligned}
\label{eqn:prior}
\end{equation}
where $\mathcal{A}^{-}$ and $\mathcal{I}^{-}$ are the sets of removed AoA and IMU measurements respectively. The marginalization can be carried out via Schur Complement~\cite{shen2016initialization}. The prior $\bm{\Gamma}_{p}$ is the initial condition computed by solving system~\eqref{eqn:cost}. Eqn.~\eqref{eqn:prior} converts the sum of the Mahalanobis norm corresponding to the removed measurements into a new prior. Note that in the LIFO scheme we have an additional operation that concatenates the IMU odometry from $\mu_{n-2}$ to $\mu_n$ for preserving additional motional information (Line 13).
This approach tries to preserve all information provided by the marginalized states. On one hand, our approach keeps removing the most recent state if the robot has small motion or is stationary. Keeping older states in this case can preserve the non-zero acceleration information that helps recover the scale. On the other hand, when the robot undergoes a constant velocity motion, older states will be removed and the priors implicitly propagate the scale information forward for subsequent estimates. Fig.~\ref{fig:marginalization} illustrates the two working cases of the flexible marginalization approach. In this way, our system needs to incorporate the prior information as follows:
\begin{equation}
\bm{\mathcal{S}}^* = \argmin_{\bm{\mathcal{S}}} \Big\{\overbrace{\left(\mathbf{b}_p - \bm{\Gamma}_{p}\bm{\mathcal{S}}\right)}^\text{Prior} + \mathbf{A}(\bm{\mathcal{S}}) + \mathbf{D}(\bm{\mathcal{S}}) \Big\},
\label{eqn:final_cost}
\end{equation}
where $\left\{\mathbf{b}_p, \bm{\Gamma}_p\right\}$ is the prior for our system. The system is then solved with all available measurements within the sliding window plus any available prior (Line 20).
\begin{algorithm}
\caption{Flexible Marginalization}
\label{alg:marginalization}
\begin{algorithmic}[1]
\REQUIRE
$$\bm{\mathcal{S}} \leftarrow \left[\bm{\mu}_0, \dotsc, \bm{\mu}_{n-1} | b_{\mathcal{L}}\right]$$
$$f = \text{FIFO} \; \text{or} \; \text{LIFO}$$
$$\left\{\mathbf{b}_p, \bm{\Gamma}_p\right\} \leftarrow \text{Prior}$$
\ENSURE $\Delta t > \delta$ \OR $b_\mathcal{L}$ changes \OR $\mathcal{M}_{n-1}^n > \varepsilon$
\STATE $\bm{\mathcal{S}} \leftarrow \bm{\mathcal{S}}\cup\left[\bm{\mu}_n | b_{\mathcal{L}^{+}}\right]$
\IF {$f = \text{FIFO}$}
\STATE $\left\{\mathbf{b}_p, \bm{\Gamma}_p, b_{\mathcal{L}^{-}}\right\} \leftarrow$ Marginalization$\left(\bm{\mu}_0\right)$
\STATE $\bm{\mathcal{S}} \leftarrow \bm{\mathcal{S}}\backslash\left[\bm{\mu}_0 | b_{\mathcal{L}^{-}}\right]$
\IF {$\mathcal{M}_{n-1}^n > \varepsilon$ \OR $b_{\mathcal{L}}$ changes}
\STATE $f \leftarrow \text{FIFO}$
\ELSE
\STATE $f \leftarrow \text{LIFO}$
\ENDIF
\ELSE
\STATE $\left\{\mathbf{b}_p, \bm{\Gamma}_p, b_{\mathcal{L}^{-}}\right\} \leftarrow$ Marginalization$\left(\bm{\mu}_{n-1}\right)$
\STATE $\bm{\mathcal{S}} \leftarrow \bm{\mathcal{S}}\backslash\left[\bm{\mu}_{n-1} | b_{\mathcal{L}^{-}}\right]$
\STATE OdometryConcatenation$\left(\bm{\mu}_{n-2}, \bm{\mu}_n\right)$
\IF {$\mathcal{M}_{n-2}^n > \varepsilon$ \OR $b_{\mathcal{L}}$ changes}
\STATE $f \leftarrow \text{FIFO}$
\ELSE
\STATE $f \leftarrow \text{LIFO}$
\ENDIF
\ENDIF
\STATE Solve $\bm{\mathcal{S}}$ using \eqref{eqn:final_cost} and \eqref{eqn:cost_specific} with $\left\{\mathbf{b}_p, \bm{\Gamma}_p\right\}$
\RETURN $\left\{f, \mathbf{b}_p, \bm{\Gamma}_p, \bm{\mathcal{S}}\right\}$
\end{algorithmic}
\end{algorithm}
\subsection{Implementation and Experimental Setup}
We implemented Rover on an Intel NUC with a 1.3 GHz Core i5 processor with $4$ cores, an $8$ GB of RAM and a $120$ GB SSD, running Ubuntu Linux equipped with Intel 5300 NICs and a LORD MicroStrain 3DM-GX4-45 IMU. We use the Linux 802.11 CSI tool~\cite{halperin2011tool} to obtain the wireless channel information for each packet. Thanks to the open-source hardware of HitchHike~\cite{zhang2016hitchhike}, we build the customized tags to backscatter commodity WiFi signals. The power consumption of the tags is only $33\mu$W, $1000\times$ lower than the mW-level power consumption of commodity WiFi. The whole system is implemented in C++. The NUC connects to the iRobot Create 2 and uses ROS (Robot Operating System) as the interfacing robotics middleware to control the robot's moving trajectory\footnote{ROS driver for iRobot Create 2, \url{https://github.com/autonomylab/create_autonomy}.}. The experimental platform is shown in Fig.~\ref{fig:sys}.
\iffalse
\begin{figure}[t!]
\centering
\includegraphics[width=5in]{irobot_test.jpg}
\caption{The experimental platform. The left shows the receiver attaches on the robot and sends commands to control its motions through the Create's 7-pin serial port. The right shows one of our customized backscatter tags.}
\label{fig:sys}
\end{figure}
\fi
In all experiments, we use two NUCs. One is the excitation source that operates in $5.825$ GHz center frequency (channel $165$) on a $20$ MHz band. The other is the receiver on the robot that performs the frequency hopping protocol to sweep all available channels in the $5$ GHz band except channel $165$.
The experiments are conducted in a $9\times 5$ square meters meeting room in our laboratory, which is a typical indoor setting. Four backscatter tags are deployed in the room. Each tag is configured to shift a frequency and backscatter signals in a separate channel. This prevents the interference between tags. In addition, the frequency shift can be an identifier to distinguish the received signal from which tag as each tag occupies a separate channel.
\begin{figure}
\centering
\begin{minipage}[b]{0.48\textwidth}\centering
\center
\includegraphics[width=1\textwidth]{irobot_test.eps}\vspace{-0.3cm}
\caption{The experimental platform. The left shows the receiver attaches on the robot and sends commands to control its motions through the Create's 7-pin serial port. The right shows one of our customized backscatter tags.} \label{fig:sys}
\end{minipage}
\hspace{0.1cm}
\begin{minipage}[b]{0.48\textwidth}\centering
\center
\includegraphics[width=1\textwidth]{trajectory3.eps}\vspace{-0.3cm}
\caption{We use the NUC to control a robot moves in a pre-defined rectangular trajectory in the meeting room. The ground truth is provided by the program of defining the trajectory that runs in the NUC.} \label{fig:trajectory}
\end{minipage}
\end{figure}
\subsection{Micro-benchmark Evaluation}
\iffalse
\begin{figure}[t!]
\centering
\includegraphics[width=3.5in]{aoa_error2.eps}
\caption{The accuracy of AoA estimation.}
\label{fig:aoa}
\end{figure}
\begin{figure}[t!]
\centering
\includegraphics[width=5in]{trajectory3.eps}
\caption{We use the NUC to control a robot moves in a pre-defined rectangular trajectory in the meeting room. The ground truth is provided by the program of defining the trajectory that runs in the NUC.}
\label{fig:trajectory}
\end{figure}
\fi
\begin{figure}
\centering
\begin{minipage}[b]{0.23\textwidth}\centering
\center
\includegraphics[width=1\textwidth]{aoa_error2.eps}\vspace{-0.3cm}
\caption{The accuracy of AoA estimation.} \label{fig:aoa}
\end{minipage}
\hspace{0.1cm}
\begin{minipage}[b]{0.23\textwidth}\centering
\center
\includegraphics[width=1\textwidth]{deg_error.eps}\vspace{-0.3cm}
\caption{The performance of robot localization under degenerated motions.} \label{fig:degerated_motions_a}
\end{minipage}
\end{figure}
\begin{table}[t!]
\centering
\caption{Computation time for each update.}
\label{table:time}
\begin{tabular}{|p{25pt}|p{80pt}|p{80pt}|}
\hline
No. of States&Robot Position Accuracy (cm)&Mean Computation Time (ms) \\
\hline
20&70.2&18.29 \\
\hline
30&45.3&27.40 \\
\hline
40&38.6&39.21 \\
\hline
50&36.5&58.50 \\
\hline
60&37.2&99.38 \\
\hline
70&37.0&158.17 \\
\hline
80&35.9&235.42 \\
\hline
\end{tabular}
\end{table}
{\bf Backscatter AoA Estimation}. We first test the accuracy of tag-to-receiver AoA estimation. The key difference in AoA estimation from the state-of-the-art~\cite{kotaru2017localizing}, WiTag, is that we empower it with time-division multiplexing so that the receiver can simultaneously measure AoAs of multiple tags who backscatter signals in different channels. We demonstrate the AoA estimation by four tags deployed in line-of-sight (LOS) and non-LOS (NLOS) settings. The CDF plotted in Fig.~\ref{fig:aoa} shows that the performance of Rover is similar to WiTag. The median errors of Rover and WiTag are $9.3\degree$ and $8.1\degree$ respectively in LOS deployment. In NLOS deployment, the median errors of Rover and WiTag are $18.1\degree$ and $14.6\degree$, respectively.
{\bf Performance under degenerated motions}. We then test Rover's tracking performance under degenerated motions, including being stationary and moving at a constant velocity. Meanwhile, we run Rover in two concurrent processes, with and without marginalization, for the evaluation of our marginalization algorithm. The robot first undergoes generic motions in both tests. Then at $24$ second, it stays stationary in the first test and moves at a constant velocity of $0.1$ m/s in the second test. Fig.~\ref{fig:degerated_motions_a} shows that the localization error accumulates in both cases of degenerated motions if there is no marginalization, but exhibits no accumulation when applied. The robot's mean localization errors are $35.5$ cm and $33.7$ cm during the first $24$ seconds of generic motions. Then the errors go up to $82.1$ cm and $148.7$ cm when being stationary and moving at a constant velocity in the case of no marginalization. When applying marginalization, the errors reduce to $39.1$ cm and $37.0$ cm in the two tests. We notice that the error accumulates faster in the constant velocity movement when marginalization is absent. This is due to the fact that near-zero linear acceleration in this case makes the moving distance unobservable from IMU measurements. Meanwhile, the AoA estimation still changes according to the movements, yielding erroneous results in the SLAM framework. In contrast, when being stationary, the measurements from the AoA and IMU do not contradict each other.
Fig.~\ref{fig:degerated_motions_b} depicts the localization error of a backscatter tag in LOS deployment in different degenerated motions, with and without marginalization. The mean errors of the two tests under generic motions are $76.5$ cm and $83.4$ cm. When the marginalization is not applied, the final errors rise to $118.7$ cm in stationariness and $121.0$ cm in constant velocity motion, respectively. In contrast, applying our marginalization algorithm eliminates the error accumulation. The errors remain $71.3$ cm and $79.6$ cm respectively, which are similar to the performance under generic motions. Again, the error in constant velocity motion accumulates faster due to the erroneous computation.
{\bf Rover's complexity}. The real-time processing is a desired property in that the real-time location estimates can be used for navigating the robot. Thus, the computation complexity analysis is required. The most time-consuming part of Rover is the SLAM framework, which is a linear system that can be computed quite efficiently. Specifically, we use the standard Cholesky decomposition implemented by Eigen to solve the linear system. The time complexity is $O(N^3)$ in theory, where $N$ denotes the number of states. In practice, the multithreaded routines make the computation time be approximate $N^2$ growth. Despite the mild time complexity, we further employs a sliding window formulation to ensure the real-time processing by bounding the parameter $N$. This is because $N$, which means the number of states in Rover, can be vast in a long-term run and thus significantly increases the computational cost if we solve the full batch SLAM for the best possible accuracy. It poses a tradeoff between localization accuracy and computation time. Essentially, the more states involved the more accurate results obtained. But this inevitably results in higher delay since a larger state vector and the corresponding measurements are involved in the optimization framework. To shed light on that, we tune the number of states in the sliding window from $20$ to $80$ to seek a balance between accuracy and computational cost. Table~\ref{table:time} lists the results in different amounts of states considered. When incorporating more than $50$ states, we can see a marginal increase of the accuracy and a significant increase of the computation time, which goes up to hundreds of milliseconds. Therefore, in our experiments, we empirically set the size of sliding window to be $50$. The overall average computation time is $58.50$ ms for each update and thus Rover achieves the real-time processing.
\begin{figure}
\centering
\begin{minipage}[b]{0.25\textwidth}\centering
\center
\includegraphics[width=1\textwidth]{deg_tag.eps}\vspace{-0.3cm}
\caption{The performance of tag localization under degenerated motions.} \label{fig:degerated_motions_b}
\end{minipage}
\hspace{0.1cm}
\begin{minipage}[b]{0.21\textwidth}\centering
\center
\includegraphics[width=1\textwidth]{position2.eps}\vspace{-0.3cm}
\caption{Robot position tracking in the meeting room.} \label{fig:experiment_result_a}
\end{minipage}
\vspace{-0.3cm}
\end{figure}
\subsection{System-level Evaluation}
\begin{figure*}
\centering
\begin{minipage}[b]{0.3\textwidth}\centering
\center
\includegraphics[width=1\textwidth]{tag.eps}\vspace{-0.3cm}
\caption{The localization errors of four tags in the meeting room.} \label{fig:experiment_result_b}
\end{minipage}
\hspace{0.1cm}
\begin{minipage}[b]{0.32\textwidth}\centering
\center
\includegraphics[width=1\textwidth]{mixed_error_marg.eps}\vspace{-0.3cm}
\caption{Robot position tracking with degenerated motions. {\bf STNRY} represents {\bf stationary}.} \label{fig:mixed_motions_a}
\end{minipage}
\hspace{0.1cm}
\begin{minipage}[b]{0.32\textwidth}\centering
\center
\includegraphics[width=1\textwidth]{mixed_tag_zoom_2.eps}\vspace{-0.3cm}
\caption{The error reports of four tags' positioning. They are zoomed in to the stationary periods for a better comparison. {\bf STNRY} represents {\bf stationary}.} \label{fig:mixed_motions_b}
\end{minipage}
\end{figure*}
{\bf Generic motions}. Fig.~\ref{fig:trajectory} shows the system deployment and the overall performance of Rover. The performance of tracking the robot's trajectory is plotted in Fig.~\ref{fig:experiment_result_a}. The mean error over the estimated trajectory is $39.3$ cm. The accuracy goes beyond the expectation from the noisy AoA estimation (Fig.~\ref{fig:aoa}). This is because our system introduces the inertial sensors that provide an additional sensing modality for positioning. Moreover, our sliding window optimization filters out the noise of heterogeneous sensors by finding the configuration of positions that best fits different spatial measurement constraints.
Fig.~\ref{fig:experiment_result_b} shows the localization results of the tags. Initially, the tags' locations are set to be $(0, 0)$. After about $20$ seconds, Rover localizes tags $1$ and $2$ as their AoAs are available. Tags $3$ and $4$ are localized at about $80$ and $90$ seconds later as the robot approaches them and received their backscattered packets. Meanwhile, Rover stops updating the location of tag $1$ after about $95$ seconds as it loses contact with the robot. The four tags' final localization errors are $73.6$ cm, $52.9$ cm, $97.2$ cm, and $145.9$ cm, respectively. Among them, the error of tag $4$ is higher due to its NLOS deployment. The mean localization error in LOS deployment is $74.6$ cm.
{\bf Mixed with degenerated motions}. To highlight the effectiveness of our marginalization approach in coping with degenerated motions, we control the robot to stop for a while at some points in the original trajectory and concurrently run Rover in two processes, \ie, with and without the marginalization respectively. Fig.~\ref{fig:mixed_motions_a} shows the position tracking results. The robot stops at $36$\spth second and $125$\spth second, both for a period of $30$ seconds. When incorporating marginalization, there is no sign of error accumulation during the stationary periods. The mean error over the whole trajectory is $43.2$ cm. In contrast, without marginalization, the overall mean error rises to $83.4$ cm.
Fig.~\ref{fig:mixed_motions_b} depicts the localization performance of four tags. For a clearer demonstration, we zoomed into the degenerated periods of each tag. For tags $1$ and $2$, they experience two periods of being stationary at $36$\spth second and $125$\spth second. In the absence of the marginalization, the two tags' final localization errors increase to $146.8$ cm and $182.3$ cm. On the other hand, when enabling the marginalization of Rover, the final errors remain almost unchanged that they are still at $46.4$ cm and $79.3$ cm for tags $1$ and $2$. After about $155$ seconds, tag $1$'s location is no longer updated as it loses the contact with the robot. Similar situation appears on tags $3$ and $4$. Their final errors rise to $124.3$ cm and $178.9$ cm without the marginalization, and remain at $78.2$ cm and $129.2$ cm when enabling the marginalization, which are similar to the performance under generic motions
In summary, the localization accuracy is decimeter-level, which is similar to the state-of-art WiFi based localization systems~\cite{kotaru2015spotfi, kotaru2017localizing}. The uniqueness of Rover is that it works without landmarks or any map of the environment, while conventional solutions need multiple APs with known positions. Conventional solutions use more APs to provide redundant positioning measurements and combat the noise of WiFi measurements. On the contrary, we take advantage of IMU and a robot's mobility to enable a new localization paradigm. The inertial measurements play the role of combating the WiFi noise and the drift-free localizability of WiFi helps correct the IMU drift in return. To bound the computation complexity, we employ a sliding window based formulation and incur a marginalization issue under degenerated motions. Our flexible marginalization algorithm succeeds in addressing the issue.
\section{Introduction}
\label{sec:intro}
\input{intro}
\section{Backscatter AoA Estimation}
\label{sec:background}
\input{background}
\section{SLAM with AoAs}
\label{sec:design}
\input{design}
\section{Implementation and Evaluation}
\label{sec:evaluation}
\input{eval}
\section{Related Work}
\label{sec:related}
\input{related}
\section{Conclusion}
\label{sec:conclusion}
\input{conclusion}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 2,423
|
Q: Which AWS services am I using? When I sign into the AWS Management Console, I just see a list of all the services. How do I know which ones I'm using? Can I hide the ones I'm not using?
I much prefer the way Heroku organizes things. It shows your apps first. Then, when you click into an app, it only shows the add-ons (services) that app is using. Imagine logging into Heroku and just seeing a list of all Heroku add-ons.
A: UPDATE: 2019-02-22 09:39:25
*
*A user on the stackexchange network reports that this answer is no longer valid, due to a change made by AWS
Quick Answer (TL;DR)
*
*Use the tag editor feature of AWS Resource Groups to report AWS services usage.
Detailed Answer
Context
*
*Amazon Web Services console (AWSConsole)
*Current version as of 2017-06-11
*Tracking any of various AWS Resources
Problem
*
*Scenario: AWSUserDipasq wants a report showing all used resources for a specific AWSConsole
*AWSUserDipasq does not have a handy record or report at hand
*
*Example: AWSUserDipasq inherited an AWS configuration from someone else
*Example: AWSUserDipasq setup the configuration a long time ago, and forgot what he did
*Example: AWSUserDipasq used some third-party service to configure one or more resources on the specific AWSConsole
*AWSUserDipasq notices that the AWSBillingReport does not show enough detail
*
*Example: AWSBillingReport only shows those items with no associated usage fee
*Example: AWSBillingReport only shows those items which have already incurred costs in the previous billing period
Solution
Use the tag editor feature of AWS Resource Groups.
Step-by-Step:
*
*STEP: Login to the relevant AWSConsole
*STEP: Choose Resource Groups from the main AWSConsole
*STEP: Choose tag editor from the Resource Groups submenu
*STEP: Under Find resources to tag :: Regions choose all the AWS regions available
*STEP: Under Find resources to tag :: Resource Types choose All resource types
*STEP: Choose Find Resources
When these steps are successfully completed, the result will be a report of all the AWS Resources that are deployed on the relevant AWSConsole
Pitfalls
*
*This approach may show resources that are allocated for deployment, but still not actually used.
See also
*
*https://docs.aws.amazon.com/awsconsolehelpdocs/latest/gsg/creating-a-resource-group.html
*http://docs.aws.amazon.com/AWSCloudFormation/latest/UserGuide/cfn-using-cloudformer.html
A: Once you figure out what services you're using, you may want to create a resource group to group them together.
A: AWS introduced AWS Config for audit purpose. AWS Config is a service that enables you to assess, audit, and evaluate the configurations of your AWS resources. Config continuously monitors and records your AWS resource configurations and allows you to automate the evaluation of recorded configurations against desired configurations.
Source: https://aws.amazon.com/config/
A: Login to your AWS account using Resource Auditor Role and check the billing. Under Billing Details you can see what you are running under which region.
Do pin the Billing server to see the same once you login.
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 5,034
|
Paralimnus cinnamomeus är en insektsart som beskrevs av Mitjaev 1971. Paralimnus cinnamomeus ingår i släktet Paralimnus och familjen dvärgstritar. Inga underarter finns listade i Catalogue of Life.
Källor
Dvärgstritar
cinnamomeus
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 9,610
|
LOOKING FOR A MODERN FAMILY HOME WITH SHEDDING IN A QUIET LOCATION ? THEN LOOK NO FURTHER.
This four bedroom solid stone home with colourbond roof and aluminium windows has been completely renovated inside and out. It has been tastefully done using neutral tones allowing you to add your own personality and offers space inside and out for comfortable family living.
– Modern kitchen with laminate timber floor, electric cooking with underbench oven,hotplates and range hood, dishwasher, pantry and island bench.
– Open Dining with laminate floor and slow combustion wood heating.
– Four double size bedrooms all carpeted and 3 with built in robes, main with a blind and two and three with curtains, Bedroom 3 also has a roller shutter.
– Renovated modern bathroom fully tiled to the ceiling. Corner spa bath with waterfall shower head over and vanity.
– Tiled laundry with built in cupboards.
– Rear rumpus room which is carpeted and has sliding glass doors leading to the pergola.
– Ducted reverse cycle air conditioning and slow combustion wood fire for heating and cooling the home.
– The shedding and undercover areas here are every man's dream. You have massive amounts of secure, lockable shedding and huge flexibility for outdoor living and entertaining. There is an 8mx5m semi enclosed rear gable roof pergola with cement floor, lighting and ceiling fans, it is a completely private area enclosed on three sides including the adjoining 7mx 6m double carport which is secured by a double roller door from the road. This makes the whole rear yard completely lockable and secure. The carport is attached to the massive, deep, two bay 16mx10m shed with multiple car spaces and workshop area it has a cement floor, storage loft and is also lockable with another roller door.
– Set on a block of 809m2 hedging makes both the small front and larger rear yards private.
– 10,000 gallons of rainwater services the house, town water is also available and town sewer is connected.
– The rear yard is lawn with garden beds, soft fall for a child's play area if needed and a garden shed and wood shed.
This solid well maintained home has been beautifully renovated and offers a lot more than meets the eye. Inspection is a must… Call today to book your appointment.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 2,870
|
This site is brand new and things will appear sporadically over the coming weeks so please feel free to come back and see how it's evolving. In the meantime if you would like to contact me you can do so here.
Our research specialises in studying the regulation of neural form and function at the molecular level. Much of our work has focused on studying the roles of transcription factors in the development and patterning of nervous systems from basic neurogenesis through to area specialisation and axonal navigation. More recent work has moved into the domain of regulatory genomics where primary miRNA, mRNA, protein expression data is integrated with a host of genomic meta-data and prior biological knowledge to build an integrated understanding of the underlying biological processes. At a higher level we are applying this systems level molecular view to understanding the regulatory processes controlling synaptic plasticity in neurological disease models and paradigms of learning, memory and cognition.
Katie Emelianova (2012-). Patterns of Molecular Evolution in Begonia [with Catherine Kidner, RBGE].
Xin He (2012-). Construction of frameworks for meta-genomic analysis of neurological diseases and their applications.
Maciej Pajak (2013-). Conserved genetic control motifs in synaptic plasticity.
PhD. studentship. Rule-Based Modelling for Neurological Disease.
Giuseppe Gallone (2012). Computational Approaches to Discovering Differentiation Genes in the Peripheral Nervous System of Drosophila melanogaster [with Andrew Jarman].
Catherine Carr (2009). Microarray investigation of the role of Pax6 at the PSPB using a novel tauGFP-Pax6 reporter mouse.
Jennifer Pinson (2005). The role of Pax6 isoforms in embryonic development.
David Tyas (2005). Generation of a Pax6 reporter mouse.
Celestial Yap (2005). The role of cofilin in glioblastoma cell behaviour.
Owen Dando (2013). Integrating gene regulation and expression data to infer genomic target sequences for the transcription factor Gli3 in the developing mammalian forebrain.
Moo Sin Yeong (2012). Evolution of the cognitive proteome.
Sthita Mohapatra (2011). Developing a web application for cross taxonomic protein-protein interaction prediction.
Eleni Flerianou (2010). Implementing a Taverna workflow architecture for regulatory genomics.
Elizabeth Watson (2009). Assessing regulome complexity during Drosophila peripheral nervous system development.
Hugh Townshend (2007). Computer construction of a gene regulatory network for neurogenesis - the use of existing literature to create a model for Drosophila neurogenesis.
Benjamin Fenby (2000). Towards a functional assay for Pax6.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 9,184
|
David Kirp is a professor at the Goldman School of Public Policy at the University of California, Berkeley, a member of the National Academy of Education, a contributing writer to The New York Times and a senior scholar at the Learning Policy Institute, a "think-and-do" tank. He is a Member of the American Academy of Arts and Sciences and the National Academy of Education. In his seventeen books and hundreds of articles, he has concentrated on pivotal education and youth issues from cradle to college and career.
Education
Kirp graduated from Amherst College and Harvard Law School.
Career
A former newspaper editor and syndicated columnist, David Kirp contributes to leading national print media outlets, including The New York Times, The Atlantic Monthly, the American Prospect and The Nation, and appears as a policy expert on nationally broadcast radio and televisions programs.
Kirp is a recipient of Berkeley's 1982 Distinguished Teaching Award.
David Kirp founded the Harvard Center on Law and Education, a national law reform organization that promotes equality of educational opportunity. He was a trustee of Amherst College and has served on numerous nonprofit boards, including Experience Corps, Friends of the Children, the Coro Leadership Center of San Francisco and the ACLU of Northern California. He served on President Barack Obama's transition team, where he drafted policy agendas for early education and community schools. He has consulted with many nonprofit groups and public agencies in the United States and abroad.
Works
Among Kirp's books are The Sandbox Investment: The Universal Preschool Movement and Kids-First Politics and Shakespeare, Einstein and the Bottom Line: The Marketing of Higher Education.
The College Dropout Scandal focuses on the under-appreciated fact that half of undergraduates who enroll in public universities fail to graduate and shows, through narratives about colleges that buck this trend, what can be done to change the arc of students' lives.
Improbable Scholars: The Rebirth of a Great American School System and a Strategy for America's Schools details how a poor, Latino school district became a national model.
References
External links
David Kirp AtGoogleTalks.
Living people
Amherst College alumni
Harvard Law School alumni
Goldman School of Public Policy faculty
Year of birth missing (living people)
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 31
|
{"url":"https:\/\/www.coursehero.com\/subjects\/annual-percentage-rate\/","text":"\u2022 ### Annual Percentage Rate Q&A\n\n##### Annual Percentage Rate Study Resources Q&A View all\n\u2022 ###### Q. Please do not use financial calculator. I want to know the formula. Suppose that the annual percentage rate (compounded semi-annually) is 10%....\n\u2022 1 file(s) attached\n\u2022 ###### Q. 1. What is the effective rate of 12% compounded annually, quarterly, monthly, and daily? 2. If the effective rate is 18%, what is the nominal...\n\u2022 1 file(s) attached","date":"2019-01-22 15:02:59","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\": 0.6520804166793823, \"perplexity\": 6117.2312813963745}, \"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-2019-04\/segments\/1547583857913.57\/warc\/CC-MAIN-20190122140606-20190122162606-00034.warc.gz\"}"}
| null | null |
fikstür, puan Durumu, ok sayda kamera ile eitli alardan, drone ile gökyüzünden ekilecek ve spiker hizmetleriyle birlikte canl olarak üzerinden l3 vpn nedir yaynlanacaktr. - Final malar, statistiksel bilgiler ve ligle ilgili bütün detaylar web sitesi ve sosyal medya kanallar üzerinden izlenebilecektir.we create solutions which works on Big Data and use Machine Learning for them. As a Full Stack Software Engineer you will build a product for machine generated l3 vpn nedir real world data. Tanm: At LAGOM, we are building software which solves complex problems.please provide some examples (preferably,) we offer l3 vpn nedir flexible working hours. Additionally, so you get to choose the best working time for yourself. At least 3) of your past projects. Many more benefits and invaluable startup experience await. We are waiting for your applications at.
build and deploy a single-page web app system from scratch l3 vpn nedir using design documents.
Then, WalkOVR could be your next destination. Here is who we are looking for: Software Engineer with prior experience Experienced in C, C, Java, Python or similar Having experience in developing on embedded systems is expected. Having worked with prototyping boards is an advantage. Part-time.
insanlara yardm etmekten holanan, disiplin l3 vpn nedir kurallarna aykr davranan oyuncularn turnuvadan diskalifiye edilmesi hakk TÜ ARI Teknokent tarafndan sakl tutulmaktadr. TÜ Teknokent'te bulunan atölyemize takm ruhunu seven, tridi ekibine katlmak ister misin? Letiim: Tridi http genius proxy list Müteri Temsilcisi Aryor!
Js Basic understanding of machine learning concepts (to be able to communicate with the team) Experience with C# and WPF Experience with Redis and timeseries databases Firma Ad: ODC özümleri Danmanlk Ticaret A. Pozisyon Ad: Müteri Deneyim Uzman Departman Ad: Sat ve Pazarlama Departman Tanm: - Kurumsal müterilerimizdeki.
here is who we are looking for: l3 vpn nedir Electronics Engineer with at least 3 years of experience Experienced in multi layer circuit design,opera Browser features The opera features shown below, for instance if you have full screenmode (F11)) and l3 vpn nedir than hit (F4)) you will get an additional bar on the left side of the screen. Are a lot keyboards shortcuts.common Name (eg,) most of the l3 vpn nedir details will default to the correct values but you will need to enter a "Common Name". As with generating the root certificate, this is best set to the hostname of the server.
instagram (instastory or just episodes of my favorite TV show,) the video would stop to buffer/load almost all l3 vpn nedir the time; I had many unpleasant video watching experiences. Best VPN I've used. In the past when I used VPN to stream videos on,best VPN I've used. Instagram (instastory or just episodes of my favorite TV show,) vPN to stream videos on, the video would stop to buffer/load l3 vpn nedir almost all the time; I had many unpleasant video watching experiences. In the past when I used.
and download aplikasi cakyenk vpn support is top notch. It works, it's simple, really Useful! This program lets you bypass firewalls and content filters to access sites that may be blocked by l3 vpn nedir your ISP or Government. By KageTora777 at m. - by ksframpton at m.it is the responsibility of the person writing the review l3 vpn nedir to be neutral and just in writing about it. User experience matters the most and specially when providing a review of a service, does PureVPN Really Works on Kodi?
either to give detailed information about the URLs accessed l3 vpn nedir by specific users, or to monitor bandwidth usage statistics. It also usually produces logs,7. It is a totally free software application that allows you to visit blocked sites anonymously. It offers full broadband speed l3 vpn nedir and is easy to use.
the behavior is same to traditional Ethernet switches. It means that SoftEther VPN can create a VPN connection beyond any kinds of firewalls l3 vpn nedir and NATs. The free vpn client download windows 7 Virtual Hub exchanges all Ethernet packets from each connected VPN session to other connected sessions.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 532
|
Q: Replacing both spaces and " - " in filenames and directorys I have been reading this this discussion and this find . -depth -name '* *' \ | while IFS= read -r f ; do mv -i "$f" "$(dirname "$f")/$(basename "$f"|tr ' ' _)" ; done
helps me deleting spaces in files and directories.
Beat Boy becomes Beat_Boy. This is ok.
What I don't get right is how to deal with this:
Beat Boy - Best of becomes Beat_Boy_-_Best_of while I want it to be Beat_Boy-Best_of.
I would appreciate any hint which way to go...
Regards
A: You can add sed to substitute "_-_" with "-"
f="Beat Boy - Best of"
echo $f | tr ' ' _ | sed 's/_-_/-/g'
#Beat_Boy-Best_of
In your case, you would want:
find . -depth -name '* *' |
while IFS= read -r f ; do
mv -i "$f" "$(dirname "$f")/$(basename "$f" |
tr ' ' _ |
sed 's/_-_/-/g')" ;
done
Edit
You can also replace tr ' ' _ | sed 's/_-_/-/g' with sed 's/ /_/g ; s/_-_/-/g'.
A: f="Beat Boy - Best of"
f1=${f// - /-}
f1=${f1// /_}
echo $f1
Beat_Boy-Best_of
A: This solution just replaces any number of [ ' ' or '-' ] with a single '_'. I assume that's probably what you want.
The find command still only searches for files with spaces in them, but you can change that to suit your needs.
while IFS= read -r f ;
mv -i "$f" "$(dirname "$f")/$(basename "$f" | sed -re 's/[ -]+/_/g')";
done < <(find . -depth -name '* *')
Full credit: this takes LC-datascientist's solution and replacing the somewhat awkward combination of tr and sed. Even Doyousketch2's comment about sed didn't use s///g option to make it simpler.
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 7,764
|
Abraham Lincoln Items Being Featured At Henry Ford Museum Near Detroit
Mark Frankhouse
Mark Frankhouse Published: April 15, 2021
Today's date of April 15th, 2021 marks the 156th anniversary of President Abraham Lincoln's death. As a kid going to the Henry Ford museum on a field trip, I remember the chills that I had when I first looked at the chair Lincoln sat in at the Ford's Theatre, when he was shot by John Wilkes Booth in 1865. Thanks to the Henry Ford Museum's goal to keep the chair preserved, the chair is still a permanent feature and will be amongst many other items of Lincoln's that will be on display at the museum.
There are many commemorative and personal items that belonged to him which is the main feature of the exhibit. Included in their inventory is:
Washstand Used in Abraham Lincoln's Springfield, Illinois Home, 1840-1860
Printing Block of Columbia Mourning President Lincoln's Death, 1865
Wardrobe Used in Abraham Lincoln's Springfield, Illinois Home, 1840-1860
Abraham Lincoln Campaign Badge, 1864
Abraham Lincoln Campaign Hat, 1860
Abraham Lincoln Mourning Badge, 1865
Life Cast of Abraham Lincoln's Hands and Face by Leonard Wells Volk
The items are featured as part of the "Liberty and Justice for all" exhibit. General admission tickets are $25 and can be purchased through their website. The Henry Ford recently resumed operations after temporarily closing to prevent the spread of COVID-19.
The most valuable of the items owned by the Henry Ford Museum of Lincoln's is the assassination chair, purchased by Henry Ford in 1930, and has been on display at the museum for the past 42 years. This is a great exhibit if you really want to take a step back in time.
Filed Under: Henry Ford Museum
Fight Over Lincoln Statue In Kalamazoo's Bronson Park
How Many of Michigan's Top 20 Attractions Have You Visited?
Ferrari From 'Ferris Bueller's Day Off' Now on Display at Henry Ford
Walt Disney Archives Tour Brings Heroes & Villains to Henry Ford Museum
Enter To Win Our Last Minute Marvel Tickets For Christmas
Enter To Win A Family 4-Pack: The Marvel Exhibit at The Henry Ford
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 6,125
|
{"url":"https:\/\/rba.gov.au\/publications\/bulletin\/2019\/jun\/cryptocurrency-ten-years-on.html","text":"# Bulletin \u2013 June 2019 Payments Cryptocurrency: Ten Years On\n\n## Abstract\n\nTen years on from the creation of Bitcoin, the term \u2018cryptocurrency\u2019 has entered the public consciousness. Despite achieving some name recognition, cryptocurrencies are not widely used for payments. This article examines why Bitcoin is unlikely to become a ubiquitous payment method in Australia, and summarises how subsequent cryptocurrencies have sought to address some of the shortcomings of Bitcoin \u2013 such as its volatility and scalability problems. It also examines the proliferation of new \u2018coins\u2019 and concludes that, despite the developments in cryptocurrencies, none are currently functioning as money in the economy.\n\n## Introduction\n\nOn 3 January 2009, the first bitcoins were created.[1] Ten years on the terms \u2018bitcoin\u2019 and \u2018cryptocurrency\u2019 are widely known. \u2018How to buy bitcoin\u2019 was the third-ranked \u2018How to \u2026\u2019 search term in Google in 2017 (Google 2018), alongside significant growth in fraudulent and phishing spam mail related to cryptocurrencies (Kaspersky Lab 2018). However, neither Bitcoin nor the many thousands of cryptocurrencies that have followed have become widely used for payments. People are more likely to view cryptocurrencies as a speculative high-risk investment class than a payment system. In this article, we look back over the decade since the launch of Bitcoin. We examine how cryptocurrencies have changed over that period in an attempt to address some of the shortcomings of Bitcoin as a payment system \u2013 such as its volatility and scalability problems.[2] We also describe the development of \u2018programmable\u2019 cryptocurrencies. Despite these changes, we see little likelihood of a material take-up of cryptocurrencies for retail payments in Australia in the foreseeable future.[3]\n\n## What is Cryptocurrency?\n\nOne definition of cryptocurrency is that it is a digital representation of value that is neither issued by a central bank or a public authority, nor necessarily attached to a national currency, but is designed to be accepted by some parties as a means of payment and can be transferred, stored or traded electronically.[4] Cryptocurrencies use computer software running across a network and rely on various established cryptographic techniques (hashing, digital signatures or one-way cryptographic functions) to control access and verify transactions. They use some form of \u2018consensus mechanism\u2019 to validate transactions; that is, a mechanism to achieve agreement across the network on whether a transaction is valid or not.\n\nThe technology underlying cryptocurrencies is often referred to as distributed ledger technology (DLT).[5] Given this, cryptocurrency is sometimes described as a \u2018digital token\u2019 on a distributed ledger that can be used to exchange value and thereby facilitate payments. DLT platforms vary in many ways, including: who can see and\/or keep a copy of the ledger, who can update the ledger, what information is required to verify a transaction on the ledger, and how tokens are created and distributed. Another way in which DLT platforms can differ is in how the data on the platform is structured; blockchain refers to one way of structuring the data. Blockchain and alternative methods are discussed later in the article.\n\nIn recent years, other types of DLT-based digital tokens have been designed and launched. Some have characteristics that are similar in some respects to securities (such as shares or bonds) and others are tokens that can be redeemed for access to a specific product or service (that is often to be provided using DLT). These are often referred to as \u2018security tokens\u2019 and \u2018utility tokens\u2019, respectively. Together cryptocurrency, security tokens and utility tokens are commonly referred to as \u2018crypto-assets\u2019. It should be noted that, while commonly used, these terms can be misleading. For example, \u2018currency\u2019 is often thought as being synonymous with money. However, no cryptocurrencies currently have the key attributes of money; and similarly, many crypto-assets have been found to fall well short of the definition of an asset as \u2018a useful thing or quality\u2019 (Macquarie Dictionary 2019).[6]\n\nCryptocurrencies (and crypto-assets more broadly) can enter circulation in a variety of ways. As described more fully below, in the case of Bitcoin, new bitcoins are created and paid out as a reward for participants of the system validating transactions. In other cases, new cryptocurrency units may be simply (and potentially arbitrarily) created by the controller of the protocol and sold (potentially via an initial coin offering) or given away for free (typically as a marketing exercise to broaden awareness of their coin). Cryptocurrency exchanges facilitate the buying and selling of cryptocurrencies in the secondary market. However, not all cryptocurrencies are listed on exchanges, or indeed have any market value.\n\n## The First Generation of Cryptocurrencies\n\nProposals for electronic versions of cash had been made and trialled at various points in the late 20th century, without success in practice.[7] Bitcoin, which launched in 2009 following the publication of a paper by an unknown author or authors in 2008, combined a series of existing technologies to provide a peer-to-peer version of electronic cash (Nakamoto 2008). Box A provides a high-level description of some of the basics of Bitcoin.\n\n## Box A Bitcoin Basics[8]\n\nBitcoin has a \u2018blockchain\u2019 of transactions. The \u2018ledger\u2019, or record of changes in ownership, consists of \u2018blocks\u2019 of information linked together in chronological order (a \u2018chain\u2019). Every 10 minutes on average, the Bitcoin blockchain is updated to include a new block of transactions. Addresses (or ownership) on the ledger are in terms of alphanumeric pseudonyms rather than legal names.\n\nMost conventional payment methods \u2013 cash is the obvious exception \u2013 rely on some central party to keep and update the ledger or record of holdings. For example, the Reserve Bank maintains the ledger of commercial banks' Exchange Settlement Account holdings. And commercial banks maintain records of their customers' deposits. By contrast, Bitcoin and other cryptocurrencies rely on a distributed ledger. The Bitcoin ledger (the blockchain) is replicated across the \u2018nodes\u2019 (i.e. computers) connected to the network. The idea is that each of the nodes ends up with an identical copy of the latest version of the ledger.\n\nIf a ledger is open to participation by any party, and any party can propose changes to the ledger, it is known as a public (or \u2018unpermissioned\u2019 or \u2018trustless\u2019) ledger. Bitcoin and many other cryptocurrencies are examples of trustless distributed ledgers. The user does not need to know or trust any party on the network but, in effect, needs to trust the algorithm and the cryptography used. This allows parties who do not necessarily trust each other to transact without the need for an intermediary.\n\nThe security of the Bitcoin system relies on public\/private-key cryptography. The transaction verification methodology is referred to as \u2018proof of work\u2019. Participants in the system (or \u2018miners\u2019 as they are known) compete to successfully verify (by solving computationally intensive calculations for) a new block of transactions, with each block consisting of around 2,500 transactions at the time of writing. The first miner to do so earns a reward of newly \u2018mined\u2019 coins, currently set at 12\u00bd bitcoins (currently, worth around US$100,000). The successful miner also earns any transaction fees offered by the people initiating the transactions contained in that block. Bitcoin demonstrated that, under certain assumptions, information about transactions could be verified and relied upon without the need for a trusted central party. The possibility of transactions being recorded securely on a distributed basis led to considerable interest in Bitcoin and other potential implementations of DLT. While Bitcoin remains the most prominent cryptocurrency, a large number of alternative cryptocurrencies and digital tokens have been created in recent years. Some are essentially replicas of Bitcoin, while others seek to introduce additional functionality or have different design features. For example, Litecoin adopts most of the features of Bitcoin but has a shorter block confirmation time of around 2\u00bd minutes and uses an alternative hashing algorithm. Dogecoin, initially created as a novelty currency, gained use for various crowd-sourced fundraising efforts. As identified by Nakamoto, the purpose of Bitcoin was to act as a peer-to-peer payment mechanism. In practice, its use for this function has been limited. However, it has seen significant use as a vehicle for speculation. This was particularly the case in late 2017 when there was a very considerable increase in the price of bitcoin, along with most other cryptocurrencies. Media reports of these price increases generated further speculative interest, with many buyers unlikely to have had familiarity with cryptocurrencies other than what they had heard or seen in the media or from acquaintances. Following this speculative episode, prices fell dramatically from their peaks, leaving many purchasers of cryptocurrencies with capital losses. Economic definitions of money typically reference three key features: a means of payment, unit of account, and store of value. Assessments of whether Bitcoin and other cryptocurrencies meet this definition usually conclude that they do not (Ali et al 2014; RBA 2014). Bitcoin's very significant fluctuations in price mean that it is a poor store of value (Graph 1). In part reflecting this price volatility, it is not used as a unit of account: goods and services sold for bitcoin are nearly always priced in some national currency, with the amount of bitcoin required to be delivered varying as its price changes. While Bitcoin and other cryptocurrencies can act as a means of payment, they are not widely used or accepted due to a number of shortcomings. There are strong network effects in payments: use and acceptance of payment methods are generally self-reinforcing \u2013 as can be seen from the rapid adoption of contactless card payment by both merchants and cardholders. A failure to generate network effects can mean that payment methods become, or remain, niche. In this context, Bitcoin has a number of shortcomings that appear to have limited its suitability for widespread household and business payment use \u2013 price volatility (discussed above), lack of scalability and uncertainty around settlement finality. The lack of scalability (see Box B) stems from the fact that Bitcoin blocks have a limit on the amount of information they can contain. This limits the number of transactions that can be validated in any individual block and restricts the system to fewer than 10 transactions per second. By contrast, the Fast Settlement Service that serves Australia's New Payments Platform is designed with the capacity of settling around 1,000 transactions per second. Another issue with Bitcoin is that a transaction cannot be assumed to be final until sometime after it is confirmed in a block. A block is validated by the network roughly every 10 minutes. Since miners compete to nominate new transaction blocks, a transaction may be included in one miner's block but not another's. Sometimes two competing blocks are mined at approximately the same time: eventually one of these will become part of the longest chain while the other becomes an \u2018orphan\u2019 block. Bitcoin transactions recorded in an orphan block are likely to eventually be picked up and included in a later block in the (main) chain but, before this occurs, transactions in the orphan block cannot be treated as settled. Even after a few subsequent blocks are mined, a given block may still be part of an orphan chain: an oft-cited guide is for parties to a transaction to wait until five subsequent blocks are mined (i.e. a total of 60 minutes) before treating a transaction as final. This lack of prompt settlement finality can be a problem for users where, say, goods or services are being delivered in exchange for bitcoins. Because Bitcoin and other first-generation cryptocurrencies rely on \u2018proof of work\u2019 to establish consensus on the state of the ledger, they consume considerable amounts of energy. Miners compete to solve a computationally intensive cryptographic puzzle that, when solved, verifies a new block of transactions. The successful miner earns a reward of new coins plus any transaction fees associated with a block. The chances of successfully mining a block are roughly proportional to the amount of processing power devoted to solving the cryptographic puzzle. This leads to an arms race in mining technology, as miners invest in more processing power to increase their chances of success. However, since the incentives for this additional investment apply to all miners, if all parties individually invest in faster computing power, then there is no change to their chances of successfully mining a block (Ma, Gans and Tourky 2018). At time of writing, it is estimated that the amount of energy used to power the Bitcoin consensus process is estimated to be equivalent to the energy consumption of Switzerland (Digiconomist 2019). This sizeable energy consumption is a key element of ensuring the validity of cryptocurrency ledgers, but generates large negative environmental externalities. This is likely to become an issue for policymakers, particularly in the context of increasing concerns about climate change.[9] While it is possible for an end user to transact in and manage their holdings of bitcoin without using a third party, most end users of cryptocurrency rely on some sort of intermediary to facilitate transactions. These include providers of cryptocurrency exchange services and cryptocurrency wallets. The roles undertaken by intermediaries effectively reinserts the need for some form of trust in a central party for most users. The central party provides services that are valuable to the end user, but also exposes the end user to risks of fraud.[10] One perceived benefit of Bitcoin and other cryptocurrencies appears to be censorship resistance. There are two main elements to this. Once a transaction is recorded on a widely distributed blockchain, the record cannot be easily erased or altered. In addition, a user who controls their own private key can undertake transactions without a central authority (be it a government, an intermediary or any other party) preventing that user from doing so. The inability of other parties to prevent, modify or censor transactions is, for some of its adherents, a key advantage of cryptocurrency. In contrast, the decentralised nature of cryptocurrencies and a lack of clarity around jurisdictional issues raises challenges for regulatory authorities, who have tended to focus not on the central protocol but rather on intermediaries providing services relating to cryptocurrencies, and on those using crypto-tokens for fundraising purposes. For example, the Australian Transaction Reports and Analysis Centre (AUSTRAC) obliges digital currency exchange providers in Australia to: register and enrol with AUSTRAC; adopt and maintain an Anti-money Laundering and Counter Terrorism Financing program that mitigates and manages the provider's money laundering and terrorism financing risks; and report suspicious matters and transactions above certain thresholds to AUSTRAC. ## Box B Bitcoin Scalability Problem As described above, Bitcoin transactions are confirmed when miners \u2013 participants in the Bitcoin system who compete to verify transactions \u2013 include those transactions in a new block that is added to the Bitcoin blockchain. This set-up limits the number of transactions in two ways: (1) each block, which records transactions, is by construction limited in size to one megabyte; and (2) a new block is added to the blockchain approximately every 10 minutes. Thus there is a hard limit on the capacity of the Bitcoin network, and fewer than 10 transactions per second can be processed. In contrast, and as noted earlier, Australia's new Fast Settlement Service has been designed with the capacity to settle around 1,000 transactions per second. The processing capacity of the international cards schemes is even greater, being in the region of tens of thousands of transactions per second.[11] Initially, this transaction limit was not binding, but this changed through 2017 and 2018 when bitcoin speculation became more popular and the number of transactions increased (Graph B1). In December 2017, to incentivise miners to prioritise their transaction, Bitcoin users had to pay, on average, almost US$30 per transaction (and more than US\\$50 on certain days).\n\nTwo categories of solutions have been proposed to address this scalability problem. The first, \u2018on-chain\u2019, seeks to change the Bitcoin protocol to allow more transactions. The second, \u2018off-chain\u2019, seeks to net offsetting transactions in a separate system, before settling the net flows on the main Bitcoin system.\n\nTwo main on-chain proposals have emerged: use blocks more efficiently; and\/or to increase block size. In late 2017, an update to the Bitcoin code was released that, by changing the way blocks are structured, roughly doubled the transaction capacity of each block. This update was designed to be backward-compatible with the existing Bitcoin system, and gained wide adoption by Bitcoin miners. At roughly the same time, a group of miners started using new code that allowed for 8 megabyte blocks. Most Bitcoin users, however, remained with the original Bitcoin and the new system (dubbed \u2018Bitcoin Cash\u2019) effectively became a new, less popular, cryptocurrency. The example of Bitcoin Cash demonstrates the challenge faced by all on-chain solutions. Proposals to change the Bitcoin code must gain widespread support across the Bitcoin community (and specifically miners) to be adopted, otherwise any modifications to the code will result in a new cryptocurrency rather than an update to Bitcoin itself.\n\nThe main off-chain solution to have emerged is the so-called Lightning Network, where Bitcoin users establish bilateral \u2018payment channels\u2019 by transferring bitcoins to a jointly controlled address. This solution is discussed further in the section \u2018Iterations to address scalability\u2019.\n\n## How Have Cryptocurrencies Changed?\n\nTen years on from its first transaction, Bitcoin remains one of the most prominent cryptocurrencies, and first generation-style coins continue to be created today (though they may not necessarily be used or traded). But there has also been innovation to address the key shortcomings of the first-generation coins and provide increased functionality. In the last two years in particular, there has been a substantial increase in the number of new crypto-assets created, some of which embody novel features or capabilities relevant for their potential use for payments. In this section we set out some prominent examples of newer coins that attempt to address the shortcomings of earlier cryptocurrencies for use in payments.\n\nOf note, while a great many crypto-assets have been created, most are small and many do not exist for long. For example, of the more than 2,000 crypto assets included on CoinMarketCap, a crypto-asset information service with the most comprehensive publicly available list of crypto-assets, the top 50 account for more than 95\u00a0per\u00a0cent of the market capitalisation of all crypto assets.[12] In addition, only around half of all crypto\u2011assets currently included on CoinMarketCap have existed for more than one year (Graph\u00a02), and of all the crypto assets removed from CoinMarketCap in the past four years around 40 per cent were less than a year old.\n\nThis short lifecycle of crypto-assets is not surprising. There are very few technical barriers to creating a crypto asset \u2013 as noted earlier, many are created through minor changes to the code of another crypto asset. Also, many exchanges will list new cryptocurrencies and other crypto-assets on a fee-for-service basis, without regard to their legitimacy. The short lifecycle may also partly reflect a rapid pace of technological development; with \u2018coins\u2019 potentially being discarded as they become \u2018old-tech\u2019.\n\n### Iterations to address price volatility\n\nAs discussed above, the price volatility of cryptocurrencies such as Bitcoin is likely to have inhibited their use as a payment method (that is, a means of exchange). If it is difficult or impossible for merchants and consumers to know what a cryptocurrency will be worth from one moment to the next, then it will be unattractive for most parties to price, or buy, goods and services in that cryptocurrency and accept payment in the cryptocurrency. Similarly, high price volatility makes cryptocurrencies a poor store of value.\n\nIn an attempt to address this, a number of so-called \u2018stablecoins\u2019 have emerged. Stablecoins are a type of cryptocurrency designed to minimise price volatility against some widely used unit of account (often the US dollar) or a common store of value (such as gold). Two broad approaches to achieve this currently exist: asset-backed stablecoins, and algorithmic stablecoins, with some offerings being a hybrid of the two.\n\nAsset-backed stablecoins are cryptocurrencies that seek to gain and maintain a stable value through being \u2013 or purporting to be \u2013 a claim on real or financial assets. For stablecoins that are fully backed by assets, this means that new coins are, in theory, only issued against an inflow of assets of the same value, and that the coins can be redeemed at a fixed price by selling these assets. Stablecoins that are fully backed by assets that match the peg they are trying to maintain (e.g. money in a US dollar bank account for a USD-pegged stable coin) will, in general, be less susceptible to price volatility, while stablecoins that are not fully backed, or that are backed by more volatile assets (e.g. other cryptocurrencies) tend to be more susceptible to price volatility. Asset-backed stablecoin issuers may seek to cover costs and\/or derive profit via seigniorage; that is, they earn interest on the backing assets but do not pay interest on their stablecoin liabilities.[13] These assets are typically controlled by the issuer of the cryptocurrency. However, the underlying details regarding legal recourse of stablecoin holders to those assets, and even whether the assets actually exist, is often unclear. The existence of a central entity that controls the asset backing the stablecoin runs somewhat counter to the original idea behind cryptocurrencies, which was to be a decentralised form of money not reliant on any central body.[14]\n\nAlgorithmic stablecoins attempt to gain and maintain value through a software protocol that manages the supply of the cryptocurrency to match demand, such that the market-clearing price tracks the underlying unit of account closely. Two broad approaches exist to achieving this. The first simply adds or removes coins from circulation (either directly or by changing their status to \u2018inactive\u2019) in order to match supply to demand. While this may succeed in maintaining the quoted stablecoin price, it does this by changing the number of active coins that users hold, such that the total value of users' holdings, being the price multiplied by the number, will still be volatile. The second approach seeks to use incentives and expectations to maintain a stable price. If supply exceeds demand, the stablecoin algorithm issues \u2018bonds\u2019 at a discount to face value, and uses the proceeds to purchase and destroy the surplus stablecoins. If demand exceeds supply, new stablecoins are issued to \u2018bondholders\u2019 to redeem the liability. If the price of the stablecoin falls but some users expect it to rise again in future, then there is an incentive for them to buy \u2018bonds\u2019 and profit from the temporary deviation. If, on the other hand, there are not enough such optimistic users, then the mechanism will fail and the stablecoin price may not recover.\n\nTether, which is one of the earliest and most prominent asset-backed stablecoins, has to date maintained a relatively tight \u2013 although imperfect \u2013 peg to the US dollar (Graph\u00a03), despite some market participants questioning the extent to which it is indeed backed by US dollars. Of note, Tether initially claimed to be fully backed by US dollars held at an undisclosed bank. However, in February 2019, it modified its terms of service indicating that its stablecoin may be backed by other US dollar-denominated assets in addition to cash and cash equivalents. Court proceedings have since indicated that only 74 per cent of Tether tokens are backed by cash and cash equivalents (Hoegner 2019). In addition, some reserves were reportedly used by the company to invest in bitcoin and \u2018other assets\u2019 (Cermak 2019). In contrast, other stablecoin issuers have partnered with established financial institutions and engaged with regulators. For example, funds backing the TrueUSD stablecoin are held in escrow accounts at a number of US-based fiduciary and banking partners that the TrueUSD issuer cannot access.[15] So far, TrueUSD has maintained a tight peg to the US dollar since it launched in 2018. NuBits is one of the few algorithmic stablecoins that has launched. It uses bond-like instruments to provide users with incentives to maintain a stable price. Its price fell substantially in early 2018 and has not recovered, highlighting the role of price expectations in algorithmic stablecoin models.\n\nIn Australia, the use of stablecoins as a payment method has been very limited, as has the supply of Australian dollar-linked stablecoins. AUDRamp, the first Australian dollar-linked stablecoin to launch, went live in September 2018. However, only 137 tokens were issued and the price has fallen to zero. More recently, TrueAUD was launched in April 2019 by TrustToken, the issuers of TrueUSD, though no tokens appear to have been issued. TrueAUD is expected to operate similarly to TrueUSD.\n\nLooking ahead, the Libra Association \u2013 whose participants include Facebook, Mastercard, Visa, PayPal and others \u2013 plans to launch a \u2018global cryptocurrency\u2019 in 2020 that would be fully backed by a reserve comprised of a basket of bank deposits and short-term government securities denominated in a range of national currencies. The initial description of the cryptocurrency, named Libra, notes that its value may fluctuate as it is not pegged to any given currency (Libra Association Members 2019).\n\nStablecoins have, in theory at least, the benefit of a stable value while retaining elements of Bitcoin's pseudonymity. However, even if the concerns about the credibility of stablecoin issuers and their coins are resolved, it is not clear that there would be material demand (at least for legitimate purposes) to pay with, or accept, stablecoins over conventional payment methods linked to deposit accounts at commercial banks. The strongest, though still niche, demand for stablecoins appears to be from holders of cryptocurrency that want to diversify into a low-volatility asset without leaving the crypto-ecosystem. Demand may also reflect a reticence to interact with the regulated banking system more generally, perhaps because of a crypto-libertarian[16] ethos, or because the cryptocurrency held may not have arisen from legitimate activities or the holder is seeking to avoid or evade taxes. It is also not obvious that all stablecoins will necessarily be attractive to crypto-libertarians. As noted above, asset-backed stablecoins rely on a central body to buy and manage the assets that back the stablecoin, which means that users have to trust that central body. This is somewhat counter to the initial idea behind cryptocurrencies, although for users who value the technical capabilities of DLT, rather than necessarily valuing the ideological aspects of Bitcoin, this may not be a problem.\n\nThe Bitcoin scalability problem (see Box B) highlighted one barrier to cryptocurrencies becoming widely used. At present, blockchain technology provides for transaction throughput orders of magnitude lower than what would be required for a widely used payment system in Australia, let alone a global payment system. This is unsurprising \u2013 the trade-off between decentralisation, scalability and security faced by blockchain developers often requires the throughput of the network to be a lower priority consideration. This trade off is known as the \u2018scalability trilemma\u2019, which claims that blockchain systems can, at most, have only two of the following three properties: (i) decentralisation, (ii) scalability and (iii) security. In practice, these trade offs are incremental; increasing the scalability of a blockchain does not require it to become entirely centralised or insecure, but more centralised or less secure. Even so, to increase throughput and not compromise on a cryptocurrency's degree of decentralisation and\/or security is a difficult task. These attributes are often decided early on in a cryptocurrency's development; for a cryptocurrency to be a reliable store of value \u2013 volatility aside \u2013 security is paramount.\n\nIncreasingly, blockchain developers are implementing alternative consensus algorithms to proof of work. These algorithms include, among others, proof of stake, byzantine fault tolerance[17] and proof of authority.[18] Generally, these alternative consensus algorithms provide for a significant increase in throughput compared with computationally expensive proof-of-work mining processes. The scalability trilemma means that this is typically achieved through centralisation. For example, proof of authority requires a centrally managed authority node to appoint block validators; similarly, byzantine fault tolerance requires a leader node to propose which transactions are included in a block. Proof of stake is less centralised than these algorithms, but remains more centralised than proof of work \u2013 it concentrates the validation of blocks in nodes that hold a large volume of cryptocurrency.\n\nOther cryptocurrencies have turned to non-blockchain solutions to address scalability. Two notable developments include off-chain \u2018payment channels\u2019 and non-blockchain applications of DLT. The Lightning Network is an off-chain network of bilateral payment channels that sits above a host blockchain. Users establish a payment channel by transferring cryptocurrency to a jointly controlled address on the host blockchain. Flows back and forth between any two participating users are then recorded off the blockchain ledger, and the net effect of these transactions is only settled on the blockchain ledger when the payment channel closes. This is comparable with the bilateral netting that occurs in some other payment systems. Transactions can be routed indirectly via multiple bilateral links if no direct link exists. A drawback of this system, however, is that cryptocurrency quarantined in payment channels is unable to be used elsewhere, until those channels close. Liquidity is effectively trapped in the payment channel. While the Lightning Network was first developed for Bitcoin, it has recently been implemented for Litecoin (another first-generation cryptocurrency). A similar off-chain network of payment channels is under development for the Ethereum blockchain.\n\nOne non-blockchain application of DLT used to address scalability is to replace the linear blockchain with a directed acyclic graph (DAG). Unlike a blockchain-based cryptocurrency, where transactions are bundled into blocks that form a linear chain, in a DAG-based cryptocurrency, individual transactions are linked together. Different nodes are able to confirm unrelated transactions in parallel, allowing multiple chains of transactions to co-exist and interconnect.[19] IOTA and Nano are two of the better-known cryptocurrencies using DAGs, though both have relatively low levels of activity outside of coordinated tests designed to demonstrate the capacity of each platform to process higher volumes of transactions.\n\nMost of these solutions are not operational or are operating at a scale much smaller than intended. In May 2019, the average number of unique, active Bitcoin addresses per day was around 700,000. By contrast, the implementation of Lightning Network for Bitcoin has less than 10,000 active nodes. Alternative consensus algorithms, such as byzantine fault tolerance or proof of authority, are unlikely to be implemented in widely used public cryptocurrencies because of the centralisation needed for proposing and\/or validating blocks. These algorithms may be better suited to private and permissioned blockchains where there is a degree of trust between the participants or with the entity operating the blockchain.\n\n### Iterations for functionality\n\nOne of the most pivotal innovations in cryptocurrencies since the creation of Bitcoin was the introduction of public distributed computing platforms, the most well-known of which is Ethereum. The Ethereum platform and its native cryptocurrency, ether, were launched in 2015. The platform's key innovation is the Ethereum virtual machine, which allows the execution of \u2018smart contracts\u2019 that, among other things, facilitate the issuing of crypto-assets or \u2018tokens\u2019 and the development of distributed software applications. Ethereum operates using a proof-of-work algorithm, with ether used to pay miners to process transactions, including the execution of smart contracts. Transaction fees differ by computational complexity, bandwidth use and storage needs. As new blocks are mined, ether is created as a reward for the successful miner.[20]\n\nSmart contracts are comprised of self-executing computer code running on a blockchain or other DLT platform.[21] The creator of a smart contract on the public Ethereum blockchain sets out the conditions under which the contract will execute and its output. As smart contracts are stored on a blockchain or other DLT platform, the conditions and associated outputs are visible to all parties to the contract and immutable. This allows parties to enter into an agreement knowing that it will be enforced without the need to trust each other. For example, a crypto-asset token can be issued using a smart contract using \u2018if, then\u2019 or other conditional statements. Here, the smart contract may be configured as: \u2018if Address A receives 1 ether from Address B, then send 10 tokens from Address A to Address B\u2019. If the token is a cryptocurrency, it is sometimes referred to as \u2018programmable money\u2019. One benefit of programmable money is that both sides of a transaction are able to settle simultaneously \u2013 a so-called \u2018atomic\u2019 transaction. Tokens may also have a broader array of features and characteristics, facilitating the creation of security and utility tokens. Around 1,300 of the crypto-assets listed on CoinMarketCap are created using smart contracts and around 90\u00a0per\u00a0cent of these were created on the Ethereum platform. Even though smart contract code on the Ethereum blockchain is typically public, and therefore can be independently verified, fraudulent activity nonetheless occurs. In 2017, researchers estimated that as many as 10\u00a0per\u00a0cent of smart contracts on the Ethereum platform were related to fraudulent activity (Bartoletti et al 2017).\n\nThe additional functionality offered by smart contracts does not, in itself, address the fundamental barriers \u2013 such as scalability and volatility \u2013 to cryptocurrencies becoming widely used for payments. Indeed, it may be the case that additional functionality offered by smart contracts can be integrated into centralised systems, including into some of Australia's existing payment systems. Indeed, a recent Data61-CBA proof of concept to apply \u2018programmable money\u2019 to National Disability Insurance Scheme payments found that a system based on a centralised database could, in theory, generate the same efficiency gains as a DLT-based approach (Royal et al 2018).\n\n## Are Cryptocurrencies Money Today?\n\nSome of the evolution in cryptocurrencies in recent years has been an attempt to address some of the key shortcomings that have prevented Bitcoin from functioning as money. However, it remains the case that no cryptocurrencies currently function as money in Australia, or as widely used payment methods. Proposals to improve scalability and volatility have had varied success. Many continue to be a work in progress and they generally come at the cost of making a cryptocurrency more centralised, a feature that may not be attractive to crypto-libertarians and in any case makes them more similar to established payment systems. Developments to date have also not added sufficiently to the overall reliability, functionality and credibility of cryptocurrencies to make them an attractive alternative to established payment systems for everyday payments for the population at large.\n\nRegardless, DLT is likely to continue to evolve, including in ways that are unrelated to cryptocurrency. For example, there are several private-sector initiatives focused on \u2018private permissioned\u2019 DLT systems, for example, Corda and Quorum, which \u2013 while not suitable for a widely used cryptocurrency \u2013 are being explored for use in financial market infrastructure and wholesale payments. Accordingly, the Reserve Bank will continue to study the implications of cryptocurrencies and DLT for the financial system, and the economy more broadly.\n\nFinally, it should also be noted that innovation continues to occur in traditional centralised payment systems \u2013 the creation and launch of Australia's New Payments Platform is an example of this. As long as the Australian dollar continues to provide a reliable, low-inflation store of value, and the payments industry continues to work on the efficiency, functionality and resilience of the Australian payments system, it is difficult to envisage cryptocurrencies presenting a compelling proposition that would lead to their widespread use in Australia.\n\n## Footnotes\n\nThe authors are from Payments Policy Department. [*]\n\nWe use (lower case) \u2018bitcoin\u2019 to refer to a unit of cryptocurrency in the Bitcoin system. [1]\n\nIn this context, scalability refers to the capacity of a system to grow to meet demand. [2]\n\nThis article focuses on privately established cryptocurrencies. It does not address issues relating to central bank digital currencies, which have been given some consideration in recent years: for a local and global perspective see Lowe (2017) and CPMI and MC (2018). Nor does this article address the potential use of distributed ledger technology in wholesale or large-value payments systems or other financial market infrastructures. [3]\n\nThis definition draws on the European Banking Authority's definition of \u2018virtual currencies\u2019, see European Banking Authority (2014). [4]\n\nAs described in the UK Cryptoassets Taskforce Final Report, \u2018DLT is a type of technology that enables the sharing and updating of records in a distributed and decentralised way. Participants can securely propose, validate, and record updates to a synchronised ledger (a form of database), that is distributed across the participants.\u2019 (HM Treasury, Financial Conduct Authority, Bank of England 2018). The term \u2018blockchain\u2019 is often used interchangeably with DLT, but it refers to a specific way of structuring data on a DLT platform. [5]\n\nASIC has issued investor warnings on both cryptocurrencies and initial coin offerings, see ASIC (2018a) and ASIC (2018b). [6]\n\nFor example, the 1990s saw trials of digicash and Mondex, early prototypes of electronic cash. [7]\n\nThis description is drawn from Richards (2018). [8]\n\nSee Debelle (2019) for a financial sector perspective on these issues. [9]\n\nA widely known early example relates to Mt Gox, which declared bankruptcy in early 2014 following the loss of 850,000 bitcoins. More recently, customers of the Canadian exchange QuadrigaCX are reported to have lost access to crypto-assets following the death of the founder of the exchange, purportedly the only person with the cryptographic keys to access the \u2018cold wallets\u2019 (offline storage) of users. [10]\n\nFor example, Visa's payment network, VisaNet, processes around 1,700 transactions per second and is capable of processing more than 65,000 transactions per second. [11]\n\nFor a cryptocurrency to be included on CoinMarketCap, it must fit the definition of a cryptocurrency, be traded publicly, and actively traded on at least two exchanges. There are around 250 exchanges currently recognised by CoinMarketCap. [12]\n\nThe term seigniorage is used to describe the income earnt from the production of money. It can refer to the profit derived from the difference between the face value of the money (such as banknotes) and the cost of its production. It can also refer to the income earnt on securities acquired in exchange for the money produced, less any interest payable on the money that is outstanding (zero in the case of banknotes). Today, it is common for banknote issuing authorities, including the Bank, to derive seigniorage using the latter approach. This is because commercial banks can and do return banknotes to the central bank in exchange for fresh electronic balances at the central bank and, as such, banknotes are treated as zero-interest liabilities. See RBA (1997) for further discussion. [13]\n\nOutside the scope of this article, there are also, in prototype form at least, commercial bank-backed stablecoins such as JPM Coin. In such a set-up, holders are likely to be exposed to the credit risk of the commercial bank, similar to a conventional deposit account (abstracting from any government deposit guarantees). [14]\n\nTrueUSD is registered as a money services business with the Financial Crimes Enforcement Network, which administers anti-money laundering, \u2018know your customer\u2019 and anti-terrorism financing regulations. [15]\n\nCrypto-libertarians are commonly characterised as mistrustful of the traditional banking system. Richards (2018) notes that \u2018Some of them [crypto-libertarians] assert that the quantitative easings undertaken by major central banks in the wake of the global financial crisis have somehow debauched the value of traditional national currencies.\u2019 [16]\n\nByzantine fault tolerance (BFT) is a concept in distributed systems, in which the participants of a system (some of whom may be malicious) can achieve consensus on its state. Consensus algorithms such as delegated BFT or practical BFT achieve BFT by appointing a leader node to propose changes to the blockchain; nodes may take turns fulfilling the leader role. If more than a defined threshold of the other nodes agree with the leader node's proposed changes, the changes are committed to the blockchain. [17]\n\nVariations on these algorithms, such as delegated proof-of-stake or democratic byzantine fault tolerance, differ mostly in how the underlying algorithm is implemented. The latter, implemented in University of Sydney and Data61's \u2018Red Belly Blockchain\u2019 has been shown to scale to more than thousands of transactions per second under experimental conditions. [18]\n\nEthereum currently uses proof of work for mining, though it has been aiming to move to proof of stake for a long time. [20]\n\nIn this section we discuss smart contracts created on the public Ethereum blockchain. Smart contracts may also be created on private blockchain or other DLT platforms, where the intended application will inform characteristics such as privacy. [21]\n\n## References\n\nAli R, J Barrdear, R Clews and J Southgate (2014), \u2018The Economics of Digital Currencies\u2019 Bank of England Quarterly Bulletin, September.\n\nASIC (2018a), \u2018Cryptocurrencies\u2019, Moneysmart site, 24 October.\n\nASIC (2018b), \u2018Initial Coin Offerings: Investment or scam?\u2019, Moneysmart site.\n\nBartoletti M, S Carta, T Cimoli and R Saia (2017), \u2018Dissecting Ponzi schemes on Ethereum: identification, analysis, and impact\u2019, 19 July.\n\nCermak L (2019), \u2018Tether admits in court to investing some of its reserves in bitcoin\u2019, The Block site, 21 May.\n\nCPMI (2017), \u2018Distributed ledger technology in payment, clearing and settlement \u2013 An analytical framework\u2019, February.\n\nCPMI and MC (2018), \u2018Central bank digital currencies\u2019, 18 March.\n\nDebelle G (2019), \u2018Climate Change and the Economy\u2019, Public Forum hosted by the Centre for Policy Development, Sydney, 12 March.\n\nDigiconomist (2019), Bitcoin Energy Consumption Index site, 21 May.\n\nDoyle M-A, C Fisher, E Tellez and A Yadav (2017), \u2018How Australians Pay: Evidence from the 2016 Consumer Payments Survey\u2019, RBA Research Discussion Paper No 2017-04.\n\nEuropean Banking Authority (2014), \u2018EBA Opinion on \u2018virtual currencies\u2019\u2019, 4 July.\n\nHM Treasury, Financial Conduct Authority, Bank of England (2018), \u2018Cryptoassets Taskforce: final report\u2019, October.\n\nHoegner S (2019), \u2018Affidavit filed in the Matter of Letitia James, Attorney General of the State of New York v iFinex Inc., BFXNA Inv, BFXWW Inc., Tether Holdings Limited, Tether Operations Limited, Tether Limited, Tether International Limited\u2019, Scribd.com site, 30 April.\n\nKaspersky Lab (2018), \u2018Spam and phishing in 2017\u2019, 15 February.\n\nLibra Association Members (2019), \u2018An Introduction to Libra\u2019, Libra site, 18 June.\n\nLowe P (2017), \u2018An eAUD?\u2019, Address to the 2017 Australian Payment Summit, Sydney, 13 December.\n\nMa J, JS Gans and R Tourky (2018), \u2018Market Structure in Bitcoin Mining\u2019, NBER Working Paper Series 24242.\n\nMacquarie Dictionary (2019), 22 May.\n\nNakamoto S (2008), \u2018Bitcoin: A Peer-to-Peer Electronic Cash System\u2019.\n\nRBA (1997), \u2018Measuring Profits from Currency Issue\u2019, Bulletin, July, pp 1\u20134.\n\nRBA (2014), \u2018Submission to the Inquiry into Digital Currency\u2019, Senate Economic References Committee Inquiry into Digital Currency, November.\n\nReserve Bank of Australia (2019), \u2018Cryptocurrencies\u2019, Reserve Bank of Australia site.\n\nRichards T (2018), \u2018Cryptocurrencies and Distributed Ledger Technology\u2019, Australian Business Economists Briefing, Sydney, 26 June.\n\nRoyal D, P Rimba, M Staples, S Gilder, AB Tran, E Williams, A Ponomarev, I Weber, C Connor and N Lim (2018), \u2018Making Money Smart: Empowering NDIS participants with Blockchain technologies\u2019, October","date":"2021-05-09 14:08:48","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\": 0.3229979872703552, \"perplexity\": 3493.388309863521}, \"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-2021-21\/segments\/1620243988986.98\/warc\/CC-MAIN-20210509122756-20210509152756-00543.warc.gz\"}"}
| null | null |
{"url":"http:\/\/math.stackexchange.com\/questions\/850798\/trying-to-explain-what-consistent-means-to-a-middle-schooler\/850805","text":"# Trying to explain what \u201cconsistent\u201d means to a middle schooler\n\nIf you were to explain what \"consistent\" means to a middle schooler in elementary Algebra would you say it is the fact that a rule continues to hold for more general cases?\n\nWith the example of the rule for positive exponents continues to hold for zero and negative exponents.\n\n-\nI would say consistent means that you cannot derive a contradiction from (whatever it is you're talking about); in the case of extending a rule, the extension of the rule would be consistent if it holds in more general cases. \u2013\u00a0Hayden Jun 28 '14 at 22:55\nFor a middle school student, maybe start with something like this: You ask your mother if you can have a cookie, and she says no. Then if you have a brownie, she can't say that you went against what she said. Or you ask you mother if you can go outside, and she says you can if your father doesn't say \"no\", so you go outside without asking your father (because by not asking him, he hasn't said \"no\"). Consistent means you haven't technically broken any rules. Then move on to math things. \u2013\u00a0Dave L. Renfro Jun 30 '14 at 13:47\n@DaveL.Renfro what would be the first math thing you would use? \u2013\u00a0skull petrol Jul 3 '14 at 8:38\nI think your exponents example is a good one, and I pretty much always used the laws for positive integer exponents to suggest the extension to negative and rational exponents. However, I think one should be careful about over emphasizing formal reasoning and proof, especially at the middle school level. In fact, I always considered the work with extending the rules of exponents at this level being mostly a way of re-discovering the rules if you forgot exactly how they went. Incidentally, you may find it useful to google the phrase \"principle of the permanence of equivalent forms\". \u2013\u00a0Dave L. Renfro Jul 3 '14 at 12:44\n\nConsistency in mathematics has to do with how a given statement $a$ relates to a set $X$ of other statements. $a$ is consistent with $X$ provided there is no proof of $\\neg a$ using the statements in $X$.\n$X$ is self-consistent if you cannot prove the opposite of one of its statements using the others. This is equivalent to saying you will never be able to prove both a statement and its negation by assuming only the statements in $X$.","date":"2015-11-27 19:25:21","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\": 0.5361087918281555, \"perplexity\": 406.7426159902474}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2015-48\/segments\/1448398450559.94\/warc\/CC-MAIN-20151124205410-00323-ip-10-71-132-137.ec2.internal.warc.gz\"}"}
| null | null |
ACCEPTED
#### According to
International Plant Names Index
#### Published in
null
#### Original name
Eremostachys tianschanica Popov
### Remarks
null
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 1,071
|
Have an everlasting memory travelling at this fascinating tropical island with the discovery tour exploring all of the most stunning attractions in Samui together with enjoy participating in activities such as snorkeling, kayaking, mountain trekking and sightseeing at the magnificent 42-island archipelago called Angthong National Marine Park. With more than 30 years experience organizing tours in Samui, we assure that your vacation with be filled with happiness and enjoyment without any dissatisfactions.
Grab your best opportunity to feel the beauty of nature and cultural heritages of Samui as well as gaining memorable adventurous experience at Angthong National Marine Park today!
- Arrive at Koh Samui, a warmly welcome by our representative at Samui Airport.
- Air-condition van transfer from the airport to the hotel.
- Check-in at the hotel and have some relaxation.
- Visit highlight travel attractions in Samui: Air-condition van with a professional driver and a tour guide.
Any other attractions or places as you wish to visit.
Day 2: Angthong National Marine Park: Discover Amazing Adventures!
- Transfer from your hotel to Nathon Pier, pick-up time depends in your hotel's location.
- Cruise towards Angthong National Marine Park by Highsea Tour.
- Visit "Koh Wua Ta Lap" where has the world-famous viewpoint of all 42 astonishing islands of Angthong Marine Park considered as definition of paradise. Enjoy swimming, sunbathing, exploring or simply relaxing on the lovely white sandy beach.
- Explore "Koh Mae Koh" where has a dramatic lagoon hidden in the middle of the island called "The Blue Lagoon". Enjoy snorkeling with colorful fishes and glamorous corals in the crystal blue sea and kayaking along the coastline to explore dramatic cliffs and stunning tunnels.
- After the excursion trip, there will be a transfer service from the pier to the hotel.
- Have a leisure time at the hotel.
- Have a buffet breakfast at the hotel.
- Free at leisure for optional tours such as Jungle eco safari tour, Koh Tao & Koh Nangyuan, ATV Adventure, Skyhawk samui or Samui Thai cooking class.
2 nights at 3-star hotel.
Transportation by air-condition vans during the whole trip.
Angthong National Marine Park entrance fee 300 baths for Adult and 150 bahts for child per person.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 8,390
|
Quick Transcription Service is Professional Transcription Company in Hamilton, Ontario. We are providing transcript, translation services and other services like Interpretation Services,Cart Services, Typing Services and Captioning Services in various cities of Ontario. Our Reasonable and Best Transcription Service rates starting at $0.70/min.
Hamilton is a port city situated in Ontario. Its inception dates back to 1872 but the city of Hamilton was formed din 2001 by amalgamating the old city along with Regional Municipality of Hamilton–Wentworth. It has a population of 519,949 and an area of 1,138.11 square kilometer. It has hot and humid type climate.
We have Professional Specialist 1000+ Translator around Hamilton, Ontario. Quick Turnaround Time and 100% accuracy is maintained at most for our major Services in Hamilton, Ontario.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 5,406
|
{"url":"http:\/\/sciencewise.info\/bookmarks\/all","text":"text color\nbackground\n\u2022 Please use in name only letters, numbers, underscores or hyphens\n\u2022 You already have a label with such name\nno labels\n\nAll bookmarked papers in (10687)\n\n\u2022 The Void Phenomenon\n\nAdvances in theoretical ideas on how galaxies formed have not been strongly influenced by the advances in observations of what might be in the voids between the concentrations of ordinary optically selected galaxies. The theory and observations are maturing, and the search for a reconciliation offers a promising opportunity to improve our understanding of cosmic evolution. I comment on the development of this situation and present an update of a nearest neighbor measure of the void phenomenon that may be of use in evaluating theories of galaxy formation.\nVoidGalaxyGalaxy FormationStatisticsLow surface brightness galaxyTwo-point correlation functionLambda-CDM modelRedshift spaceSpiral galaxyGas clouds...\n\u2022 Neutrino Masses from Loop-Induced Dirac Yukawa Couplings\n\nWe consider a possibility to naturally explain tiny neutrino masses without the lepton number violation. We study a simple model with SU(2)_L singlet charged scalars (s_1^+, s_2^+) as well as singlet right-handed neutrino (nu_R). Yukawa interactions for Dirac neutrinos, which are forbidden at the tree level by a softly-broken Z_2 symmetry, are induced at the one-loop level via the soft-breaking term in the scalar potential. Consequently neutrinos obtain small Dirac masses after the electroweak symmetry breaking. It is found that constrains from neutrino oscillation measurements and lepton flavor violation search results (especially for mu to e gamma) can be satisfied. We study the decay pattern of the singlet charged scalars, which could be tested at the LHC and the ILC. We discuss possible extensions also, e.g. to introduce dark matter candidate.\nMajorana massCoupling constantStandard ModelCharged leptonLepton flavour violationHiggs bosonDark matterBosonizationTri Bimaximal mixingScalar field...\n\u2022 Loop Suppression of Dirac Neutrino Mass in the Neutrinophilic Two Higgs Doublet Modelver. 2\n\nWe extend the scalar sector of the neutrinophilic two Higgs doublet model, where small masses of Dirac neutrinos are obtained via a small vacuum expectation value v_nu of the neutrinophilic SU(2)_L-doublet scalar field which has a Yukawa interaction with only right-handed neutrinos. A global U(1)_X symmetry is used for the neutrinophilic nature of the second SU(2)_L-doublet scalar field and also for eliminating Majorana mass terms of neutrinos. By virtue of an appropriate assignment of the U(1)_X-charges to new particles, our model has an unbroken Z_2 symmetry, under which the lightest Z_2-odd scalar boson can be a dark matter candidate. In our model, v_nu is generated by the one-loop diagram to which Z_2-odd particles contribute. We briefly discuss a possible signature of our model at the LHC.\nVacuum expectation valueNeutrinoNeutrino massScalar fieldDark matter candidateScalar bosonStandard ModelDark matterMass eigen stateYukawa interaction...\n\u2022 Warmth Elevating the Depths: Shallower Voids with Warm Dark Matter\n\nWarm dark matter (WDM) has been proposed as an alternative to cold dark matter (CDM), to resolve issues such as the apparent lack of satellites around the Milky Way. Even if WDM is not the answer to observational issues, it is essential to constrain the nature of the dark matter. The effect of WDM on haloes has been extensively studied, but the small-scale initial smoothing in WDM also affects the present-day cosmic web and voids. It suppresses the cosmic \"sub-web\" inside voids, and the formation of both void haloes and subvoids. In N-body simulations run with different assumed WDM masses, we identify voids with the zobov algorithm, and cosmic-web components with the origami algorithm. As dark-matter warmth increases, the initial-conditions smoothing increases, and the number of voids and subvoids is suppressed. Also, void density profiles change, their shapes become flatter inside the void radius, while edges of the voids remain unchanged. Also, filaments and walls become cleaner, as the sub-structures in between have been smoothed out; this leads to a clear, mid-range peak in the density PDF. These distinct features of voids make them possible observational indicators of the warmth of dark matter.\nDark matterWDM particlesGalaxyWarm dark matterThermalisationAbundanceCosmologyStructure formationRedshift-space distortionLambda-CDM model...\n\u2022 Cosmological Perturbation Theory in the Synchronous and Conformal Newtonian Gauges\n\nThis paper presents a systematic treatment of the linear theory of scalar gravitational perturbations in the synchronous gauge and the conformal Newtonian (or longitudinal) gauge. It differs from others in the literature in that we give, in both gauges, a complete discussion of all particle species that are relevant to any flat cold dark matter (CDM), hot dark matter (HDM), or CDM+HDM models (including a possible cosmological constant). The particles considered include CDM, baryons, photons, massless neutrinos, and massive neutrinos (an HDM candidate), where the CDM and baryons are treated as fluids while a detailed phase-space description is given to the photons and neutrinos. Particular care is applied to the massive neutrino component, which has been either ignored or approximated crudely in previous works. Isentropic initial conditions on super-horizon scales are derived. The coupled, linearized Boltzmann, Einstein and fluid equations that govern the evolution of the metric and density perturbations are then solved numerically in both gauges for the standard CDM model and two CDM+HDM models with neutrino mass densities $\\onu=0.2$ and 0.3, assuming a scale-invariant, adiabatic spectrum of primordial fluctuations. We also give the full details of the cosmic microwave background anisotropy, and present the first accurate calculations of the angular power spectra in the two CDM+HDM models including photon polarization, higher neutrino multipole moments, and helium recombination. The numerical programs for both gauges are available at http:\/\/arcturus.mit.edu\/cosmics\/ .\nHorizonMetric perturbationBoltzmann transport equationPhase space densityThomson scatteringIonizationEinstein field equationsRadiation-dominated epochEvolution equationScalar mode fluctuation...\n\u2022 On the perturbation of the luminosity distance by peculiar motions\n\nWe consider some aspects of the perturbation to the luminosity distance $d(z)$ that are of relevance for SN1a cosmology and for future peculiar velocity surveys at non-negligible redshifts. 1) Previous work has shown that the correction to the lowest order perturbation $\\delta d \/ d = -\\delta v \/ c z$ has the peculiar characteristic that it appears to depend on the absolute state of motion of sources, rather than on their motion relative to that of the observer. The resolution of this apparent violation of the equivalence principle is that it is necessary to allow for evolution of the velocities with time, and also, when considering perturbations on the scale of the observer-source separation, to include the gravitational redshift effect. We provide an expression for $\\delta d \/ d$ that provides a physically consistent way to compute the impact of peculiar motions for SN1a cosmology and peculiar velocity surveys. 2) We then calculate the perturbation to the redshift as a function of source flux density, which has been proposed as an alternative probe of large-scale motions. We show how the inclusion of surface brightness modulation modifies the relation between $\\delta z(m)$ and the peculiar velocity, and that, while the noise properties of this method might appear promising, the velocity signal is swamped by the effect of galaxy clustering for most scales of interest. 3) We show how, in linear theory, peculiar velocity measurements are biased downwards by the effect of smaller scale motions or by measurement errors (such as in photometric redshifts). Our results nicely explain the effects seen in simulations by Koda et al.\\ 2013. We critically examine the prospects for extending peculiar velocity studies to larger scales with near-term future surveys.\nGalaxyRedshift spaceVelocity dispersionLine of sightPrimordial density perturbationThe Dark Energy SurveyWeak lensingCosmic microwave backgroundLuminosityTully-Fisher relation...\n\u2022 A unified solution to the small scale problems of the $\\Lambda$CDM model II: introducing parent-satellite interactionver. 2\n\nWe continue the study of the impact of baryon physics on the small scale problems of the $\\Lambda$CDM model, based on a semi-analytical model (Del Popolo, 2009). Withsuch model, we show how the cusp\/core, missing satellite (MSP), Too Big to Fail (TBTF) problems and the angular momentum catastrophe can be reconciled with observations, adding parent-satellite interaction. Such interaction between darkmatter (DM) and baryons through dynamical friction (DF) can sufficiently flattenthe inner cusp of the density profiles to solve the cusp\/core problem. Combining, in our model, a Zolotov et al. (2012)-like correction, similarly to Brooks et al. (2013), and effects of UV heating and tidal stripping, the number of massive, luminous satellites, as seen in the Via Lactea 2 (VL2) subhaloes,is in agreement with the numbers observed in the MW, thus resolving the MSP and TBTF problems. The model also produces a distribution of the angular spin parameter and angular momentum in agreement with observations of the dwarfs studied by van den Bosch, Burkert, \\\\& Swaters (2001).\nEllipticityCircular velocitySmoothed-particle hydrodynamicsN-body simulationStellar massCold dark matterStarHost galaxyStar formationGalaxy...\n\u2022 Higgs-field Portal into Hidden Sectors\n\nThe Higgs field mass term, being superrenomalizable, has a unique status within the standard model. Through the opening it affords, $SU(3) \\times SU(2) \\times U(1)$ singlet fields can have renormalizable couplings to standard model fields. We present examples that are neither grotesque nor unnatural. A possible consequence is to spread the Higgs particle resonance into several weaker ones, or to afford it additional, effectively invisible decay channels.\nHidden sectorStandard ModelHiggs fieldHiggs bosonStandard Model fieldQuarkGauge fieldNucleosynthesisChiral symmetry breakingVacuum expectation value...\n\u2022 The odd couple: quasars and black holes\n\nQuasars emit more energy than any other objects in the universe, yet are not much bigger than the solar system. We are almost certain that quasars are powered by giant black holes of up to $10^{10}$ times the mass of the Sun, and that black holes of between $10^6$ and $10^{10}$ solar masses---dead quasars---are present at the centers of most galaxies. Our own galaxy contains a black hole of $4.3\\times10^6$ solar masses. The mass of the central black hole appears to be closely related to other properties of its host galaxy, such as the total mass in stars, but the origin of this relation and the role that black holes play in the formation of galaxies are still mysteries.\nParsecEvent horizonAstrophysical jetNearby galaxiesMilky WayAccretion diskMassive black holeGround telescopesGravitational fieldsAccretion...\n\u2022 Magnetic Reconnection in Astrophysical Environments\n\nMagnetic reconnection is a process that changes magnetic field topology in highly conducting fluids. Traditionally, magnetic reconnection was associated mostly with solar flares. In reality, the process must be ubiquitous as astrophysical fluids are magnetized and motions of fluid elements necessarily entail crossing of magnetic frozen in field lines and magnetic reconnection. We consider magnetic reconnection in realistic 3D geometry in the presence of turbulence. This turbulence in most astrophysical settings is of pre-existing nature, but it also can be induced by magnetic reconnection itself. In this situation turbulent magnetic field wandering opens up reconnection outflow regions, making reconnection fast. We discuss Lazarian \\& Vishniac (1999) model of turbulent reconnection, its numerical and observational testings, as well as its connection to the modern understanding of the Lagrangian properties of turbulent fluids. We show that the predicted dependences of the reconnection rates on the level of MHD turbulence make the generally accepted Goldreich \\& Sridhar (1995) model of turbulence self-consistent. Similarly, we argue that the well-known Alfv\\'en theorem on flux freezing is not valid for the turbulent fluids and therefore magnetic fields diffuse within turbulent volumes. This is an element of magnetic field dynamics that was not accounted by earlier theories. For instance, the theory of star formation that was developing assuming that it is only the drift of neutrals that can violate the otherwise perfect flux freezing, is affected and we discuss the consequences of the turbulent diffusion of magnetic fields mediated by reconnection.\nMagnetohydrodynamicsEddyRichardson diffusionDissipationLundquist numberCompressibilityInstabilityNumerical simulationMagnetosphere of a starSolar wind...\n\u2022 Determination of the Local Dark Matter Density in our Galaxyver. 2\n\nThe rotation curve, the total mass and the gravitational potential of the Galaxy are sensitive measurements of the dark matter halo profile. In this publication cuspy and cored DM halo profiles are analysed with respect to recent astronomical constraints in order to constrain the shape of the Galactic DM halo and the local DM density. All Galactic density components (luminous matter and DM) are parametrized. Then the total density distribution is constrained by astronomical observations: 1) the total mass of the Galaxy, 2) the total matter density at the position of the Sun, 3) the surface density of the visible matter, 4) the surface density of the total matter in the vicinity of the Sun, 5) the rotation speed of the Sun and 6) the shape of the velocity distribution within and above the Galactic disc. The mass model of the Galaxy is mainly constrained by the local matter density (Oort limit), the rotation speed of the Sun and the total mass of the Galaxy from tracer stars in the halo. It is shown from a statistical chi^2 fit to all data that the local DM density is strongly positively (negatively) correlated with the scale length of the DM halo (baryonic disc). Since these scale lengths are poorly constrained the local DM density can vary from 0.2 to 0.4 GeV\/cm^3 (0.005 - 0.01 M_sun\/pc^3) for a spherical DM halo profile and allowing total Galaxy masses up to 2 * 10^12 M_sun. For oblate DM halos and dark matter discs, as predicted in recent N-body simulations, the local DM density can be increased significantly.\nGlobular clusterScale heightMass distributionMilky WayNavarro-Frenk-White profileThin stellar diskDark Matter Density ProfileDark matter haloLocal dark matter densityCircular velocity...\n\u2022 Constraints on ionising photon production from the large-scale Lyman-alpha forestver. 2\n\nRecent work has shown that the z~2.5 Lyman-alpha forest on large scales encodes information about the galaxy and quasar populations that keep the intergalactic medium photoionized. We present the first forecasts for constraining the populations with data from current and next-generation surveys. At a minimum the forest should tell us whether galaxies or, conversely, quasars dominate the photon production. The number density and clustering strength of the ionising sources might be estimated to sub-10% precision with a DESI-like survey if degeneracies (e.g., with the photon mean-free-path, small-scale clustering power normalization and potentially other astrophysical effects) can be broken by prior information. We demonstrate that, when inhomogeneous ionisation is correctly handled, constraints on dark energy do not degrade.\nCosmologyBaryon acoustic oscillationsTwo-point correlation functionLine of sightRadiative transferCovariance matrixRedshift-space distortionCosmological parametersUltraviolet sourcesFisher information matrix...\n\u2022 Dark Matter Fraction in Lens Galaxies: New Estimates from Microlensing\n\nWe present a joint estimate of the stellar\/dark matter mass fraction in lens galaxies and the average size of the accretion disk of lensed quasars from microlensing measurements of 27 quasar image pairs seen through 19 lens galaxies. The maximum likelihood estimate for the fraction of the surface mass density in the form of stars is $\\alpha=0.2^{+0.1}_{-0.1}$ near the Einstein radius of the lenses ($\\sim 1 - 2$ effective radii). The estimate for the average accretion disk size is $r_s=6.0^{+3.0}_{-1.1}\\sqrt{M\/0.3M_\\sun}$ light-days. The fraction of mass in stars at these radii is significantly larger than previous estimates from microlensing studies assuming quasars were point-like. The corresponding local dark matter fraction of 80\\ is in good agreement with other estimates based on strong lensing or kinematics. The size of the accretion disk inferred in the present study is slightly larger than previous estimates.\nStellar massStatisticsStellar dynamicsStellar surfacesExtinctionMass distributionAccretion diskQuasarPierre Auger ObservatoryMass profile...\n\u2022 Is there a \"too big to fail\" problem in the field?ver. 2\n\nWe use the Arecibo Legacy Fast ALFA (ALFALFA) 21cm survey to measure the number density of galaxies as a function of their rotational velocity, Vrot,HI (as inferred from the width of their 21cm emission line). Based on the measured velocity function we statistically connect galaxies with their host halos, via abundance matching. In a LCDM cosmology, low-velocity galaxies are expected to be hosted by halos that are significantly more massive than indicated by the measured galactic velocity; allowing lower mass halos to host ALFALFA galaxies would result in a vast overestimate of their number counts. We then seek observational verification of this predicted trend, by analyzing the kinematics of a literature sample of field dwarf galaxies. We find that galaxies with Vrot,HI<25 km\/s are kinematically incompatible with their predicted LCDM host halos, in the sense that hosts are too massive to be accommodated within the measured galactic rotation curves. This issue is analogous to the \"too big to fail\" problem faced by the bright satellites of the Milky Way, but here it concerns extreme dwarf galaxies in the field. Consequently, solutions based on satellite-specific processes are not applicable in this context. Our result confirms the findings of previous studies based on optical survey data, and addresses a number of observational systematics present in these works. Furthermore, we point out the assumptions and uncertainties that could strongly affect our conclusions. We show that the two most important among them, namely baryonic effects on the abundances and rotation curves of halos, do not seem capable of resolving the reported discrepancy.\nVector fieldRotation CurveToo big to fail problemInclinationMilky WayDark matter subhaloWDM particlesTHINGS surveyWarm dark matterVelocity Width Function...\n\u2022 The radial velocity dispersion profile of the Galactic halo: Constraining the density profile of the dark halo of the Milky Wayver. 2\n\nWe have compiled a new sample of 240 halo objects with accurate distance and radial velocity measurements, including globular clusters, satellite galaxies, field blue horizontal branch stars and red giant stars from the Spaghetti survey. The new data lead to a significant increase in the number of known objects for Galactocentric radii beyond 50 kpc, which allows a reliable determination of the radial velocity dispersion profile out to very large distances. The radial velocity dispersion shows an almost constant value of 120 km\/s out to 30 kpc and then continuously declines down to 50 km\/s at about 120 kpc. This fall-off puts important constraints on the density profile and total mass of the dark matter halo of the Milky Way. For a constant velocity anisotropy, the isothermal profile is ruled out, while both a dark halo following a truncated flat model of mass $1.2^{+1.8}_{-0.5}\\times 10^{12}$ M_sun and an NFW profile of mass $0.8^{+1.2}_{-0.2}\\times 10^{12}$ M_sun and c=18 are consistent with the data. The significant increase in the number of tracers combined with the large extent of the region probed by these has allowed a more precise determination of the Milky Way mass in comparison to previous works. We also show how different assumptions for the velocity anisotropy affect the performance of the mass models.\nNavarro-Frenk-White profileCircular velocityVelocity dispersionStellar haloProper motionVirial massThomas-Fermi modelGalaxyCore radiusA giants...\n\u2022 Mass models of the Milky Way\n\nWe present a simple method for fitting parametrized mass models of the Milky Way to observational constraints. We take a Bayesian approach which allows us to take into account input from photometric and kinematic data, and expectations from theoretical modelling. This provides us with a best-fitting model, which is a suitable starting point for dynamical modelling. We also determine a probability density function on the properties of the model, which demonstrates that the mass distribution of the Galaxy remains very uncertain. For our choices of parametrization and constraints, we find disc scale lengths of 3.00 \\pm 0.22 kpc and 3.29 \\pm 0.56 kpc for the thin and thick discs respectively; a Solar radius of 8.29 \\pm 0.16 kpc and a circular speed at the Sun of 239 \\pm 5 km\/s; a total stellar mass of 6.43 \\pm 0.63 * 10^10 M_sun; a virial mass of 1.26 \\pm 0.24 * 10^12 M_sun and a local dark matter density of 0.40 \\pm 0.04 GeV\/cm^3. We find some correlations between the best-fitting parameters of our models (for example, between the disk scale lengths and the Solar radius), which we discuss. The chosen disc scale-heights are shown to have little effect on the key properties of the model.\nGalaxyKinematicsMilky WayScale heightVirial massStellar massSunCold dark matterThin stellar diskThick stellar disk...\n\u2022 The Dark Matter Halo of the Milky Way, AD 2013ver. 2\n\nWe derive the mass model of the Milky Way (MW) using a cored dark matter (DM) halo profile and recent data. The method used consists in fitting a spherically symmetric model of the Galaxy with a Burkert DM halo profile to available data: MW terminal velocities in the region inside the solar circle, circular velocity as recently estimated from maser star forming regions at intermediate radii, and velocity dispersions of stellar halo tracers for the outermost Galactic region. The latter are reproduced by integrating the Jeans equation for every modeled mass distribution, and by allowing for different velocity anisotropies for different tracer populations. For comparison we also consider a Navarro-Frenk-White profile. We find that the cored profile is the preferred one, with a shallow central density of rho_H~4x10^7M_s\/kpc^3 and a large core radius R_H~10 kpc, as observed in external spirals and in agreement with the mass model underlying the Universal Rotation Curve of spirals. We describe also the derived model uncertainties, which are crucially driven by the poorly constrained velocity dispersion anisotropies of halo tracers. The emerging cored DM distribution has implications for the DM annihilation angular profile, which is much less boosted in the Galactic center direction with respect to the case of the standard \\Lambda CDM, NFW profile. Using the derived uncertainties we discuss finally the limitations and prospects to discriminate between cored and cusped DM profile with a possible observed diffuse DM annihilation signal. The present mass model aims to characterize the present-day description of the distribution of matter in our Galaxy, which is needed to frame current crucial issues of Cosmology, Astrophysics and Elementary Particles.\nNavarro-Frenk-White profileSunKinematicsDark Matter Density ProfileThin stellar diskStellar diskBlue horizontal-branch starMilky WayRotation CurveProper motion...\n\u2022 The Milky Way's Circular Velocity Curve to 60 kpc and an Estimate of the Dark Matter Halo Mass from Kinematics of ~2400 SDSS Blue Horizontal Branch Starsver. 5\n\nWe derive new constraints on the mass of the Milky Way's dark matter halo, based on a set of halo stars from SDSS as kinematic tracers. Our sample comprises 2401 rigorously selected Blue Horizontal-Branch (BHB) halo stars drawn from SDSS DR-6. To interpret these distributions, we compare them to matched mock observations drawn from two different cosmological galaxy formation simulations designed to resemble the Milky Way, which we presume to have an appropriate orbital distribution of halo stars. We then determine which value of $\\rm V_{cir}(r)$ brings the observed distribution into agreement with the corresponding distributions from the simulations. This procedure results in an estimate of the Milky Way's circular velocity curve to $\\sim 60$ kpc, which is found to be slightly falling from the adopted value of $\\rm 220 km s^{-1}$ at the Sun's location, and implies M$(<60 \\rm kpc) = 4.0\\pm 0.7\\times 10^{11}$M$_\\odot$. The radial dependence of $\\rm V_{cir}(r)$, derived in statistically independent bins, is found to be consistent with the expectations from an NFW dark matter halo with the established stellar mass components at its center. If we assume an NFW halo profile of characteristic concentration holds, we can use the observations to estimate the virial mass of the Milky Way's dark matter halo, M$_{\\rm vir}=1.0^{+0.3}_{-0.2} \\times 10^{12}$M$_\\odot$, which is lower than many previous estimates. This estimate implies that nearly 40% of the baryons within the virial radius of the Milky Way's dark matter halo reside in the stellar components of our Galaxy. A value for M$_{\\rm vir}$ of only $\\sim 1\\times10^{12}$M$_\\odot$ also (re-)opens the question of whether all of the Milky Way's satellite galaxies are on bound orbits.\nStarBlue horizontal-branch starRadial velocityGalaxyMilky Way haloJeans equationNavarro-Frenk-White profileVelocity dispersionAbsolute magnitudeVirial mass...\n\u2022 A Tale of Tails: Dark Matter Interpretations of the Fermi GeV Excess in Light of Background Model Systematics\n\nSeveral groups have identified an extended excess of gamma rays over the modeled foreground and background emissions towards the Galactic center (GC) based on observations with the Fermi Large Area Telescope. This excess emission is compatible in morphology and spectrum with a telltale sign from dark matter (DM) annihilation. Here, we present a critical reassessment of DM interpretations of the GC signal in light of the foreground and background uncertainties that some of us recently outlaid in Calore et al. 2014. We find that a much larger number of DM models fits the gamma-ray data than previously noted. In particular: (1) In the case of DM annihilation into $\\bar{b}b$, we find that even large DM masses up to $m_\\chi \\simeq$ 74 GeV are allowed with a $p$-value $> 0.05$. (2) Surprisingly, annihilation into non-relativistic hh gives a good fit to the data. (3) The inverse Compton emission from $\\mu^+\\mu^-$ with $m_\\chi\\sim$ 60-70 GeV can also account for the excess at higher latitudes, $|b|>2^\\circ$, both in its spectrum and morphology. We also present novel constraints on a large number of mixed annihilation channels, including cascade annihilation involving hidden sector mediators. Finally, we show that the current limits from dwarf spheroidal observations are not in tension with a DM interpretation when uncertainties on the DM halo profile are accounted for.\nInverse ComptonIntensityDiffuse emissionCosmic rayQuarkBranching ratioStandard ModelPositronBremsstrahlungDwarf spheroidal galaxy...\n\u2022 Two Local Volume Dwarf Galaxies Discovered in 21 cm Emission: Pisces A and B\n\nWe report the discovery of two dwarf galaxies, Pisces A and B, from a blind 21 cm HI search. These were the only two galaxies found via optical imaging and spectroscopy of 22 HI clouds identified in the GALFA-HI survey as dwarf galaxy candidates. They have properties consistent with being in the Local Volume ($<10$ Mpc), and one has resolved stellar populations such that it may be on the outer edge of the Local Group ($\\sim 1 \\, {\\rm Mpc}$ from M31). While the distance uncertainty makes interpretation ambiguous, these may be among the faintest starforming galaxies known. Additionally, rough estimates comparing these galaxies to $\\Lambda$CDM dark matter simulations suggest consistency in number density, implying that dark matter halos likely to host these galaxies are primarily HI-rich. The galaxies may thus be indicative of a large population of dwarfs at the limit of detectability that are comparable to the faint satellites of the Local Group. Because they are outside the influence of a large dark matter halo to alter their evolution, these galaxies can provide critical anchors to dwarf galaxy formation models.\nPoint sourceStarSloan Digital Sky SurveyTelescopesGalaxyExploring the Local Volume in SimulationsStar formingObservatoriesHubble flowHertzsprung-Russell diagram...\n\u2022 In-orbit background of X-ray microcalorimeters and its effects on observations\n\nMethods.There are no experimental data about the background experienced by microcalorimeters in the L2 orbit, and thus the particle background levels were calculated by means of Monte Carlo simulations: we considered the original design configuration and an improved configuration aimed to reduce the unrejected background, and tested them in the L2 orbit and in the low Earth orbit, comparing the results with experimental data reported by other X-ray instruments.To show the results obtainable with the improved configuration we simulated the observation of a faint, high-redshift, point source (F[0.5-10 keV]~6.4E-16 erg cm-2 s-1, z=3.7), and of a hot galaxy cluster at R200 (Sb[0.5-2 keV]=8.61E-16 erg cm-2 s-1 arcmin-2,T=6.6 keV). Results.First we confirm that implementing an active cryogenic anticoincidence reduces the particle background by an order of magnitude and brings it close to the required level.The implementation and test of several design solutions can reduce the particle background level by a further factor of 6 with respect to the original configuration.The best background level achievable in the L2 orbit with the implementation of ad-hoc passive shielding for secondary particles is similar to that measured in the more favorable LEO environment without the passive shielding, allowing us to exploit the advantages of the L2 orbit.We define a reference model for the diffuse background and collect all the available information on its variation with epoch and pointing direction.With this background level the ATHENA mission with the X-IFU instrument is able to detect ~4100 new obscured AGNs with F>6.4E-16 erg cm-2 s-1 during three years, to characterize cluster of galaxies with Sb(0.5-2 keV)>9.4E-16 erg cm-2 s-1 sr-1 on timescales of 50 ks (500 ks) with errors <40% (<12%) on metallicity,<16% (4.8%) on temperature,2.6% (0.72%) on the gas density, and several single-element abundances.\nCluster of galaxiesObscured AGNAbundanceAthena+ missionLow Earth orbitMicrocalorimeterVirial radiusPoint sourceMonte Carlo methodOrbit...\n\u2022 Attempts at a determination of the fine-structure constant from first principles: A brief historical overview\n\nIt has been a notably elusive task to find a remotely sensical ansatz for a calculation of Sommerfeld's electrodynamic fine-structure constant alpha_QED ~ 1\/137.036 based on first principles. However, this has not prevented a number of researchers to invest considerable effort into the problem, despite the formidable challenges, and a number of attempts have been recorded in the literature. Here, we review a possible approach based on the quantum electrodynamic (QED) beta function, and on algebraic identities relating alpha_QED to invariant properties of \"internal\" symmetry groups, as well as attempts to relate the strength of the electromagnetic interaction to the natural cut-off scale for other gauge theories. Conjectures based on both classical as well as quantum-field theoretical considerations are discussed. We point out apparent strengths and weaknesses of the most prominent attempts that were recorded in the literature. This includes possible connections to scaling properties of the Einstein-Maxwell Lagrangian which describes gravitational and electromagnetic interactions on curved space-times. Alternative approaches inspired by string theory are also discussed. A conceivable variation of the fine-structure constant with time would suggest a connection of alpha_QED to global structures of the Universe, which in turn are largely determined by gravitational interactions.\nRenormalization groupQuantum fluctuationQuantizationCoupling constantCasimir energyClassical electron radiusPhase transitionsGravitonThe age of the UniverseElectron-positron pair...\n\u2022 Stability of Force-Free Magnetospheresver. 2\n\nWe analyze the dynamical evolution of a perturbed force-free magnetosphere of a rotating black hole, which is described by the Blandford-Znajek solution in the stationary limit. We find that the electromagnetic field perturbations can be classified into two categories: \"trapped modes\" and \"traveling waves\". The trapped modes are analogous to the vacuum (without plasma) electromagnetic quasinormal modes in rotating black hole spacetimes, but with different eigenfrequencies and wave functions, due to their coupling with the background electromagnetic field and current. The traveling waves propagate freely to infinity or the black hole horizon along specific null directions, and they are closely related to the no-scattering Poynting flux solutions discovered by Brennan, Gralla and Jacobson. Our results suggest that the Blandford-Znajek solution is mode stable, and more importantly we expect this study to illuminate the dynamical behavior of force-free magnetospheres as well as to shed light on the path to new exact solutions.\nBlack holeWave equationDifferential formBlack hole spinKerr black holeHamiltonianHorizonEvolution equationSchwarzschild black holesMagnetosphere of a star...\n\u2022 Twisted Fermionic Oscillator Algebra in $\\kappa$-Minkowski space-time\n\nIn this paper, we investigate the twisted algebra of the fermionic oscillators associated with Dirac field defined in $\\kappa$-Minkowski space-time. Starting from $\\kappa$-deformed Dirac theory, which is invariant under the undeformed $\\kappa$-Poincare algebra, using the twisted flip operator, we derive the deformed algebra of the creation and annihilation operators corresponding to the Dirac field quanta in $\\kappa$-Minkowski space-time. In the limit $a\\rightarrow 0$, the deformed algebra reduces to the commutative result.\nSymmetry algebraStatisticsHopf algebraFermionic fieldSymmetry groupStar productQ-deformed oscillator algebraDirac fieldQuantum gravityQuantization...\n\u2022 An anomalous propulsion mechanism\n\nWe consider a gas of free chiral fermions trapped inside a uniform rotating spherical shell. Once the shell becomes transparent the fermions are emitted along the axis of rotation due to the chiral and mixed anomaly. In return, owing to momentum conservation, the shell is propelled forward. We study the dependence of the magnitude of this effect on the shell parameters in a controlled setting and find that it is sensitive to the formation of an ergosphere around the rotating shell. A brief discussion on a possible relation to pulsar kicks is provided.\nProto-neutron starNeutron starConstitutive relationVorticityStarNeutrinoThermalisationCoolingSchwarzschild radiusDecay rate...\n\u2022 Effective Lagrangian approach to the EWSB sector\n\nIn a model independent framework, the effects of new physics at the electroweak scale can be parametrized in terms of an effective Lagrangian expansion. Assuming the $SU(2)_L x U(1)_Y$ gauge symmetry is linearly realized, the expansion at the lowest order span dimension--six operators built from the observed Standard model (SM) particles, in addition to a light scalar doublet. After a proper choice of the operator basis we present a global fit to all the updated available data related to the electroweak symmetry breaking sector: triple gauge boson vertex (TGV) collider measurements, electroweak precision tests and Higgs searches. In this framework modifications of the interactions of the Higgs field to the electroweak gauge bosons are related to anomalous TGV's, and given the current experimental precision, we show that the analysis of the latest Higgs boson data at the LHC and Tevatron gives rise to strong bounds on TGV's that are complementary to those from direct TGV measurements. Interestingly, we present how this correlated pattern of deviations from the SM predictions could be different for theories based on a non--linear realization of the $SU(2)_L x U(1)_Y$ symmetry, characteristic of for instance composite Higgs models. Furthermore, anomalous TGV signals expected at first order in the non--linear realization may appear only at higher orders of the linear one, and viceversa. Their study could lead to hints on the nature of the observed boson.\nTri-Linear Gauge Boson CouplingsChiralityReachabilityHiggs bosonComplementarityStandard ModelEffective theoryElectroweak precision testGauge coupling constantElectroweak symmetry breaking...\n\u2022 Model-independent evidence in favor of an end to reionization by z~6\n\nWe present new upper limits on the volume-weighted neutral hydrogen fraction, <xHI>, at z~5-6 derived from spectroscopy of bright quasars. The fraction of the Lyman-alpha and Lyman-beta forests that is \"dark\" (with zero flux) provides the only model-independent upper limit on <xHI>, requiring no assumptions about the physical conditions in the intergalactic medium or the quasar's unabsorbed UV continuum. In this work we update our previous results using a larger sample (22 objects) of medium-depth (~ few hours) spectra of high-redshift quasars obtained with the Magellan, MMT, and VLT. This significantly improves the upper bound on <xHI> derived from dark pixel analysis to <xHI> <= 0.06 + 0.05 (1{\\sigma}) at z=5.9, and <xHI> <= 0.04 + 0.05 (1{\\sigma}) at z=5.6. These results provide robust constraints for theoretical models of reionization, and provide the strongest available evidence that reionization has completed (or is very nearly complete) by z~6.\nStatisticsIntergalactic mediumRedshift binsAbsorptivityEffective optical depthTelescopesInverse-variance weightingSpectrographsQuasarCosmology...\n\u2022 A high order special relativistic hydrodynamic and magnetohydrodynamic code with space-time adaptive mesh refinementver. 3\n\nWe present a high order one-step ADER-WENO finite volume scheme with space-time adaptive mesh refinement (AMR) for the solution of the special relativistic hydrodynamic and magnetohydrodynamic equations. By adopting a local discontinuous Galerkin predictor method, a high order one-step time discretization is obtained, with no need for Runge--Kutta sub-steps. This turns out to be particularly advantageous in combination with space-time adaptive mesh refinement, which has been implemented following a \"cell-by-cell\" approach. As in existing second order AMR methods, also the present higher order AMR algorithm features time-accurate local time stepping (LTS), where grids on different spatial refinement levels are allowed to use different time steps. We also compare two different Riemann solvers for the computation of the numerical fluxes at the cell interfaces. The new scheme has been validated over a sample of numerical test problems in one, two and three spatial dimensions, exploring its ability in resolving the propagation of relativistic hydrodynamical and magnetohydrodynamical waves in different physical regimes. The astrophysical relevance of the new code for the study of the Richtmyer--Meshkov instability is briefly discussed in view of future applications.\nInstabilityStencilShock waveLorentz factorRiemann problemRelativistic magnetohydrodynamicsAlfv\u00e9n waveContact discontinuityAdaptive mesh refinementExact solution...\n\u2022 Frequentism and Bayesianism: A Python-driven Primer\n\nThis paper presents a brief, semi-technical comparison of the essential features of the frequentist and Bayesian approaches to statistical inference, with several illustrative examples implemented in Python. The differences between frequentism and Bayesianism fundamentally stem from differing definitions of probability, a philosophical divide which leads to distinct approaches to the solution of statistical problems as well as contrasting ways of asking and answering questions about unknown parameters. After an example-driven discussion of these differences, we briefly compare several leading Python statistical packages which implement frequentist inference using classical methods and Bayesian inference using Markov Chain Monte Carlo.\nConfidence intervalMonte Carlo Markov chainFrequentist approachNuisance parameterMaximum likelihoodPoint estimationStarBayesian approachPythonAlice and Bob...\n\u2022 Mass Accretion and its Effects on the Self-Similarity of Gas Profiles in the Outskirts of Galaxy Clusters\n\nGalaxy clusters exhibit remarkable self-similar behavior which allows us to establish simple scaling relationships between observable quantities and cluster masses, making galaxy clusters useful cosmological probes. Recent X-ray observations suggest that self-similarity may be broken in the outskirts of galaxy clusters. In this work, we analyze a mass-limited sample of massive galaxy clusters from the Omega500 cosmological hydrodynamic simulation to investigate the self-similarity of the diffuse X-ray emitting intracluster medium (ICM) in the outskirts of galaxy clusters. We find that the self-similarity of the outer ICM profiles is better preserved if they are normalized with respect to the mean density of the universe, while the inner profiles are more self-similar when normalized using the critical density. However, the outer ICM profiles as well as the location of accretion shock around clusters are sensitive to their mass accretion rate, which causes the apparent breaking of self-similarity in cluster outskirts. We also find that the collisional gas does not follow the distribution of collisionless dark matter perfectly in the infall regions of galaxy clusters, leading to 10% departures in the gas-to-dark matter density ratio from the cosmic mean value. Our results have a number implications for interpreting observations of galaxy clusters in X-ray and through the Sunyaev-Zel'dovich effect and their application to cluster cosmology.\n\u2022 The power of relativistic jets is larger than the luminosity of their accretion disks\n\nTheoretical models for the production of relativistic jets from active galactic nuclei predict that jet power arises from the spin and mass of the central black hole, as well as the magnetic field near the event horizon. The physical mechanism mechanism underlying the contribution from the magnetic field is the torque exerted on the rotating black hole by the field amplified by the accreting material. If the squared magnetic field is proportional to the accretion rate, then there will be a correlation between jet power and accretion luminosity. There is evidence for such a correlation, but inadequate knowledge of the accretion luminosity of the limited and inhomogeneous used samples prevented a firm conclusion. Here we report an analysis of archival observations of a sample of blazars (quasars whose jets point towards Earth) that overcomes previous limitations. We find a clear correlation between jet power as measured through the gamma-ray luminosity, and accretion luminosity as measured by the broad emission lines, with the jet power dominating over the disk luminosity, in agreement with numerical simulations. This implies that the magnetic field threading the black hole horizon reaches the maximum value sustainable by the accreting matter.\nFlat spectrum radio quasarAccretionAstrophysical jetEGRETMagnetic energyLorentz factorBlack hole spinBroad-line regionSpectral energy distributionActive Galactic Nuclei...\n\u2022 When Higgs Meets Starobinsky in the Early Universever. 2\n\nThe measurement of the Higgs mass at the LHC has confirmed that the Standard Model electroweak vacuum is a shallow local minimum and is not absolutely stable. In addition to a probable unacceptably fast tunneling to the deep true minimum, it is not clear how the observable present-day vacuum could be reached from the early Universe particularly following inflation. In this note it is shown that these problems can be alleviated if the Higgs field is non-minimally coupled to a higher-curvature theory of gravity which is effective in deriving inflation a la Starobinsky. Moreover, it implies that the Higgs self-coupling could be enhanced and have an observable effect at the next generation of particle colliders.\nStandard ModelPlanck scaleEinstein frameHiggs potentialPlanck missionHiggs bosonMixing angleE-foldingScalar fieldHiggs quartic coupling...\n\u2022 Bayesian empirical likelihood for quantile regression\n\nBayesian inference provides a flexible way of combining data with prior information. However, quantile regression is not equipped with a parametric likelihood, and therefore, Bayesian inference for quantile regression demands careful investigation. This paper considers the Bayesian empirical likelihood approach to quantile regression. Taking the empirical likelihood into a Bayesian framework, we show that the resultant posterior from any fixed prior is asymptotically normal; its mean shrinks toward the true parameter values, and its variance approaches that of the maximum empirical likelihood estimator. A more interesting case can be made for the Bayesian empirical likelihood when informative priors are used to explore commonality across quantiles. Regression quantiles that are computed separately at each percentile level tend to be highly variable in the data sparse areas (e.g., high or low percentile levels). Through empirical likelihood, the proposed method enables us to explore various forms of commonality across quantiles for efficiency gains. By using an MCMC algorithm in the computation, we avoid the daunting task of directly maximizing empirical likelihood. The finite sample performance of the proposed method is investigated empirically, where substantial efficiency gains are demonstrated with informative priors on common features across several percentile levels. A theoretical framework of shrinking priors is used in the paper to better understand the power of the proposed method.\nBayesian approachClimateFrequentist approachStatisticsEstimating equationsCoverage probabilityIndicator functionUniform convergenceWettingCovariance...\n\u2022 QCD corrections to H -> gg in FDR\n\nI apply FDR -- a recently introduced Four Dimensional Regularization approach to quantum field theories -- to compute the NLO QCD corrections to H -> gg in the large top mass limit. The calculation involves all key ingredients of massless QCD, namely ultraviolet, infrared and collinear divergences, besides alpha_s renormalization. I show in detail how the correct result emerges in FDR, and discuss the translation rules to dimensional regularization.\nDimensional ReductionQuantum field theoryPhase spaceFDRStrong coupling constantPartonInfrared divergenceGauge invarianceFeynman rulesTransition rule...\n\u2022 Search for Heavy Right Handed Neutrinos at the FCC-ee\n\nThe Standard Model of particle physics is still lacking an understanding of the generation and nature of neutrino masses. A favorite theoretical scenario (the see-saw mechanism) is that both Dirac and Majorana mass terms are present, leading to the existence of heavy partners of the light neutrinos, presumably massive and nearly sterile. These heavy neutrinos can be searched for at high energy lepton colliders of very high luminosity, such as the Future electron-positron e+e- Circular Collider, FCC-ee (TLEP), presently studied within the Future Circular Collider design study at CERN, as a possible first step. A first look at sensitivities, both from neutrino counting and from direct search for heavy neutrino decay, are presented. The number of neutrinos should be measurable with a precision between 0.001 - 0.0004, while the direct search appears very promising due to the long lifetime of heavy neutrinos for small mixing angles. A sensitivity down to a heavy-light mixing of 10^{-12} is obtained, covering a large phase-space for heavy neutrino masses between 10 and 80 GeV\/c2.\nSterile neutrinoNeutrinoColliderTLEP experimentMixing angleCERNNeutrino massStandard ModelLuminosityMajorana mass...\n\u2022 Unveiling the nature of dark matter with high redshift 21 cm line experimentsver. 2\n\nObservations of the redshifted 21 cm line from neutral hydrogen will open a new window on the early Universe. By influencing the thermal and ionization history of the intergalactic medium (IGM), annihilating dark matter (DM) can leave a detectable imprint in the 21 cm signal. Building on the publicly available 21cmFAST code, we compute the 21 cm signal for a 10 GeV WIMP DM candidate. The most pronounced role of DM annihilations is in heating the IGM earlier and more uniformly than astrophysical sources of X-rays. This leaves several unambiguous, qualitative signatures in the redshift evolution of the large-scale ($k\\approx0.1$ Mpc$^{-1}$) 21 cm power amplitude: (i) the local maximum (peak) associated with IGM heating can be lower than the other maxima; (ii) the heating peak can occur while the IGM is in emission against the cosmic microwave background (CMB); (iii) there can be a dramatic drop in power (a global minimum) corresponding to the epoch when the IGM temperature is comparable to the CMB temperature. These signatures are robust to astrophysical uncertainties, and will be easily detectable with second generation interferometers. We also briefly show that decaying warm dark matter has a negligible role in heating the IGM.\nGalaxyIntergalactic mediumCoolingCosmologyAbsorptivityAstronomical X-ray sourceKinetic temperatureDark AgesReionizationHydrogen 21 cm line...\n\u2022 Bounds on QCD axion mass and primordial magnetic field from CMB $\\mu$-distortionver. 3\n\nThe oscillation of the CMB photons into axions can cause CMB spectral distortion in the presence of large scale magnetic field. With the COBE limit on the $\\mu$ parameter and a homogeneous magnetic field with strength $B\\lesssim 3.2$ nG at the horizon scale, stronger lower limit on the axion mass in comparison with the limit of the ADMX experiment is found to be, $4.8\\times 10^{-5}$ eV $\\lesssim m_a$ for the KSVZ axion model. On the other hand, using the experimental limit on the axion mass $3.5\\times 10^{-6}$ eV $\\lesssim m_a$ from the ADMX experiment together with the COBE bound on $\\mu$, is found $B\\lesssim 53$ nG for the KSVZ axion model and $B\\lesssim 141$ nG for DFSZ axion model, for a homogeneous magnetic field with coherence length at the present epoch $\\lambda_B\\sim 1.3$ Mpc. Limits on $B$ and $m_a$ for PIXIE\/PRISM expected sensitivity on $\\mu$ are derived. If CMB $\\mu$ distortion would be detected by the future space missions PIXIE\/PRISM and assuming that the strength of the large scale magnetic field is close to its canonical value, $B\\sim 1-3$ nG, axions in the mass range $2\\, \\mu$eV - $3\\, \\mu$eV would be potential candidates of CMB $\\mu$-distortion.\nMagnetic field strengthFaraday rotationIndex of refractionCMB temperature anisotropyCosmologyAxion modelCoupling constantQuantum electrodynamicsAxionFaraday effect...\n\u2022 Search for heavy neutrinos in $K^+\\to\\mu^+\\nu_H$ decays\n\nEvidence of a heavy neutrino, $\\nu_H$, in the $K^+\\to\\mu^+\\nu_H$ decays was sought using the E949 experimental data with an exposure of $1.70\\times 10^{12}$ stopped kaons. With the major background from the radiative $K^+\\to\\mu^+\\nu_\\mu\\gamma$ decay understood and suppressed, upper limits (90% C.L.) on the neutrino mixing matrix element between muon and heavy neutrino, $|U_{\\mu H}|^2$, were set at the level of $10^{-7}$ to $10^{-9}$ for the heavy neutrino mass region 175 to 300 MeV\/$c^2$.\nPionKaonBranching ratioStatisticsMonte Carlo methodScintillationStandard ModelKinematicsKaon decayBig bang nucleosynthesis...\n\u2022 Magnetic Fields in a Sample of Nearby Spiral Galaxiesver. 2\n\nBoth observations and modelling of magnetic fields in the diffuse interstellar gas of spiral galaxies are well developed but the theory has been confronted with observations for only a handful of individual galaxies. There is now sufficient data to consider statistical properties of galactic magnetic fields. We have collected data from the literature on the magnetic fields and interstellar media (ISM) of 20 spiral galaxies, and tested for various physically motivated correlations between magnetic field and ISM parameters. Clear correlations emerge between the total magnetic field strength and molecular gas density as well as the star formation rate. The magnetic pitch angle exhibits correlations with the total gas density, the star formation rate and the strength of the axisymmetric component of the mean magnetic field. The total and mean magnetic field strengths exhibit noticeable degree of correlation, suggesting a universal behaviour of the degree of order in galactic magnetic fields. We also compare the predictions of galactic dynamo theory to observed magnetic field parameters and identify directions in which theory and observations might be usefully developed.\nMean fieldSteady stateTurbulenceSpiral armHelicityAzimuthDifferential rotationMagnetic helicityCompressibilityIntensity...\n\u2022 Production Mechanisms and Signatures of Isosinglet Neutral Heavy Leptons in $\\Z^0$ Decays\n\nNeutrinoInterferenceGauge fieldLepton numberWeak neutral current interactionLeptonic model of particle accelerationCharged currentSterile neutrinoElectronParticles...\n\u2022 Tau decays to pions\n\nSemileptonic decayTau leptonParity violationChiralityChiral modelDalitz plotMassLeptonsP-symmetryVector...\n\u2022 Measurement of the Strong Coupling Constant and the Vector and Axial-Vector Spectral Functions in Hadronic Tau Decays\n\nThe spectral functions of the vector current and the axial-vector current have been measured in hadronic tau decays using the OPAL detector at LEP. Within the framework of the Operator Product Expansion a simultaneous determination of the strong coupling constant alpha_s, the non-perturbative operators of dimension 6 and 8 and of the gluon condensate has been performed. Different perturbative descriptions have been compared to the data. The Contour Improved Fixed Order Perturbation Theory gives alpha_s(mtau**2) = 0.348 +- 0.009 +- 0.019 at the tau-mass scale and alpha_s(mz**2) = 0.1219 +- 0.0010 +- 0.0017 at the Z-mass scale. The values obtained for alpha_s(mz**2) using Fixed Order Perturbation Theory or Renormalon Chain Resummation are 2.3% and 4.1% smaller, respectively. The running of the strong coupling between s_0 ~1.3 GeV**2 and s_0 = mtau**2 has been tested from direct fits to the integrated differential hadronic decay rate R_tau. A test of the saturation of QCD sum rules at the tau-mass scale has been performed.\nMonte Carlo methodRegularizationBranching ratioStatisticsSystematic errorQuantum chromodynamicsPionRenormalization schemeQuark massPerturbative QCD...\n\u2022 Too Many, Too Few, or Just Right? The Predicted Number and Distribution of Milky Way Dwarf Galaxies\n\nWe predict the spatial distribution and number of Milky Way dwarf galaxies to be discovered in the DES and LSST surveys, by completeness correcting the observed SDSS dwarf population. We apply most massive in the past, earliest forming, and earliest infall toy models to a set of dark matter-only simulated Milky Way\/M31 halo pairs from Exploring the Local Volume In Simulations (ELVIS). The observed spatial distribution of Milky Way dwarfs in the LSST-era will discriminate between the earliest infall and other simplified models for how dwarf galaxies populate dark matter subhalos. Inclusive of all toy models and simulations, at 90% confidence we predict a total of 37-114 L $\\gtrsim 10^3$L$_{\\odot}$ dwarfs and 131-782 L $\\lesssim 10^3$L$_{\\odot}$ dwarfs within 300 kpc. These numbers of L $\\gtrsim 10^3$L$_{\\odot}$ dwarfs are dramatically lower than previous predictions, owing primarily to our use of updated detection limits and the decreasing number of SDSS dwarfs discovered per sky area. For an effective $r_{\\rm limit}$ of 25.8 mag, we predict: 3-13 L $\\gtrsim 10^3$L$_{\\odot}$ and 9-99 L $\\lesssim 10^3$L$_{\\odot}$ dwarfs for DES, and 18-53 L $\\gtrsim 10^3$L$_{\\odot}$ and 53-307 L $\\lesssim 10^3$L$_{\\odot}$ dwarfs for LSST. These enormous predicted ranges ensure a coming decade of near-field excitement with these next generation surveys.\nDark matter subhaloMilky WayA dwarfsUltra-faint dwarf spheroidal galaxyGalaxyAzimuthStatisticsStarAndromeda galaxyInfall model...\n\u2022 The flat density profiles of massive, and relaxed galaxy clusters\n\nIn the present paper, we studied by means of the SIM introduced in Del Popolo (2009), the total and DM density profiles, and the correlations among different quantities, observed by Newman et al. (2012a,b), in seven massive and relaxed clusters, namely MS2137, A963, A383, A611, A2537, A2667, A2390. Similarly to Newman et al. (2012a,b), the total density profile, in the radius range 0.003 - 0.03$r_{200}$, has a mean total density profile in agreement with dissipationless simulations. The slope of the DM profiles of all clusters is flatter than -1. The slope, $\\alpha$, has a maximum value (including errors) of $\\alpha=-0.88$ in the case of A2390, and minimum value $\\alpha=-0.14$ for A2537. The baryonic component dominates the mass distribution at radii $< 5-10$ kpc, while the outer distribution is dark matter dominated. We found an anti-correlation among the slope $\\alpha$, the effective radius, $R_e$, and the BCG mass, and a correlation among the core radius $r_{core}$, and $R_e$. Moreover, the mass in 100 kpc (mainly dark matter) is correlated with the mass inside 5 kpc (mainly baryons). The behavior of the total mass density profile, the DM density profile, and the quoted correlations can be understood in a double phase scenario. In the first dissipative phase the proto-BCG forms, and in the second dissipationless phase, dynamical friction between baryonic clumps (collapsing to the center) and the DM halo flattens the inner slope of the density profile. In simple terms, the large scatter in the inner slope from cluster to cluster, and the anti-correlation among the slope, $\\alpha$ and $R_e$ is due to the fact that in order to have a total mass density profile which is NFW-like, clusters having more massive BCGs at their centers must contain less DM in their center. Consequently the inner profile has a flatter slope.\nBaryon contentNavarro-Frenk-White profileCluster of galaxiesAbell 383GalaxyStarVirial massAdiabatic contraction of dark matterN-body simulationDM mass...\n\u2022 Exact theory of freeze out\n\nBy considering the kinetic equations for the relic particles and the bath particles supposed in thermal and chemical equilibrium in the early Universe, we show that the problem of finding the present relic abundance is exactly defined by a system of two equations, the usual Boltzmann equation and a new one previously not recognized. The analytical solution of the latter gives the abundance down to a matching temperature that can be identified with freeze out temperature $x_f=m\/T_f$, while the usual Boltzmann equation is valid only for $x \\ge x_f$. The dependence of the present relic abundance on the abundance at an intermediate temperature is an exact result and not the consequence of the so called freeze out approximation. We also suggest an analytical approximation that furnishes the relic abundance accurate at the level of $1\\%-2\\%$ in the case of $S$-wave and $P$-wave scattering cross sections.\nWeakly interacting massive particleStatisticsRelic abundanceDegree of freedomFreeze-outEntropyDark matterAbundanceStandard ModelBoltzmann transport equation...\n\u2022 XMM-Newton Measurement of the Galactic Halo X-ray Emission using a Compact Shadowing Cloud\n\nObservations of interstellar clouds that cast shadows in the soft X-ray background can be used to separate the background Galactic halo emission from the local emission due to solar wind charge exchange (SWCX) and\/or the Local Bubble (LB). We present an XMM-Newton observation of a shadowing cloud, G225.60-66.40, that is sufficiently compact that the on- and off-shadow spectra can be extracted from a single field of view (unlike previous shadowing observations of the halo with CCD-resolution spectrometers, which consisted of separate on- and off-shadow pointings). We analyzed the spectra using a variety of foreground models: one representing LB emission, and two representing SWCX emission. We found that the resulting halo model parameters (temperature $T_h \\approx 2 \\times 10^6$ K, emission measure $E_h \\approx 4 \\times 10^{-3}$ cm$^{-6}$ pc) were not sensitive to the foreground model used. This is likely due to the relative faintness of the foreground emission in this observation. However, the data do favor the existence of a foreground. The halo parameters derived from this observation are in good agreement with those from previous shadowing observations, and from an XMM-Newton survey of the Galactic halo emission. This supports the conclusion that the latter results are not subject to systematic errors, and can confidently be used to test models of the halo emission.\nSolar windSurface brightnessSoft X-ray backgroundAbundanceThermalisationIntensityScience analysis systemCollisional ionization equilibriumAtomDBSpectral analysis...\n\u2022 Particle Physics Models of Inflation and the Cosmological Density Perturbationver. 4\n\nThis is a review of particle-theory models of inflation, and of their predictions for the primordial density perturbation that is thought to be the origin of structure in the Universe. It contains mini-reviews of the relevant observational cosmology, of elementary field theory and of supersymmetry, that may be of interest in their own right. The spectral index $n(k)$, specifying the scale-dependence of the spectrum of the curvature perturbation, will be a powerful discriminator between models, when it is measured by Planck with accuracy $\\Delta n\\sim 0.01$. The usual formula for $n$ is derived, as well as its less familiar extension to the case of a multi-component inflaton; in both cases the key ingredient is the separate evolution of causally disconnected regions of the Universe. Primordial gravitational waves will be an even more powerful discriminator if they are observed, since most models of inflation predict that they are completely negligible. We treat in detail the new wave of models, which are firmly rooted in modern particle theory and have supersymmetry as a crucial ingredient. The review is addressed to both astrophysicists and particle physicists, and each section is fairly homogeneous regarding the assumed background knowledge.\nHorizonInflatonSlow rollSlow-roll inflationCosmic Background ExplorerSupergravityGravitational waveVacuum expectation valueScalar fieldHubble time...\n\u2022 Gravitational wave emission from oscillating millisecond pulsars\n\nNeutron stars undergoing r-mode oscillation emit gravitational radiation that might be detected on earth. For known millisecond pulsars the observed spindown rate imposes an upper limit on the possible gravitational wave signal of these sources. Taking into account the physics of r-mode evolution, we show that only sources spinning at frequencies above a few hundred Hertz can be unstable to r-modes, and we derive a more stringent universal r-mode spindown limit on their gravitational wave signal, exploiting the fact that the r-mode saturation amplitude is insensitive to the structural properties of individual sources. We find that this refined bound limits the gravitational wave strain from millisecond pulsars to values below the detection sensitivity of next-generation detectors. Young sources are therefore a more promising option for the detection of gravitational waves emitted by r-modes and to probe the interior composition of compact stars in the near future.","date":"2014-11-26 01:14:17","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 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\": 0.6870273947715759, \"perplexity\": 1711.8087300547581}, \"config\": {\"markdown_headings\": false, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2014-49\/segments\/1416931004988.25\/warc\/CC-MAIN-20141125155644-00049-ip-10-235-23-156.ec2.internal.warc.gz\"}"}
| null | null |
Nohoch Tata (pronunciación: Nojoch Tata) es un apelativo en idioma maya que se aplica, entre los mayas de Quintana Roo, México, a la figura del gran sacerdote, esto es, al personaje de mayor jerarquía en la organización eclesiástica de las comunidades indígenas.
Datos históricos
A partir de la llamada Guerra de Castas, los indígenas mayas del actual estado de Quintana Roo en México, practicaron el culto a la denominada Santa Cruz, mezcla de rito católico y de creencia maya precolombina. En tales ritos de culto la figura que ejercía el cargo sacerdotal más elevado recibió el nombre de Nohoch Tata (gran abuelo).
Alfonso Villa Rojas etnólogo que escribió Los elegidos de Dios, Etnografía de los mayas de Quintana Roo señala que el Nohoch Tata equivale a la figura del Ah Kin, o del sacerdote que oficiaba la misa y cuya misión principal fue la de resguardar y asegurarse de la calidad de los servicios religiosos que corresponden a la Santísima Cruz Protectora.
Es un personaje comunitario que debe tener un prestigio intachable y resulta tabú criticarlo en ninguno de sus actos. No hace la milpa ni se ocupa de ninguna actividad o trabajo común. Todos sus gastos son cubiertos con los dineros que recauda la iglesia por concepto de misas, casamientos, bautizos. Villa Rojas considera que el Nohoch Tata es equiparable al Ahau Kan o gran sacerdote de tiempos prehispánicos quien, como los describe fray Diego de Landa, daba consejos a los señores y respuestas a sus preguntas.
Más recientemente se ha llamado Nohoch Tata, por antonomasia, al personaje de mayor edad y de mayor sabiduría en una comunidad dada.
Véase también
Felipe Carrillo Puerto (Quintana Roo)
Cruzoob
Referencias
Bibliografía
Alfonso Villa Roja (1978), Los elegidos de Dios. Etnografía de los mayas de Quintana Roo Serie de Antropología Social. No. 56, Instituto Nacional Indigenista, 571 págs. Ilustr. México.
Vocablos en lengua maya
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 3,006
|
\section{Introduction}
A horospherical product is a metric space constructed from two Gromov hyperbolic spaces $H_p$ and $H_q$. It is included in their cartesian product $H_p\times H_q$ and can be seen as a diagonal in it. The definition of this horospherical product makes use of the so-called Busemann functions. Let us assume that there exists a unique geodesic ray $k$ in $H_p$ starting at a given base point $w_p\in H_p$ and leading in the direction of a given point on the boundary $a_p\in\partial H_p$. Then the Busemann function with respect to $a_p$ and $w_p$ associates to a point $x_p\in H_p$ the delay it has in a race towards $a_p$ against $k$. Given a base point and a point on the boundary on $H_p$ and $H_q$ we have two respective Busemann functions. We define the height functions of these spaces $H_p$ and $H_q$ to be the opposite of the Busemann functions. Hence the level-lines of the Busemann functions, which are called horospheres, are also the level-lines of the height functions. Then the horospherical product $\mathcal{H}=H_p\bowtie H_q$ is built by gluing $H_p$ with an upside down copy of $H_q$ along their respective horospheres. More precisely with a given height $h_p$ on $H_p$ (Definition \ref{DefHaut}) and a given height $h_q$ on $H_q$, the horospherical product $\mathcal{H}=H_p\bowtie H_q$ is defined as follows.
\begin{equation}
\mathcal{H}:=\lbrace (x_p,x_q)\in H_p\times H_q\ /\ h_p(x_p)+h_q(x_q)=0 \rbrace.\nonumber
\end{equation}
Since we are considering only couples of points with opposite heights in this set, we define the height on the horospherical product $\mathcal{H}$ as the height on the first component $H_p$. This notion of horospherical product generalizes the description of the Diestel-Leader graphs, the SOL geometry and the Cayley 2-complexes of Baumslag-Solitar groups $BS(1,n)$. In the second chapter of \cite[Woess]{Woess}, the last three exemples are presented as horocyclic products of metric spaces. We choose the name horospherical product instead of horo\textit{cyclic} product since in higher dimension, level-lines according to a Busemann function are not horocycles but horospheres. As Woess suggested in \cite[W]{Woess}, we explore here a generalization for horospherical products.
\\The Diestel-Leader graphs are horospherical products of two regular trees. If the two trees' degree are equal, their horospherical product is the Cayley graph of a lamplighter group, see \cite[Woess]{Woess2} for further details. A motivation to study this construction are the results from \cite[Eskin, Fisher, Whyte]{EFW0}, \cite[E,F,W]{EFW1} and \cite[E,F,W]{EFW2}. They state that the Diestel-Leader graphs constructed from two regular trees with no common divisor in their degree are vertex-transitive graphs which are not quasi-isometric to any Cayley Graphs. The existence of such a graph was a long open problem.
\\The SOL geometry, one of the eight Thurston geometries, is presented in \cite[Woess]{Woess} as the horospherical product of two hyperbolic planes. In \cite[Eskin, Fisher, Whyte]{EFW2}, they also prove rigidity results on lattices of the SOL geometry. A third example is related to the family of Baumslag-Solitar groups $BS(1,n)$, their Cayley 2-complex are described in \cite[Bendikov, Saloff-Coste, Salvatori, Woess]{Treebol} as the horospherical product of a hyperbolic plane and a homogeneous tree. Similar rigidity results as in \cite[Eskin, Fisher, Whyte]{EFW0} are presented in \cite[Farb, Mosher]{FB1} and \cite[F,M]{FB2} for Baumslag-Solitar groups.
\\\\For our generalization, we require that our components $H_p$ and $H_q$ are two proper geodesically complete Gromov hyperbolic Busemann spaces. A Busemann space is a metric space where the distance between any two geodesics is convex, and metric space $X$ is geodesically complete if and only if a geodesic segment $\alpha:I\to X$ can be prolonged into a geodesic line $\hat{\alpha} :\mathbb{R}\to X$. The Busemann hypothesis suits with the definition of horospherical product since we require that the opposite heights are exactly equal. Furthermore, adding the hypothesis that $H_p$ and $H_q$ are geodesically complete allows us to prove that the horospherical product $\mathcal{H}=H_p\bowtie H_q$ is connected.
\\\\There are many possible choices for the distance on $H_p\bowtie H_q$. In this paper we work with a family of length path metrics induced by distances on $H_p\times H_q$ (see precise definition \ref{DefNDistHoro}). We require that the distance on $H_p\bowtie H_q$ comes from a norm $N$ on $\mathbb{R}^2$ that is greater than the normalized $\ell_1$ norm. Such norms are called admissible norms. A description of the distances on horospherical products is given by Corollary \ref{lengthGeod}. This corollary shows that any distance we described earlier provides the same geodesic shapes, up to an additive constant depending only on $H_p$, $H_q$ and on the norm $N$. To do so we introduce a notion of vertical geodesics, which are geodesics heuristically "normal" to horospheres (see precise definition \ref{DefVertGeodInHoro}). The shapes of geodesic segments are described in the following theorem.
\begin{thm}\label{THMAINTRO}
Let $\delta\geq 1$ and let $N$ be an admissible norm. Let $H_p$ and $H_q$ be two proper, geodesically complete, $\delta$-hyperbolic, Busemann spaces. Let $x=(x_p,x_q)$ and $y=(y_p,y_q)$ be two points of $\mathcal{H}=H_p\bowtie H_q$ and let $\alpha$ be a geodesic segment of $(\mathcal{H},d_{\mathcal{H},N})$ linking $x$ to $y$. There exists a constant $\kappa$ depending only on $\delta$ and $N$, and there exist two vertical geodesics $V_1=(V_{1,p},V_{1,q})$ and $V_2=(V_{2,p},V_{2,q})$ such that:
\begin{enumerate}
\item If ~ $h(x)\leq h(y)-\kappa$ ~ then $\alpha$ is in the $\kappa$-neighbourhood of $V_1\cup(V_{1,p},V_{2,q})\cup V_2$
\item If ~ $h(x)\geq h(y)+\kappa$ ~ then $\alpha$ is in the $\kappa$-neighbourhood of $ V_1\cup(V_{2,p},V_{1,q})\cup V_2$
\item If ~ $|h(x)-h(y)|\leq \kappa$ ~ then at least one of the conclusions of $1.$ or $2.$ holds.
\end{enumerate}
Specifically, $V_1$ and $V_2$ can be chosen such that $x$ is close to $V_1$ and $y$ is close to $V_2$.
\end{thm}
\begin{figure}
\begin{center}
\includegraphics[scale=0.4]{FigTHMAINTRO.pdf}
\captionof{figure}{Shape of geodesic segments when $h(x)\leq h(y)-\kappa$ in $\mathcal{H}=H_p\bowtie H_q$. The neighbourhoods' shape are distorted since when going upward, distances are contracted in the "direction" $H_p$ and expanded in the "direction" $H_q$.}
\label{FigTHMAINTRO}
\end{center}
\end{figure}
This behaviour is illustrated on Figure \ref{FigTHMAINTRO} for $h(x)\leq h(y)-\kappa$. This result is similar to the hyperbolic case, where a geodesic segment is in the constant neighbourhood of two vertical geodesics. The heuristic comprehension of Theorem \ref{THMAINTRO} is, say in the case $h(x)\leq h(y)-\kappa$, that a geodesic segment travels first along a copy of the component $H_q$ (which is upside down) as a geodesic in it, and last travels along a copy of the component $H_p$ as a geodesic in it.
\\To prove Theorem \ref{THMAINTRO} we need to control the lengths of the geodesics' projections on $H_p$ and $H_q$. This work is done in section \ref{SecMetricEstimat}. The relative distance is defined as the distance minus the difference of height, it can be understood as the distance on horospheres. We first exhibit that in a hyperbolic space the maximal height of a geodesic segment and the relative distance between the end points of that geodesic segment are tightly related. We also have a lower bound on the length of paths avoiding horoballs as in Proposition $1.6$ p400 of \cite[Bridson, Haefliger]{BH}. Then we refine this last result into a control on the length of paths which avoid horoballs and which reach a given point. Since the projections on $H_p$ and $H_q$ of geodesics in $\mathcal{H}$ are such paths, Theorem \ref{THMAINTRO} follows.
\\This result leads us to show the existence of unextendabled geodesics, which are called dead-ends. This was well known for lamplighter groups. This description of geodesic segments also allows us to prove that for any geodesic ray $k$ of $\mathcal{H}=H_p\bowtie H_q$, there exists a vertical geodesic ray at finite Hausdorff distance. Therefore we classify all possible shapes for geodesic lines and then give a description of the visual boundary of $\mathcal{H}$. The notion of $H_p$-type and $H_q$-type geodesics at scale $\kappa$ are described in Definition \ref{DefHpTypeHqType} and illustrated on Figure \ref{FinalThmInIntro}. They are essentially geodesics of $\mathcal{H}$ in a constant $\kappa$-neighbourhood of geodesics in a copy of $H_p$ or in a copy of $H_q$ in $\mathcal{H}$. We show that the geodesic lines of $H_p\bowtie H_q$ are either $H_p$-type, $H_q$-type or both.
\begin{thm}\label{THMBINTRO}
Let $\delta\geq 1$ and let $N$ be an admissible norm. Let $H_p$ and $H_q$ be two proper, geodesically complete, $\delta$-hyperbolic, Busemann spaces. Let $\mathcal{H}=H_p \bowtie H_q$ be the horospherical product of $H_p$ and $H_q$. Then there exists $\kappa\geq 0$ depending only on $\delta$ and $N$ such that for all geodesic $\alpha:\mathbb{R}\rightarrow \mathcal{H}$ of $(\mathcal{H},d_{\mathcal{H},N})$ at least one of the two following statements holds.
\begin{enumerate}
\item $\alpha$ is a $H_p$-type geodesic at scale $\kappa$ of $\mathcal{H}$
\item $\alpha$ is a $H_q$-type geodesic at scale $\kappa$ of $\mathcal{H}$
\end{enumerate}
\end{thm}
If a geodesic is both $H_p$-type and $H_q$-type at scale $\kappa$, it is in the $\kappa$-neighbourhood of a vertical geodesic of $H_p\bowtie H_q$.
\begin{figure}
\begin{center}
\includegraphics[scale=0.25]{FinalThm.pdf}
\captionof{figure}{Different type of geodesics in $\mathcal{H}=H_p\bowtie H_q$.}
\label{FinalThmInIntro}
\end{center}
\end{figure}
The notion of visual boundary of $\mathbb{H}^2\bowtie \mathbb{H}^2$ is presented in the work of Troyanov in \cite[Troyanov]{Troya} through several definitions of horizons. We expand the definition and the description of the visual boundary in the general case of horospherical products as follows. Two geodesics are called asymptotic if they are at finite Hausdorff distance from each other. Let $o\in\mathcal{H}$, the visual boundary of $\mathcal{H}$ is then denoted by $\partial_o(\mathcal{H})$ and stands for the set of families of asymptotic geodesic rays starting at $o$. We have:
\begin{thm}\label{THMCINTRO}
Let $\delta\geq 1$ and let $H_p$ and $H_q$ be two proper, geodesically complete, $\delta$-hyperbolic, Busemann spaces. We fix base points and directions on $H_p$ and $H_q$ as follows, $(w_{p},a_p)\in H_p\times\partial H_p$, $(w_{q},a_q)\in H_q\times\partial H_q$. Let $\mathcal{H}=H_p\bowtie H_q$ be the horospherical product with respect to $(w_{p},a_p)$ and $(w_{q},a_q)$. Then the visual boundary of $\mathcal{H}$ with respect to a given point $o=(o_p,o_q)$ is:
\begin{align*}
\partial_o \mathcal{H}=&\Big(\big(\partial H_p\setminus \lbrace a_p\rbrace\big)\times\lbrace a_q\rbrace\Big)\bigcup\Big(\lbrace a_p\rbrace\times\big(\partial H_q\setminus \lbrace a_q\rbrace\big) \Big)
\\=&\Big(\big(\partial H_p\times\lbrace a_q\rbrace\big)\bigcup\big(\lbrace a_p\rbrace\times\partial H_q\big)\Big)\setminus \lbrace(a_p,a_q)\rbrace
\end{align*}
\end{thm}
This last result is similar to the Proposition 6.4 of \cite[Troyanov]{Troya}. However, unlike Troyanov in his work, we are focusing on minimal geodesics and not on local ones. One can see that this visual boundary neither depends on the chosen admissible norm $N$ nor the base point $o$.
\\\\The figures of this paper depict lemmas and theorems when the two components $H_p$ and $H_q$ are hyperbolic planes $\mathbb{H}^2$, hence when $\mathcal{H}= H_p\bowtie H_q$ is the SOL geometry. In the $2$ dimensional figures, we picture the vertical geodesics as getting closer when going upward since the distance contracts in this direction. In the $3$ dimensional case we picture the vertical geodesics as straight lines in order to match with their shapes in the SOL geometry.
\\\\The paper is organised with first Section \ref{SectContext} which presents Gromov hyperbolic spaces, the notion of vertical geodesics in them and the impact of the Busemann hypothesis on the vertical geodesics. Then Section \ref{SecMetricEstimat} provides us with an estimate on the length of paths avoiding horoballs in hyperbolic spaces, namely Lemma \ref{ExpLengthWhenBelowAndReachPoint}, which will be central in our control of the distances in $\mathcal{H}$. In Section \ref{SectHoroDefn} we define the horospherical products and give an estimate of their distance through Corollary \ref{lengthGeod}. We hence discuss the fact that an entire family of distances are close to each others in $\mathcal{H}$. Last, in Section \ref{SectionThm}, we prove our three main results. Theorem \ref{THMAINTRO} follows from the estimates of Corollary \ref{lengthGeod} on the length of geodesic segments. The description of geodesic lines of Theorem \ref{THMBINTRO} follows from Theorem \ref{THMAINTRO} and gives us the tools to prove Theorem \ref{THMCINTRO}.
\section{Context}\label{SectContext}
\subsection{Gromov hyperbolic spaces}
The goal of this section is to recall what is a Gromov hyperbolic space and what are vertical geodesics in such a space. Let $H$ be a proper geodesic metric space, and $d$ be a distance on $H$. A geodesic line of $H$ is the isometric image of an Euclidean line in $H$. A geodesic ray of a metric space $H$ is the isometric image of a half Euclidean line in $H$. A geodesic segment of a metric space $H$ is the isometric image of an Euclidean interval in $H$. By slight abuse, we will call geodesic, geodesic ray or geodesic segment, a map $\alpha:I\rightarrow H$ which parametrises our given geodesic by arclength.
\\\\Let $\delta\geq 0$ be a non-negative number. Let $x$, $y$ and $z$ be three points of $H$. The geodesic triangle $[x,y]\cup[y,z]\cup[z,x]$ is called $\delta$-slim if any of its sides is included in the $\delta$-neighbourhood of the remaining two. The metric space $H$ is called $\delta$-hyperbolic if every geodesic triangle is $\delta$-slim. A metric space $H$ is called Gromov hyperbolic if there exists $\delta\geq 0$ such that $H$ is a $\delta$-hyperbolic space.
\\\\An important property of Gromov hyperbolic spaces is that they admit a nice compactification. Indeed the Gromov boundary allows that. We call two geodesic rays of $H$ equivalent if their images are at finite Hausdorff distance. Let $o\in H$ be a base point. We define $\partial_{o} H$ the Gromov boundary of $H$ as the set of families of equivalent rays starting from $o$. In fact, the boundary $\partial_{o} H$ does not depend on the base point $o$, hence we will simply denote it by $\partial H$. For more details, see \cite[Ghys, De La Harpe]{GDLH} or chap.III H p.399 of \cite[Bridson, Haefliger]{BH}.
\subsection{Vertical geodesics with respect to a boundary point}
In this section we fix $\delta\geq 0$, $H$ a proper geodesic $\delta$-hyperbolic space, $w\in H$ a base point and $a\in\partial H$ a point on the boundary of $H$. We recall the definition of Busemann function firstly presented in the introduction.
\begin{equation}
\forall\ x \in H,\ \beta_a(x,w)=\sup\lbrace \limsup\limits_{t\rightarrow + \infty}(d(x,k(t))-t)\mid k\in a,\text{ starting from }w \rbrace.\nonumber
\end{equation}
We want a notion of height on our hyperbolic spaces, a number tending to $+\infty$ when following a selected direction. It is the reason why we define the height on $H$ as the opposite of the Busemann function.
\begin{defn}[height with respect to $a\in \partial H$ and $w\in H$]\label{DefHaut}
Let $a\in \partial H$ be a direction in $H$ and let $w\in H$ be a base point. Then we define:
\begin{equation}
\forall x\in H,\quad h_{(a,w)}(x)=-\beta_a (x,w).\nonumber
\end{equation}
\end{defn}
Let us write Proposition 2 chap.8 p.136 of \cite[Ghys, De La Harpe]{GDLH} with our notations.
\begin{propo}[\cite{GDLH}, chap.8 p.136]\label{PropHautGDLH}
Let $H$ be a hyperbolic proper geodesic metric space. Let $a\in \partial H$ and $w\in H$, then:
\begin{enumerate}
\item $ \lim\limits_{x\rightarrow a}h_{(a,w)}(x)=+\infty$
\item $ \lim\limits_{x\rightarrow b}h_{(a,w)}(x)=-\infty$, $\forall b \in \partial H \setminus \lbrace a\rbrace$
\item $\forall x,y,z\in H, | \beta_a(x,y)+\beta_a(y,z)-\beta_a(x,z)|\leq 200\delta$.
\end{enumerate}
\end{propo}
Furthermore, a geodesic ray is in $a\in\partial H$ if and only if its height tends to $+\infty$.
\begin{cor}\label{PropoGeodVertVersa}
Let $H$ be a hyperbolic proper geodesic metric space. Let $a\in \partial H$ and $w\in H$, and let $\alpha:[0,+\infty[\to H$ be a geodesic ray. The two following properties are equivalent:
\begin{enumerate}
\item $\lim\limits_{t\rightarrow +\infty} h_{(a,w)}(\alpha(t))= +\infty$
\item $\alpha([0,+\infty[)\in a$.
\end{enumerate}
\end{cor}
\begin{proof}\
As for any geodesic ray $\alpha:[0,+\infty[\to H$ there exists $b\in\partial H$ such that $\alpha ([0,+\infty[)\in b$, this proposition is a particular case of Proposition \ref{PropHautGDLH}.
\end{proof}
We will picture our hyperbolic spaces in a way similar to the Log model for the hyperbolic plane. We send $a\in\partial H$ upward to infinity and $\partial H\setminus \lbrace a\rbrace$ downward to infinity. We then call vertical the geodesic rays that are in the equivalence class $a$.
\begin{defn}[Vertical geodesics with repsect to $a\in \partial H$]\label{DefGeodVert}
A geodesic of $H$ which satisfies one of the properties of Corollary \ref{PropoGeodVertVersa} is called a vertical geodesic relatively to the point $a$.
\end{defn}
An important property of the height is to be Lipschitz.
\begin{propo}\label{PropHautLipsch}
Let $a\in\partial H$ and $w\in H$. The height function $h_a:=-\beta_a (\cdot,w)$ is Lipschitz:
\begin{equation}
\forall x,y\in H, |h_{(a,w)}(x)-h_{(a,w)}(y)|\leq d (x,y).\nonumber
\end{equation}
\end{propo}
\begin{proof}
By using the triangular inequality we have for all $x,y\in H$:
\begin{align}
-h_{(a,w)}(x)&=\beta_a (x,w)=\sup\lbrace \limsup\limits_{t\rightarrow + \infty}(d(x,k(t))-t)\mid \text{k vertical rays starting at } w \rbrace\nonumber
\\&\leq d(x,y)+\sup\lbrace \limsup\limits_{t\rightarrow + \infty}(d( y,k(t))-t)\mid \text{k vertical rays starting at } w \rbrace \nonumber
\\&\leq d(x,y)+\beta_a (y,w) \leq d(x,y)-h_{(a,w)} (y).\nonumber
\end{align}
The result follows by exchanging the roles of $x$ and $y$.
\end{proof}
From now on, we fix a given $a\in\partial H$ and a given $w\in H$. Therefore we simply denote the height by $h$ instead of $h_{(a,w)}$.
\begin{propo}\label{PropoQuaisLinGeodVert}
Let $\alpha$ be a vertical geodesic of $H$. We have the following control on the height along $\alpha$:
\begin{equation}
\forall t_1,t_2\in\mathbb{R},\ t_2-t_1-200\delta \leq h\bigl( \alpha(t_2)\bigr)-h\big(\alpha(t_1)\big)\leq t_2-t_1+200\delta.\nonumber
\end{equation}
\end{propo}
\begin{proof}\
Let $t_1,t_2\in\mathbb{R}$, then:
\begin{align}
h( \alpha(t_2))-h(\alpha(t_1))&=\beta\big( \alpha(t_1),w\big)-\beta\big(\alpha(t_2),w\big)\nonumber
\\&= \beta\big( \alpha(t_1),\alpha(t_2)\big)-\Big(\beta\big( \alpha(t_2),w\big)-\beta\big(\alpha(t_1),w\big)+\beta\big( \alpha(t_1),\alpha(t_2)\big)\Big).\nonumber
\end{align}
The third point of Proposition \ref{PropHautGDLH} applied to the last bracket gives:
\begin{equation}\label{formule1}
\beta\big( \alpha(t_1),\alpha(t_2)\big)-200\delta\leq h( \alpha(t_2))-h(\alpha(t_1))\leq \beta\big( \alpha(t_1),\alpha(t_2)\big)+200\delta.
\end{equation}
Since $t\mapsto \alpha(t+t_2)$ is a vertical geodesic starting at $\alpha(t_2)$ we have:
\begin{align}
\beta\big( \alpha(t_1),\alpha(t_2)\big)&=\sup\Big\lbrace \limsup\limits_{t\rightarrow + \infty}\big(d(\alpha(t_1),k(t))-t\big)\Big\mid \text{k vertical rays starting at } \alpha(t_2) \Big\rbrace\nonumber
\\&\geq\limsup\limits_{t\rightarrow + \infty}\Big(d\big(\alpha(t_1),\alpha(t+t_2)\big)-t\Big)\nonumber
\\&\geq\limsup\limits_{t\rightarrow + \infty}\big(|t+t_2-t_1|-t\big)\geq t_2-t_1\nonumber \text{, for t large enough.}\nonumber
\end{align}
Using this last inequality in inequality (\ref{formule1}) we get $t_2-t_1-200\delta\leq h( \alpha(t_2))-h(\alpha(t_1))$. The result follows by exchanging the roles of $t_1$ and $t_2$.
\end{proof}
Using Proposition \ref{PropoQuaisLinGeodVert} with $t_1=0$ and $t_2=t$, the next corollary holds.
\begin{cor}\label{CoroGeodVertQuasiLin}
Let $\alpha$ be a vertical geodesic parametrised by arclength and such that $h(\alpha(0))=0$. We have:
\begin{equation}
\forall t\in\mathbb{R},\ |h(\alpha(t))-t| \leq 200\delta.\nonumber
\end{equation}
\end{cor}
In the sequel we want to apply the slim triangles property on ideal triangles, hence we need the following result of \cite[Coornaert, Delzant, Papadopoulos]{Papa1}.
\begin{propr}[Proposition $2.2$ page $19$ of \cite{Papa1}]\label{ThinTrianglePropr}
Let $a,b$ and $c$ be three points of $X\cup\partial X$. Let $\alpha,\beta,\gamma$ be three geodesics of $X$ linking respectively $b$ to $c$, $c$ to $a$, and $a$ to $b$. Then every point of $\alpha$ is at distance less than $24\delta$ from the union $\beta\cup\gamma$.
\end{propr}
\subsection{Busemann spaces}
We recall here some material from Chap.8 and Chap.12 of \cite[Papadopoulos]{Papa} about Busemann spaces. Busemann spaces are metric spaces where the distance between geodesics are convex functions. To make it more precise, a metric space $X$ is called Busemann if it is geodesic, and if for every pair of geodesics parametrized by arclength $\gamma:[a,b]\rightarrow X$ and $\gamma ':[a',b']\rightarrow X$, the following function is convex:
\begin{align*}
D_{\gamma ,\gamma '}:[a,b]\times[a',b']&\rightarrow X
\\(t,t')&\mapsto d_X(\gamma(t),\gamma '(t')).
\end{align*}
As an example, all $CAT(0)$ spaces are Busemann spaces. However, being $CAT(0)$ is stronger than being Busemann convex by Theorem $1.3$ of \cite[Foertsch, Lytchak, Schroeder]{FLS}. As an example, strictly convex Banach spaces are all Busemann spaces, but they are $CAT(0)$ if and only if they are Hilbert spaces. Something interesting in Busemann spaces is that two points are always linked by a unique geodesic (see $8.1.4$ p.$203$ of Papadopoulos \cite[Papadopoulos]{Papa} for further details). The next proposition gives us informations on the height functions.
\begin{propr}[Prop. $12.1.5$ in p.263 of Papadopoulos \cite{Papa}]\label{PropConvBuseFonction}
Let $\delta\geq 0$ be a non negative number. Let $H$ be a proper $\delta$-hyperbolic, Busemann space. For every geodesic $\alpha$, the function $t\mapsto -h(\alpha(t))$ is convex.
\end{propr}
From now on, $H$ will be a proper, Gromov hyperbolic, Busemann space. The Busemann hypothesis implies that the height along geodesic behaves nicely. This means that we can drop the constant $200\delta$ from Corollary \ref{CoroGeodVertQuasiLin}. It is the main reason why we require our spaces to be Busemann spaces.
\begin{propo}\label{PropoHautLin}
Let $H$ be a $\delta$-hyperbolic and Busemann space and let $V$ be a path of $H$. Then $V$ is a vertical geodesic if and only if $\exists c\in\mathbb{R}$ such that $\forall t\in\mathbb{R},\ h(V(t))=t+c$.
\end{propo}
\begin{proof} Let $V$ be a vertical geodesic in $H$. By Property \ref{PropConvBuseFonction} we have that $t\mapsto -h(V(t))$ is convex. Furthermore, from Corollary \ref{CoroGeodVertQuasiLin}, we get $|h(V(t))-t|\leq 200\delta$. Thereby the bounded convex function $t\mapsto t-h(V(t))$ is constant. Then there exists a real number $c$ such that $\forall t\in\mathbb{R},\ h(V(t))=t+c$.
\\We now assume that there exists a real number $c$ such that $\forall t\in\mathbb{R},\ h(V(t))=t+c$. Therefore, for all real numbers $t_1$ and $t_2$ we have $d\big(V(t_1),V(t_2)\big)\geq \Delta h\big(V(t_1),V(t_2)\big)=|t_1-t_2|$. By definition $V$ is a connected path, hence $|t_1-t_2|\geq d\big(V(t_1),V(t_2)\big)$ which implies with the previous sentence that $|t_1-t_2|=d\big(V(t_1),V(t_2)\big)$, then $V$ is a geodesic. Furthermore $\lim\limits_{t\rightarrow+\infty}h(V(t))=+\infty$, which implies by definition that $V$ is a vertical geodesic.
\end{proof}
A metric space is called geodesically complete if all its geodesic segments can be prolonged into geodesic lines. By adding the hypothesis of geodesically completeness on a hyperbolic Busemann space $H$ we get that any point of $H$ is included in a vertical geodesic line.
\begin{propr}\label{ExistsVertGeodInx}
Let $H$ be a $\delta$-hyperbolic Busemann geodesically complete space. Then for all $x\in H$ there exists a vertical geodesic $V_x:\mathbb{R}\rightarrow H$ such that $V_x$ contains $x$
\end{propr}
\begin{proof}
Let us consider in this proof $w\in H$ and $a\in\partial H$, from which we constructed the height $h$ of our space $H$. Then by definition we have $h_{(a,w)}=h$. Proposition 12.2.4 of \cite[Papadopoulos]{Papa} ensures the existence of a geodesic ray $R_x\in a$ starting at $x$. Furthermore as $H$ is geodesically complete $R_x$ can be prolonged into a geodesic $V_x:\mathbb{R}\rightarrow H$ such that $V_x([0;+\infty[)\in a$. Hence $V_x$ is a vertical geodesic from Definition \ref{DefGeodVert}.
\end{proof}
In this section we defined all the objects we will use in hyperbolic spaces. We will now focus on proving length estimates on specific paths. They will appear in Section \ref{SectHoroDefn} as the projection of geodesics in a horospherical product.
\section{Metric estimates in Gromov hyperbolic Busemann spaces}\label{SecMetricEstimat}
\subsection{Metric description of geodesics}
This section focuses on length estimates in Gromov hyperbolic Busemann spaces. The central result is Lemma \ref{ExpLengthWhenBelowAndReachPoint}, which present a lower bound on the length of a path staying between two horospheres. Before moving to the technical results of this section, let us introduce some notations.
\begin{nota}
Unless otherwise specified, $H$ will be a Gromov hyperbolic Busemann geodesically complete proper space. Let $\gamma:I\rightarrow H$ be a connected path. Let us denote the maximal height and the minimal height of this path as follows:
\begin{align*}
h^+(\gamma)&=\sup\limits_{t\in I}\big\lbrace h(\gamma(t))\big\rbrace,
\\h^-(\gamma)&=\inf\limits_{t\in I}\big\lbrace h(\gamma(t))\big\rbrace.
\end{align*}
Let $x$ and $y$ be two points of $H$, we denote the height difference between them by:
\begin{equation}
\Delta h(x,y)=|h(x)-h(y)|.\nonumber
\end{equation}
We define the relative distance between two points $x$ and $y$ of $H$ as:
\begin{equation}
d_r(x,y)=d(x,y)-\Delta h(x,y).\nonumber
\end{equation}
Let us denote $V_x$ a vertical geodesic containing $x$, we will consider it to be parametrised by arclength. Thanks to Proposition \ref{PropoHautLin} we choose a parametrisation by arclength such that $\forall t\in\mathbb{R},\ h(V_x(t))=t+0$.
\end{nota}
The relative distance between two points quantifies how far a point is from the nearest vertical geodesic containing the other point. Next lemma tells us that in order to connect two points a geodesic needs to go sufficiently high. This height is controlled by the relative distance between those two points.
\begin{lemma}\label{LEM0}
Let $H$ be a $\delta$-hyperbolic and Busemann metric space, let $x$ and $y$ be two elements of $H$ such that $h(x)\leq h(y)$, and let $\alpha$ be a geodesic linking $x$ to $y$. Let us denote $z=\alpha\left(\Delta h(x,y)+\frac{1}{2}d_r(x,y)\right)$, $x_1:=V_x\left(h(y)+\frac{1}{2}d_r(x,y)\right)$ the point of $V_x$ at height $h(y)+\frac{1}{2}d_r(x,y)$ and $y_1:=V_y\left(h(y)+\frac{1}{2}d_r(x,y)\right)$ the point of $V_y$ at the same height $h(y)+\frac{1}{2}d_r(x,y)$. Then we have:
\begin{enumerate}
\item $h^+(\alpha)\geq h(y)+\frac{1}{2}d_r(x,y)-96\delta$
\item $d\left(z,x_1\right)\leq 144\delta$
\item $d\left(z,y_1\right)\leq 144\delta$
\item $d\left(x_1,y_1\right)\leq 288\delta$.
\end{enumerate}
\end{lemma}
\begin{figure}
\begin{center}
\includegraphics[scale=1]{LEM0.pdf}
\caption{Proof of Lemma \ref{LEM0}}\label{FigLEM0}
\end{center}
\end{figure}
\begin{proof} The lemma and its proof are illustrated on Figure \ref{FigLEM0}. Following Property \ref{ThinTrianglePropr}, the triple of geodesics $\alpha$, $V_x$ and $V_y$ is a $24\delta$-slim triangle. Since the sets $\lbrace t\in[0,d(x,y)]|d(\alpha(t),V_x)\leq 24\delta\rbrace$ and $\lbrace t\in[0,d(x,y)]|d(\alpha(t),V_y)\leq 24\delta\rbrace$ are closed sets covering $[0,d(x,y)]$, their intersection is non empty. Hence there exists $t_0\in[0,d(x,y)]$, $x_2\in V_x$ and $y_2\in V_y$ such that $d(\alpha(t_0),x_2)\leq 24\delta$ and $d(\alpha(t_0),y_2)\leq 24\delta$. Let us first prove that $t_0$ is close to $\Delta h(x,y)+\frac{1}{2}d_r(x,y)$. By the triangular inequality we have that:
\begin{align*}
|t_0-d(x,x_2)|=|d(x,\alpha(t_0))-d(x,x_2)|\leq d(x_2,\alpha(t_0))\leq 24\delta.
\end{align*}
Let us denote $x_3:=V_x(h(x)+t_0)$ the point of $V_x$ at height $h(x)+t_0$, and $y_3=V_y(h(y)+d(x,y)-t_0)$ the point of $V_y$ at height $h(y)+d(x,y)-t_0$. Then by the triangular inequality:
\begin{align}
d(\alpha(t_0),x_3)&\leq d(\alpha(t_0),x_2)+d(x_2,x_3)=d(\alpha(t_0),x_2)+|d(x,x_2)-d(x,x_3)|\nonumber
\\&\leq d(\alpha(t_0),x_2)+|d(x,x_2)-t_0|\leq 48\delta.\label{distprocheentregeod}
\end{align}
In the last inequality we used that $d(x,x_3)=t_0$, which holds by the definition of $x_3$. We show in the same way that $d(\alpha(t_0),y_3)\leq 48\delta$. By the triangular inequality we have $d(x_3,y_3)\leq 96\delta$. As the height function is Lipschitz we have $\Delta h(x_3,y_3)\leq d(x_3,y_3)\leq 96\delta$, which provides us with:
\begin{align}
\left|\frac{1}{2}d_r(x,y)+\Delta h(x,y)-t_0\right|&=\frac{1}{2}\big|d_r(x,y)+\Delta h(x,y)+h(y)-h(x)-2t_0\big|\nonumber
\\&=\frac{1}{2}|h(y)+d(x,y)-t_0-(h(x)+t_0)|=\frac{1}{2}\Delta h(x_3,y_3)\leq \frac{96\delta}{2}\leq 48\delta.\label{t0ettempshautproche}
\end{align}
In particular it gives us that $d(z,\alpha(t_0))\leq 48\delta$. We are now ready to prove the first point using inequalities (\ref{distprocheentregeod}) and (\ref{t0ettempshautproche}):
\begin{align*}
h^+(\alpha)\geq& h(\alpha(t_0))\geq h(x_3)-\Delta h(\alpha(t_0),x_3)\geq h(x)+t_0-48\delta
\\\geq & h(x)+\frac{1}{2}d_r(x,y)+\Delta h(x,y)-96\delta\geq h(y)+\frac{1}{2}d_r(x,y)-96\delta,\text{ as we have }h(x)\leq h(y).
\end{align*}
The second point of our lemma is proved by the sequel:
\begin{align*}
d(z,x_1)&\leq d(z,\alpha(t_0))+d(\alpha(t_0),x_1)\leq 48\delta+d(\alpha(t_0),x_3)+d(x_3,x_1)
\\&\leq 96\delta+\left|t_0+h(x)-\left(\frac{1}{2}d_r(x,y)+h(y)\right)\right|=96\delta+\left|t_0-\left(\Delta h(x,y) +\frac{1}{2}d_r(x,y)\right)\right|\leq 144\delta.
\end{align*}
The proof of $3.$ is similar, and $4.$ is obtained from $2.$ and $3.$ by the triangular inequality.
\end{proof}\
The next lemma shows that in the case where $h(x)\leq h(y)$ a geodesic linking $x$ to $y$ is almost vertical until it reaches the height $h(y)$.
\begin{lemma}\label{LinkDrAndDSameHeight}
Let $H$ be a $\delta$-hyperbolic and Busemann space. Let $x$ and $y$ be two points of $H$ such that $h(x)\leq h(y)$. We define $x':=V_x(h(y))$ to be the point of the vertical geodesic $V_x$ at the same height as $y$. Then:
\begin{equation}
|d_r(x,y)-d(x',y)|\leq 54\delta.
\end{equation}
\end{lemma}
\begin{proof}
Since $H$ is $\delta$-hyperbolic, the geodesic triangle $[x,y]\cup[y,x']\cup[x',x]$ is $\delta$-slim. Then there exists $p_1\in[x,x']$, $p_2\in[x',y]$ and $m\in[x,y]$ such that $d(p_1,m)\leq \delta$ and $d(p_2,m)\leq \delta$. Hence, $h^-([x',y])-\delta\leq h(m)\leq h^+([x,x'])+\delta$. Let $R_{x'}$ and $R_y$ be two vertical geodesic rays respectively contained in $V_x$ and $V_y$ and respectively starting at $x'$ and $y$. Then Property \ref{ThinTrianglePropr} used on the ideal triangle $R_x\cup R_y \cup [x',y]$ implies that $h^-([x',y])\geq h(y)-24\delta$, therefore we have $h^+([x,x'])=h(y)$. Then $h(y)-25\delta\leq h(m)\leq h(y)+\delta$ holds.
It follows that $m$ and $x'$ are close to each other:
\begin{align}
d(m,x')&\leq d(m,p_1)+d(p_1,x')\leq \delta + \Delta h(p_1,x')\leq \delta + \Delta h(p_1,m)+ \Delta h(m,y) +\Delta h(y,x')\nonumber
\\&\leq \delta + d(p_1,m)+ 25\delta + 0\leq 27\delta.\label{EqRandLem1}
\end{align}
Then we give an estimate on the distance between $x$ and $m$:
\begin{equation}
|d(x,m)-\Delta h(x,y)|= |d(x,m)-d(x,x')|\leq d(m,x')\leq 27\delta.\label{EqRandLem2}
\end{equation}
However $d_r(x,y)=d(x,y)-\Delta h(x,y)$ and $d(x,y)=d(x,m)+d(m,y)$, therefore:
\begin{equation}
d_r(x,y)=d(x,m)+d(m,y)-\Delta h(x,y).\label{EqRandLem3}
\end{equation}
Combining inequalities (\ref{EqRandLem2}) and (\ref{EqRandLem3}) we have $|d_r(x,y)-d(m,y)|\leq 27\delta$. Then:
\begin{align*}
|d_r(x,y)-d(x',y)|\leq 27\delta +d(x',m) \leq 54\delta.
\end{align*}
\end{proof}
The lemmas of this last section allow us to prove the estimate lemmas of the next one.
\subsection{Length estimate of paths avoiding horospheres}\label{SecPathAvoidHoro}
Consider a path $\gamma$ and a geodesic $\alpha$ that links the two same points of a proper, Gromov hyperbolic, Busemann space. We prove in this section that if the height of $\gamma$ does not reach the maximal height of the geodesic $\alpha$, then $\gamma$ is much longer than $\alpha$. Furthermore, its length increases exponentially on the difference of maximal height between $\gamma$ and $\alpha$. To do so we need Proposition $1.6$ p400 of \cite[Bridson, Haefliger]{BH}. We denote by $l(c)$ the length of a path $c$.
\begin{propo}[\cite{BH}]\label{LemmeBrid}
Let $X$ be a $\delta$-hyperbolic geodesic space. Let $c$ be a continuous path in X. If $[p,q]$ is a geodesic segment connecting the endpoints of $c$, then for every $x\in[p,q]$: $$d(x,im(c))\leq \delta |\log_2 l(c)|+1.$$
\end{propo}
This result implies that a path of $H$ between $x$ and $y$ which avoids the ball centred in the middle of a geodesic $[x,y]$ has length greater than an exponential in the distance $d(x,y)$. From now on we will add as convention that $\delta\geq 1$. For all $\delta_1\leq\delta_2$ a $\delta_1$-slim triangle is also $\delta_2$-slim, hence all $\delta_1$-hyperbolic spaces are $\delta_2$-hyperbolic spaces. That is why we can assume that all Gromov hyperbolic spaces are $\delta$-hyperbolic with $\delta\geq 1$. It allows us to consider $\frac{1}{\delta}$ as a well defined term, we hence avoid different cases in the proof of the following lemma. We also use this assumption to simplify constants appearing in the proof. The next result is a similar control on the length of path as Proposition \ref{LemmeBrid}, but we consider that the path is avoiding a horosphere instead of avoiding a ball in~$H$.
\begin{lemma}\label{LemmeAmande}
Let $\delta\geq 1$ and $H$ be a proper, $\delta$-hyperbolic, Busemann space. Let $x$ and $y\in H$ and let $V_x$ (respt. $V_y$) be a vertical geodesic containing $x$ (respt. $y$). Let us consider $t_0\geq\max(h(x),h(y))$ and let us denote $x_0:=V_x(t_0)$ and $y_0:=V_y(t_0)$. Assume that $d(x_0,y_0)> 768\delta$.
\\Then for all connected path $\gamma:[0,T]\rightarrow H$ such that $\gamma(0)=x$, $\gamma(T)=y$ and $h^+(\gamma)\leq h(x_0)$ we have:
\begin{equation}
l(\gamma)\geq\Delta h(x,x_0)+\Delta h(y,y_0) +2^{-386}2^{\frac{1}{2\delta}d(x_0,y_0)}-24\delta .
\end{equation}
\end{lemma}
\begin{figure}
\includegraphics[scale=0.3]{ExplosionLongueurSiPasHaut.pdf}
\centering
\caption{Proof of Lemma \ref{LemmeAmande}}
\label{FigLemmaAmande}
\end{figure}
For trees when $\delta=0$ this Lemma still makes sense. Indeed, if $\delta$ tends to $0$ then the length of the path described in this Lemma tends to infinity, which is consistent with the fact that such a path does not exist in trees. The proof would use the fact that in Proposition \ref{LemmeBrid} we have $d(x,im(c))=0$ when $\delta=0$ since $0$-hyperbolic spaces are real trees.
\begin{proof}
One can follow the idea of the proof on Figure \ref{FigLemmaAmande}. We will consider $\gamma$ to be parametrised by arclength. Let $B(x,\Delta h(x_0,x))\subset H$ be the ball of radius $h(x_0)-h(x)$ centred on $x$, and let $m\in B(x,\Delta h(x_0,x))$ be a point in this ball. Then:
\begin{equation}
d_r(m,x)=d(m,x)-\Delta h(m,x)\leq \Delta h(x,x_0)-\Delta h(m,x)\leq \Delta h(x_0,m).\nonumber
\end{equation}
Let us first assume that $h(m)\geq h(x)$, then:
\begin{align}
h(m)+\frac{d_r(m,x)}{2}&\leq h(m)+\frac{\Delta h(x_0,m)}{2}\leq h(m)+\frac{h(x_0)-h(m)}{2}=\frac{h(x_0)}{2}+\frac{h(m)}{2} \leq h(x_0).\label{EqDrEtX0}
\end{align}
By Lemma \ref{LEM0} we have:
\begin{align}
d\left(V_x\left(h(m)+\frac{d_r(m,x)}{2}\right),V_m\left(h(m)+\frac{d_r(m,x)}{2}\right)\right)\leq 288\delta.\nonumber
\end{align}
We now assume that $h(m)\leq h(x)$, then:
\begin{equation}
h(x)+\frac{d_r(x,m)}{2}\leq h(x) +\frac{d(x,m)}{2}\leq h(x)+\frac{\Delta h(x,x_0)}{2}\leq h(x_0).\nonumber
\end{equation}
Then Lemma \ref{LEM0} provides:
\begin{align}
d\left(V_x\left(h(x)+\frac{d_r(m,x)}{2}\right),V_m\left(h(x)+\frac{d_r(m,x)}{2}\right)\right)\leq 288\delta.\nonumber
\end{align}
Since $H$ is a Busemann space, the function $t\to d(V_x(t),V_m(t))$ is convex. Furthermore $t\to d(V_x(t),V_m(t))$ is bounded on $[0;+\infty[$ as $H$ is Gromov hyperbolic, hence $t\to d(V_x(t),V_m(t))$ is a non increasing function. Therefore both cases $h(m)\leq h(x)$ and $h(x)\leq h(m)$ give us that:
\begin{align}
d\Big(x_0,V_m\left(h(x_0)\right)\Big)=d\Big(V_x\left(h(x_0)\right),V_m(h(x_0))\Big)\leq 288\delta.\label{EqDistProjHx0}
\end{align}
In other words, all points of $B(x,\Delta h(x_0,x))$ belong to a vertical geodesic passing nearby $x_0$. By the same reasoning we have $\forall n\in B(y,\Delta h(y_0,y))$ :
\begin{align}
d\Big(y_0,V_n\left(h(y_0)\right)\Big)\leq 288\delta.\label{EqDistProjHx02}
\end{align}
Then by the triangular inequality:
\begin{align}
d\Big(V_m(h(x_0)),V_n (h(y_0))\Big)&\geq -d\Big(x_0,V_m\left(h(x_0)\right)\Big)+d(x_0,y_0)-d\Big(y_0,V_n\left(h(y_0)\right)\Big)\nonumber
\\&\geq 768\delta -288\delta -288\delta\geq 192\delta.\label{EqX1Y155}
\end{align}
Specifically $d(V_m(h(x_0)),V_n (h(y_0)))=d(V_m(h(x_0)),V_n (h(x_0)))>0$ which implies that $m\neq n$. Then $B(x,\Delta h(x_0,x))\cap B(y,\Delta h(y_0,y)) = \emptyset$. By continuity of $\gamma$ we deduce the existence of the two following times $t_x\leq t_y$ such that:
\begin{align}
t_x&=\inf\lbrace t\in[0,T]\ |\ d(\gamma(t),x)=\Delta h(x,x_0)\rbrace,\nonumber
\\t_y&=\sup\lbrace t\in[0,T]\ |\ d(\gamma(t),y)=\Delta h(y,y_0)\rbrace.\nonumber
\end{align}
In order to have a lower bound on the length of $\gamma$ we will need to split this path into three parts:
\begin{equation}
\gamma=\gamma_{|[0,t_x]}\cup\gamma_{|[t_x,t_y]}\cup\gamma_{|[t_y,T]}.\nonumber
\end{equation}
As $\gamma$ is parametrised by arclength and $d(\gamma(0),\gamma(t_x))=\Delta h(x,x_0)$ we have that:
\begin{equation}
l\left(\gamma_{|[0,t_x]}\right)\geq \Delta h(x,x_0).\label{refXX0}
\end{equation}
For similar reasons we also have:
\begin{equation}
l\left(\gamma_{|[t_y,T]}\right)\geq \Delta h(y,y_0).\label{refYY0}
\end{equation}
We will now focus on proving a lower bound for the length of $\gamma_{|[t_x,t_y]}$.
\\\\We want to construct a path $\gamma'$ joining $x_1=V_{\gamma(t_x)}(h(x_0))$ to $y_1=V_{\gamma(t_y)}(h(x_0))$, that stays below $h(x_0)$ and such that $\gamma_{|[t_x,t_y]}$ is contained in $\gamma'$. Let $x_1:=V_{\gamma(t_x)}(h(x_0))$ and $y_1:=V_{\gamma(t_y)}(h(x_0))$. We construct $\gamma'$ by gluing paths together:
\begin{equation}
\gamma' =
\left\{
\begin{array}{ll}
V_{\gamma(t_x)} & \mbox{from } x_1 \mbox{ to } \gamma(t_x)\\
\gamma & \mbox{from } \gamma(t_x) \mbox{ to } \gamma(t_y)\\
V_{\gamma(t_y)} & \mbox{from } \gamma(t_y) \mbox{ to } y_1\\
\end{array}
\right.\nonumber
\end{equation}
Applying inequalities (\ref{EqDistProjHx0}) and (\ref{EqDistProjHx02}) used on $\gamma(t_x)$ and $\gamma(t_y)$ we get:
\begin{align}
d(x_0,x_1)&\leq 288\delta ,\label{EqX01108}
\\d(y_0,y_1)&\leq 288\delta.\label{EqY01108}
\end{align}
In order to apply Proposition \ref{LemmeBrid} to $\gamma'$ we need to check that there exists a point $A$ of the geodesic segment $[x_1,y_1]$ such that $h(A)\geq h(x_0)$. Applying Lemma \ref{LEM0} to $[x_1,y_1]$ and since $h(x_1) = h(y_1)$ we get:
\begin{align}
h^+([x_1,y_1])&\geq \frac{d_r(x_1,y_1)}{2}+h(x_0)-96\delta= \frac{d(x_1,y_1)}{2}+h(x_0)-96\delta.\nonumber
\end{align}
Thanks to the triangular inequality and inequalities (\ref{EqX01108}) and (\ref{EqY01108}):
\begin{align}
h^+([x_1,y_1])&\geq \frac{d(y_0,x_0)-d(x_0,x_1)-d(y_0,y_1)}{2}+h(x_0)-96\delta\geq \frac{d(x_0,y_0)}{2}+h(x_0)-384\delta.\nonumber
\end{align}
Since by hypothesis $d(x_0,y_0)>768\delta$, there exists a point $A$ of $[x_1,y_1]$ exactly at the height:
\begin{equation}
h(A)=\frac{d(x_0,y_0)}{2}+h(x_0)-384\delta.\nonumber
\end{equation}
We can then apply Proposition \ref{LemmeBrid} to get:
\begin{align*}
\delta | \log_2(l(\gamma'))|+1&\geq d(A,\gamma')\geq\Delta h(A,x_0)\geq\frac{d(x_0,y_0)}{2}+h(x_0)-384\delta-h(x_0)
\\&\geq\frac{d(x_0,y_0)}{2}-384\delta.
\end{align*}
Since $\delta\geq 1$, last inequality implies that $l(\gamma')\geq 2^{-385}2^{\frac{1}{2\delta}d(x_0,y_0)}$. Now we use this inequality to have a lower bound on the length of $\gamma_{|[t_x,t_y]}$:
\begin{align}
l(\gamma_{|[t_x,t_y]})&\geq l(\gamma')-\Delta h(\gamma(t_x),x_0)-\Delta h(\gamma(t_y),y_0)\nonumber
\\&\geq 2^{-385}2^{\frac{1}{2\delta}d(x_0,y_0)}-\Delta h(\gamma(t_x),x_0)-\Delta h(\gamma(t_y),y_0).\label{FirstPieceAdding}
\end{align}
We claim that $l\left(\gamma_{|[t_x,t_y]}\right)\geq \Delta h(\gamma(t_x),x_0)+\Delta h(\gamma(t_y),y_0)-48\delta$, hence:
\begin{align}
l\left(\gamma_{|[t_x,t_y]}\right)&\geq 2^{-386}2^{\frac{1}{2\delta}d(x_0,y_0)}-24\delta,\label{IneqUseHereDontNow}
\end{align}
which ends the proof by combining inequality (\ref{IneqUseHereDontNow}) with inequalities (\ref{refXX0}) and (\ref{refYY0}).
\\\\\hspace*{0.6cm}Proof of the claim. Inequality (\ref{EqX1Y155}) with $m=\gamma(t_x)$ and $n=\gamma(t_y)$ gives $d(x_1,y_1)\geq 192\delta$. We want to prove that $h^+([\gamma(t_x),\gamma(t_y)])\geq h(x_1)-24\delta$. First, by Lemma \ref{ThinTrianglePropr} we have that $[\gamma(t_x),\gamma(t_y)]\cup V_{\gamma(t_x)} \cup V_{\gamma(t_y)}$ is a $24\delta$-slim triangle. Then there exist three times $t_0$, $t_1$ and $t_2$ such that $d\left(V_{\gamma(t_x)}(t_1),\gamma (t_0)\right)\leq 24\delta$ and such that $d\left(V_{\gamma(t_y)}(t_2),\gamma (t_0)\right)\leq 24\delta$. Then:
\begin{align}
|t_1-t_2|&=\Delta h\left( V_{\gamma(t_x)}(t_1),V_{\gamma(t_y)}(t_2)\right)\leq d\left(V_{\gamma(t_x)}(t_1),V_{\gamma(t_y)}(t_2)\right)\nonumber
\\&\leq d\left(V_{\gamma(t_x)}(t_1),\gamma (t_0)\right)+d\left(\gamma (t_0),V_{\gamma(t_y)}(t_2)\right)\leq 48\delta.\label{InegT1T218D}
\end{align}
We will show by contradiction that either $t_1=h(V_{\gamma(t_x)}(t_1))\geq h(x_0)$ or $t_2=h(V_{\gamma(t_y)}(t_2))\geq h(x_0)$.
\\Assume that $t_1< h(x_0)$ and $t_2< h(x_0)$. Then by the triangular inequality:
\begin{align*}
d\big(V_{\gamma(t_x)}(t_1),V_{\gamma(t_y)}(t_2)\big)&\geq d\big(V_{\gamma(t_y)}(t_2),V_{\gamma(t_x)}(t_2)\big)-d\big(V_{\gamma(t_x)}(t_2),V_{\gamma(t_x)}(t_1)\big)
\\&\geq d\big(V_{\gamma(t_y)}(t_2),V_{\gamma(t_x)}(t_2)\big)-48\delta\text{, since }|t_1-t_2|\leq 48\delta\text{ by equation (\ref{InegT1T218D}).}
\end{align*}
As $H$ is a Busemann space, the function $t\mapsto d\big(V_{\gamma(t_x)}(t),V_{\gamma(t_y)}(t)\big)$ is non increasing. Furthermore, $h(x_0)\geq t_2$ hence:
\begin{align*}
48\delta&\geq d\big(V_{\gamma(t_x)}(t_1),V_{\gamma(t_x)}(t_2)\big)\geq d\big(V_{\gamma(t_x)}(t_2),V_{\gamma(t_y)}(t_2)\big)-48\delta
\\&\geq d\big(V_{\gamma(t_x)}(h(x_0)),V_{\gamma(t_y)}(h(x_0))\big)-48\delta \geq d(x_1,y_1)-48\delta
\\&\geq d(x_0,y_0)-d(x_0,x_1)-d(y_0,y_1)-48\delta\geq d(x_0,y_0)-624\delta\text{, by inequalities }(\ref{EqX01108})\text{ and }(\ref{EqY01108}),
\\&\geq 49\delta\text{, since }d(x_0,y_0)\geq 768\delta\text{ by hypothesis},
\end{align*}
which is impossible. Therefore $t_1\geq h(x_0)$ or $t_2\geq h(x_0)$. We assume without loss of generality that $t_1\geq h(x_0)$, then:
\begin{equation}
\Delta h\big(\gamma(t_0),V_{\gamma(t_x)}(t_1)\big) \leq d\big(\gamma(t_0),V_{\gamma(t_x)}(t_1)\big)\leq 24\delta,\nonumber
\end{equation}
which implies:
\begin{align*}
h^+([\gamma(t_x),\gamma(t_y)])\geq h(\gamma(t_0))\geq h\left(V_{\gamma(t_x) }(t_1)\right)-\Delta h\big(\gamma(t_0),V_{\gamma(t_x)}(t_1)\big)\geq h(x_0)-24\delta,
\end{align*}
and gives us:
\begin{align}
l\left(\gamma_{|[t_x,t_y]}\right)&\geq h^+([\gamma(t_x),\gamma(t_y)])-h(\gamma(t_x))+h^+([\gamma(t_x),\gamma(t_y)])-h(\gamma(t_y))\nonumber
\\&\geq h(x_0)-24\delta-h(\gamma(t_x))+h(x_0)-24\delta-h(\gamma(t_y))\nonumber
\\&\geq \Delta h(\gamma(t_x),x_0)+\Delta h(\gamma(t_y),y_0)-48\delta.\label{SecondPieceAdding}
\end{align}
\end{proof}
Next lemma shows that we are able to control the relative distance of a couple of points travelling along two vertical geodesics.
\begin{lemma}[Backwards control]\label{ControleRelativeDistGoingBackward}
Let $\delta\geq 0$ and $H$ be a proper, $\delta$-hyperbolic, Busemann space. Let $V_1$ and $V_2$ be two vertical geodesics of $H$. Then for all couple of times $(t_1,t_2)$ and for all $t\in\left[0,\frac{1}{2}d_r(V_1(t_1),V_2(t_2))\right]$:
\begin{align*}
\left|d_r\left(V_1\left(t_1+\frac{1}{2}d_r(V_1(t_1),V_2(t_2))-t\right),V_2\left(t_2+\frac{1}{2}d_r(V_1(t_1),V_2(t_2))-t\right)\right)-2t\right|\leq 288\delta.
\end{align*}
\end{lemma}
\begin{figure}
\begin{center}
\includegraphics[scale=0.3]{BackwardControl.pdf}
\caption{Proof of Lemma \ref{ControleRelativeDistGoingBackward}}\label{FigBackwardControl}
\end{center}
\end{figure}
\begin{proof}
To simplify the computations, we use the following notation, $D:=t_2+\frac{1}{2}d_r(V_1(t_1),V_2(t_2))$ and $\Delta=|t_1-t_2| $. The term $\Delta$ is the difference of height between $V_1(t_1)$ and $V_2(t_2)$ since vertical geodesics are parametrised by their height. Then we have to prove that $\forall t\in\left[0,\frac{1}{2}d_r(V_1(t_1),V_2(t_2))\right]$, $|d_r(V_1(D-\Delta-t),V_2(D-t))-2t|\leq 288\delta$. We can assume without loss of generality that $t_1\leq t_2$. Lemma \ref{LEM0} applied with $x=V_1(t_1)$ and with $y=V_2(t_2)$ gives us $d(V_1(D),V_2(D))\leq 288\delta$. Furthermore, the relative distance is smaller than the distance, hence $d_r(V_1(D),V_2(D))\leq 288\delta$. Now if we move the two points backward from $V_1(D-\Delta)$ and $V_2(D)$ along $V_1$ and $V_2$, we have for $t\in[0,D]$:
\begin{align}
d_r(V_1(D-\Delta-t),V_2(D-t))=&d(V_1(D-\Delta-t ),V_2(D-t))-\Delta
\\\leq &d(V_1(D-\Delta-t ),V_1(D-\Delta))+d(V_1(D-\Delta),V_2(D))\nonumber
\\&+d(V_2(D ),V_2(D-t))-\Delta, \nonumber
\\&\text{furthermore }V_1\text{ and }V_2\text{ are geodesics, then:}\nonumber
\\\leq &t+d(V_1(D-\Delta),V_1(D))+d(V_1(D),V_2(D))+t-\Delta \nonumber
\\\leq &t+\Delta+288\delta+t-\Delta\leq 2t+288\delta.\label{ControlDrelatDown}
\end{align}
Let us consider a geodesic $\alpha$ between $V_1(t_1)$ and $V_2(t_2)$. Since $H$ is a Busemann space, and thanks to Lemma \ref{LEM0} we have $d\left(V_1(D-\Delta-t),\alpha(D-\Delta-t_1-t)\right)\leq 144\delta$ and $d\left(V_2(D-t),\alpha(D-t_1+t)\right)\leq 144\delta$. Then the second part of our inequality follows:
\begin{align}
d_r(V_1(D-\Delta-t),V_2(D-t))=&d(V_1(D-\Delta-t ),V_2(D-t))-\Delta \nonumber
\\\geq& d(\alpha(D-\Delta-t_1-t),\alpha(D-t_1+t))\nonumber
\\&-d(V_1(D-\Delta-t ),\alpha(D-\Delta-t_1-t))\nonumber
\\&-d(V_2(D-t),\alpha(D-t_1+t))-\Delta\nonumber
\\\geq& d(\alpha(D-\Delta-t_1-t),\alpha(D-t_1+t)) -288\delta-\Delta\nonumber
\\\geq& 2t+\Delta -288\delta-\Delta\geq 2t -288\delta.\label{ControlDrelatUp}
\end{align}
\end{proof}
The next lemma is a slight generalisation of Lemma \ref{LemmeAmande}. The difference is we control the length of a path with its maximal height instead of the distance between the projection of its extremities on a horosphere.
\begin{lemma}\label{ExpLengthWhenBelowSameHeight}
Let $\delta\geq 1$ and $H$ be a proper, $\delta$-hyperbolic, Busemann space. Let $x,y\in H$ such that $h(x)\leq h(y)$. Let $\alpha$ be a path connecting $x$ to $y$ with $h^+(\alpha)\leq h(y)+\frac{1}{2}d_r(x,y)-\Delta H$ and where $\Delta H$ is a positive number such that $\Delta H> 555\delta$. Then:
\begin{align*}
l(\alpha)\geq d(x,y)+2^{-530}2^{\frac{1}{\delta}\Delta H}-2\Delta H-24\delta.
\end{align*}
\end{lemma}
\begin{figure}
\begin{center}
\includegraphics[scale=0.3]{ExplosionLongueurNoReachLowPoint.pdf}
\captionof{figure}{Proof of Lemma \ref{ExpLengthWhenBelowSameHeight}}
\label{FigExpLengthWhenBelowSameHeight}
\end{center}
\end{figure}
\begin{proof}
This proof is illustrated on Figure \ref{FigExpLengthWhenBelowSameHeight}. Since $h^+(\alpha)\geq h(y)$ we have that $\frac{1}{2}d_r(x,y)\geq \Delta H$. Applying Lemma \ref{ControleRelativeDistGoingBackward} with $V_1=V_x$, $V_2=V_y$, $t_1=h(x)$, $t_2=h(y)$ and $t=\Delta H$ we have:
\begin{align*}
\left|d_r\left(V_x\left(h(x)+\frac{1}{2}d_r(x,y)-\Delta H\right),V_y\left(h(y)+\frac{1}{2}d_r(x,y)-\Delta H\right)\right)-2\Delta H\right|\leq 288\delta.
\end{align*}
Then we have:
\begin{align*}
d_r\left(V_x\left(h(x)+\frac{1}{2}d_r(x,y)-\Delta H\right),V_y\left(h(y)+\frac{1}{2}d_r(x,y)-\Delta H\right)\right)\geq 2\Delta H- 288\delta.
\end{align*}
Furthermore, Lemma \ref{LinkDrAndDSameHeight} applied on $V_x\left(h(x)+\frac{1}{2}d_r(x,y)-\Delta H\right)$ and $V_y\left(h(y)+\frac{1}{2}d_r(x,y)-\Delta H\right)$ gives (notice that the only difference between the two sides of the following inequality is the height in the vertical geodesic $V_x$):
\begin{align*}
&d_r\left(V_x\left(h(x)+\frac{1}{2}d_r(x,y)-\Delta H\right),V_y\left(h(y)+\frac{1}{2}d_r(x,y)-\Delta H\right)\right)\\&\leq d\left(V_x\left(h(y)+\frac{1}{2}d_r(x,y)-\Delta H\right),V_y\left(h(y)+\frac{1}{2}d_r(x,y)-\Delta H\right)\right)+54\delta.
\end{align*}
Then:
\begin{align}
d\left(V_x\left(h(y)+\frac{1}{2}d_r(x,y)-\Delta H\right),V_y\left(h(y)+\frac{1}{2}d_r(x,y)-\Delta H\right)\right)\geq 2\Delta H -342\delta>768\delta.\label{ControleDHInproof}
\end{align}
Let us denote $t_0=h(y)+\frac{1}{2}d_r(x,y)-\Delta H$. Thanks to inequality (\ref{ControleDHInproof}) the hypothesis of Lemma \ref{LemmeAmande} holds with $x_0=V_x\left(h(y)+\frac{1}{2}d_r(x,y)-\Delta H\right)$ and $y_0=V_y\left(h(y)+\frac{1}{2}d_r(x,y)-\Delta H\right) $. Applying this lemma on $\alpha$ provides:
\begin{align*}
l(\alpha)&\geq\Delta h(x,x_0)+\Delta h(y,y_0) +2^{-386}2^{\frac{1}{2\delta}d(x_0,y_0)}-24\delta
\\&\geq h(y)+\frac{1}{2}d_r(x,y)-\Delta H-h(x)+h(y)+\frac{1}{2}d_r(x,y)-\Delta H-h(y)+2^{-386}2^{\frac{1}{2\delta}d(x_0,y_0)}-24\delta
\\&\geq \Delta h(y,x)+d_r(y,x)-2\Delta H+2^{-386}2^{\frac{1}{2\delta}d(x_0,y_0)}-24\delta
\\&\geq d(x,y)-2\Delta H+2^{-386}2^{\frac{1}{2\delta}(2\Delta H -288\delta)}-24\delta \text{, by equation (\ref{ControleDHInproof}).}
\\&\geq d(x,y)+2^{-530}2^{\frac{1}{\delta}\Delta H}-2\Delta H-24\delta .
\end{align*}
\end{proof}
This previous lemma tells us that a path needs to reach a sufficient height for its length not to increase to much. We give now a generalization of Lemma \ref{ExpLengthWhenBelowSameHeight}, where the path reaches a given low height before going to its end point. This lemma will be the central result for the understanding of the geodesic shapes in a horospherical product.
\begin{lemma}\label{ExpLengthWhenBelowAndReachPoint}
Let $\delta\geq 1$ and $H$ be a proper, $\delta$-hyperbolic, Busemann space. Let $x,y,m\ \in H$ such that $h(m)\leq h(x)\leq h(y)$ and let $\alpha:[0,T]\to H$ be a path connecting $x$ to $y$ such that $h^-(\alpha)=h(m)$. With the notation $\Delta H=h(y)+\frac{1}{2}d_r(x,y)-h^+(\alpha)$ we have:
\begin{align*}
l(\alpha)\geq 2\Delta h(x,m)+d(x,y)+2^{-850}2^{\frac{1}{\delta}\Delta H}-1-\max(0,2\Delta H)-1700\delta.
\end{align*}
\end{lemma}
\begin{figure}
\begin{center}
\includegraphics[scale=0.3]{ExplosionLongueurReachLowPoint.pdf}
\captionof{figure}{Proof of Lemma \ref{ExpLengthWhenBelowAndReachPoint}}
\label{FigExpLengthWhenBelowAndReachPoint}
\end{center}
\end{figure}
\begin{proof}
This proof is illustrated on Figure \ref{FigExpLengthWhenBelowAndReachPoint}. We first assume that $\Delta H>850\delta$, we postpone the other cases to the end of this proof. Let $V_x$ and $V_m$ be vertical geodesics respectively containing $x$ and $m$. We call $x_1=V_x(h(y))$ and $m_1=V_m(h(y))$ the points of $V_x$ and $V_m$ at height $h(y)$. First, Lemma \ref{LinkDrAndDSameHeight} provides $|d(x_1,y)-d_r(x,y)|\leq 54\delta$. Then we consider a geodesic triangle between the three points $x_1$, $m_1$ and $y$. Lemma \ref{LEM0} tells us that $h^+([x_1,y])\geq h(y)+\frac{1}{2} d_r(x_1,y)-96\delta\geq h(y)+\frac{1}{2}d_r(x,y)-123\delta$. Since $[x_1,y]$ is included in the $\delta$-neighbourhood of the two other sides of the geodesic triangle, one of the two following inequalities holds:
\begin{align*}
1)&\ h^+([x_1,m_1])\geq h(y)+\frac{1}{2}d_r(x,y)-124\delta
\\2)&\ h^+([m_1,y])\geq h(y)+\frac{1}{2}d_r(x,y)-124\delta.
\end{align*}
\hspace*{0.6cm}We first assume $1)$ that $h^+([x_1,m_1])\geq h(y)+\frac{1}{2}d_r(x,y)-124\delta$, hence:
\begin{equation}
d(x_1,m_1)\geq d_r(x,y)-248\delta.\label{UseInRP2}
\end{equation}
Let us denote $m_0=V_m(h(x))$ the point of $V_m$ at height $h(x)$. By considering the $2\delta $-slim quadrilateral between the points $x,x_1,m_0,m_1$ we have that $[x_1,m_1]$ is in the $2\delta$- neighbourhood of $[x_1,x]\cup[x,m_0]\cup[m_0,m]$. Furthermore $d_r(x,y)\geq2(h^+(\alpha)-h(y))+2\Delta H\geq 2\Delta H\geq 1700\delta$ by assumption, then $h^+([x_1,m_1])\geq h(y)+\frac{1}{2}d_r(x,y)-124\delta\geq h(y)+726\delta$. Since $h^+([x_1,x])=h^+([m_0,m_1])=h(y)$ we have that $h^+([x,m_0])\geq h^+([x_1,m_1])-2\delta\geq h(y)+724\delta$. Moreover:
\begin{align*}
d_r(x,m_0)=d(x,m_0)\geq h^+([x,m_0])-h(x)\geq h(y)-h(x)+724\delta \geq \Delta h(x,y)+724\delta,
\end{align*}
which allows us to use Lemma \ref{ControleRelativeDistGoingBackward} on $V_x$ and $V_m$ with $t=\frac{1}{2}d_r(x,m_0)-\Delta h(x,y)\geq 0$ and $t_1=t_2=h(x)$. It gives:
\begin{align*}
\left| d_r\Big(V_x\big(h(x)+\Delta h(x,y)\big),V_m\big(h(x)+\Delta h(x,y)\big)\Big)-d_r(x,m_0)+2\Delta h(x,y)\right|\leq 288\delta,
\end{align*}
which implies in particular:
\begin{equation}
d_r\Big(V_x\big(h(y)\big),V_m\big(h(y)\big)\Big)+2\Delta h(x,y)-288\delta\leq d_r(x,m_0).\label{UseInRP3}
\end{equation}
Combining inequalities (\ref{UseInRP2}) and (\ref{UseInRP3}) we have $d(x,m_0)=d_r(x,m_0)\geq d_r(x,y)+2\Delta h(x,y)-536\delta$. Lemma \ref{LinkDrAndDSameHeight} used on $x$ and $m$ then gives:
\begin{align}\label{UseInRP1}
d_r(x,m)\geq d(x,m_0)-54\delta\geq d_r(x,y)+2\Delta h(x,y)-590\delta.
\end{align}
Let us denote $\alpha_1$ the part of $\alpha$ linking $x$ to $m$ and $\alpha_2$ the part of $\alpha$ linking $m$ to $y$. We have:
\begin{align*}
h^+(\alpha_1)\leq& h^+(\alpha)\leq h(y)+\frac{1}{2}d_r(x,y)-\Delta H \leq h(x)+\Delta h(x,y)+\frac{1}{2}d_r(x,y)-\Delta H
\\\leq& h(x) +\frac{1}{2}\left(2\Delta h(x,y)+d_r(x,y)\right)-\Delta H \leq h(x)+\frac{1}{2}\left(d_r(x,m)+590\delta\right)-\Delta H \text{, by inequality }(\ref{UseInRP1}).
\\\leq& h(x)+\frac{1}{2}d_r(x,m)+295\delta-\Delta H \leq h(x)+\frac{1}{2}d_r(x,m)-\Delta H',
\end{align*}
with $\Delta H '=\Delta H-295\delta$. By assumption $\Delta H>850\delta$, hence $\Delta H'> 555 \delta$ which allows us to apply Lemma \ref{ExpLengthWhenBelowSameHeight} on $\alpha_1$. It follows:
\begin{align*}
l(\alpha_1)\geq& d(x,m)+2^{-530}2^{\frac{1}{\delta}\Delta H'}-2\Delta H'-24\delta
\\\geq & \Delta h(x,m)+d_r(x,m)+2^{-825}2^{\frac{1}{\delta}\Delta H}-2\Delta H-614\delta \text{, since }\Delta H'=\Delta H-295\delta.
\\\geq & \Delta h(x,m)+d_r(x,y)-590\delta+2^{-825}2^{\frac{1}{\delta}\Delta H}-2\Delta H-614\delta \text{, by inequality (\ref{UseInRP1})}
\\\geq & \Delta h(x,m)+d_r(x,y)+2^{-825}2^{\frac{1}{\delta}\Delta H}-2\Delta H-1204\delta .
\end{align*}
We use in the following inequalities that $l(\alpha_2)\geq d(m,y)\geq\Delta h(m,y)$, we have:
\begin{align*}
l(\alpha)&\geq l(\alpha_1)+l(\alpha_2) \geq \Delta h(x,m)+d_r(x,y)+2^{-825}2^{\frac{1}{\delta}\Delta H}-2\Delta H-1204\delta +\Delta h (m,y)
\\&\geq 2\Delta h(x,m)+\Delta h(x,y)+d_r(x,y)+2^{-825}2^{\frac{1}{\delta}\Delta H}-2\Delta H-1204\delta
\\&\geq 2\Delta h(x,m)+d(x,y)+2^{-825}2^{\frac{1}{\delta}\Delta H}-2\Delta H-1204\delta
\\&\geq 2\Delta h(x,m)+d(x,y)+2^{-850}2^{\frac{1}{\delta}\Delta H}-1-2\Delta H-1700\delta,
\\&\geq 2\Delta h(x,m)+d(x,y)+2^{-850}2^{\frac{1}{\delta}\Delta H}-1-\max(0,2\Delta H)-1700\delta\text{, since }\Delta H>850\delta\geq 0,
\end{align*}
which ends the proof for case 1).
\\\\Now assume that $2)$ holds, which is $h^+([m_1,y])\geq h(y)+\frac{1}{2}d_r(x,y)-124\delta$. It implies $d(m_1,y)\geq d_r(x,y)-248\delta$, then:
\begin{align*}
h^+(\alpha_2)\leq& h^+(\alpha)\leq h(y)+\frac{1}{2}d_r(x,y)-\Delta H \leq h(y)+\frac{1}{2}d_r(m_1,y)+124\delta-\Delta H
\\&\leq h(y)+\frac{1}{2}d_r(m_1,y)-\Delta H '',
\end{align*}
with $\Delta H ''=\Delta H-124\delta$. Lemma \ref{LinkDrAndDSameHeight} provides us with:
\begin{equation}
d_r(m,y)\geq d(m_1,y)-54\delta\geq d_r(x,y)-302\delta.\label{UseInRP4}
\end{equation}
Since $\Delta H> 850\delta$, we have $\Delta H''> 726\delta$ which allows us to apply Lemma \ref{ExpLengthWhenBelowSameHeight} on $\alpha_2$. It follows that:
\begin{align*}
l(\alpha_2)\geq& d(y,m)+2^{-530}2^{\frac{1}{\delta}\Delta H''}-2\Delta H''-24\delta
\\\geq & \Delta h(y,m)+d_r(y,m)+2^{-654}2^{\frac{1}{\delta}\Delta H}-2\Delta H-272\delta \text{, since }\Delta H''=\Delta H-124\delta.
\\\geq & \Delta h(y,m)+d_r(x,y)+2^{-654}2^{\frac{1}{\delta}\Delta H}-2\Delta H-574\delta\text{, by inequality (\ref{UseInRP3})} .
\end{align*}
Hence:
\begin{align*}
l(\alpha)&\geq l(\alpha_1)+l(\alpha_2) \geq \Delta h(x,m)+\Delta h(y,m)+d_r(x,y)+2^{-654}2^{\frac{1}{\delta}\Delta H}-2\Delta H-574\delta
\\&\geq 2\Delta h(x,m)+\Delta h(y,x)+d_r(x,y)+2^{-654}2^{\frac{1}{\delta}\Delta H}-2\Delta H-574\delta
\\&\geq 2\Delta h(x,m)+d(x,y)+2^{-654}2^{\frac{1}{\delta}\Delta H}-2\Delta H-574\delta
\\&\geq 2\Delta h(x,m)+d(x,y)+2^{-850}2^{\frac{1}{\delta}\Delta H}-1-\max(0,2\Delta H)-1700\delta.
\end{align*}
There remains to treat the case when $\Delta H \leq 850\delta$, where $\Delta H=h(y)+\frac{1}{2}d_r(x,y)-h^+(\alpha)$. Let $n$ denote a point of $\alpha$ such that $h(n)=h^+(\alpha)$. If $m$ comes before $n$, we have $l(\alpha)\geq d(x,m)+d(m,n)+d(n,y)$. Otherwise $n$ comes before $m$ and we have $l(\alpha)\geq d(x,n)+d(n,m)+d(m,y)$. Since $h(m)\leq h(x)\leq h(y)\leq h(n)$ we always have:
\begin{align*}
l(\alpha)&\geq \Delta h(x,m)+\Delta h(m,n)+\Delta h(n,y)
\\&\geq \Delta h(x,m) + \Delta h(m,x) +\Delta h(x,y)+\Delta h(y,n) + \Delta h(y,n)\geq 2\Delta h(x,m) +\Delta h(x,y)+2(h^+(\alpha)-h(y))
\\&\geq 2\Delta h(x,m) +\Delta h(x,y)+d_r(x,y)-2\Delta H\geq 2 \Delta h(m,x) +d(x,y)-1700\delta.
\end{align*}
Furthermore $\Delta H \leq 850\delta$, then $2^{-850}2^{\frac{1}{\delta}\Delta H}\leq 1$. Therefore:
\begin{align*}
l(\alpha)&\geq 2 \Delta h(m,x) +d(x,y)+2^{-850}2^{\frac{1}{\delta}\Delta H}-1-\max(0,2\Delta H)-1700\delta,
\end{align*}
which ends the proof for the remaining case.
\end{proof}
\section{Horospherical products}\label{SectHoroDefn}
\subsection{Definitions}
In this part we generalize the definition of horospherical product, as seen in \cite[Eskin, Fisher, Whyte]{EFW1} for two trees or two hyperbolic planes, to any pair of proper, geodesically complete, Gromov hyperbolic, Busemann spaces. We recall that given a proper, $\delta$-hyperbolic space $H$ with distinguished $a\in\partial H$ and $w\in H$, we defined the height function on $H$ in Definition \ref{DefHaut} from the Busemann functions with respect to $a$ and $w$.
\begin{defn}[Horospherical product]\label{DefHoro}
Let $H_p$ and $H_q$ be two $\delta-$hyperbolic spaces. We fix the base points $w_p\in H_p,\ w_q\in H_q$ and the directions in the boundaries $a_p\in\partial H_p,\ a_q\in\partial H_q$. We consider their heights functions $h_p$ and $h_q$ respectively on $H_p$ and $H_q$. We define the horospherical product of $H_p$ and $H_q$, denoted $H_p\bowtie H_q=\mathcal{H}$, by:
\begin{equation}
\mathcal{H}:=\big\lbrace (x_p,x_q)\in H_p\times H_q\ /\ h_p(x_p)+h_q(x_q)=0 \big\rbrace.\nonumber
\end{equation}
\end{defn}
From now on, with slight abuse, we omit the base points and fixed points on the boundary in the construction of the horospherical product. The metric space $\mathcal{H}$ refers to a horospherical product of two Gromov hyperbolic Busemann spaces. We choose to denote $H_p$ and $H_q$ the two components in order to identify easily which objects are in which component.
\\One of our goals is to understand the shape of geodesics in $\mathcal{H}$ according to a given distance on it. In a cartesian product the chosen distance changes the behaviour of geodesics. However we show that in a horopsherical product the shape of geodesics does not change for a large family of distances, up to an additive constant.
\\\\We will define the distances on $H_p\bowtie H_q=\mathcal{H}$ as length path metrics induced by distances on $H_p\times H_q$. A lot of natural distances on the cartesian product $H_p\times H_q$ come from norms on the vector space $\mathbb{R}^2$. Let $N$ be such a norm and let us denote $d_N:=N(d_{H_p},d_{H_q})$, the length $l_N(\gamma)$ of a path $\gamma=(\gamma_p,\gamma_q)$ in the metric space $\Big(H_p\times H_q,d_N\Big)$ is defined by:
\begin{equation}
l_N(\gamma)=\sup\limits_{\theta\in\Theta([t_1,t_2])}\left(\sum\limits_{i=1}^{n_{\theta}-1}d_{N}(\gamma(\theta_i),\gamma(\theta_{i+1})) \right).\nonumber
\end{equation}
Where $\Theta([t_1,t_2])$ is the set of subdivisions of $[t_1,t_2]$. Then the $N$-path metrics on $\mathcal{H}$ is:
\begin{defn}[The $N$-path metrics on $\mathcal{H}$]\label{DefNDistHoro}
Let $N$ be a norm on the vector space $\mathbb{R}^2$. The $N$-path metric on $\mathcal{H}:=H_p\bowtie H_q$, denoted by $d_{\mathcal{H},N}$, is the length path metric induced by the distance $N(d_{H_p},d_{H_q})$ on $H_p \times H_q$. For all $x$ and $y$ in $\mathcal{H}$ we have:
\begin{align}
d_{\mathcal{H},N}(x,y)=\inf\lbrace l_N(\gamma)\vert \gamma\ path\ in\ \mathcal{H}\ linking\ x\ to\ y\rbrace.
\end{align}
\end{defn}
Any norm $N$ on $\mathbb{R}^2$ can be normalized such that $N(1,1)=1$. We call admissible any such norm which satisfies an additional condition.
\begin{defn}[Admissible norm]\label{DefDistHoro}
Let $N$ be a norm on the vector space $\mathbb{R}^2$ such that $N(1,1)=1$. The norm $N$ is called admissible if and only if for all real $a$ and $b$ we have:
\begin{equation}
N(a,b)\geq \frac{a+b}{2}.
\end{equation}
Since all norms are equivalent in $\mathbb{R}^2$, there exists a constant $C_N\geq 1$ such that:
\begin{equation}
N(a,b)\leq C_N\frac{a+b}{2}.
\end{equation}
\end{defn}
As an example, any $l_p$ norm with $p\geq 1$ is admissible.
\begin{propr}\label{ProprSplitLenght}
Let $N$ be an admissible norm on the vector space $\mathbb{R}^2$. Let $\gamma:=(\gamma_p,\gamma_q)\subset H_p\times H_q$ be a connected path. Then we have:
\begin{equation}
\frac{l_{H_p}(\gamma_p)+l_{H_q}(\gamma_q)}{2}\leq l_N(\gamma)\leq C_N\frac{l_{H_p}(\gamma_p)+l_{H_q}(\gamma_q)}{2}.\nonumber
\end{equation}
\end{propr}
\begin{proof}
Let $\gamma:=(\gamma_p,\gamma_q):[t_1,t_2]\rightarrow H_p\times H_q$ be a connected path and $\theta$ a subdivision of $[t_1,t_2]$, then by the definition of the length:
\begin{align*}
l_N(\gamma)&\geq\sum\limits_{i=1}^{n_{\theta}-1}d_{N}(\gamma(\theta_i),\gamma(\theta_{i+1}))=\sum\limits_{i=1}^{n_{\theta}-1}N\Big(d_{H_p}\big(\gamma_p(\theta_i),\gamma_p(\theta_{i+1})\big),d_{ H_q}\big(\gamma_q(\theta_i),\gamma_q(\theta_{i+1})\big)\Big)
\\&\geq\sum\limits_{i=1}^{n_{\theta}-1}\frac{1}{2}\Big(d_{H_p}\big(\gamma_p(\theta_i),\gamma_p(\theta_{i+1})\big)+d_{ H_q}\big(\gamma_q(\theta_i),\gamma_q(\theta_{i+1})\big)\Big),\ \text{since }N\text{ is admissible}.
\\&\geq\frac{1}{2}\left(\sum\limits_{i=1}^{n_{\theta}-1}d_{H_p}\big(\gamma_p(\theta_i),\gamma_p(\theta_{i+1})\big)+\sum\limits_{i=1}^{n_{\theta}-1}d_{ H_q}\big(\gamma_q(\theta_i),\gamma_q(\theta_{i+1})\big)\right).
\end{align*}
Any couple of subdivision $\theta_1$ and $\theta_2$ can be merge into a subdivision $\theta$ that contains $\theta_1$ and $\theta_2$. Furthermore the last inequality holds for any subdivision $\theta$, hence by taking the supremum on all the subdivisions we have:
\begin{equation}
l_N(\gamma)\geq \frac{l_{H_p}(\gamma_p)+l_{H_q}(\gamma_q)}{2}.\nonumber
\end{equation}
Furthermore, we have that $\forall a,b\in\mathbb{R}$, $N(a,b)\leq C_N\frac{a+b}{2}$, hence:
\begin{align*}
\sum\limits_{i=1}^{n_{\theta}-1}d_{N}(\gamma(\theta_i),\gamma(\theta_{i+1}))&\leq \frac{C_N}{2}\left(\sum\limits_{i=1}^{n_{\theta}-1}d_{H_p}(\gamma_p(\theta_i),\gamma(\theta_{i+1}))+\sum\limits_{i=1}^{n_{\theta}-1}d_{H_q}(\gamma_q(\theta_i),\gamma_q(\theta_{i+1}))\right)
\\&\leq C_N\frac{l_{H_p}(\gamma_p)+l_{H_p}(\gamma_p)}{2}
\end{align*}
Since last inequality holds for any subdivision $\theta$, we have that $l_N(\gamma)\leq C_N\frac{l_{H_p}(\gamma_p)+l_{H_p}(\gamma_p)}{2}$.
\end{proof}
The definition of height on $H_p$ and $H_q$ is used to construct a height function on $H_p\bowtie H_q$.
\begin{defn}[Height on $\mathcal{H}$]
The height $h(x)$ of a point $x=(x_p,x_q)\in H_p\bowtie H_q$ is defined as $h(x)=h_p(x_p)=-h_q(x_q)$.
\end{defn}
On Gromov hyperbolic spaces we have that de distance between two points is greater than their height difference. The same occurs on horospherical products given with an admissible norm. Let $x$ and $y$ be two points of $\mathcal{H}$, and let us denote $\Delta h(x,y) := |h(x)-h(y)|$ their height difference.
\begin{lemma}\label{LemDistBigHaut}
Let $N$ be a admissible norm, and let $d_{\mathcal{H},N}$ the distance on $\mathcal{H}=H_p\bowtie H_q$ induced by $N$. Let $x=(x_p,x_q)$ and $y=(y_p,y_q)$ be two points of $\mathcal{H}$, we have:
\begin{equation}
\forall x,y \in\mathcal{H},\quad d_{\mathcal{H},N}(x,y)\geq \Delta h(x,y).
\end{equation}
\end{lemma}
\begin{proof}
Since $N$ is admissible we have:
\begin{align*}
d_{\mathcal{H},N}(x,y)&\geq \frac{d_{H_p}(x_p,y_p)+d_{H_q}(y_p,y_q)}{2}\geq \frac{\Delta h(x_p,y_p)+\Delta h(x_q,y_q)}{2}
\\&\geq\Delta h(x_p,y_p)=\Delta h(x,y).
\end{align*}
\end{proof}
Following Proposition \ref{PropoHautLin}, we define a notion of vertical paths in a horospherical product.
\begin{defn}[Vertical paths in $\mathcal{H}$]\label{DefVertGeodInHoro}
Let $V:\mathbb{R}\to \mathcal{H}$ be a connected path. We say that $V$ is vertical if and only if there exists a parametrisation by arclength of $V$ such that $h(V(t))=t$ for all $t$.
\end{defn}
Actually, a vertical path of a horospherical product is a geodesic.
\begin{lemma}
Let $N$ be an admissible norm. Let $V:\mathbb{R}\to \mathcal{H}$ be a vertical path. Then $V$ is a geodesic of $(\mathcal{H},d_{\mathcal{H},N})$.
\end{lemma}
\begin{proof}
Let $t_1,t_2\in\mathbb{R}$. The path $V$ is vertical therefore $\Delta h\big(V(t_1),V(t_2)\big)=|t_1-t_2|$. Since $V$ is connected and parametrised by arclength, we have that:
\begin{align*}
|t_1-t_2|=l_N\left(V_{|[t_1,t_2]}\right)&\geq d_{\mathcal{H},N}\big(V(t_1),V(t_2)\big)
\\&\geq \Delta h\big(V(t_1),V(t_2)\big)=|t_1-t_2|.
\end{align*}
Then $d_{\mathcal{H},N}\big(V(t_1),V(t_2)\big)=|t_1-t_2|$, which ends the proof.
\end{proof}
Such geodesics are called vertical geodesics. Next proposition tells us that vertical geodesics of $H_p\bowtie H_q$ are exactly couples of vertical geodesics of $H_p$ and $H_q$.
\begin{propo}\label{PropGeodVertInHoro}
Let $N$ be an admissible norm and let $V=(V_p,V_q):\mathbb{R}\to \mathcal{H}$ be a geodesic of $(\mathcal{H},d_{\mathcal{H},N})$. The two following properties are equivalent:
\begin{enumerate}
\item $V$ is a vertical geodesic of $(\mathcal{H},d_{\mathcal{H},N})$
\item $V_p$ and $V_q$ are respectively vertical geodesics of $H_p$ and $H_q$.
\end{enumerate}
\end{propo}
\begin{proof}\
Let us first assume that $V$ be a vertical geodesic, we have for all real $t$ that $h(V_p(t))=h(V(t))=t$, hence $\forall t_1,t_2\in\mathbb{R}$:
\begin{align}
d_{H_p}\big(V_p(t_1),V_p(t_2)\big)\geq \Delta h \big(V_p(t_1),V_p(t_2)\big)=|t_1-t_2|.\label{lowboundprojgeod}
\end{align}
Similarly we have that $d_{H_q}\big(V_q(t_1),V_q(t_2)\big)\geq |t_1-t_2|$. Using that $N$ is admissible and that $V$ is a geodesic we have:
\begin{align*}
d_{H_p}\big(V_p(t_1),V_p(t_2)\big)&=2\frac{d_{H_p}\big(V_p(t_1),V_p(t_2)\big)+d_{H_q}\big(V_q(t_1),V_q(t_2)\big)}{2}-d_{H_q}\big(V_q(t_1),V_q(t_2)\big)
\\&\leq 2d_{\mathcal{H},N}\big(V(t_1),V(t_2)\big)-|t_1-t_2|=|t_1-t_2|.
\end{align*}
Combine with inequality (\ref{lowboundprojgeod}) we have that $d_{H_p}\big(V_p(t_1),V_p(t_2)\big)=|t_1-t_2|$, hence $V_p$ is a vertical geodesic of $H_p$. Similarly, $V_q$ is a vertical geodesic $H_q$.
\\Let us assume that $V_p$ and $V_q$ are vertical geodesics of $H_p$ and $H_q$. Let $t_1,t_2\in\mathbb{R}$, we have:
\begin{align*}
d_{\mathcal{H},N}(V(t_1),V(t_2))&=\sup\limits_{\theta\in\Theta ([t_1,t_2])} \left( \sum\limits_{i=1}^{n_{\theta}-1}d_{N}(V(\theta_i),V(\theta_{i+1}))\right)
\\&=\sup\limits_{\theta\in\Theta ([t_1,t_2])} \left( \sum\limits_{i=1}^{n_{\theta}-1}N\Big(d_{H_p}\big(V_p(\theta_i),V_p(\theta_{i+1})\big),d_{H_q}\big(V_q(\theta_i),V_q(\theta_{i+1})\big)\Big)\right)
\\&=\sup\limits_{\theta\in\Theta ([t_1,t_2])} \left( \sum\limits_{i=1}^{n_{\theta}-1}N\Big(\Delta h\big(V_p(\theta_i),V_p(\theta_{i+1})\big),\Delta h\big(V_q(\theta_i),V_q(\theta_{i+1})\big)\Big)\right)
\\&=\sup\limits_{\theta\in\Theta ([t_1,t_2])} \left( N(1,1)\sum\limits_{i=1}^{n_{\theta}-1}\Delta h\big(V_p(\theta_i),V_p(\theta_{i+1})\big)\right)
\\&=N(1,1)\Delta h\big(V_p(t_1),V_p(t_2)\big)=|t_1-t_2|,\text{ since }N(1,1)=1.
\end{align*}
Where $\Theta ([t_1,t_2])$ is the set of subdivision of $[t_1,t_2]$. Hence the proposition is proved.
\end{proof}
This previous result is the main reason why we are working with distances which came from admissible norms.
\begin{defn}
A geodesic ray of $\mathcal{H}=H_p\bowtie H_q$ is called vertical if it is a subset of a vertical geodesic.
\end{defn}
A metric space is called geodesically complete if all its geodesic segments can be prolonged into geodesic lines. If $H_p$ and $H_q$ are proper hyperbolic geodesically complete Busemann spaces, their horospherical product $\mathcal{H}$ is connected.
\begin{propr}\label{HoroProdConnected}
Let $H_p$ and $H_q$ be two proper, geodesically complete, $\delta$-hyperbolic, Busemann spaces. Let $\mathcal{H}=H_p\bowtie H_q$ be their horospherical product. Then $\mathcal{H}$ is connected, furthermore $\frac{1}{2}(d_{H_p}+d_{H_q})\leq d_{\mathcal{H}}\leq 2C_N(d_{H_p}+d_{H_q})$.
\end{propr}
\begin{proof}
Let $x=(x_p,x_q)$ and $y=(y_p,y_q)$ be two points of $\mathcal{H}$. From Property \ref{ExistsVertGeodInx}, there exists a vertical geodesic $V_{x_q}$ such that $x_q$ is in the image of $V_{x_q}$, and there exists a vertical geodesic $V_{y_p}$ such that $y_p$ is in the image of $V_{y_p}$. Let $y_q'$ be the point of $V_{x_q}$ at height $h(y_q)$. Let $\alpha_p$ be a geodesic of $H_p$ linking $x_p$ to $y_p$ and let $\alpha_q'$ be a geodesic of $H_q$ linking $y_q'$ to $y_q$. We will connect $x$ to $y$ with a path composed with pieces of $\alpha_p$, $\alpha_q'$, $V_{x_q}$ and $V_{y_p}$.
\\We first link $(x_p,x_q)$ to $(y_p,y_q')$ with $\alpha_p$ and $V_{x_q}$. It is possible since $V_{x_q}$ is parametrised by its height. More precisely we construct the following path $c_1$:
\begin{align*}
\forall t\in[0,d(x_p,y_p)],\ c_1(t)=\Big(\alpha_p(t), V_{x_q}\big( -h(\alpha_p(t))\big)\Big).
\end{align*}
Since $V_{x_q}$ is parametrised by its height, we have $h\left( V_{x_q}\big( -h(\alpha_p(t))\big)\right)=-h(\alpha_p(t))$ which implies $c_1(t)\in\mathcal{H}$. Furthermore, using the fact that the height is 1-Lipschitz, we have $\forall t_1,t_2\in[0,d(x_p,y_p)]$:
\begin{align*}
d_{H_q}\Big(V_{x_q}\big( -h(\alpha_p(t_1))\big),V_{x_q}\big( -h(\alpha_p(t_2))\big)\Big)=| h(\alpha_p(t_1))-h(\alpha_p(t_2))|\leq d_{H_p}(\alpha_p(t_1),\alpha_p(t_2)).
\end{align*}
Hence $c_{1,q}:t\mapsto V_{x_q}\big( -h(\alpha_p(t))\big)$ is a connected path such that $l(c_{1,q})\leq l(\alpha_p)\leq d_{H_p}(x_p,y_p)$. Hence $c_1$ is a connected path linking $(x_p,x_q)$ to $(y_p,y_q')$. Using
Property \ref{ProprSplitLenght} on $c_1$ provides us with:
\begin{align*}
l_N(c_1)&\leq \frac{C_N}{2} (l(c_{1,q})+l(\alpha_p))\leq C_N l(\alpha_p)
\\&\leq C_N d_{H_p}(x_p,y_p)
\end{align*}
We recall that by definition $y_q'=V_{x_q}(h(y_q))$.
We show similarly that $c_{2}:t\mapsto \Big(V_{y_p}\big( -h(\alpha_q'(t))\big),\alpha_q'(t) \Big)$ is a connected path linking $(y_p,y_q')$ to $(y_p,y_q)$ such that:
\begin{align*}
l(c_2)&\leq C_N d_{H_q}(y_q',y_q)\leq C_N\big(d_{H_q}(y_q',x_q)+d_{H_q}(x_q,y_q)\big)
\\&= C_N\big(\Delta h(x_q,y_q)+d_{H_q}(x_q,y_q)\big)\text{, since }y_q'=V_{x_q}(h(y_q))
\\&\leq 2C_N d_{H_q}(x_q,y_q).
\end{align*}
Hence, there exists a connected path $c=c_1\cup c_2$ linking $x$ to $y$ such that:
\begin{equation}
l(c)\leq C_N d_{H_p}(x_p,y_p)+2C_N d_{H_q}(x_q,y_q)\leq 2C_N\big(d_{H_p}(x_p,y_p)+d_{H_q}(x_q,y_q)\big).
\end{equation}
\end{proof}
However if the two components $H_p$ and $H_q$ are not geodesically complete, $\mathcal{H}$ may not be connected.
\begin{example}
Let $H_p$ and $H_q$ be two graphs, constructed from an infinite line $\mathbb{Z}$ (indexed by $\mathbb{Z}$) with an additional vertex glued on the $0$ for $H_p$ and on the $-2$ for $H_q$. Their construction are illustrated on figure \ref{FigUnconnectedHoroProd}. They are two 0-hyperbolic Busemann spaces which are not geodesically complete. Let $w_{p}\in H_p$ be the vertex indexed by $0$ in $H_p$, and let $w_{q}\in H_q$ be the vertex indexed by $-2$ in $H_q$. We choose them to be the base points of $H_p$ and $H_q$. Since $\partial H_p$ and $\partial H_q$ contain two points each, we fix in both cases the point of the boundary $a_p$ or $a_q$ to be the one that contains the geodesic ray indexed by $\mathbb{N}$. On figure \ref{FigUnconnectedHoroProd}, we denoted the height of a vertex inside this one. Then the horospherical product $\mathcal{H}=H_p\bowtie H_q$ taken with the $\ell_1$ path metric is not connected. Since some vertices of $H_p$ and $H_q$ are not contained in a vertical geodesic, one may not be able to adapt its height correctly while constructing a path joining $\left(x^p_{-1},x^q_{(2,1)}\right)$ to $\left(x^p_{(0,-1)},x^q_{(2,1)}\right)$.
\end{example}
\begin{figure}
\includegraphics[scale=0.25]{ProduitNonConnexe.pdf}
\centering
\caption{Example of horospherical product which is not connected. The number in a vertex is the height of that vertex.}
\label{FigUnconnectedHoroProd}
\end{figure}
It is not clear that a horospherical product is still connected without the hypothesis that $H_p$ and $H_q$ are Busemann spaces. In that case we would need a "coarse" definition of horospherical product. Indeed, the height along geodesics would not be smooth as in Proposition \ref{PropoHautLin}, therefore the condition requiring to have two exact opposite heights would not suits.
\subsection{Examples}
A first example of horospherical product is the family of Diestel-Leader graphs. They are by construction horospherical products of two trees.
\begin{defn}[Diestel-Leader graph $DL(p,q)$]
Let $p\geq2$ and $q\geq2$ be two integers. Let $T_p$ be the $p$-homogeneous tree and $T_q$ be the $q$-homogeneous tree. The two graphs $T_p$ and $T_q$ are $0$-hyperbolic proper geodesically complete Busemann spaces. The Diestel-Leader graph $DL(p,q)$ is defined by $DL(p,q)=T_p\bowtie T_q$.
\end{defn}
We see $T_p$ and $T_q$ as connected metric spaces with the usual distance on them. By choosing half of the $\ell_1$ path metric on $DL(p,q)$, this horospherical product becomes a graph with the usual distance on it. Indeed, the set of vertices of $DL(p,q)$ is then defined by the subset of couples of vertices of $T_p\times T_q$ included in $DL(p,q)$. In this horospherical product, two points $(x_p,x_q)$ and $(y_p,y_q)$ of $DL(p,q)$ are connected by an edge if and only if $x_p$ and $y_p$ are connected by an edge in $T_p$ and if $x_q$ and $y_q$ are connected by an edge in $T_q$. Furthermore, when $p=q$, there is a one-to-one correspondance between $DL(q,q)$ and the Cayley graph of the lamplighter group $\mathbb{Z}_q\wr \mathbb{Z}$, see \cite[Woess]{Woess2} for further details.
\\\\The SOL geometry is the Riemannian manifold with coordinates $(x,y,z)\in\mathbb{R}^3$ and with the Riemannian metric $ds^2=dz^2+e^{2z}dx^2+e^{-2z}dy^2$. It is the horospherical product of two hyperbolic planes, it is described in \cite[Woess]{Woess}. Let us consider $\mathbb{H}^2$ the Log model of the hyperbolic plane, defined as the Riemannian manifold with coordinates $(x,z)\in\mathbb{R}^2$ and with the Riemannian metric $ds^2=dz^2+e^{-2z}dx^2$. We fix $w=(0,0)$ as the base point of $\mathbb{H}$ and the "upward" direction $a$ as the point on the boundary. In that case the height function in regards to $(a,w)$ taken on a point $(x,z)\in\mathbb{H}$ is $h_{(a,w)}(x,z)=z$. We now look at the horospherical product $\mathbb{H}^2\bowtie\mathbb{H}^2:=\lbrace (x_1,z_1,x_2,z_2)\in\mathbb{R}^2\times\mathbb{R}^2 \vert z_1=-z_2\rbrace$ taken with the $\ell_2$ path metric. Since the second and the fourth variable are exactly opposite, we merge them into one. Hence we have that $\mathbb{H}^2\bowtie\mathbb{H}^2$ is isometric to the space $\lbrace (x_1,x_2,z_1)\in\mathbb{R}^3\rbrace$ with the metric
\begin{equation}
ds^2=dz_1^2+e^{-2z_1}dx_1^2+dz_1^2+e^{2z_1}dx_2^2=2dz_1^2+e^{-2z_1}dx_1^2+e^{2z_1}dx_2^2.\nonumber
\end{equation}
Changing the coordinates by dividing $x_1$ and $x_2$ by two tells us that this space is isometric to SOL.
\\\\Depending on the case, we either used the $\ell_1$ path metric or the $\ell_2$ path metric. Proposition \ref{l1samel2} tells us that it does not matter, up to an additive uniform constant. Quasi-isometric rigidity results have been proved in the Diestel-Leader graphs and the SOL geometry with the same techniques in \cite[Eskin, Fisher, Whyte]{EFW1} and \cite[E,F,W]{EFW2}.
\\\\The horospherical product of a hyperbolic plane and a regular tree has been studied as the 2-complex of Baumslag-Solitar groups in \cite[Bendikov, Saloff-Coste, Salvatori, Woess]{Treebol}. They are called the treebolic spaces. The distance they choose on the treebolic spaces is similar to ours. In fact our Proposition \ref{lengthGeod} and their Proposition $2.8$ page 9 (in \cite{Treebol}) tell us they are equal up to an additive constant. Rigidity results on the treebolic spaces were brought up in \cite[Farb, Mosher]{FB1} and \cite[F,M]{FB2}.
\\\\The previous examples were already known, however our construction still works for many other spaces. As an example, a geodesically complete manifold with a curvature lower than a negative constant could be used as the component $H_p$ or $H_q$ in the horospherical product.
\subsection{Length of geodesic segments in $\mathcal{H}$}
From now on, unless otherwise specified, $H_p$ and $H_q$ will always be two proper, geodesically complete, $\delta$-hyperbolic, Busemann spaces with $\delta\geq 1$, and $N$ will always be an admissible norm. Let $x$ and $y$ be two points of $\mathcal{H}:=H_p\bowtie H_q$, and let $\alpha$ be a geodesic of $\mathcal{H}$ connecting them. We first prove an upper bound on the length of $\alpha$ by computing the length of a path $\gamma\subset\mathcal{H}$ linking $x$ to $y$
\begin{lemma}\label{PathConnectingPointsInHoroProduct}
Let $x$ and $y$ be points of the horospherical product $\mathcal{H}=H_p\bowtie H_q$. There exists a path $\gamma$ connecting $x=(x_p,x_q)$ to $y=(y_p,y_q)$ such that:
\begin{align*}
l_N(\gamma)\leq d_r(x_q,y_q)+d_r(x_p,y_p)+\Delta h(x,y)+1152\delta C_N.
\end{align*}
\end{lemma}
\begin{proof}
Without loss of generality, we assume $h(x)\leq h(y)$. One can follow the idea of the proof on Figure \ref{FigureConstructionPathHoroProduct}. We consider $V_{x_p}$ and $V_{y_p}$ two vertical geodesics of $H_p$ containing $x_p$ and $y_p$ respectively. Similarly let $V_{x_q}$ and $V_{y_q}$ be two vertical geodesics of $H_q$ containing $x_q$ and $y_q$ respectively. We will use them to construct $\gamma$. Let $A_1$ be the point of the vertical geodesic $(V_{x_p},V_{x_q})\subset\mathcal{H}$ at height $h(x)-\frac{1}{2}d_r(x_q,y_q)$ and $A_2$ be the point of the vertical geodesic $(V_{x_p},V_{y_q})\subset\mathcal{H}$ at the same height $h(x)-\frac{1}{2}d_r(x_q,y_q)$. Let $A_3$ be the point of the vertical geodesic $(V_{x_p},V_{y_q})$ at height $h(y)+\frac{1}{2}d_r(x_p,y_p)$ and $A_4$ be the point of the vertical geodesic $(V_{y_p},V_{y_q})$ at the same height $h(y)+\frac{1}{2}d_r(x_p,y_p)$. Then $\gamma:=\gamma_1\cup\gamma_2\cup\gamma_3\cup\gamma_4\cup\gamma_5$ is constructed as follows:
\\\\\hspace*{0.6cm}- $\gamma_1$ is the part of $(V_{x_p},V_{x_q})$ linking $x$ to $A_1$.
\\\hspace*{0.6cm}- $\gamma_2$ is a geodesic linking $A_1$ to $A_2$. Such a geodesic exists by Property \ref{HoroProdConnected}.
\\\hspace*{0.6cm}- $\gamma_3$ is the part of $(V_{x_p},V_{y_q})$ linking $A_2$ to $A_3$.
\\\hspace*{0.6cm}- $\gamma_4$ is a geodesic linking $A_3$ to $A_4$. Such a geodesic exists by Property \ref{HoroProdConnected}.
\\\hspace*{0.6cm}- $\gamma_5$ is the part of $(V_{y_p},V_{y_q})$ linking $A_4$ to $y$.
\\\\In fact $A_1$ and $A_2$ are close to each other. Indeed, the two points $A_1=(A_{1,p},A_{1,q})$ and $A_2=(A_{2,p},A_{2,q})$ are characterised by the two geodesics $(V_{x_p},V_{x_q})$ and $(V_{x_p},V_{y_q})$. Then, because $-h(y)=h_q(y_q)\leq h_q(x_q)$, Lemma \ref{LEM0} applied on $x_q$ and $y_q$ in $H_q$ gives us $d_{H_q}(A_{1,q},A_{2,q})\leq 288\delta$. Furthermore Property \ref{HoroProdConnected} provides us with $d_{\mathcal{H},N}\leq 2C_N(d_{H_p}+d_{H_q})$, however we have that $A_{1,p}=A_{2,p}$ hence:
\begin{align}
d_{\mathcal{H},N}(A_1,A_2)\leq 576\delta C_N.\label{IneqA1A2}
\end{align}
Lemma \ref{LEM0} applied on $x_p$ and $y_p$ provides similarly:
\begin{align}
d_{\mathcal{H},N}(A_3,A_4)\leq 576\delta C_N,\label{IneqA3A4}
\end{align}
which gives us:
\begin{align*}
l_N(\gamma)=&l_N(\gamma_1)+l_N(\gamma_2)+l_N(\gamma_3)+l_N(\gamma_4)+l_N(\gamma_5)
\\=& d_{\mathcal{H},N}(x,A_1)+d_{\mathcal{H},N}(A_1,A_2)+d_{\mathcal{H},N}(A_2,A_3)+d_{\mathcal{H},N}(A_3,A_4)+d_{\mathcal{H},N}(A_4,y)
\\&\text{Since }\gamma_1,\ \gamma_3\text{ and }\gamma_5\text{ are vertical geodesics, we have:}
\\=& \Delta h(x,A_1)+d_{\mathcal{H},N}(A_1,A_2)+\Delta h(A_2,A_3)+d_{\mathcal{H},N}(A_3,A_4)+\Delta h(A_4,y)
\\=& \frac{1}{2}d_r(x_q,y_q)+d_{\mathcal{H},N}(A_1,A_2)+\frac{1}{2}d_r(x_q,y_q)+\frac{1}{2}d_r(x_p,y_p)+\Delta h(x,y)+d_{\mathcal{H},N}(A_3,A_4)+\frac{1}{2}d_r(x_p,y_p)
\\\leq& d_r(x_q,y_q)+d_r(x_p,y_p)+\Delta h(x,y)+1152\delta C_N\text{, by inequalities (\ref{IneqA1A2}) and (\ref{IneqA3A4}).}
\end{align*}
\begin{figure}
\begin{center}
\includegraphics[scale=0.35]{GammaProofGeodHorocycleDifLevel.pdf}
\captionof{figure}{Construction of the path $\gamma$ when $h(x)\leq h(y)$ for Lemma \ref{PathConnectingPointsInHoroProduct}.}
\label{FigureConstructionPathHoroProduct}
\end{center}
\end{figure}
\end{proof}
We are aiming to use Lemma \ref{ExpLengthWhenBelowAndReachPoint} on the two components $\alpha_p\subset H_p$ and $\alpha_q\subset H_q$ of $\alpha$ to obtain lower bounds on their lengths. We hence need the following lemma to ensure us that when $\alpha$ is a geodesic, the exponential term in the inequality of Lemma \ref{ExpLengthWhenBelowAndReachPoint} will be small.
\begin{lemma}\label{AnalyticStudy}
Let $C= 2853\delta C_N+2^{851}$ and let $e:\mathbb{R}\rightarrow\mathbb{R}$ be a map defined by $\forall t\in\mathbb{R}$, $e(t)=\frac{1}{C}2^{C^{-1}t}-2\max(0,t)$. Then $\forall t\in\mathbb{R}$:
\begin{enumerate}
\item $e(t)\geq -7C^2$
\item $(\ e(t)\leq 2853\delta C_N\ )\Rightarrow(\ t\leq 3C^2 \ )$.
\end{enumerate}
\end{lemma}
\begin{proof}
For all time $t$, we have that $e(t)=\frac{1}{C}2^{C^{-1}t}-2\max(0,t)\leq \frac{1}{C}2^{C^{-1}t}-2t=:e_1(t)$. The derivative of $e_1$ is $e_1'(t)=\frac{\log(2)}{C^2}2^{C^{-1}t}-2$, which is non negative $\forall t\geq C \log_2\left(\frac{2}{\log(2)}C^2\right)$ and non positive otherwise. Then $\forall t\in\mathbb{R}$:
\begin{align*}
e_1(t)&\geq e_1\left(\log_2\left(\frac{2}{\log(2)}C^2\right)\right)\geq \frac{2C}{\log(2)}-2C \log_2\left(\frac{2}{\log(2)}C^2\right)\geq \frac{2C}{\log(2)}-4C \log_2\left(\sqrt{\frac{2}{\log(2)}}C\right)
\\&\geq \frac{2C}{\log(2)}-4\sqrt{\frac{2}{\log(2)}}C^2\geq -4\sqrt{\frac{2}{\log(2)}}C^2\geq -7C^2.
\end{align*}
Since $C\geq \frac{2}{\log(2)}$ we have $3C^2\geq C\log_2(C^3)\geq C \log_2\left(\frac{2}{\log(2)}C^2\right)$, then $e_1$ is non decreasing on $[C\log_2(C^3);+\infty[$. We show that $e_1(3C^2)\geq 2853\delta C_N$:
\begin{align*}
e_1(3C^2)\geq e_1(C\log_2(C^3))=&\frac{1}{C}2^{\frac{C\log_2(C^3)}{C}}-2C\log_2(C^3)=C(C-6\log_2(C)).
\end{align*}
Since $C\geq 2^{851}$ we have $C-6\log_2(C)\geq 1$ and since $C\geq 2853\delta C_N$ we have that $e_1(3C^2)\geq C\times 1\geq 2853\delta C_N$ which provides $\forall t\in [3C^2;+\infty[$ we have $e_1(t)\geq 2853\delta C_N$. Furthermore $\forall t\in \mathbb{R}^+$, $e_1(t)=e(t)$, hence $\forall t\in [3C^2;+\infty[$ we have $e(t)\geq 2853\delta C_N$ which implies point $2.$ of this lemma.
\end{proof}
The following lemma provides us with a lower bound matching Lemma \ref{PathConnectingPointsInHoroProduct}, and a first control on the heights a geodesic segment must reach.
\begin{lemma}\label{LowerBoundLengthGeod}
Let $x=(x_p,x_q)$ and $y=(y_p,y_q)$ be two points of $\mathcal{H}=H_p\bowtie H_q$ such that $h(x)\leq h(y)$. Let $\alpha=(\alpha_p,\alpha_q)$ be a geodesic segment of $\mathcal{H}$ linking $x$ to $y$. Let $C_0=(2853\delta C_N+2^{851})^2$, we have:
\begin{enumerate}
\item $l(\alpha)\geq \Delta h (x,y)+d_r(x_q,y_q)+d_r(x_p,y_p)-15C_0$
\item $h^+(\alpha)\geq h(y)+\frac{1}{2}d_r(x_p,y_p)-3C_0$
\item $h^-(\alpha)\leq h(x)-\frac{1}{2}d_r(x_q,y_q)+3C_0$.
\end{enumerate}
\end{lemma}
\begin{proof}
Let us denote $\Delta H^+=h(y)+\frac{1}{2}d_r(x_p,y_p)-h^+(\alpha)$ and $\Delta H^-=h^-(\alpha)-\left(h(x)-\frac{1}{2}d_r(x_q,y_q)\right)$. Let $m$ be a point of $\alpha$ at height $h^-(\alpha)=h(x)-\frac{1}{2}d_r(x_q,y_q)+\Delta H^-$, and $n$ be a point of $\alpha$ at height $h^+(\alpha)=h(y)+\frac{1}{2}d_r(x_p,y_p)-\Delta H^+$. Then Lemma \ref{ExpLengthWhenBelowAndReachPoint} used on $\alpha_p$ gives us:
\begin{align*}
l(\alpha_p)\geq& 2\Delta h(x_p,m_p)+d(x_p,y_p)+2^{-850}2^{\frac{1}{\delta}\Delta H^+}-1-2\max(0,\Delta H^+)-1700\delta
\\\geq& 2h(x_p)-2\left(h(x_p)-\frac{1}{2}d_r(x_q,y_q)+\Delta H^-\right)+d(x_p,y_p)+2^{-850}2^{\frac{1}{\delta}\Delta H^+}-1
\\&-2\max(0,\Delta H^+)-1700\delta
\\\geq& d_r(x_q,y_q)+d_r(x_p,y_p)+\Delta h(x,y)+2^{-850}2^{\frac{1}{\delta}\Delta H^+}-1-2\max(0,\Delta H^+)-2\Delta H^--1700\delta.
\end{align*}
Since $h(x_q)\geq h(y_q)$ and $h(n_q)=h(y_q)-\frac{1}{2}d_r(x_p,y_p)+\Delta H^+$, Lemma \ref{ExpLengthWhenBelowAndReachPoint} used on $\alpha_q$ provides similarly:
\begin{align*}
l(\alpha_q)\geq d_r(x_p,y_p)+d_r(x_q,y_q)+\Delta h(x,y)+2^{-850}2^{\frac{1}{\delta}\Delta H^-}-1-2\max(0,\Delta H^-)-2\Delta H^+-1700\delta.
\end{align*}
Hence by Property \ref{ProprSplitLenght}:
\begin{align}
l_N(\alpha)\geq\frac{1}{2}(l(\alpha_p)+l(\alpha_q))
\geq& d_r(x_p,y_p)+d_r(x_q,y_q)+\Delta h(x,y)-1700\delta+2^{-851}2^{\frac{1}{\delta}\Delta H^-}\nonumber\\&+2^{-851}2^{\frac{1}{\delta}\Delta H^+}-2\max(0,\Delta H^-)-2\max(0,\Delta H^+)-1.\label{UseEq1InThis}
\end{align}
Furthermore, we know by Lemma \ref{PathConnectingPointsInHoroProduct} that $l_N(\alpha)\leq \Delta h (x,y)+d_r(x_p,y_p)+d_r(x_q,y_q) +1152\delta C_N$. Since $C_N\geq1$ we have:
\begin{align*}
2852\delta C_N\geq& 2^{-851}2^{\frac{1}{\delta}\Delta H^-}-2\max(0,\Delta H^-)+2^{-851}2^{\frac{1}{\delta}\Delta H^+}-2\max(0,\Delta H^+)-1.
\end{align*}
Let us denote $S:=\max\{\Delta H^-,\Delta H^+\}$. Therefore we have $2^{-851}2^{\frac{1}{\delta}S}-2\max(0,S)-1\leq 2852\delta C_N$. By assumption $\delta\geq1$ hence $2^{-851}2^{\frac{1}{\delta}S}-2\max(0,S)\leq 2853\delta C_N$. Furthermore, for $C=2853\delta C_N+2^{851}$, we have both $2^{-851}\geq\frac{1}{C}$ and $\frac{1}{\delta}\geq \frac{1}{C}$. Then we have $\frac{1}{C}2^{\frac{S}{C}}-2\max(0,S)\leq 2853\delta C_N$. Lemma \ref{AnalyticStudy} provides $S\leq 3C^2=3C_0$ which implies points $2.$ and $3.$ of our lemma. Lemma \ref{AnalyticStudy} also provides us with:
\begin{align*}
-14C_0\leq &2^{-851}2^{\frac{1}{\delta}\Delta H^-}-2\max(0,\Delta H^-)+2^{-851}2^{\frac{1}{\delta}\Delta H^+}-2\max(0,\Delta H^+).
\end{align*}
Last inequality is a lower bound of the term we want to remove in inequality (\ref{UseEq1InThis}). The first point of our lemma hence follows since $1700\delta+1\leq C_0$.
\end{proof}
Combining Lemma \ref{PathConnectingPointsInHoroProduct} and \ref{LowerBoundLengthGeod} we get the following corollary.
\begin{cor}\label{lengthGeod}
Let $N$ be an admissible norm and let $C_0= (2853\delta C_N+2^{851})^2$. The length of a geodesic segment $\alpha$ connecting $x$ to $y$ in $(\mathcal{H},d_{\mathcal{H},N})$ is controlled as follows:
\begin{align*}
\big|l_N(\alpha)-\big(\Delta h (x,y)+d_r(x_p,y_p)+d_r(x_q,y_q)\big)\big|\leq 15C_0,
\end{align*}
which gives us a control on the $N$-path metric, for all points $x$ and $y$ in $\mathcal{H}$ we have:
\begin{align*}
\big|d_{\mathcal{H},N}(x,y)-\big(\Delta h (x,y)+d_r(x_p,y_p)+d_r(x_q,y_q)\big)\big|\leq 15C_0.
\end{align*}
\end{cor}
This result is central as it shows that the shape of geodesics does not depend on the $N$-path metric chosen for the distance on the horospherical product.
\begin{cor}\label{l1samel2}
Let $r\geq 1$. For all $x$ and $y$ in $\mathcal{H}=H_p\bowtie H_q$ we have:
\begin{equation}
\big|d_{\mathcal{H},\ell_r}(x,y)-d_{\mathcal{H},\ell_1}(x,y)\big|\leq 30(5706\delta+2^{851})^2.\nonumber
\end{equation}
\end{cor}
\begin{proof}
The $\ell_r$ norm inequalities provide us with:
\begin{equation}
\sqrt[r]{{d_{H_p}}^r+{d_{H_q}}^r}\leq d_{H_p}+d_{H_q}\leq 2^{\frac{r-1}{r}}\sqrt[r]{{d_{H_p}}^r+{d_{H_q}}^r}.\nonumber
\end{equation}
Hence we have $\frac{\sqrt[r]{2}}{2}\left(d_{H_p}+d_{H_q}\right)\leq \sqrt[r]{{d_{H_p}}^r+{d_{H_q}}^r}\leq d_{H_p}+d_{H_q}$. Then the $\ell_r$ norms are admissible norms with $C_{\ell_r}\leq 2$, which ends the proof.
\end{proof}
The next corollary tells us that changing this distance does not change the large scale geometry of $\mathcal{H}$.
\begin{cor}
Let $N_1$ and $N_2$ be two admissible norms. Then the metric spaces $\left(\mathcal{H}, d_{\mathcal{H},N_1}\right)$ and $\left(\mathcal{H}, d_{\mathcal{H},N_2}\right)$ are quasi-isometric.
\end{cor}
The control on the distances of Lemma \ref{lengthGeod} will help us understand the shape of geodesic segments and geodesic lines in a horospherical product.
\section{Shapes of geodesics and visual boundary of $\mathcal{H}$}\label{SectionThm}
\subsection{Shapes of geodesic segments}
In this section we focus on the shape of geodesics. We recall that in all the following $H_p$ and $H_q$ are assumed to be two proper, geodesically complete, $\delta$-hyperbolic, Busemann spaces with $\delta\geq 1$, and $N$ is assumed to be an admissible norm.
The next lemma gives a control on the maximal and minimal height of a geodesic segment in a horospherical product. It is similar to a traveller problem, who needs to walk from $x$ to $y$ passing by $m$ and $n$. This result follows from the inequalities on maximal and minimal heights of Lemma \ref{LowerBoundLengthGeod} combined with Lemma \ref{PathConnectingPointsInHoroProduct}.
\begin{lemma}\label{HPlusHMinusGeod}
Let $x=(x_p,x_q)$ and $y=(y_p,y_q)$ be two points of $\mathcal{H}=H_p\bowtie H_q$ such that $h(x)\leq h(y)$. Let $N$ be an admissible norm and let $\alpha=(\alpha_p,\alpha_q)$ be a geodesic of $(\mathcal{H},d_{\mathcal{H},N})$ linking $x$ to $y$. Let $C_0=(2853\delta C_N+2^{851})^2$, we have:
\begin{enumerate}
\item $\left|h^-(\alpha) -\left(h(x)-\frac{1}{2}d_r(x_q,y_q)\right)\right|\leq 4C_0$
\item $\left|h^+(\alpha) -\left(h(y)+\frac{1}{2}d_r(x_p,y_p)\right)\right|\leq 4C_0$.
\end{enumerate}
\end{lemma}
\begin{proof}
Let us consider a point $m$ of $\alpha$ such that $h(m)=h^-(\alpha)$ and a point $n$ of $\alpha$ such that $h(n)=h^+(\alpha)$. Then $m$ comes before $n$ or $n$ comes before $m$. In both cases, since $h(m)\leq h(x)\leq h(y)\leq h(n)$ and by Lemma \ref{LemDistBigHaut} we have:
\begin{align*}
l_N(\alpha)&\geq \Delta h(x,y)+2(h(x)-h^-(\alpha))+2(h^+(\alpha)-h(y))
\\&\geq\Delta h(x,y)+2(h(x)-h^-(\alpha))+d_r(x_p,y_p)-6C_0,\text{ by Lemma \ref{LowerBoundLengthGeod}}.
\end{align*}
Furthermore Lemma \ref{PathConnectingPointsInHoroProduct} provides $l_N(\alpha)\leq \Delta h (x,y)+d_r(x_p,y_p)+d_r(x_q,y_q)+C_0$ , hence:
\begin{align*}
\Delta h (x,y)+d_r(x_p,y_p)+d_r(x_q,y_q)+C_0\geq\Delta h(x,y)+2(h(x)-h^-(\alpha))+d_r(x_p,y_p)-6C_0,
\end{align*}
which implies $\left(h(x)-\frac{1}{2}d_r(x_q,y_q)\right) -h^-(\alpha)\leq 4C_0$. In combination with the third point of Lemma \ref{LowerBoundLengthGeod} it proves the first point of our Lemma \ref{HPlusHMinusGeod}. The second point is proved similarly.
\end{proof}
\begin{lemma}\label{TechShapeGeod}
Let $N$ be an admissible norm and let $C_0=(2853\delta C_N+2^{851})^2$. Let$x=(x_p,x_q)$ and $y=(y_p,y_q)$ be two points of $\mathcal{H}=H_p\bowtie H_q$. Let $\alpha=(\alpha_p,\alpha_q)$ be a geodesic of $(\mathcal{H},d_{\mathcal{H},N})$ linking $x$ to $y$. Then there exist two points $a=(a_p,a_q),\ b=(b_p,b_q)$ of $\alpha$ such that $h(a)=h(x)$, $h(b)=h(y)$ with the following properties:
\begin{enumerate}
\item If $h(x)\leq h(y)-7C_0$ then:
\begin{enumerate}
\item $h^-(\alpha)=h^-([x,a])$ and $h^+(\alpha)=h^+([b,y])$
\item $\left|d_r(x_q,a_q)-d_r(x_q,y_q)\right| \leq 16C_0\ \text{and}\ d_r(x_p,a_p)\leq 22C_0$
\item $\left|d_r(y_p,b_p)-d_r(x_p,y_p)\right| \leq 16C_0\ \text{and}\ d_r(y_q,b_q)\leq 22C_0$
\item $|d_{\mathcal{H},N}(a,b)-\Delta h(a,b)|\leq 13C_0$.
\end{enumerate}
\item If $h(y)\leq h(x)-7C_0$ then $(a)$, $(b)$, $(c)$ and $(d)$ hold by switching the roles of $x$ and $y$ and switching the roles of $a$ and $b$.
\item If $|h(x)-h(y)|\leq 7C_0$ at least one of the two previous conclusions is satisfied.
\end{enumerate}
\end{lemma}
Lemma \ref{TechShapeGeod} is illustrated on Figure \ref{NotaSectThm}. Its notations will be used in all section \ref{SectionThm}.
\begin{figure}
\begin{center}
\includegraphics[scale=0.25]{ResumeNotProofThm.pdf}
\captionof{figure}{Notations of Lemma \ref{TechShapeGeod}.}
\label{NotaSectThm}
\end{center}
\end{figure}
\begin{proof}
Let us consider a point $m$ of $\alpha$ such that $h(m)=h^-(\alpha)$ and a point $n$ of $\alpha$ such that $h(n)=h^+(\alpha)$. We first assume that $m$ comes before $n$ in $\alpha$ oriented from $x$ to $y$. Let us call $a$ the first point between $m$ and $n$ at height $h(x)$ and $b$ the last point between $m$ and $n$ at height $h(y)$. Property $(a)$ of our Lemma is then satisfied. Let us denote $\alpha_1$ the part of $\alpha$ linking $x$ to $a$, $\alpha_2$ the part of $\alpha$ linking $a$ to $b$ and $\alpha_3$ the part of $\alpha$ linking $b$ to $y$. We have that $m$ is a point of $\alpha_1$ and that $n$ is a point of $\alpha_3$. Inequalities $2.$ and $3.$ of Lemma \ref{LowerBoundLengthGeod} used on $\alpha_1$ provide $l_N(\alpha_1)\geq d(x,m) +d(m,a)\geq 2\Delta h(x,m) \geq d_r(x_q,y_q)-6C_0$ and similarly $l_N(\alpha_3)\geq d_r(x_p,y_p)-6C_0$. Furthermore we have $l_N(\alpha_2)\geq \Delta h (x,y)$. Combining $l_N(\alpha_1)=l_N(\alpha)-l_N(\alpha_2)-l_N(\alpha_3)$ and Lemma \ref{PathConnectingPointsInHoroProduct} we have:
\begin{align}
l_N(\alpha_1)&\leq\Delta h (x,y)+d_r(x_p,y_p)+d_r(x_q,y_q)+C_0-\Delta h (x,y)-d_r(x_p,y_p)+6C_0\nonumber
\\&\leq d_r(x_q,y_q)+7C_0.\label{EquseInther2}
\end{align}
We have similarly that $l_N(\alpha_3)\leq d_r(x_p,y_p)+7C_0$ and that $d_{\mathcal{H},N}(a,b)=l_N(\alpha_2)\leq\Delta h (x,y) +13C_0$. It gives us $|d_{\mathcal{H},N}(a,b)-\Delta h (x,y)|\leq 13C_0$, point $(d)$ of our lemma. Furthermore, using Lemma \ref{HPlusHMinusGeod} on $\alpha$ and $\alpha_1$ provides:
\begin{align*}
\left|h^-(\alpha) -\left(h(x)-\frac{1}{2}d_r(x_q,y_q)\right)\right|&\leq 4C_0,
\\\left|h^-(\alpha_1) -\left(h(x)-\frac{1}{2}d_r(x_q,a_q)\right)\right|&\leq 4C_0.
\end{align*}
Since $h^-(\alpha)=h^-(\alpha_1)$ we have:
\begin{equation}
\left|d_r(x_q,a_q)-d_r(x_q,y_q)\right|\leq 16C_0,\label{EquseInther3}
\end{equation}
which is the first inequality of $(b)$. Using the first point of Lemma \ref{LowerBoundLengthGeod} on $\alpha_1$ in combination with inequality (\ref{EquseInther2}) gives us:
\begin{align*}
d_r(x_q,y_q)+7C_0\geq& l_N(\alpha_1)\geq \Delta h(x,a) +d_r(x_p,a_p)+d_r(x_q,a_q)-15C_0
\\\geq&d_r(x_p,a_p)+d_r(x_q,a_q)-15C_0
\\\geq&d_r(x_p,a_p)+d_r(x_q,y_q)-31C_0\text{, by inequality (\ref{EquseInther3}).}
\end{align*}
Then $d_r(x_p,y_p)\leq 38C_0$ the second inequality of point $(b)$ holds. We prove similarly the inequality $(c)$ of this lemma. This ends the proof when $m$ comes before $n$. If $n$ comes before $m$, the proof is still working by orienting $\alpha$ from $y$ to $x$ hence switching the roles between $x$ and $y$.
\\\\We will now prove that if $h(x)\leq h(y)-7C_0$ then $m$ comes before $n$ on $\alpha$ oriented from $x$ to $y$. Let us assume that $h(x)\leq h(y)-7C_0$. We will proceed by contradiction, let us assume that $n$ comes before $m$, using $h(m)\leq h(x)\leq h(y)\leq h(n)$ it implies:
\begin{align*}
l_N(\alpha)\geq& d_{\mathcal{H},N}(x,n)+d_{\mathcal{H},N}(n,m)+d_{\mathcal{H},N}(m,y) \geq \Delta h(x,n)+\Delta h(n,m)+\Delta h(m,y)
\\\geq&\Delta h(x,y)+\Delta h(y,n)+\Delta h(m,x)+\Delta h(x,y)+\Delta h(y,n)+\Delta h(m,x)+\Delta h(x,y)
\\\geq&2\Delta h(x,y)+\Delta h(x,y)+2\Delta h(m,x)+2\Delta (y,n)
\\\geq&14C_0+\Delta h(x,y)+2(h(x)-h^-(\alpha))+2(h^+(\alpha)-h(y)).
\end{align*}
However Lemma \ref{LowerBoundLengthGeod} applied on $\alpha$ provides $h^+(\alpha)\geq h(y)+\frac{1}{2}d_r(x_p,y_p)-3C_0$ and $h^-(\alpha)\leq h(x)-\frac{1}{2}d_r(x_q,y_q)+3C_0$. Then:
\begin{align*}
l_N(\alpha)\geq& 14C_0+\Delta h(x,y) +d_r(x_p,y_p)+d_r(x_q,y_q)-12C_0
\\\geq&\Delta h(x,y) +d_r(x_p,y_p)+d_r(x_q,y_q)+2C_0,
\end{align*}
which contradict Lemma \ref{PathConnectingPointsInHoroProduct}. Hence, if $h(x)\leq h(y)-7C_0$, the point $m$ comes before the point $n$ and by the first part of the proof, $1.$ holds. Similarly, if $h(y)\leq h(x)-7C_0$ then $n$ comes before $m$ and then $2.$ holds. Otherwise when $|h(x)-h(y)|\leq 7C_0$ both cases could happened, then $1.$ or $2.$ hold.
\end{proof}
This previous lemma essentially means that if $x$ is sufficiently below $y$, the geodesic $\alpha$ first travels in a copy of $H_q$ in order to "loose" the relative distance between $x_q$ and $y_q$, then it travels upward using a vertical geodesic from $a$ to $b$ until it can "lose" the relative distance between $x_p$ and $y_p$ by travelling in a copy of $H_p$. It looks like three successive geodesics of hyperbolic spaces, glued together. The idea is that the geodesic follows a shape similar to the path $\gamma$ we constructed in Lemma \ref{PathConnectingPointsInHoroProduct}. We formalize this in the following theorem, which tells us that a geodesic segment is in the constant neighbourhood of three vertical geodesics. It can be understood as an extension of the fact that in a hyperbolic space, a geodesic segment is in a constant neighbourhood of two vertical geodesics.
\begin{thm}\label{THMA}
Let $N$ be an admissible norm. Let $x=(x_p,x_q)$ and $y=(y_p,y_q)$ be two points of $\mathcal{H}=H_p\bowtie H_q$ and let $\alpha$ be a geodesic segment of $(\mathcal{H},d_{\mathcal{H},N})$ linking $x$ to $y$. Let $C_0=(2853\delta C_N+2^{851})^2$, there exist two vertical geodesics $V_1=(V_{1,p},V_{1,q})$ and $V_2=(V_{2,p},V_{2,q})$ such that:
\begin{enumerate}
\item If ~ $h(x)\leq h(y)-7C_0$ ~ then $\alpha$ is in the $196C_0C_N$-neighbourhood of $V_1\cup(V_{1,p},V_{2,q})\cup V_2$
\item If ~ $h(x)\geq h(y)+7C_0$ ~ then $\alpha$ is in the $196C_0C_N$-neighbourhood of $ V_1\cup(V_{2,p},V_{1,q})\cup V_2$
\item If ~ $|h(x)-h(y)|\leq 7C_0$ ~ then at least one of the conclusions of $1.$ or $2.$ holds.
\end{enumerate}
Specifically $V_1$ and $V_2$ can be chosen such that $x$ is close to $V_1$ and $y$ is close to $V_2$.
\end{thm}
\begin{figure}
\begin{center}
\includegraphics[scale=0.75]{FigTHMA.pdf}
\captionof{figure}{Theorem \ref{THMA}. The neighbourhood's shapes are distorted since when going upward, distances are contracted in the "direction" $H_p$ and expanded in the "direction" $H_q$.}
\label{FigThmA}
\end{center}
\end{figure}
Figure \ref{FigThmA} pictures the $196C_0C_N$-neighbourhood of such vertical geodesics when $h(x)\leq h(y)-7C_0$.
When $|h(x)-h(y)|\leq 7C_0$, there are two possible shapes for a geodesic segment. In some cases, two points can be linked by two different geodesics, one of type $1$ and one of type $2$.
\begin{proof}
Let $m=(m_p,m_q)$ be a point of $\alpha$ such that $h(m)=h^-(\alpha)$, and $n=(n_p,n_q)$ be a point of $\alpha$ such that $h(n)=h^+(\alpha)$. Then by Lemma \ref{HPlusHMinusGeod} we have:
\begin{equation}
\left|\Delta h(x,m)-\frac{1}{2}d_r(x_q,y_q)\right|\leq 4C_0.\label{UseAfter2}
\end{equation}
We show similarly that:
\begin{equation}
\left|\Delta h(y,n)-\frac{1}{2}d_r(x_p,y_p)\right|\leq 4C_0.\label{UseAfter3}
\end{equation}
In the first case we assume that $h(x)\leq h(y)-7C_0$. With notations as in Lemma \ref{TechShapeGeod}, and by inequality (\ref{EquseInther2}), we have that $l_N([x,a])\leq d_r(x_q,y_q)+7C_0$, hence:
\begin{align}
l_N([x,m])=&l_N([x,a])-l_N([a,m])\leq d_r(x_q,y_q)+7C_0-\Delta h(a,m)\nonumber
\\\leq&\frac{1}{2}d_r(x_q,y_q)+11C_0\text{, since }\Delta h(x,m)=\Delta h(a,m).\label{UseAfter1}
\end{align}
It follows from this inequality that:
\begin{align*}
d_{H_p}(x_p,m_p)=& 2d_{H_p\times H_q}(x,m)-d_{H_q}(x_q,m_q)\leq 2d_{\mathcal{H},N}(x,m)-d_{H_q}(x_q,m_q)
\\\leq& 2l_N([x,m])-d_{H_q}(x_q,m_q)\leq d_r(x_q,y_q)+22C_0-\Delta h(x,m)\leq \frac{1}{2}d_r(x_q,y_q)+26C_0.
\end{align*}
Then:
\begin{align*}
d_r(x_p,m_p)=& d_{H_p}(x_p,m_p)-\Delta h(x,m)\leq \frac{1}{2}d_r(x_q,y_q)+26C_0-\Delta h(x,m)
\\\leq&30C_0 \text{, by inequality }(\ref{UseAfter2}).
\end{align*}
Similarly $d_r(x_q,m_q)\leq 30C_0$. Let us consider the vertical geodesic $V_{m_p}$ of $H_p$ containing $m_p$, and the vertical geodesic $V_{x_q}$ of $H_q$ containing $x_q$. Let us denote $x'_p$ the point of $V_{m_p}$ at the height $h(x)$. Since $d_r(x_p,m_p)\leq 30C_0$, Lemma \ref{LinkDrAndDSameHeight} applied on $x_p$ and $m_p$ provides $d_{H_p}(x_p,x'_p)\leq 31C_0$.
We will then consider two paths of $H_p$. The first one is $\alpha_{1,p}=[x_p,m_p]$, the part of $\alpha_p$ linking $x_p$ to $m_p$. The second one is $[m_p,x'_p]$ a piece of vertical geodesic linking $m_p$ to $x'_p$. We show that these two paths have close length. Using Property \ref{ProprSplitLenght} with inequalities (\ref{UseAfter2}) and (\ref{UseAfter1}) provides us with:
\begin{align*}
l_{H_p}([x_p,m_p])&\leq 2l_N([x,m])-l_{H_q}([x_q,m_q])\leq 2\left(\frac{1}{2}d_r(x_q,y_q)+11C_0\right) -\Delta h(x,m)
\\&\leq\Delta h(x,m)+30C_0
\end{align*}
Furthermore $l_{H_p}([x_p,m_p])\geq \Delta h(x,m)$ and we know that $l_{H_p}([m_p,x_p'])=\Delta h(x,m)$, hence:
\begin{align*}
\big\vert l_{H_p}([x_p,m_p])-l_{H_p}([m_p,x_p'])\big\vert\leq 30 C_0
\end{align*}
We already proved that their end points are also close to each other $d(x_p,x'_p)\leq 31C_0$. Since $\delta\leq C_0$, the property of hyperbolicity of $H_p$ gives us that $\alpha_{1,p}$ is in the $(31+30+1)C_0=62C_0$-neighbourhood of $[m_p,x'_p]$, a part of the vertical geodesic $V_{m_p}$. We show similarly that $\alpha_{1,q}$ is in the $62C_0$-neighbourhood of $V_{x_q}$. Since $N$ is an admissible norm, Property \ref{HoroProdConnected} gives us that $\alpha_{1}$ is in the $124C_0C_N$-neighbourhood of $(V_{m_p},V_{x_q})$. We show similarly that $\alpha_3$, the portion of $\alpha$ linking $n$ to $y$, is in the $124C_0C_N$-neighbourhood of $(V_{y_p},V_{n_q})$.
We now focus on $\alpha_2$, the portion of $\alpha$ linking $m$ to $n$. Let us denote $[m_p,n_p]$ the path $\alpha_{2,p}$ and $[m_q,n_q]$ the path $\alpha_{2,q}$. Then Lemma \ref{HPlusHMinusGeod} provides us with:
\begin{equation}
\left|\Delta h(m,n)-\Big(\Delta h(x,y)+\frac{1}{2}d_r(x_q,y_q)+\frac{1}{2}d_r(x_p,y_p)\Big)\right|\leq 8C_0.\label{UseAfter4}
\end{equation}
However from Lemma \ref{PathConnectingPointsInHoroProduct} and since $1152\delta C_N\leq C_0$:
\begin{align*}
l_N(\alpha_2)=&l_N(\alpha)-l_N(\alpha_1)-l_N(\alpha_3)
\\\leq& \Delta h(x,y)+d_r(x_p,y_p)+d_r(x_q,y_q)+C_0-\Delta h(x,m)-\Delta h(n,y)
\\\leq& \Delta h(x,y)+\frac{1}{2}d_r(x_p,y_p)+\frac{1}{2}d_r(x_q,y_q)+9C_0\text{, by inequalities }(\ref{UseAfter2})\text{ and }(\ref{UseAfter3}).
\end{align*}
It follows from this inequality and the fact that $N$ is admissible that:
\begin{align*}
d_{H_p}(m_p,n_p)&\leq 2l_N(\alpha_2)-d_{H_q}(m_q,n_q)\leq 2\Delta h(x,y)+d_r(x_p,y_p)+d_r(x_q,y_q)+18C_0-\Delta h(m,n)
\\&\leq \Delta h(m,n)+34C_0\text{, by inequality }(\ref{UseAfter4}).
\end{align*}
Thus:
\begin{align*}
d_r(m_p,n_p)=& d_{H_p}(m_p,n_p)-\Delta h(m,n)\leq 34C_0 .
\end{align*}
In the same way we have $d_r(m_q,n_q)\leq 34C_0$. Let us denote $n_p'$ the point of $V_{m_p}$ at the height $h(n_p)$. Since $d_r(x_p,m_p)\leq 34C_0$, Lemma \ref{LinkDrAndDSameHeight} applied on $m_p$ and $n_p$ provides:
\begin{equation}
d_{H_p}(m_p,n'_p)\leq 35C_0\label{UseAfter25}
\end{equation}
Hence we have proved that $\alpha_{2,p}$ and $[m_p,n_p']$ have their end points close to each other. Let us now prove that these paths have close lengths. We have that $l_{H_p}([m_p,n_p'])=\Delta h (m,n)$, and from inequalities (\ref{UseAfter2}) and (\ref{UseAfter3}) we have:
\begin{align*}
l_{H_p}([m_p,n_p])&\leq 2l_N(\alpha_{2,p})-l_{H_q}([m_q,n_q])=2\Big(l_N(\alpha)-l_N(\alpha_1)-l_N(\alpha_3)\Big) -\Delta h(m,n)
\\&\leq 2\Big(15C_0+\Delta h (x,y) +d_r(x_p,y_p)+d_r(x_q,y_q)-\Delta h(x,m)-\Delta h(n,y)\Big) -\Delta h(m,n)
\\&\leq 2\Big(\Delta h (x,y) +d_r(x_p,y_p)+d_r(x_q,y_q)-\Delta h(x,m)-\Delta h(n,y)\Big) -\Delta h(m,n)
\\&\leq 2\Big(\Delta h (x,y) +\Delta h(x,m)+\Delta h(n,y)+16C_0\Big) -\Delta h(m,n)+30C_0\leq\Delta h(m,n)+62C_0
\end{align*}
As $l_{H_p}([m_p,n_p])\geq \Delta h(m,n)$ we obtain:
\begin{equation}
|l_{H_p}([m_p,n_p])-l_{H_p}([m_p,n_p'])|\leq 62 C_0\label{UseAfter26}
\end{equation}
Then by similar arguments as for the path $\alpha_{1,p}$, inequalities (\ref{UseAfter25}) and (\ref{UseAfter26}) show that $\alpha_{2,p}$ is in the $(35+62+1)C_0=98C_0$ neighbourhood of $V_{m_p}$. Similarly we prove that $\alpha_{2,q}$ is in the $98C_0$ neighbourhood of $V_{n_q}$. Since $N$ is an admissible norm, Property \ref{HoroProdConnected} gives us that $\alpha_{2}$ is in the $196C_0C_N$-neighbourhood of $(V_{m_p},V_{n_q})$.
\\\\In the second case, we assume that $h(y)\leq h(x)-7C_0$. Then by switching the role of $x$ and $y$, Lemma \ref{TechShapeGeod} gives us the result identically.
\\\\In the third case, we assume that $|h(x)- h(y)|\leq 7C_0$. Then Lemma \ref{TechShapeGeod} tells us that on of the two previous situations prevails, which proves the result.
\end{proof}
\subsection{Coarse monotonicity}
The fact that a geodesic is following a vertical geodesic is related to the next definition.
\begin{defn}
Let $C$ be a non negative number. A geodesic $\alpha:I\to\mathcal{H}$ of $\mathcal{H}=H_p\bowtie H_q$ is called $C$-coarsely increasing if $\forall t_1,t_2\in I$:
\begin{align*}
\big(\ t_2> t_1+C\ \big)\Rightarrow\big(\ h(\alpha(t_2))> h(\alpha(t_2))\ \big).
\end{align*}
The geodesic $\alpha$ is called $C$-coarsely decreasing if $\forall t_1,t_2\in I$:
\begin{align*}
\big(\ t_2> t_1+C\ \big)\Rightarrow\big(\ h(\alpha(t_2))< h(\alpha(t_2))\ \big).
\end{align*}
\end{defn}
The next lemma links the coarse monotonicity and the fact that a geodesic segment is close to vertical geodesics.
\begin{lemma}\label{ShapeCoarsMonotGeodHoroPoduct}
Let $N$ be an admissible norm and let $C_0=(2853\delta C_N+2^{851})^2$. Let $x=(x_p,x_q)$ and $y=(y_p,y_q)$ be two points of $\mathcal{H}=H_p\bowtie H_q$ and let $\alpha$ be a geodesic segment of $(\mathcal{H},d_{\mathcal{H},N})$ linking $x$ to $y$. Let $m\in\alpha$ and $n\in\alpha$ be two points in $\mathcal{H}$ such that $h^-(\alpha)=h(m)$ and $h^+(\alpha)=h(n)$. We have:
\begin{enumerate}
\item If ~ $h(x)\leq h(y)-7C_0$, then $\alpha$ is $17C_0$-coarsely decreasing on $[x,m]$ and $17C_0$-coarsely increasing on $[m,n]$ and $17C_0$-coarsely decreasing on $[n,y]$.
\item If ~ $h(x)\geq h(y)+7C_0$, then $\alpha$ is $17C_0$-coarsely increasing on $[x,n]$ and $17C_0$-coarsely decreasing on $[n,m]$ and $17C_0$-coarsely increasing on $[m,n]$.
\item If ~ $|h(x)-h(y)|\leq 7C_0$ ~ then the conclusions of $1.$ or $2.$ holds.
\end{enumerate}
\end{lemma}
\begin{proof}
Assume that $h(x)\leq h(y)-7C_0$. Then from inequality (\ref{UseAfter1}) in the proof of Theorem \ref{THMA}, $l_N([x,m])\leq \frac{1}{2} d_r(x_q,y_q)+11C_0$. Furthermore Lemma \ref{HPlusHMinusGeod} gives us that $\left|\Delta h(x,m)-\frac{1}{2}d_r(x_q,y_q)\right|\leq 4C_0$. Then:
\begin{align}
l_N([x,m])\leq \Delta h(x,m)+15C_0.\label{useInHere123}
\end{align}
We will proceed by contradiction, assume that $[x,m]$ is not $15C_0$-coarsely decreasing, then there exists $i_1\in\alpha$, $i_2\in\alpha$ such that $h(i_1)=h(i_2)$ and $l([i_1,i_2])> 15C_0$. Hence:
\begin{align*}
l_N([x,m])&\geq l_N([x,i_1])+l_N([i_1,i_2])+l_N([i_2,m])\geq\Delta h(x,i_1)+l_N([i_1,i_2])+\Delta h(i_2,m)
\\&>\Delta h(x,m)+15C_0,
\end{align*}
which contradicts inequality (\ref{useInHere123}). Then $[x,m]$ is $15C_0$-coarsely decreasing. We show in a similar way that $[m,n]$ is $17C_0$-coarsely increasing and that $[n,y]$ is $15C_0$-coarsely decreasing. This proves the first point of our lemma. The second point is proved by switching the roles of $x$ and $y$. We now assume $|h(x)-h(y)|\leq 7C_0$, as in the proof of Theorem \ref{THMA} the inequality (\ref{UseAfter1}) or a corresponding inequality holds, which ends the proof.
\end{proof}
\subsection{Shapes of geodesic rays and geodesic lines}
In this section we are focusing on using the previous results to get informations on the shapes of geodesic rays and geodesic lines. We first link the coarse monotonicity of a geodesic ray to the fact that it is close to a vertical geodesic. Let $\lambda\geq 1$ and $c\geq0$, a $(\lambda,c)$-quasigeodesic of the metric space $(\mathcal{H},d_{\mathcal{H},N})$ is the image of a function $\phi :\mathbb{R}\to \mathcal{H}$ verifying that $\forall t_1,t_2\in\mathbb{R}$:
\begin{equation}
\frac{|t_1-t_2|}{\lambda}-c\leq d_{\mathcal{H},N}\big(\phi(t_1),\phi(t_2)\big)\leq\lambda|t_1-t_2|+c
\end{equation}
\begin{lemma}\label{ProjAreQuasiGeod}
Let $N$ be an admissible norm and let $C_0=(2853\delta C_N+2^{851})^2$. Let $\alpha=(\alpha_p,\alpha_q)$ be a geodesic ray of $(\mathcal{H},d_{\mathcal{H},N})$ and let $K$ be a positive number such that $\alpha$ is $K$-coarsely monotone. Then $\alpha_p$ and $\alpha_q$ are $(1,26C_0+8K)$-quasigeodesics.
\end{lemma}
\begin{proof}
Let $t_1$ and $t_2$ be two times. Let us denote $x=(x_p,x_q)=\alpha(t_1)$ and $y=(y_p,y_q)=\alpha(t_2)$. We apply Lemma \ref{TechShapeGeod} on the part of $\alpha$ linking $x$ to $y$ denoted by $[x,y]$. By $K$-coarse monotonicity of $\alpha$ we have that $d(x,a)_{\mathcal{H},N}\leq K$ and $d_{\mathcal{H},N}(b,y)\leq K$. Hence using $d)$ of Lemma \ref{TechShapeGeod}:
\begin{align*}
\Delta h(x,y)\leq d_{\mathcal{H},N}(x,y)&\leq d_{\mathcal{H},N}(x,a)+d_{\mathcal{H},N}(a,b)+d_{\mathcal{H},N}(b,y)\leq K+\Delta h(a,b)+13C_0+K
\\&\leq \Delta h(x,y)+\Delta h(x,a)+\Delta h(b,y)+13C_0+2K\leq\Delta h(x,y)+13C_0+4K.
\end{align*}
Furthermore, $d_{H_p}(x_p,y_p)\geq \Delta h(x_p,y_p)=\Delta h(x,y)$ and $d_{H_q}(x_q,y_q)\geq \Delta h(x,y)$. Since $N$ is an admissible norm we have:
\begin{align*}
\Delta h(x,y)\leq d_{H_p}(x_p,y_p)&=2d_{H_p\times H_q}(x,y)-d_{H_q}(x_q,y_q)\leq 2d_{\mathcal{H},N}(x,y)-d_{H_q}(x_q,y_q)
\\&\leq 2\Delta h(x,y)+13C_0+4K-\Delta h(x,y)\leq\Delta h(x,y)+13C_0+4K .
\end{align*}
Hence:
\begin{align*}
d_{\mathcal{H},N}(x,y)-26C_0-8K\leq d_{H_p}(x_p,y_p)\leq d_{\mathcal{H},N}(x,y)+26C_0+8K ,
\end{align*}
By definition we have $x_p=\alpha_p(t_1)$, $y_p=\alpha_p(t_2)$ and $d_{\mathcal{H},N}(x,y)=|t_1-t_2|$. Then $\alpha_p$ is a $(1,26C_0+8K)$-quasigeodesic ray. We prove similarly that $\alpha_q$ is a $(1,26C_0+8K)$-quasigeodesic ray.
\end{proof}
We will now make use of the rigidity property of quasi-geodesics in Gromov hyperbolic spaces, presented in Theorem 3.1 p.41 of \cite[Coornaert, Delzant, Papadopoulos]{Papa1}.
\begin{thm}[\cite{Papa1}]\label{THMPAPADO}
Let $H$ be a $\delta$-hyperbolic geodesic space. If $f:\mathbb{R}\rightarrow H$ is a $(\lambda,k)$-quasi geodesic, then there exists a constant $\kappa>0$ depending only on $\delta,\lambda$ and $k$ such that the image of $f$ is in the $\kappa$-neighbourhood of a geodesic in $H$.
\end{thm}
\begin{lemma}\label{LemCoarsClosVert}
Let $N$ be an admissible norm and let $T_1$ and $T_2$ be two real numbers. Let $\alpha=(\alpha_p,\alpha_q):[T_1,+\infty[\to \mathcal{H}$ be a geodesic ray of $(\mathcal{H},d_{\mathcal{H},N})$. Let $K$ be a positive number such that $\alpha$ is $K$-coarsely monotone.
Then there exists a constant $\kappa>0$ depending only on $K$, $\delta$ and $N$ such that $\alpha$ is in the $\kappa$-neighbourhood of a vertical geodesic ray $V:[T_2;+\infty[\to \mathcal{H}$ and such that $d_{\mathcal{H},N}\big(\alpha(T_1),V(T_2)\big)\leq\kappa$.
\end{lemma}
\begin{proof}
We assume without loss of generality that $\lim\limits_{t\rightarrow +\infty}h(\alpha(t))=+\infty$. Let $C_0=(2853\delta C_N+2^{851})^2$, by Lemma \ref{ProjAreQuasiGeod}, $\alpha_p$ is a $(1,26C_0+8K)$-quasi geodesic ray. Then Theorem \ref{THMPAPADO} says there exists $\kappa_p>0$ depending only on $26C_0+8K$ and $\delta$ such that $\alpha_p$ is in the $\kappa_p$-neighbourhood of a geodesic $V_p$. Since $C_0$ depends only on $\delta$ and $N$, $\kappa_p$ depends only on $K$, $\delta$ and $N$. Then $\lim\limits_{t\rightarrow +\infty}h(\alpha(t))=+\infty$ gives us $\lim\limits_{t\rightarrow +\infty}h(V_p(t))=+\infty$ which implies that $V_p$ is a vertical geodesic of $H_p$.
We will now build the vertical geodesic we want in $H_q$. We have $\lim\limits_{t\rightarrow +\infty}h(\alpha_q(t))=-\infty$ and by Lemma \ref{ProjAreQuasiGeod}:
\begin{align*}
\Delta h(\alpha_q(t_1),\alpha_q(t_2))-26C_0-8K\leq d_{H_q}(\alpha_q(t_1),\alpha_q(t_2))\leq \Delta h(\alpha_q(t_1),\alpha_q(t_2))+26C_0+8K .
\end{align*}
Since $H_q$ is Busemann, there exists a vertical geodesic ray $\beta$ starting at $\alpha_q(T_1)$. Since $\beta$ is parametrised by its height, $\alpha_q\cup\beta$ is also a $(1,26C_0+8K)$-quasi geodesic, hence there exists $\kappa_q$ and $V_q$ depending only on $K$, $\delta$ and $N$ such that $\alpha_q\cup\beta$ is in the $\kappa_q$-neighbourhood of $V_q$. Since $\lim\limits_{t\rightarrow -\infty}h(V_q(t))=+\infty$, $V_q$ is a vertical geodesic of $H_q$.
Furthermore, by Property \ref{HoroProdConnected}, $d_{\mathcal{H},N}\leq 2C_N(d_{H_p}+d_{H_q})$, hence there exists $\kappa$ depending only on $K$, $\delta$ and $N$ such that $\alpha$ is in the $\kappa$-neighbourhood (for $d_{\mathcal{H},N}$) of $(V_p,V_q)$, a vertical geodesic of $(\mathcal{H},d_{\mathcal{H},N})$.
Since $h(\alpha(t))\geq h(\alpha(T_1))-26C_0-8K=:M$, $\alpha$ is in the $\kappa$-neighbourhood of $\Big(V_p\big([M-\kappa;+\infty[\big),V_q\big(]-\infty;-M+\kappa]\big)\Big)$ which is a vertical geodesic ray.
\\We will now show that the starting points of $\alpha$ and $V$ are close to each other. Let us denote $T_1'$ a time such that $d_{\mathcal{H},N}\big(\alpha(T_1) , V(T_1')\big)\leq \kappa$, then $\Delta h \big(\alpha(T_1) , V(T_1')\big)\leq \kappa$, hence $|T_1'-M|\leq 26C_0+8K+\kappa$. Then by the triangular inequality:
\begin{align*}
d_{\mathcal{H},N}\Big( \alpha(T_1), V(M-\kappa)\Big)\leq &d_{\mathcal{H},N}\Big( \alpha(T_1), V(T_1')\Big)+d_{\mathcal{H},N}\Big( V(T_1'), V(M-\kappa)\Big)
\\\leq& \kappa +26C_0+8K+\kappa + \kappa=26C_0+8K+3 \kappa
\end{align*}
Let us denote $\kappa':=26C_0+8K+3 \kappa\geq\kappa$ and $T_2:=M-\kappa$. Hence $\alpha:[T_1;+\infty[\to\mathcal{H}$ is in the $\kappa'$-neighbourhood of a vertical geodesic ray $V:[T_2:+\infty[\to\mathcal{H}$, we have $d_{\mathcal{H},N}\big(\alpha(T_1),V(T_2)\big)\leq\kappa'$ and $\kappa'$ depends only on $\delta$ and $K$.
\end{proof}
\begin{lemma}\label{RayChangesOnce}
Let $N$ be an admissible norm and let $\alpha:\mathbb{R}^+\to\mathcal{H}$ be a geodesic ray of $(\mathcal{H},d_{\mathcal{H},N})$. Then $\alpha$ changes its $17C_0$-coarse monotonicity at most once.
\end{lemma}
\begin{proof}
Let $\alpha:\mathbb{R}^+\to\mathcal{H}$ be a geodesic ray. Thanks to Lemma \ref{ShapeCoarsMonotGeodHoroPoduct} $\alpha$ changes at most twice of $17C_0$-coarse monotonicity. Indeed, assume it changes three times, applying Lemma \ref{ShapeCoarsMonotGeodHoroPoduct} on the geodesic segment which includes these three times provides a contradiction. We will show in the following that it actually only changes once.
\\\hspace*{0.6cm}Assume $\alpha$ changes twice of $17C_0$-coarse monotonicity. Then $\alpha$ must be first $17C_0$-coarsely increasing or $17C_0$-coarsely decreasing. We assume without loss of generality that $\alpha$ is first $17C_0$-coarsely decreasing. Then there exist $t_1,t_2,t_3\in\mathbb{R}$ such that $\alpha$ is $17C_0$-coarsely decreasing on $[\alpha(t_1),\alpha(t_2)]$ then $17C_0$-coarsely increasing on $[\alpha(t_2),\alpha(t_3)]$ then $17C_0$-coarsely decreasing on $[\alpha(t_3),\alpha(+\infty)[$.
Hence Lemma \ref{LemCoarsClosVert} applied on $[\alpha(t_3),\alpha(+\infty)[$ implies that there exists $\kappa>0$ depending only on $\delta$ (since the constant of coarse monotonicity depends only on $\delta$) and a vertical geodesic ray $V=(V_p,V_q)$ such that $[\alpha(t_3),\alpha(+\infty)[$ is in the $\kappa$-neighbourhood of $V$.
Since $h^+([\alpha(t_3),\alpha(+\infty)[)<+\infty$, we have that $\lim\limits_{t\rightarrow +\infty}h(\alpha(t))=-\infty$, hence there exists $t_4\geq t_3$ such that $h(\alpha(t_4))\leq h(\alpha(t_1))-7C_0$. Then Lemma \ref{ShapeCoarsMonotGeodHoroPoduct} tells us that $\alpha$ is first $17C_0$-coarsely increasing, which contradicts what we assumed.
\end{proof}
We have classified the possible shapes of geodesic rays. Since geodesics lines are two geodesic rays glued together, we will be able to classify their shapes too.
\begin{defn}\label{DefHpTypeHqType}
Let $N$ be an admissible norm and let $\alpha=(\alpha_p,\alpha_q):\mathbb{R}\rightarrow \mathcal{H}$ be a path of $(\mathcal{H},d_{\mathcal{H},N})$. Let $\kappa\geq 0$.
\begin{enumerate}
\item $\alpha$ is called $H_p$-type at scale $\kappa$ if and only if:
\begin{enumerate}
\item $\alpha_p$ is in a $\kappa$-neighbourhood of a geodesic of $H_p$
\item $\alpha_q$ is in a $\kappa$-neighbourhood of a vertical geodesic of $H_q$.
\end{enumerate}
\item $\alpha$ is called $H_q$-type at scale $\kappa$ if and only if:
\begin{enumerate}
\item $\alpha_q$ is in a $\kappa$-neighbourhood of a geodesic of $H_q$
\item $\alpha_p$ is in a $\kappa$-neighbourhood of a vertical geodesic of $H_p$.
\end{enumerate}
\end{enumerate}
\end{defn}
The $H_p$-type paths follow geodesics of $H_p$, meaning that they are close to a geodesic in a copy of $H_p$ inside $\mathcal{H}$. The $H_q$-type paths follow geodesics of $H_q$.
\begin{figure}
\begin{center}
\includegraphics[scale=0.3]{FinalThm.pdf}
\captionof{figure}{Different type of geodesics in $\mathcal{H}=H_p\bowtie H_q$.}
\label{FinalThm}
\end{center}
\end{figure}
\begin{rem}
In a horospherical product, being close to a vertical geodesic is equivalent to be both $H_p$-type and $H_q$-type.
\end{rem}
\begin{thm}\label{THMB}
Let $N$ be an admissible norm. There exists $\kappa\geq 0$ depending only on $\delta$ and $N$ such that for any $\alpha:\mathbb{R}\rightarrow \mathcal{H}$ geodesic of $(\mathcal{H},d_{\mathcal{H},N})$ at least one of the two following statements holds.
\begin{enumerate}
\item $\alpha$ is a $H_p$-type geodesic at scale $\kappa$ of $(\mathcal{H},d_{\mathcal{H},N})$
\item $\alpha$ is a $H_q$-type geodesic at scale $\kappa$ of $(\mathcal{H},d_{\mathcal{H},N})$
\end{enumerate}
\end{thm}
\begin{proof}
It follows from Lemma \ref{RayChangesOnce} that $\alpha$ changes its coarse monotonicity at most once. Otherwise there would exist a geodesic ray included in $\alpha$ that changes at least two times of coarse monotonicity. We cut $\alpha$ in two coarsely monotone geodesic rays $\alpha_1:[0,+\infty[\rightarrow \mathcal{H}$ and $\alpha_2:[0,+\infty[\rightarrow \mathcal{H}$ such that up to a parametrization $\alpha_1(0)=\alpha_2(0)$ and $\alpha_1\cup\alpha_2=\alpha$.
By Lemma \ref{LemCoarsClosVert} there exists $\kappa_1$ and $\kappa_2$ depending only on $\delta$ such that $\alpha_1$ is in the $\kappa_1$-neighbourhood of a vertical geodesic ray $V_1=(V_{1,p},V_{1,q}):[0;+\infty[\to \mathcal{H}$ and such that $\alpha_2$ is in the $\kappa_2$-neighbourhood of a vertical geodesic ray $V_2=(V_{2,p},V_{2,q}):[0;+\infty[\to \mathcal{H}$. This lemma also gives us $d_{\mathcal{H},N}\big(\alpha_1(0),V_1(0)\big)\leq\kappa_1$ and $d_{\mathcal{H},N}\big(\alpha_2(0),V_2(0)\big)\leq\kappa_2$.
\\Assume that $\lim\limits_{t\rightarrow +\infty}h(V_{1,p}(t))=\lim\limits_{t\rightarrow +\infty}h(V_{2,p}(t))=+\infty$, then they are both vertical rays hence are close to a common vertical geodesic ray. Furthermore $\lim\limits_{t\rightarrow +\infty}h(V_{1,q}(t))=\lim\limits_{t\rightarrow +\infty}h(V_{2,q}(t))=-\infty$ in that case. Let $W_q$ be the non continuous path of $H_q$ defined as follows.
\begin{equation}
W_q(t) =
\left\{
\begin{array}{ll}
V_{1,q}(-t) & \forall t\in ]-\infty;0]\\
V_{2,q}(t) & \forall t\in ]0;+\infty[\\
\end{array}
\right.\nonumber
\end{equation}
We now prove that $W_q:\mathbb{R}\to H_q$ is a quasigeodesic of $H_q$. Let $t_1$ and $t_2$ be two real numbers. Since $V_{1,q}$ and $V_{2,q}$ are geodesics, $d_{H_q}(W_q(t_1),W_q(t_2))=|t_1-t_2|$ if $t_1$ and $t_2$ are both non positive or both positive. Thereby we can assume without loss of generality that $t_1$ is non positive and that $t_2$ is positive. We also assume without loss of generality that $|t_1|\geq|t_2|$. The quasi-isometric upper bound is given by:
\begin{align*}
d_{H_q}\big(W_q(t_1),W_q(t_2)\big)&=d_{H_q}\big(V_{1,q}(-t_1),V_{2,q}(t_2)\big)\nonumber
\\&\leq d_{H_q}\big(V_{1,q}(-t_1),V_{1,q}(0)\big)+d_{H_q}\big(V_{1,q}(0),V_{2,q}(0)\big)+d_{H_q}\big(V_{2,q}(0),V_{2,q}(t_2)\big)\nonumber
\\&\leq |t_1|+\kappa_1+\kappa_2+|t_2|
\\&\leq |t_1-t_2|+\kappa_1+\kappa_2,\text{ since }t_1\text{ and }t_2\text{ have different signs.}
\end{align*}
It remains to prove the lower bound of the quasi-geodesic definition on $W_q$.
\begin{align}
d_{H_q}\big(W_q(t_1),W_q(t_2)\big)&=d_{H_q}\big(V_{1,q}(-t_1),V_{2,q}(t_2)\big)\nonumber
\\&\geq \frac{1}{2C_N}d_{\mathcal{H},N}\big(V_1(-t_1),V_2(t_2)\big)-d_{H_p}\big(V_{1,p}(-t_1),V_{2,p}(t_2)\big)\nonumber
\\&\geq \frac{1}{2C_N}d_{\mathcal{H},N}\big(\alpha(t_1),\alpha(t_2)\big)-\frac{\kappa_1+\kappa_2}{C_N}-d_{H_p}\big(V_{1,p}(-t_1),V_{2,p}(t_2)\big).\label{lala2}
\end{align}
The Busemann assumption on $H_p$ provides us with:
\begin{align*}
d_{H_p}\big(V_{1,p}(-t_1),V_{2,p}(-t_1)\big)\leq d_{H_p}\big(V_{1,p}(0),V_{2,p}(0)\big)\leq\kappa_1+\kappa_2.
\end{align*}
Since $\alpha$ is a geodesic and by using the triangular inequality on (\ref{lala2}) we have:
\begin{align*}
d_{H_q}\big(W_q(t_1),W_q(t_2)\big)&\geq \frac{|t_1-t_2|}{2C_N}-d_{H_p}\big(V_{1,p}(-t_1),V_{2,p}(-t_1)\big)-d_{H_p}\big(V_{2,p}(-t_1),V_{2,p}(t_2)\big)-\frac{\kappa_1+\kappa_2}{C_N}
\\&\geq \frac{|t_1-t_2|}{2C_N}-\Delta h\big(V_{2,q}(-t_1),V_{2,q}(t_2\big)-\left(\frac{1}{C_N}+1\right)(\kappa_1+\kappa_2).
\end{align*}
Assume that $\Delta h\big(V_{2,q}(-t_1),V_{2,q}(t_2)\big)\leq \frac{|t_1-t_2|}{4C_N}$, then:
$$d_{H_q}\big(W_q(t_1),W_q(t_2)\big)\geq \frac{|t_1-t_2|}{4C_N}-\left(\frac{1}{C_N}+1\right)(\kappa_1+\kappa_2).$$
Hence $W_q$ is a $\left(\frac{1}{4C_N},\left(\frac{1}{C_N}+1\right)(\kappa_1+\kappa_2)\right)$ quasi-geodesic, which was the remaining case. Since $\kappa_1$ and $\kappa_2$ depend only on $\delta$ and $N$, there exists a constant $\kappa'$ depending only on $\delta$ and $N$ such that $V_{1,q}\cup V_{2,q}$ is in the $\kappa'$-neighbourhood of a geodesic of $H_q$. The geodesic $\alpha$ is a $H_q$-type geodesic in this case.
\\ Assume $\lim\limits_{t\rightarrow +\infty}h(V_{1,p}(t))=\lim\limits_{t\rightarrow +\infty}h(V_{2,p}(t))=-\infty$, we prove similarly that $\alpha$ is a $H_p$-type geodesic.
\end{proof}
If a geodesic is both $H_p$-type at scale $\kappa$ and $H_q$-type at scale $\kappa$, then it is in a $\kappa$-neighbourhood of a vertical geodesic of $\mathcal{H}$.
\subsection{Visual boundary of $\mathcal{H}$}
We will now look at the visual boundary of our horospherical products. This notion is described for the SOL geometry in the work of Troyanov \cite[Troyanov]{Troya} through the objects called geodesic horizons. We extend one of the definitions presented in page 4 of \cite[Troyanov]{Troya} for horospherical products.
\begin{defn}
Two geodesic of a metric space $X$ are called asymptotically equivalent if they are at finite Hausdorff distance from each other.
\end{defn}
\begin{defn}
Let $X$ be a metric space and let $o$ be a base point of $X$. The visual boundary of $X$ is the set of asymptotic equivalence classes of geodesic rays $\alpha:\mathbb{R^+}\rightarrow $ such that $\alpha(0)=o$. It is denoted $\partial_o X$.
\end{defn}
We will use a result of \cite[Papadopoulos]{Papa} to describe the visual boundary of horospherical products.
\begin{propr}[Property $10.1.7$ p.234 of \cite{Papa}]\label{PropertyPapadoRayStartPoint}
Let $X$ be a proper Busemann space, let $q$ be a point in $X$ and let $r:[0,+\infty[\to X$ be a geodesic ray. Then, there exists a unique geodesic ray $r'$ starting at $q$ that is asymptotic to $r$.
\end{propr}
\begin{thm}\label{THMC}
Let $N$ be an admissible norm. We fix base points and directions $(w_{p},a_p)\in H_p\times\partial H_p$, $(w_{q},a_q)\in H_q\times\partial H_q$. Let $\mathcal{H}=H_p\bowtie H_q$ be the horospherical product with respect to $(w_{p},a_p)$ and $(w_{q},a_q)$. Then the visual boundary of $(\mathcal{H},d_{\mathcal{H},N})$ with respect to a base point $o=(o_p,o_q)$ is given by:
\begin{align*}
\partial_o \mathcal{H}=&\Big(\big(\partial H_p\setminus \lbrace a_p\rbrace\big)\times\lbrace a_q\rbrace\Big)\bigcup\Big(\lbrace a_p\rbrace\times\big(\partial H_q\setminus \lbrace a_q\rbrace\big) \Big)
\\=&\Big(\big(\partial H_p\times\lbrace a_q\rbrace\big)\bigcup\big(\lbrace a_p\rbrace\times\partial H_q\big)\Big)\setminus \lbrace(a_p,a_q)\rbrace
\end{align*}
\end{thm}
The fact that $(a_p,a_q)$ is not allowed as a direction in $\mathcal{H}$ is understandable since both heights in $H_p$ and $H_q$ would tend to $+\infty$, which is impossible by the definition of $\mathcal{H}$.
\begin{proof}
Let $\alpha$ be a geodesic ray. Lemma \ref{RayChangesOnce} implies that there exists $t_0\in\mathbb{R}$ such that $\alpha$ is coarsely monotone on $[t_0,+\infty[$. Then Lemma \ref{LemCoarsClosVert} tells us that $\alpha([t_0,+\infty[)$ is at finite Hausdorff distance from a vertical geodesic ray $V=(V_p,V_q)$, hence $\alpha$ is also at finite Hausdorff distance from $V$. Since $H_p$ is Busemann and proper, Property \ref{PropertyPapadoRayStartPoint} ensure us there exists $V_p'$ a vertical geodesic ray such that $V_p$ and $V_p'$ are at finite Hausdorff distance with $V_p'(0)=o_{p}$. Similarly, there exists $V_q'$ a vertical geodesic ray of $H_q$ with $V_q'(0)=o_q$ such that $V_q$ and $V_q'$ are at finite Hausdorff distance. Since there is at least one vertical geodesic ray $V'=(V_q',V_p')$ in every asymptotic equivalence class of geodesic rays, $\partial_o \mathcal{H}$ is the set of asymptotic equivalence classes of vertical geodesic rays starting at $o$. Hence an asymptotic equivalence class can be identified by the couple of directions of a vertical geodesic ray. Then $\partial_o \mathcal{H}$ can be identified to:
\begin{equation}
\Big(\big(\partial H_p\setminus \lbrace a_p\rbrace\big)\times\lbrace a_q\rbrace\Big)\bigcup\Big(\lbrace a_p\rbrace\times\big(\partial H_q\setminus \lbrace a_q\rbrace\big) \Big).\nonumber
\end{equation}
the union between downward directions and upward directions, which proves the theorem.
\end{proof}
\begin{example}
In the case of SOL, $H_p$ and $H_q$ are hyperbolic planes $\mathbb{H}_2$, hence their boundaries are $\partial H_p =\partial\mathbb{H}_2=S^1$ and $\partial H_q =S^1$. Then $\partial_o SOL$ can be identified to the following set:
\begin{equation}
\big(S^1\setminus \lbrace a_p\rbrace\big)\times\lbrace a_q\rbrace\bigcup\lbrace a_p\rbrace\times\big(S^1\setminus \lbrace a_q\rbrace\big) .
\end{equation}
It can be seen as two lines at infinity, one upward $\lbrace a_p\rbrace\times\big(S^1\setminus \lbrace a_q\rbrace\big)$ and the other one downward $\big(S^1\setminus \lbrace a_p\rbrace\big)\times\lbrace a_q\rbrace$ .
\end{example}
It is similar to Proposition 6.4 of \cite[Troyanov]{Troya}, however it is not the same result.
\\\\A possible way of generalising Theorems \ref{THMA}, \ref{THMB} and \ref{THMC} is looking at what happens when the Busemann hypothesis of our components $H_p$ and $H_q$ is removed. However in that case it is already unclear how to make a relevant definition for the horospherical product.
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 6,434
|
Q: Using expex across pages I am using the expex package to align two types of text, doing it as if it were a gloss, and it works fine. There is one problem, though: Many of the texts I'm working on are longer than a page, and instead of continuing on the next one, which would be desirable, they violate the lower margin, into oblivion. I could just split the text across more than one gloss, but that really is a pain because it forces me to take the appearance and not the logical structure of the document into account. Also, any changes to other aspects of my document's layout force me to reorganize what text goes into what gloss every time.
To sum it all up: I would like to be able to span one gloss across pages using expex. Is there a way of doing this?
A: I just ran across your question. You should have listened to Alan Munn and posted to the Ling-Tex list.
At present, glosses don't break. But I think perhaps there is no really strong reason for this. If you still need this feature, I might be able to add an option to the ExPex package to allow page breaking at the cost of controlling the width of the gloss. It actually seems to be a good idea.
You can communicate with me directly at j dot frampton at neu dot edu. I don't get by this website very often.
A: I don't think there is any way to do this. For this particular question you might have more luck posting on the Ling-TeX mailing list. John Frampton is on that list and very responsive to questions about ExPex.
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 4,029
|
Build Your Own Wind Turbine
Irish site for home built wind turbines
The Turbines
Wind speed Conversion table
Posted on January 28, 2010 by office
Debate Continues over Controversial Wind Farm Noise Regulations
The debate over government regulations for wind turbines noise should be based more on engineering issues
and robust scientific evidence and less on politics, according to UK professional body, Institute Of
Acoustics.
There has been criticism of the regulations, known officially as 'ETSU-R-97', as being outdated and in need
of revision, given they are more than a decade old and are still being used to assess wind farm noise in
local government planning applications in the UK. Opponents variously describe the guidelines as "daft",
"confusing" and designed for much smaller wind turbines than can now be built.
The IOA, which has more than 3000 members in the fields of acoustics, noise and vibration worldwide, hosted
a Wind Turbine Noise meeting in Cardiff on January 27, with experts referring to the controversial
President-elect of the IOA, Trevor Cox, said "it might surprise people to know that the number of complaints
about wind farm noise is actually rather small – maybe evidence that ETSU isn't working too badly at the
moment".
"Most, if not all, regulations have some imperfections because they are necessarily drawn up with the
available data at the time. ETSU is no different; it it was being drawn up today, the chances are that
slightly different procedures or criteria might be used. But are substantial changes needed? That is what
the meeting in Cardiff will try to find out."
Trevor, who is Professor of Acoustic Engineering at the University of Salford, referred to a presentation at
the the IOA's recent international Euronoise conference in Edinburgh.
That paper compared the number of people highly annoyed by road traffic noise in the Netherlands to the
number of people likely to be highly annoyed by wind farm noise, if all proposed wind farms for this country
were to be built.
"For every person who might be annoyed by wind farms, there are hundreds more annoyed by roads," he said.
"We mustn't forget the potential political ramifications if a decision is made to revise the ETSU
guidelines. Undermining the noise regulations is a useful tactic for campaigners who are trying to stop
planning permission being granted. A revision of the guidelines could be used by campaigners to cast doubt
in the minds of planners."
The IOA would consider recommendations from experts at the Wind Turbine Noise meeting.
Trevor said that the organisation would "like to see the politics taken out of ETSU so that proper
engineering decisions can be made on the best possible scientific evidence".
In future, the IOA may call for more research into Aerodynamic Modulation (AM) – the 'swishing' noise made
by turbine blades, he said.
"Although complaints due to AM are rare, there are a small number of high profile cases where it has
happened and caused significant problems to a small number of people.
"Currently the causes and treatment of the problem need further research."
Source British Institute of Acoustics
The debate over British government regulations for wind turbines noise should be based more on engineering issues and robust scientific evidence and less on politics, according to UK professional body, Institute Of Acoustics.
There has been criticism of the regulations, known officially as 'ETSU-R-97', as being outdated and in need of revision, given they are more than a decade old and are still being used to assess wind farm noise in local government planning applications in the UK. Opponents variously describe the guidelines as "daft", "confusing" and designed for much smaller wind turbines than can now be built.
The IOA, which has more than 3000 members in the fields of acoustics, noise and vibration worldwide, hosted a Wind Turbine Noise meeting in Cardiff on January 27, with experts referring to the controversial regulations.
President-elect of the IOA, Trevor Cox, said "it might surprise people to know that the number of complaints about wind farm noise is actually rather small – maybe evidence that ETSU isn't working too badly at the moment". "Most, if not all, regulations have some imperfections because they are necessarily drawn up with the available data at the time. ETSU is no different; it it was being drawn up today, the chances are that slightly different procedures or criteria might be used. But are substantial changes needed? That is what the meeting in Cardiff will try to find out."
Trevor, who is Professor of Acoustic Engineering at the University of Salford, referred to a presentation at the the IOA's recent international Euronoise conference in Edinburgh.
That paper compared the number of people highly annoyed by road traffic noise in the Netherlands to the number of people likely to be highly annoyed by wind farm noise, if all proposed wind farms for this country were to be built. "For every person who might be annoyed by wind farms, there are hundreds more annoyed by roads," he said. "We mustn't forget the potential political ramifications if a decision is made to revise the ETSU guidelines. Undermining the noise regulations is a useful tactic for campaigners who are trying to stop planning permission being granted. A revision of the guidelines could be used by campaigners to cast doubt in the minds of planners."
The IOA would consider recommendations from experts at the Wind Turbine Noise meeting. Trevor said that the organisation would "like to see the politics taken out of ETSU so that proper engineering decisions can be made on the best possible scientific evidence". In future, the IOA may call for more research into Aerodynamic Modulation (AM) – the 'swishing' noise made by turbine blades, he said. "Although complaints due to AM are rare, there are a small number of high profile cases where it has happened and caused significant problems to a small number of people.
CategoriesNews, Uncategorized Tagswind turbines noise
Previous PostPrevious American Researcher Blames Wind Turbine Noise on Vibration
Next PostNext Energy from osmosis
If you would like to host a workshop contact us here
Take part in a workshop
If you would like to learn how to build a wind turbine contact us here
Archives Select Month September 2019 July 2019 November 2017 February 2017 June 2016 February 2016 November 2014 July 2014 June 2014 January 2014 December 2013 September 2013 August 2013 February 2013 January 2013 December 2012 July 2012 June 2012 May 2012 April 2012 March 2012 January 2012 December 2011 November 2011 October 2011 September 2011 May 2011 April 2011 March 2011 February 2011 December 2010 October 2010 September 2010 August 2010 May 2010 March 2010 February 2010 January 2010 September 2009 March 2009 February 2009 November 2008 October 2008 September 2008
Powered by Eirbyte
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 4,043
|
require 'test_helper'
class UserTest < ActiveSupport::TestCase
test "get boxes for user" do
assert_equal 2, users(:one).boxes.count
end
end
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 4,518
|
The Sunday reader
By Brett Ballah on February 3, 2019
A weekly roundup of Canadian aviation news
Calgary International Airport reported record traffic in 2018.
It seems Canadians can't get enough of flying.
In case there wasn't already enough evidence, airports continued to report that it was a banner year for aviation in Canada.
Calgary, Montreal and Halifax were the latest airports this week to report record traffic in 2018. And the growth is coming in all sectors – across Canada, to the United States, and overseas. Scroll down to see airport passenger numbers across Canada.
Ultra low-cost carriers claim some of the credit for the increased traffic by lowering airfares and enticing more people to fly.
On Friday Swoop celebrated the sale of its first ticket one year ago – on a flight between Hamilton and Abbotsford, British Columbia. Still, they fly limited routes, and millions of Canadians are wondering when they might be included in ULCC plans.
Takin' a stroll down memory lane! It's been 365 days since we sold our very first seat and we have countless more to look forward to. Here's a swoop back over the past year … #FlySwoop pic.twitter.com/8WEDdZqlzM
— FlySwoop (@FlySwoop) February 1, 2019
Get every story delivered straight to your inbox. Free!
All that growth comes with a dark side.
The Transportation Safety Board issued its report on runway incursions at Toronto Pearson International Airport. As Canada's busiest airport, it's logical that Pearson have the greatest number of incursions. But the airport and airlines aren't helping themselves.
The TSB concentrated on a particular set of parallel runways at the south end of YYZ, 06R/24L and 06L/24R, and found 27 incursions over a five year period. Incursions happen when a plane or vehicle are on a runway when they shouldn't be. In the worst cases, planes collide, and people die.
The TSB found that procedures required pilots to conduct arrival checklists as they approached the adjacent runway, depriving them of vital visual cues, communications weren't clear, and the runway layout contributed to the confusion.
It released the following video to show what pilots see out the front as they land on runway 24L at Pearson and have to cross 24R to get to the terminal. Notice in particular how the adjacent runway appears after a sharp right turn.
Source: Transportation Safety Board
While the TSB recommended changes to procedures and communications to make things clearer, its most expensive idea would see the Greater Toronto Airport Authority alter taxiways to make the setup safer. Intriguingly, in its response to the TSB report, the GTAA did not commit to making any changes.
This week, we'll start to get a picture of the aviation industry's financial health. Westjet, which this summer reported its first quarterly loss in 13 years, will report its 2018 results on Tuesday. Air Canada will follow the next week. It will be interesting to watch the two as they compete for premium customers on overseas routes.
Enjoy the Super Bowl, featuring the New England Patriots and Los Angeles Rams. Los Angeles World Airport handled more than 87.5 million passengers in 2018 at a facility that covers 3,500 acres. Boston-Logan International 38.4 million passengers in 2017 at a facility that covers 1,700 acres. When you do the math, the airports handled roughly the same number of passengers per acre! Hope they're as closely matched on the field.
2018 passengers
Abbotsford, B.C. 842,212* 1,008,176*
Calgary 17,343,402* 17,957,780*
Charlottetown, P.E.I. 370,730* 383,183*
Edmonton 8,254,212* 8,151,532
Fredericton, N.B. 423,234* 427,085*
Halifax 4,316,079* 4,188,443
Hamilton 725,630
Kamloops, B.C. 351,631 361,586*
Kelowna, B.C. 2,080,372* 2,032,144
Moncton, N.B. 681,473* 674,406
Montreal-Trudeau 19,425,588* 20,305,106*
Nanaimo, B.C. 435,394
Ottawa 5,111,801* 5,106,487
Prince George, B.C. 506,486
Quebec City 1,774,841*
Saskatoon 1,518,980* 1,490,000 (est.)
Thunder Bay 869,404*
Toronto-Pearson 49,507,418* 50,499,431*
Vancouver 25,936,907* 26,395,197*
Victoria 2,048,627* 1,924,385
Winnipeg 4,500,000* (estimate) 4,500,000 (est.)
* – record (sources: airport reports)
Tagged as: Air Canada, canada, Flair, flying, industry, Swoop, Ultra low-cost, Westjet
As Swoop marks milestone, some Canadians wonder when they'll be invited to the ULCC party
Routes conference: airports prepare their pitches for new service
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 1,432
|
var crypto = require('crypto'),
fs = require('fs'),
path = require('path'),
config = require('../../config'),
urlService = require('../../services/url');
// ### servePublicFile Middleware
// Handles requests to robots.txt and favicon.ico (and caches them)
function servePublicFile(file, type, maxAge) {
var content,
publicFilePath = config.get('paths').publicFilePath,
filePath,
blogRegex = /(\{\{blog-url\}\})/g,
apiRegex = /(\{\{api-url\}\})/g;
filePath = file.match(/^public/) ? path.join(publicFilePath, file.replace(/^public/, '')) : path.join(publicFilePath, file);
return function servePublicFile(req, res, next) {
if (req.path === '/' + file) {
if (content) {
res.writeHead(200, content.headers);
res.end(content.body);
} else {
fs.readFile(filePath, function readFile(err, buf) {
if (err) {
return next(err);
}
if (type === 'text/xsl' || type === 'text/plain' || type === 'application/javascript') {
buf = buf.toString().replace(blogRegex, urlService.utils.urlFor('home', true).replace(/\/$/, ''));
buf = buf.toString().replace(apiRegex, urlService.utils.urlFor('api', {cors: true}, true));
}
content = {
headers: {
'Content-Type': type,
'Content-Length': buf.length,
ETag: '"' + crypto.createHash('md5').update(buf, 'utf8').digest('hex') + '"',
'Cache-Control': 'public, max-age=' + maxAge
},
body: buf
};
res.writeHead(200, content.headers);
res.end(content.body);
});
}
} else {
return next();
}
};
}
module.exports = servePublicFile;
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 6,689
|
Parque das Nações é um pequeno bairro da cidade brasileira de Goiânia, localizado na região norte do município.
O bairro localiza-se à margem direita da Avenida Nerópolis e possui uma pequena extensão. É um dos bairros de Goiânia que não conta com pavimentação asfáltica. Segundo dados do Instituto Brasileiro de Geografia e Estatística (IBGE), divulgados pela prefeitura, no Censo 2010 a população do Parque das Nações era de pessoas.
Bairros de Goiânia
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 6,388
|
Top: Daniel Cartier; Bottom: ABBA, Barry Manilow, and Dan Fogelberg.
Every year, I try to bring in the New Year with great music. Daniel Cartier's cover of Auld Lang Syne is haunting and beautiful. The song, a traditional greeting of the new year, is based on a poem written by Robert Burns in 1788. That poem was set to a traditional Scottish melody, and the song was born. Daniel Cartier recorded it, and I just love it.
It seems like I would not be able to bypass the 1980 song from super-group Abba, Happy New Year. It was written by the "B's", Benny Andersson and Björn Ulvaeus. They, along with Agnetha Fältskog and Anni-Frid Lyngstad, make up all the letters in ABBA.
And how about the 1977 song from Pop Maestro Barry Manilow? It's Just Another New Year's Eve was a poignant song released in between the uplifting songs Can't Smile Without You and Daybreak. It was based on a melody from Johann Sebastian Bach's Goldberg Variations.
In 1980, singer/songwriter Dan Fogelberg released Same Old Lang Syne. It was later put on the album The Innocent Age. Like the best of Fogelberg's work, it told a story we could all relate to. It went to #9 on the Billboard Hot 100. It remains a favorite holdiay song for many, 30-some years later.
Here's wishing us all prosperity and lots of love in 2012!
Labels: abba, auld lang syne, barry manilow, dan fogelberg, daniel cartier, happy new year
Great 2011 Releases
Clockwise: Hotels & Highways, Nathan Leigh Jones, Angus & Julia Stone, and Mikey Wax.
With my next to the last post in 2011, I thought I would try to show some appreciation for some of the breeders on my playlist. Look, I know you must feel like a real minority on my iTunes playlists, but you really are appreciated. I refuse to discriminate against you just because of who you sleep with. That said, there was some great music from this group, and I loved listening to that music whenever I could.
I first found out about the music of Hotels & Highways because I was a big fan of Syd's music. So when he got together with Lisa Piccirillo and Patrick Thomas, I couldn't wait to hear what came of it. When they released Lost River, I was blown away, and couldn't hear it enough. They fuse together the rootsy sound with a modern edge like few can, and made a great, complete album. Watch this video from a live performance of Train Whistle from their debut.
You can purchase Lost River from iTunes and Amazon.
I have David Raleigh to blame for my preoccupation with the music of Nathan Leigh Jones. David and the handsome Aussie are friends, and Nathan has produced some music of David's, including the beautiful That's What Friends Are For with Raleigh, Sir Ari Gold, Alan Cumming, and Billy Porter. But it was his great music that really won me over, from his 2008 EP, The Way I'm Missing You, to the newly released Sooner Or Later, I just love it all. In fact, I had to go to New York City to see Jones and Raleigh perform with my dear friend David Dust, and it was a magical night. Only recently, Nathan released the video for Beautiful You, off the latest album.
You can purchase Sooner Or Later from iTunes and Amazon.
I still remember the point when I first decided I would be a Mikey Wax fan for a long time to come. It was when I happened across his video for La Vie En Rose, looking for something to use on the blog. Well, I hit play, and developed a big crush on him, one that has not ended yet. I bought the last couple of EPs and a full album he put out, but with the release of his latest album, I was blown away. Mikey focused his energy on the music, and put out a Pop wonder called Constant Motion. I just love it, and think it should be a mandatory listen for all music lovers. Give a listen as Mikey sings Counting On You, which has recently started to get some airplay on the radio!
You can purchase Constant Motion from iTunes and Amazon.
I don't know where I've been for the last few years, but for some reason, it hasn't been on the same plane as Australian siblings Angus & Julia Stone. However, since finding them, I am completely loopy about their quirky music, and lap it up like it was pudding. I found some of their older music, and love it, just like the latest stuff. And it doesn't hurt I am totally crushing on Angus, damn, he's beautiful. They started the year with a single at the top of the Australian charts, and soon that song made it on to a commercial in the US, and I discovered my new obsession. Watch the video for Big Jet Plane off the album Down The Way.
You can purchase Down The Way from iTunes and Amazon.
Labels: angus stone, hotels and highways, julia stone, lisa piccirillo, mikey wax, nathan leigh jones, patrick thomas, syd
Even More Great Singles from 2011
Clockwise: Anthony Callea, Brendan MacLean, David Raleigh, and Wes Carr.
In my final look at the singles from 2011, I couldn't resist checking out my friends Down Under. This group is made up of 3 Australians, and one American who splits his time between New York and Australia. The group is made up of three very sexy out gay men, and one very handsome straight rocker. All are talented musicians who made my life just a little bit nicer when I heard their songs.
I have been a fan of Anthony Callea ever since the first time I heard that amazing voice of his. I have run out of adjectives to adequately describe it, so suffice it to say I listen to it whenever I can. So, you can imagine my joy when he released a new single this year, Oh Oh Oh Oh. It is a dance tune, filled with vibrance and joy, and I still can't get enough of it. Watch the amazing video for Oh Oh Oh Oh.
You can purchase Oh Oh Oh Oh on iTunes and Amazon. You can also purchase the video on iTunes.
I was directed to listen to the music of Brendan MacLean by another musician, David Raleigh. As I have mentioned before, when I get a recommendation from another musician, I will listen. And this is yet another time I am grateful to Raleigh, for I love Brendan's music, with it's humor and zest. Watch his video for Cold And Happy from the White Canvas EP.
You can purchase the White Canvas EP on iTunes.
Wes Carr is another artist who captivated me the first time I heard his voice. And he is more than just the token straight man... I find his singing to be original and strong, just a joy to hear. Like Callea, I have ordered Carr's album's to be imported, since I just had to have them. This year, while I waited for a new album to come out, I was so pleased to discover he had a new single. Check out the new video for Been A Long Time.
You can purchase the Been A Long Time video on iTunes.
I just love David Raleigh pm just so many levels, and the first is the great music he makes. His piano-driven songs are just so melodic, so beautiful. And then there is that smile of his, it could light up all of Manhattan. And that is where he lives when he is not in Australia. While he released his great Beginning Again album in 2010, the latest single only recently premiered with a strong music video. Watch as he sings One Together.
You can purchase Beginning Again off iTunes and Amazon.
Labels: anthony callea, brendan maclean, david raleigh, wes carr
Great Albums of 2011
Clockwise: Casey Stratton, Gregory Douglass, Chadwick, and Justin Utley.
You'd think with all the posts so far, how could there still be great music that was released in 2011? It is easy, you just listen to the music by the four outstanding men above, how put out wonderful music whenever they sit with a microphone. And, if I am not mistaken, they are all out and proud men who also happen to look very good in their pictures...
That is certainly true for Casey Stratton, who has been making great music since he was quite young, releasing his first EP, Driving To The Moon, in 1995. This year he released two albums, Hear The City and The Vigil. The latter was a response to the loss of his beloved pet, Henry, and it is just beautiful. The former, Hear The City, is a wonderful and so evocative.
<a href="http://store.caseystratton.com/album/hear-the-city">Hear the City by Casey Stratton</a>
I swear that Casey writes his music so that it is addictive, and I must have it all. You can purchase Hear The City at Casey's online store, iTunes or Amazon.
Another man whose music is just totally irresistible to me is Vermont's own Gregory Douglass. It still annoys me I have yet to be able to see him perform live, but hope I get to rectify that very soon. His latest album, Lucid, is a moody and vital work, with honesty pouring off it. I am particularly fond of the song Dream Come True. In the video below Gregory sings Lucid from the latest release.
You can purchase Lucid at Gregory's online store, iTunes, or Amazon.
Well, once you get past Justin Utley's Hulk-like build and dashing good looks, you get to know that he is also a talented singer/songwriter. His vivid and uplifting music touches me so, and let's me know he has lived a life that has not always been easy, but will always be a path for growth. The former-Mormon sings from the heart, and that can't be missed. Watch as he sings Stand For Something from Nothing This Real.
You can purchase Nothing This Real at Justin's online store, iTunes, or Amazon.
I happened across the music of Chadwick while working on this blog, and can't believe I hadn't heard his amazing voice before. The crispness of his tone is amazing, and how he manages to use it while singing great songs is impressive. His latest album, Live & Unplugged, shows off that voice, allowing it to tell the story with simple instrumentation. Watch as he sings What About Love from Live & Unplugged. The song was written by Brian Allen, Sheron Alton, and Jim Vallance and originally performed by the legendary rock band, Heart.
You can purchase Live & Unplugged on iTunes or Amazon.
Labels: casey stratton, chadwick johnson, gregory douglass, justin utley, lucid
Last Friday Night of 2011
Clockwise: Elephant, Jimmy Somerville, The Young Professionals, and Sir Ari Gold.
As it is the last Friday night of 2011, I thought I would end it with a review of some great party/dance music from the year to date. And some very hot gay men, too. Well, that is just a very nice bonus point, at least for me. And, as you will be able to hear for yourself, some of my favorite dance music comes in all kinds, from Punky Hip-Hop to Neo-Disco to Euro-beats.
I will start off with one of my favorite tracks from the homo-twins, Coleman and Jackson Vrana, with their biting social commentary set to their own brand of Hop-Hop that sounds more Punk than Pop. Using the group name Elephant, the twins assault the listeners with strong language, hard beats, and bold ideas on the four songs off their debut. Take, for example, their video for the song Notorious H.I.V. off the Queer Nation EP. Being a Friday night post, I just think I will mention this is not safe for work, but great for everywhere else.
You can purchase the Queer Nation EP on iTunes and Amazon.
I have made no attempt to hide my complete infatuation with Ivri Lider and his music. I tell you, if I were to ever meet him, I fear I would embarrass myself, and ask him to marry me or something along those lines. Well, that aside, I was eagerly awaiting his first English-language album, which still has yet to hit the stores. However, we were treated to a release by The Young Professionals, an electronic duo featuring Ivri and Yonathan Goldshtein. Their first album, 9:00 to 17:00, 17:00 to Whenever, is a pure electronic pleasure, one irresistible song after another. Check out their video for the single D.I.S.C.O., and just try to not dance while you listen.
You can purchase 9:00 to 17:00, 17:00 to Whenever on iTunes and Amazon.
Not only is Sir Ari Gold unmistakably hot, he is also incredibly talented. And if you pair him with a legendary voice like Miss Sarah Dash, and you have a single that is impossible to resist. And that would give you the song Sparkle, the second single off Between The Spirit & The Flesh. That is a great album, starting with the sexy first single, Make My Body Rock. But here is the video for Sparkle.
You can purchase Between The Spirit & The Flesh on iTunes and Amazon.
And finally, a night of dancing isn't complete without a some Jimmy Somerville to shake my groove-thang to. And this year, Jimmy released the Bright Things EP, and I just had to buy it. I mean, I've been buying Jimmy's music since he was with the Bronski Beat 27 years ago, and I've been addicted to that voice since. Jimmy might have turned 50 this year, but he hasn't lost a step with that voice, and just makes me hungry for more from him. Check out Overload, off Bright Things.
You can purchase Bright Things on iTunes and Amazon.
Labels: coleman vrana, elephant, Ivri Lider, jackson vrana, Jimmy Somerville, sir ari gold, the young professionals, yonathan goldshtein
Great Club Music From 2011
Clockwise: Yovanni, Kris Searle, Cazwell, and Simulover.
When you hit the clubs in 2011, it would be surprising to NOT hear some if not all of the acts pictures above. Especially if you are hitting a LGBT club! They put out some fantastic music, an not just this year.
At the beginning of the year, Cuban-born Yovanni released his single Hello. The song, with the strong elements of Dance and Rock, showed the countless influences of the boy who grew up in Miami. After studying music, he ventured out to make his own statement. This he did. Bold, futuristic, and spicy hot are just a few of the ways you could describe the video. Watch Hello.
You can purchase Hello on iTunes and Amazon.
Earlier this year, a new release came out by Simulover. It is a duo made up of SIRPAUL and Alex Lauterstein, two talented men working in New York City. I am a huge fan of SIRPAUL's work, and had seen him live where he was assisted by the strikingly handsome DJ, Alex. So I was excited to hear the music they made together, and once it hit the internet, I was not disappointed at all. The Simulover album was great stuff, a combination of dance, electronica and industrial music that showed no limits. Check out their first video for the song Tourniquet.
You can purchase the Simulover album on iTunes and Amazon.
For the fifth consecutive year, Kris Searle has won the prestigious 21st annual Los Angeles Music Award for Best Dance Electronica Artist of the year. The British-born Kris splits his time between his home in the UK and his new adopted home in Los Angeles. Searle recently released Falling For Your Light, a great Electronic Pop song.
You can purchase Falling For Your Light on iTunes and Amazon.
It is sometimes tough to write about someone like Cazwell, who has been making great music for several years, and who is just so damned fun to watch and listen to. He recruited a bunch of hot dancers and they made some videos for songs like Ice Cream Truck and Get My Money Back off the 2010 release, Watch My Mouth. Whether it is more fun to watch the video, dance to the song, or just listen to his music on the iPod, you can decide. Cause I just can't, I love to do it all.
You can purchase Watch My Mouth on iTunes and Amazon.
Labels: alex lauterstein, cazwell, falling for your light, get my money back, hello, kris searle, simulover, sirpaul, tourniquet, yovanni
More Great Singles from 2011
Clockwise: David Geftakys, Angelo, Cassidy Haley, Darryl Stephens, and Brian Kent.
This afternoon, I will be talking about another group of talented musicians who put out fantastic singles in 2011. It was such a great year for music, and these singles are shining examples of that. These might not be songs you are hearing on Pop radio, but if I were hearing them there, I might listen to the radio more often.
I first heard of David Geftakys when David Raleigh told me I should check out his video. I always will follow the advice of musicians, for they rarely steer me wrong. Well, I hit play on YouTube, I was pretty much a goner. That first song was his single this year, Games We Play. It has so much charm, and such a great melody line, I think it is a total winner. I also downloaded a previous release, Lines In My Hand, which I also love.
You can purchase Games We Play on iTunes and Amazon.
Funny enough, I first discovered Angelo and his music when I found his "It Get's Better" video on YouTube. Hey, here is a good-looking, out and proud man, so being the curious sort, I sought out his music, and found that it was quite good! I love his most recent single, Hands Down, and I think if you give it a listen, you would love it too.
You can purchase Hands Down on iTunes and Amazon.
I discovered the music of Brian Kent through Rich Overton of RJO Artists, who has represented so many talented people, I pay attention when he is involved. Brian has put out some great music in the last few years, like Breathe Life. This year, he had a new single, and it was all kinds of fun! Watch the video directed by Mike Ruiz for Su-Su-Su-Superstar, the latest from Kent.
You can purchase Su-Su-Su-Superstar on iTunes and Amazon.
There was a bit of buzz circulating around about the music of Cassidy Haley when Adam Lambert was on American Idol. I decided to check it out, and discovered that I really love Haley's music. He has a great blend of Rock and Pop, showing off the darker side of soul. Did I forget to mention he is also gorgeous and gay? Well, he is. You can make the call for yourself when you watch his video for This Time, released earlier this year. The song is from his 2010 album, The Fool.
You can purchase This Time on iTunes and Amazon.
I first became familiar with Darryl Stephens when he played the lead in the television series and subsequent movie, Noah's Arc. I loved the show, and was also happy to see him get other work in movies, for he is quite talented. Well, sometime this year he mentioned he was about to release a song he had written, and my interest was piqued. When Envious Moon came out, I bought it, and was quite impressed, not only for his writing skills, but his singing, too. Seems Darryl has talent in many different areas, and I hope we get to see/hear his musical bent a bit more. Here is the video for Envious Moon.
You can purchase Envious Moon on iTunes.
Labels: angelo, brian kent, darryl stephens, david geftakys, envious moon, games we play, hands down
Even More Great Music from 2011
Clockwise: Toby Madigan, Chad D, EvOn, and Matt Zarley.
I am closing out the year by revisiting the great music released in it, for there has been some great music out there, especially by LGBT artists. Of course, that might not be what you hear on the radio, but if you put your ear to the ground, you might be surprised by both the quality and quantity you can discover.
I first discovered Toby Madigan when I saw the video for Chatroom Romance, and was immediately thrilled by the combination of humor and intelligence in it. So I went out and purchased the first album, and really liked it. Soon, it was time for a second release, and Symphony of Sweat was soon part of my music library. I love Toby's style, and find his songwriting to be quite good. Of course, his stunning good looks don't hurt, either. Watch as Toby sings Arrested from his latest album.
You can find Symphony of Sweat on his online store. There you can also find his first album, Left Brain/Right Brain.
Philly's own Chad D is a young rapper with a dream, and he is making his dreams come true. Part of that dream includes equality for all, something the gay man understands far too well. In his music, which is a combination of Hip-Hop and old school rapping, he tells you not what you wanna hear, but what people need to hear. Watch the video for Ask & Tell off the album The Human Link.
You can find The Human Link on iTunes and Amazon.
Well, when I first saw a picture of Matt Zarley, I have to admit my jaw dropped just a little. He is most certainly a sexy man, but those good looks did not overshadow what I quickly discovered were big talents. He can sing just about anything, and has the voice to do it well. Watch the video he made for WTF off his latest album, Change Begins With Me.
You can find Change Begins With Me on iTunes and Amazon.
EvOn calls herself The Music Bully, and I see why. The British lesbian is laying down some great music, and putting some amazing freestyle over it, taking it to the audience and the music. I am so glad I happened across her on the internet, for I am loving her music. Check out the video she made for Listen Up, a new song from earlier this year.
Check out EvOn on Bandcamp here, where you can download The Stolen Mixtape for FREE. It includes Listen Up.
Labels: arrested, ask and tell, chad d, evon, listen up, matt zarley, toby madigan, wtf
More Great Music From 2011
Clockwise: Brett Every, Christopher Dallman, Matt Alber and Declan Bennett.
Last night I started talking about the great music that was released in 2011, and today I have continued that trend. That is because there was just that much great music out there, and then some. And one of the things I love about this group, is that they are four massively talented gay men, all very different. And all are valued part of my music collection, and I would urge you to take the opportunity to add them to yours.
Since I first heard the music of Australian Brett Every, I have been a fan, and a bit enamored of his talent. He combines classic Pop with Jazz and Folk to make he sound of his very own style of storytelling entertaining and very real. I have all three of his albums, but still think his latest just might be his best. Watch and listen to the video for Man Walks Into A Bar, from the album Menu.
You can find Menu on iTunes and Amazon.
I have been a fan of Christopher Dallman since I stumbled across his debut album, Race The Light, several years ago. I thought it brilliant, and couldn't wait for a follow-up. Well, I had to wait a while, but finally there were a series of releases in 2009 and 2010, and the amazing Light The Love earlier this year. The EP contains five songs that communicate the love and beauty in Dallman's life, and I adore it. Watch as Christopher sings the title track, Light The Love, at a live show in California.
You can find Light The Love on iTunes and Amazon.
Once I found the music of Declan Bennett, I knew I was in trouble. It immediately spoke to me, whether he was recording under the name "sumladfromcov" or under his given name. From 2005's The Painter's Ball to the new release, I could, and have, listen to him all day. So when I first listened to Record: Breakup, I was not surprised I was deeply moved, and almost addicted to listening to it. Tell me what you think after watching Declan sing Freer from the album.
You can find Record: Breakup on iTunes and Amazon.
Matt Alber can, and most likely can, sing anything he would like to sing. He performed as a part of the award-winning group Chanticleer, has written and performed Country, and had a magnificent debut album of great Pop music. He co-wrote Who We Are with Tom Goss, a moving song supporting the LGBT veterans and the movement to take down Don't Ask, Don't Tell. So when it was time to pre-order his new album, I thought it was a no-brainer, and stepped up right away. And I can't tell you how glad I am, for Constant Crows is a beautiful collection, a little different from his debut. It has a little more Folk feel to it, more personal, more introspective. He wrote most of the music on it, and included one cover song. Here is a video of Matt as he sings Take A Bow, a cover of the Madonna song, from a live performance at Joe's Pub in New York City.
You can find Constant Crows on iTunes and Amazon.
Labels: brett every, Christopher Dallman, constant crows, declan bennett, freer, light the love, man walks into a bar, matt alber, menu, take a bow
Great EPs in 2011
Clockwise: Matt Doyle, Chris Riffle, Stewart Lewis, Andy Moore, and Shaun Hague.
This year several Eps were released from some great musicians. EP stood for Extended Play Single, a single with a few supplemental tracks. Now, they are more of a demi-album, a smaller collection of songs put out by an artist. It can be more affordable for all concerned - the independent artist who has to pay the costs, and the fan who can get new and fresh music at a lower cost. Take, for example, Broadway star Matt Doyle, who is an out singer/songwriter when not appearing on stage. Currently, he is featured in the New York production of War Horse. But earlier this year, he released the EP Daylight. It is a wonderful collection, beautifully written and sung. Check out this clip as he sings If Morning Can't Wait.
You can find Daylight on iTunes and Amazon.
Though he was born and raised in the Pacific Northwest, Chris Riffle now calls New York City home as he pursues his career in music. Earlier in the year, the out performer released I Am Not From Here, a strong acoustic collection of songs song from the heart. Here he sings the title track from the EP, I Am Not From Here.
You can find I Am Not From Here on iTunes and Amazon.
Stewart Lewis sings Shine from the album In Formation. Earlier this year, he released the EP Stumbling For Truth. I have seen the out singer/songwriter perform a few times, and have loved him every time. The five-song collection is filled with honesty and love, a welcome addition to any collection.
You can find Stumbling For Truth on iTunes and Amazon.
I have been fascinated with the music of Andy Moore since I saw her performing with Eric Himan many years ago. So I was quite thrilled to hear she was releasing new music, and had to buy it right away. 5 In Common is a beautiful group of songs, sung with a simplicity and beauty that is hard to match. I have the first two album from the out lesbian, and love them both. Check out as she sings Cemetery off the EP.
You can find 5 In Common on iTunes and Amazon.
I first heard of Shaun Hague when Jake Walden announced they would be touring together. When I went to see them, I wasn't sure what to expect, but was blown away by him and his music. Shaun adds a bluesy touch to his Rock-infused Pop, with plenty of heart and soul. Watch as he sings Make It A Great Day from the EP The Time Is Now. I took this video at the show at the MilkBoy Coffee this summer.
You can find The Time Is Now on iTunes and Amazon.
Labels: Andy Moore, chris riffle, matt doyle, shaun hague, stewart lewis
Great Singles from 2011
Clockwise: Nhojj, Gavin Creel, Gareth Asher, and Ricky Martin.
There were many singles released this year that were of special interest to this blog, and four of them are appearing here on this post. In fact, all four are of similar theme, of people coming together, finding acceptance for the common good. Take, for instance, when the gifted Nhojj released a video for his version of the classic song, Amazing Grace, in support of marriage equality.
You can purchase Amazing Grace on iTunes, Amazon or visit Nhojj's official website.
Broadway star Gavin Creel has proven to be a talented and masterful voice on the New York stage, garnering Tony Award nominations for Best Actor in 2002 and 2009. He proved to have talents as a songwriter as well, working on a couple of non-Broadway releases. Recently, he wrote and recorded the song Noise, a song supporting equality nationwide. The proceeds from the sale of the single will go to Broadway Impact, which Creel co-founded with Rory O'Malley and Jenny Kanelos. Here he is, to make some Noise.
This single will be included on an album due out in the Spring. You can purchase Noise on iTunes, Amazon or visit Gavin's official website. You can also check out the official website for Broadway Impact.
After coming out as a happy gay man, Ricky Martin released his first single and video for The Best Thing About Me Is You. The video was a call for inclusivity, for the people of the world to fight against discrimination of any kind. And he looked damn good doing it.
You can purchase The Best Thing About Me Is You on iTunes, Amazon or visit Ricky's official website.
In early November, Atlanta-based singer/songwriter Gareth Asher released a new version of his song Get It Right. The new recroding was a collaboration with Nappy Roots, and was a call for the world community to strive to live together, to move past our differences and just Get It Right.
The song was originally found on Gareth's beautiful album, Between The Smiles And Tears. You can purchase Get It Right on iTunes, Amazon or visit Gareth's official website.
Labels: amazing grace, gareth asher, gavin creel, get it right, nhojj, noise, ricky martin, the best thing about me is you
Great Music From 2011
Clockwise: Derek Nicoletto, Darren Hayes, Jason Walker, and B.Slade.
As I continue to look back on the great music released in 2011, I can't help but give a listen to Derek Nicoletto's amazing Kind Ghosts. As an album, it explored Derek as a solo artists, giving some great pop, a little rock and a lot of Derek. The lead single was also the title track, Kind Ghosts.
You can purchase Kind Ghosts on iTunes, Amazon and Derek's online store.
And with his first new release since 2007, handsome Darren Hayes was back on the scene with Secret Codes & Battleships, a collection that proved his still making great Pop music after a hiatus. I, of course, had to purchase the Deluxe Version of the album, because you can't ever have too much Darren in your life. Check out the video for the single, Blood-stained Heart.
You can purchase Secret Codes & Battleships on iTunes, Amazon and check out Darren's online store.
You could also get the latest release from the magnificent voice of Jason Walker. Jason made a dream come true for his father when he released Live And Unplugged, an acoustic album his proud father wanted him to make. The five-song collection of songs showcased his magnificent instrument on songs like I Am Changing, off the Leave It All Behind album.
You can purchase Live And Unplugged on iTunes, Amazon and you can visit his official website.
I have to admit I am relatively knew on the B.Slade™ train, after he was pointed out to me by Wonder Man and Nhojj. And I am grateful to both, as I immediately fell in love this B.Slade's inventive sound on the album Diesel. I have to admit I went a bit crazy, also purchasing A Brilliant Catastrophe (Alpha) and A Brilliant Catastrophe (Beta). B.Slade's voice is also amazing, as you can hear ion the title track, Diesel.
You can purchase Diesel on iTunes, Amazon, his Bandcamp site, or his official website.
Labels: bslade, darren hayes, derek nicoletto, jason walker
Looking Back at the Year 2011
I Support Angel Adams
Dark Monday • Let Them Entertain You
Christmas Morn with Mahalia Jackson
Merry 1940s Christmas
Christmas Garland • Judy at Home
Christmas Spirit
Friday Night Disco Christmas
Robert German • Xmas Bells/ White Xmas
Doctor Who • Christmas 2011
X-Factor Results • And The Winner Is...
Loco Ninja • Jingle Bells • Free Download
Pet Shop Boys • Please
X-Factor Final • Who Will Win?
All I Want For Christmas Is My Two Front Teeth
Baby, It's Cold Outside • Chris Salvatore & Mister...
Suzy Snowflake
Theo Tams & Ali Slight
Invite Josh Zuckerman to your Christmas
Dark Monday • Mitzi Sings Jerry Herman
Tom Goss • Christmas, Chicago Time
Happy Birthday, Gregory Douglass!
Eric Himan @ MilkBoy Coffee
Sunday Morning With Whitney & CeCe
Swingin' Christmas
The Specials • Friday Night, Saturday Morning
Fridays Can Be A Drag!
Dangerous Muse • Give Me Danger
X-Factor Results • No Diggity For Someone
Laughing With Jim Stafford
X-Factor Top 4
Amy Winehouse • Lioness Released
GLEE Redux • Extraordinary Merry Christmas
Aiden James • Best Shot on iTunes
Gavin Creel Makes Some "Noise"
Namoli Brennet • We Were Born To Rise
Sunday Morning With Johnny Cash
Swinging With Betty Hutton
James Morrison • Broken Strings
Friday Night Disco
NeverEnding One-Hit-Wonder
X-Factor Results • Who's Going Down?
Elephant Live Chat Tonight!
Cover Boy • Chris Salvatore
December 7, 1941 • A Day of Infamy
GLEE Redux • Hold On To Sixteen
Eric Himan • You're Gonna Need Me Single
Constant Crows by Matt Alber Available!
Five on the 5th • December 2011
Levi Kreis • Live at Joe's Pub
Aretha Was Born To Sing The Gospel
Hoagy At The Movies • Hoagy Carmichael
Jamie Cullum Reminds Us @ Five on the 5th
Rock Palace 1973
RightOut TV Awards - Best (DIY) Video
RightOut TV Awards - Best (PRO) Video
RightOut TV Awards - Pop/Rock (DIY) Video
X-Factor Results • Who Get's To Beat It?
World AIDS Day • Read My Lips
RightOut TV Awards - Best Folk/Roots/Jazz (Pro) Vi...
RightOut TV Awards - Best Hip Hop/Urban/R&B Video
RightOut TV Awards - Best Folk/Roots/Jazz (DIY) Vi...
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 8,593
|
Dhimitër Orgocka (24 October 1936 – 1 January 2021) was an Albanian film and theater actor and director, and People's Artist of Albania for his artistical merits.
Personal life
He was born in 1936 in Korçë, Albania, when Zog I was King of Albania, and graduated in the Faculty of Albanian Language in the University of Tirana. He was married to Dhorkë Orgocka, a Merited Artist of Albania actress.
He died of cerebral hemorrhage.
Working career
Orgocka started to work as a director right after school in the Andon Zako Çajupi theater of Korçë, in which he has directed around 100 premières.
His first role as an actor was that of Gjergj in the "Great Love" () drama from Fatmir Gjata, whereas his first work as a director was that of "The house on the lane" () from Teodor Laço. He has also acted in movies such as in "The Gramaphone General" (), and "Nothing can be forgotten" ().
Awards
He was a recipient of the following national and international awards:
People's Artist of Albania
Best role for the monodrama Amok from Stephan Zweig (in the 8th Festival of Theaters in Kiev Ukraine, 2005)
Best role for the monodrama Amok from Stephan Zweig (in the Festival of International Theaters in Bitola and Macedonia, 2005).
Grand Prize Sulejman Pitarka for directing the drama "Dhëndër për Kristinën" of Skënder Demollit in the 5th festival of the Albanian Theaters (in Macedonia, "Dibra 2006").
Cup of Festival for the monodrama Amok from Stephan Zweig (in the international festival of Monodramas në Vroslav, Poland 2007)
Recognition
In 2007, The House of Culture of Maliq was named after him, "Dhimitër Orgocka House of Culture".
References
External links
The New York Times Movies
1936 births
2021 deaths
Albanian male film actors
People from Korçë
University of Tirana alumni
People's Artists of Albania
Albanian male stage actors
20th-century Albanian male actors
21st-century Albanian male actors
Albanian theatre directors
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 4,382
|
Hot, it's one of the cheapest ways to get that amount of sugar delivered.
Was this not desugared ??
3 for a pound in Herron so 24 for 8 quid. Saves on delivery.
I thought they were £2.99 then and I was going to order loads!
The new less sugar ones taste awful. Same with the non fizz one with half the sugar. Ruined it.
Have not tasted a single drink since they've reduced the sugar content due to the new sugar tax that has tasted as good as it previously did!
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 4,304
|
The Jama Masjid is a mosque located in Delanipur area of Port Blair in Andaman and Nicobar Islands in the India.
It is also known as Delanipur Mosque or Jama Mosque.
Prayer
This mosque is a venue of celebration during festivals of Id-Ul-Fitr and Id-Ul-Zuha, by the local Muslim community. The mosque holds prayer sessions every day.
References
Mosques in the Andaman and Nicobar Islands
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 6,620
|
\section{Introduction}
Let $(M,d)$ be a metric space with a distinguished point $0\in M$. Denote $\operatorname{Lip}_0(M)$ the space of all Lipschitz functions $f:M\to\R$ with the property $f(0)=0$. Such a space can be equipped with the Lipschitz norm $\| f\|=\operatorname{sup}_{x\neq y}\frac{|f(x)-f(y)|}{d(x,y)}$, which turns it into a Banach space. We see that each point in $M$ can be naturally embedded into $\operatorname{Lip}_0(M)^*$ via the Dirac mapping $\delta$: $\delta_x(f)=f(x)$, $f\in\operatorname{Lip}_0(M)$, $x\in M$. The norm-closure of the subspace generated by functionals $\delta_x$, $x\in M$, i.e.
$$\overline{\operatorname{span}}^{\operatorname{Lip}_0(M)^*}\{\delta_x|x\in M\}$$
is the Lipschitz Free space over $M$, denoted $\mathcal F(M)$. Lipschitz Free spaces were introduced already by Arens and Eells in \cite{AE}, although the authors did not use the name Lipschitz Free spaces. Free spaces are called Arens-Eells spaces in \cite{W}, where a lot of results regarding the topic is presented.
Lipschitz Free spaces gained a lot of interest in last decades, connecting nonlinear theory with the linear one. Given two pointed metric spaces $M,N$, every Lipschitz mapping $\varphi:M\to N$ which fixes the point $0$ extends to a bounded linear map $F:\mathcal F(M)\to\mathcal F(N)$, making the following diagram commute:
$$\begin{CD}
\mathcal F(M) @>{F}>> \mathcal F(N)\\
@A{\delta_M}AA @AA{\delta_N}A\\
M @>{\varphi}>> N
\end{CD}$$
We focus on structural properties of Lipschitz Free spaces. It is well-known that $\operatorname{Lip}_0(\R)= L_\infty$, which yields $\mathcal F(\R)= L_1$ isometrically and similarly $\mathcal F(\N)=\ell_1$. In \cite{CDW}, the authors prove that $\mathcal F(M)$ contains a complemented copy of $\ell_1(\N)$ if $M$ is infinite (has at least cardinality $\aleph_0$), which was further extended from $\N$ to all cardinalities in \cite{HN}. However, $\mathcal F(\R^2)$ cannot be embedded in $\mathcal F(\R)=L_1$ (see \cite{NS}).
Certain results were obtained concerning approximation properties in Free spaces, including \cite{PS},\cite{LP},\cite{HLP},\cite{K},\cite{Godefroy},\cite{GO} and of course \cite{GK}. However, not much is known yet about Schauder bases in Free spaces. H\'{a}jek and Perneck\'{a} \cite{HP} constructed a Schauder basis for the Free spaces $\mathcal F(\ell_1)$ and $\mathcal F(\R^n)$. From \cite{Kaufmann} we have $\mathcal F(M)$ is isomorphic to $\mathcal F(\R^n)$ for every $M$ with non-empty interior, which gives existence of Schauder basis on such $\mathcal F(M)$.
This article follows up the article \cite{HN}, where the authors proved existence (and in the case of $c_0$ constructively) of a Schauder basis on $\mathcal F(N)$, for any net $N$ in spaces $C(K)$ for $K$ metrizable compact (hence for $c_0$ and $\R^n$). In section \ref{nonexistence} we show that the same construction as in \cite{HN} cannot be used for constructing bases in $\mathcal F(N)$ for arbitrary uniformly discrete subset $N$. In section \ref{unconditionality} we prove that bases constructed in \cite{HN} are not unconditional and that for nets in $\R^n$, no Schauder basis on $\mathcal F(N)$ arising from the technique using retractions can be unconditional.
\section{Preliminaries}
As we mentioned, we are interested in constructing a Schauder basis on Lipschitz Free space. However, constructing such basis directly on the Free space is rather complicated, wherefore we prefer to work with its adjoint space and transfer the results to the Free space. The next theorem shows a way to construct a Schauder basis through operators on $\operatorname{Lip}_0(M)$.
\begin{theorem} \label{operator} Let $M$ be a pointed metric space. Suppose there exists a sequence of linear operators $E_n:\operatorname{Lip}_0(M)\to \operatorname{Lip}_0(M)$, which satisfies the following conditions:
\begin{enumerate}
\item $\dim E_n \left(\operatorname{Lip}_0(M)\right)=n$ for every $n\in\N$,
\item There exists $K>0$ such that $E_n$ is $K$-bounded for every $n\in\N$,
\item $E_m E_n=E_n E_m=E_n$ for every $m,n\in\N$, $n\leq m$,
\item \label{weak}For every $n$, the operator $E_n$ is continuous with respect to topology of pointwise convergence on $\operatorname{Lip}_0(M)$,
\item \label{continuity} For every $f\in\operatorname{Lip}_0(M)$ the function sequence $E_n f$ converges pointwise to $f$.
\end{enumerate}
Then the space $\mathcal F(M)$ has a Schauder basis with the basis constant at most $K$.
\end{theorem}
\begin{proof}
Note first that the topology of pointwise convergence coincides with the $w^*$-topology on bounded subsets of $\operatorname{Lip}_0(M)$. Therefore, from the condition (\ref{weak}), the operators $E_n$ are $w^*$ to $w^*$ continuous on bounded subsets of $\operatorname{Lip}_0(M)$ and hence there exist linear operators $P_n:\mathcal F(M)\to\mathcal F(M)$ such that $P^*_n=E_n$ for every $n\in\N$. It is now clear that $\| P_n\|\leq K$, $\dim P_n \left(\mathcal F(M)\right)=n$ and that $P_m P_n=P_n P_m=P_n$ for every $m,n\in\N$, $n\leq m$. Furthermore (\ref{continuity}) together with the fact that the topology of pointwise convergence coincides with the $w^*$-topology on bounded subsets of $\operatorname{Lip}_0(M)$ means, that for every $f\in \operatorname{Lip}_0(M)$ the sequence $E_n f$ converges $w^*$ to $f$, and that for every $\mu\in\mathcal F(M)$ the sequence $P_n\mu$ converges weakly to $\mu$. But that means $\| P_n\mu-\mu\|\to 0$ for every $\mu\in\mathcal F(M)$. Indeed, if there were $\mu\in\mathcal F(M)$, $c>0$ and a subsequence $P_{n_k}$, such that $\| P_{n_k}\mu-\mu\|>c$ for all $k\in\N$, then for every $n\geq n_1$, there exists a $k\in\N$ such that $n\leq n_k$, which yields
$$c<\| P_{n_k}\mu-\mu\|\leq\| P_{n_k}\mu-P_n\mu\| + \| P_{n}\mu-\mu\|\leq (K+1)\| P_n\mu-\mu\|.$$
From $P_1(\mathcal F(M))\subseteq P_2(\mathcal F(M))\subseteq P_3(\mathcal F(M))\subseteq...$ we get $E=\bigcup_{n=1}^{\infty}P_n(\mathcal F(M))$ is a convex set and as all $P_n$ are commuting projections, we have that $\mu\notin\overline E$. Indeed, if $\mu \in \overline E$, then there is a sequence $\{x_k\}_{k=1}^\infty\subseteq E$, such that $x_k\to \mu$. If we choose an increasing sequence of numbers $l_k\in\N$, $l_k>n_1$, which satisfy $P_{l_k}x_k=x_k$, we get that
$$\| P_{l_k}x_k-\mu\|\geq \| P_{l_k}\mu-\mu\|-\| P_{l_k}\mu-P_{l_k}x_k\|\geq \frac{c}{K+1}-K\| \mu-x_k\|.$$
Limiting $k\to\infty$ yields $0\geq \frac{c}{K+1}$, which is a contradiction. Therefore $\mu\notin\overline E$. Hence Hahn-Banach theorem gives us the existence of a linear functional $f\in\operatorname{Lip}_0(M)$, $\| f\|=1$ with $f|_E=0$ and $f(\mu)>0$. But that is a contradiction as $P_n\mu\overset{w}\to\mu$. Therefore $P_n \mu\to \mu$.
\end{proof}
The following corollary appears already in \cite{HN}, p.12. It gives us a way to construct the Schauder basis on $\mathcal F(M)$ only by using the metric space $M$.
\begin{corollary}\label{one} Let $M$ be a metric space with a distinguished point $0$. Suppose there exists a sequence of distinct points $\{\mu_n\}_{n=0}^{\infty}\subseteq M$, $\mu_0=0$, together with a sequence of retractions
$\{\varphi_n\}_{n=0}^\infty$, $\varphi_n:M\to M$, $n\in\N_0$ which satisfy the following conditions:
\begin{enumerate}[(i)]
\item $\varphi_n(M)=\{\mu_j\}_{j=0}^{n}$ for every $n\in\N_0$,\label{bed1}
\item $\overline{\bigcup_{j=0}^{\infty}\{\mu_j\}}=M$, \label{bed2}
\item There exists $K>0$ such that $\varphi_n$ is $K$-Lipschitz for every $n\in\N_0$,\label{bed3}
\item $\varphi_m\varphi_n=\varphi_n\varphi_m=\varphi_n$ for every $m,n\in\N_0$, $n\leq m$. \label{bed4}
\end{enumerate}
Then the space $\mathcal F(M)$ has a Schauder basis with the basis constant at most $K$.
\end{corollary}
\begin{proof}
It is not difficult to see that for each $n\in\N$ the formula $E_nf=f\circ\varphi_n$, $f\in\operatorname{Lip}_0(M)$ defines a linear
operator $E_n:\operatorname{Lip}_0(M)\to\operatorname{Lip}_0(M)$, such that the sequence $E_n$ satisfies the assumptions of Theorem \ref{operator}.
\end{proof}
The last two theorems lead us to the following definition.
\begin{definition} Let $M$ be an infinite metric space such that $\mathcal F(M)$ has a Schauder basis $E$ with projections $P_n$, $n\in\N$. We say $E$ is an extensional Schauder basis if there exist finite sets $\{0\}=M_0\subseteq M_1\subseteq M_2\subseteq...$ such that $\bigcup_{n=1}^\infty M_n$ is dense in $M$ and we have that for every $n\in\N$ the adjoint $P_n^*$ is a linear extension operator $P_n^*:\operatorname{Lip}_0(M_n)\to\operatorname{Lip}_0(M)$ with $P_n^*f|_{M_n}=f$ (or equivalently $P_n$ is a projection onto $\mathcal F(M_n)$). We say $E$ is a retractional Schauder basis, if there exist retractions $\{\varphi_n\}_{n=0}^\infty$, $\varphi_n:M\to M$ which satisfy the conditions of Corollary \ref{one} and such that they give rise to the basis $E$, i.e. the adjoints $P_n^*$ satisfy $P_n^*f=f\circ\varphi_n$, $f\in\operatorname{Lip}_0(M)$.
\end{definition}
It is clear that in the definition we actually have $|M_n\setminus M_{n-1}|=1$ for every $n\in\N$. Note also that every retractional Schauder basis is a special case of an extensional Schauder basis. The next lemma shows in more detail what form the basis vectors take.
\begin{lemma}\label{char}
Let $M$ be a metric space such that there is a sequence of distinct points $0=\mu_0,\mu_1,\mu_2,...\in M$ such that $\bigcup_{n=1}^\infty \{\mu_0,\mu_1,...,\mu_n\}$ is dense in $M$. For every $n\in\N_0$ denote $M_n=\{\mu_0,...,\mu_n\}$. Suppose $\mathcal F(M)$ has a Schauder basis $B=\{e_n\}_{n=1}^\infty$. Then the following are equivalent:
\begin{enumerate}
\item\label{extb} $B$ is an extensional Schauder basis with extension operators $E_n:\operatorname{Lip}_0(M_n)\to\operatorname{Lip}_0(M)$.
\item\label{basf} For every $n\in\N$, there are constants $0\neq c_n,a^n_i\in\R$, $i\in\{1,...,n-1\}$ such that we have $c_n e_n=\delta_{\mu_n}-\sum_{i=1}^{n-1}a_i^{n}\delta_{\mu_i}$.
\end{enumerate}
\end{lemma}
\begin{proof}
$(\ref{basf})\Rightarrow(\ref{extb})$. Note first that for every $n\in\N$, we have $e_n\in \operatorname{Im} P_n\cap\ker P_{n-1}$. From that it follows inductively for every $n\in\N$ that $\operatorname{Im} P_n=\operatorname{span}\{\delta_{\mu_1},...,\delta_{\mu_n}\}$.
$(\ref{extb})\Rightarrow(\ref{basf})$ The fact that $E_n=P^*_n$ is a bounded linear extension from $M_n$ to $M$ implies that each $P_n$ maps $\mathcal F(M)$ onto $\mathcal F(M_n)$, which means each basis vector $e_n$ is a linear combination of Dirac functionals at the points of $M_n$, such that the coefficients at $\delta_{\mu_n}$ do not vanish.
\end{proof}
Keeping the notation from previous lemma, we see that for each $n\in\N$ we may define a finite dimensional operator $R_{n}:\operatorname{Lip}_0(M_{n-1})\to\operatorname{Lip}_0(M_{n})$ via
$$R_nf(\mu_{j})=\begin{cases}
f(\mu_j) & j\in\{0,...,n-1\}\,,\\
\sum_{i=1}^{n-1}a_i^{n}f(\mu_{i}) & j=n\,.\\
\end{cases}$$
The operator $E_n=P^*_n$ can be then reconstructed through a $w^*$-limit of operator composition $\lim_k R_kR_{k-1}...R_{n+1}$. The constants $c_n$ were in the lemma only for scaling of the basis vectors $e_n$.
In case of a retractional basis, the basis vectors take form of two-point molecules: For every $n\in\N$ and $i\in\{1,...,n-1\}$ exactly one of the coefficients $a_i^n$ is non-zero, namely has the value $1$. If for example $a_j^n=1$, then $\varphi_j(\mu_n)=\mu_j$, which means $e_n=\delta_{\mu_n}-\delta_{\mu_{j}}$.
Throughout this article, given a metric space $M$, $d$ will denote its metric. If $M$ is a countable (even finite) uniformly discrete metric space with $\mathcal F(M)$ having a retractional Schauder basis, by symbols $\mu_0,\mu_1,\mu_2...$, resp. $\varphi_0,\varphi_1,\varphi_2,...$ we will always mean points $\mu_i\in M$, resp. retractions $\varphi_i:M\to M$ which satisfy Corollary \ref{one}. Obviously the finite analogues of Corollary \ref{one} and Theorem \ref{operator} also hold. We are going to look in more detail on some properties of retractional Schauder basis.
Following the notation of Corollary \ref{one} (or the proof of Lemma 14 in \cite{HN}) we find useful to denote the set-valued functions $F_i=\varphi_i^{-1}:M\to 2^M$, $F_i(x)=\{y|\ \varphi_i(y)=x\}$, $i\in\N_0$. Clearly $F_0(0)=M$. From the commutativity of the $\varphi_i$'s further follows that for any $i<j$ we have
$$F_i(\mu_i)\cap F_j(\mu_j)\in\{\emptyset,F_j(\mu_j)\}.$$
\begin{definition} Let $M$ and $\mu_i$, $\varphi_i$, $i\in\N_0$ satisfy the assumptions from Corollary \ref{one} and $M=\{\mu_i\}_{i=0}^\infty$. A finite or infinite sequence of points $(\mu_{k_1},\mu_{k_2},\mu_{k_3},...)$ is called a chain whenever $k_1<k_2<k_3<...$ and $\varphi_{k_i-1}(\mu_{k_i})=\mu_{k_{i-1}}$ for every $i\in\{2,3,...\}$.
\end{definition}
Note that for every chain $(\mu_{k_1},\mu_{k_2},\mu_{k_3}...)$ we have $F_{k_1}(\mu_{k_1})\supseteq F_{k_2}(\mu_{k_2})\supseteq F_{k_3}(\mu_{k_3})\supseteq ...$. We can also introduce partial order on $M$ by $\mu_i\prec\mu_j$ if and only if there exist $n\in\N_0$ points $\mu_{k_1},...,\mu_{k_n}\in M$ such that $(\mu_i,\mu_{k_1},...,\mu_{k_n},\mu_j)$ is a chain. Note also that for two chains $S,T$ the difference $S\setminus T$ and intersection $S\cap T$ are also chains, if nonempty. For a finite chain $(x_1,x_2,...,x_n)$ we call the point $x_1$ its initial point and $x_n$ its final point.
Every chain can be viewed as a path or its segment from $0\in M$ to a given point $x\in M$. Indeed, for every $x\in M$ there exists $n\in\N$ such that for every $i\geq n$ one has $\varphi_i(x)=x$. Assuming $n$ is the least number with that property we can define the set $T^{x}_0=\bigcup_{i=0}^{n}\{\varphi_i(x)\}$ which contains exactly the points of the chain with initial point $0$ and final point $x$. Regarding $T_0^x$ as an ordered set (the order $\prec$ is linear on $T_0^x$), it is clear that given $x\in M$, there exists exactly one chain $T_0^x$ from $0$ to $x$.
Note also that for every chain $(\mu_{n_1},...,\mu_{n_k})$, $k\geq 2$ there exist constants $c_{n_i}$ (the constants from Lemma \ref{char}) such that for basis vectors $e_{n_1},...,e_{n_k}$ we have
$$\sum_{i=2}^kc_{n_i}e_{n_i}=\delta_{\mu_{n_k}}-\delta_{\mu_{n_1}}.$$
The following lemma says that, if the space is not too "porous", basis vectors can be made only of two-point molecules in points which are not too far from each other.
\begin{lemma}[Step lemma]\label{step} Let $M$ be a countable metric space, $\alpha>0, K\geq 1$ and $\varphi_n:M\to M$ a system of retractions from Corollary \ref{one}. If $(\mu_{i_1},...,\mu_{i_j})$, $j>1$ is a chain and there exist distinct points $x_1,...,x_k\in M$ with $d(x_l,x_{l+1})\leq\alpha$, $l\in\{1,...,k-1\}$, $x_1=\mu_{i_j}$, $x_k=\mu_{i_1}$ and $\operatorname{sup}_{i_1\leq n\leq i_j}\operatorname{Lip}\varphi_n\leq K$, then $d(\mu_{i_{m-1}},\mu_{i_{m}})\leq 2K\alpha$ for all $m\in\{2,...,j\}$.
\end{lemma}
\begin{proof}
Suppose $d(\mu_{i_{m-1}},\mu_{i_{m}})> 2K\alpha$ for some $m\in\{2,...,j\}$. We know $\varphi_{i_m}(\mu_{i_j})=\mu_{i_m}$ and $\varphi_{i_m-1}(\mu_{i_j})=\mu_{i_{m-1}}$. We prove by induction for all $l\in\{1,...,k\}$ that $\varphi_{i_m}(x_l)=\mu_{i_m}$ and $\varphi_{i_m-1}(x_l)=\mu_{i_{m-1}}$, which is a contradiction as $x_k=\mu_{i_1}$ and $\varphi_{i_m}(\mu_{i_1})=\mu_{i_1}\neq \mu_{i_m}$. For $l=1$ we have $x_l=\mu_{i_j}$ and the statement clearly holds. Suppose it holds for all $l=1,...,s-1<k$. From $d(x_{s-1},x_{s})\leq\alpha$ it follows that $d(\mu_{i_m},\varphi_{i_m}(x_{s}))\leq K\alpha$ and $d(\mu_{i_{m-1}},\varphi_{i_{m}-1}(x_{s}))\leq K\alpha$. From commutativity of all $\varphi_n$'s follows that either $\varphi_{i_{m}-1}(x_s)=\varphi_{i_m}(x_s)\notin\{\mu_{i_m}\}$ holds or $\varphi_{i_m}(x_s)=\mu_{i_m}$ and $\varphi_{i_m-1}(x_s)=\mu_{i_{m-1}}$ is true. Since $B_{K\alpha}(\mu_{i_m})\cap B_{K\alpha}(\mu_{i_{m-1}})=\emptyset$ we conclude the latter is true, which completes the induction step and the contradiction is obtained.
\end{proof}
In the following section, we are going to prove that there are spaces $\mathcal F(M)$ with no retractional Schauder basis yet having Schauder basis, moreover extensional.
\section{Nonexistence of retractional Schauder bases}\label{nonexistence}
\begin{definition} Let $x_0,x_1,...,x_n$, $n\in\N$ be distinct points. The set $C^0_n=\{x_0,x_1,x_2...,x_n\}$ with the (standard graph) metric $d(x_k,x_0)=n$, $k\neq 0$, $d(x_k,x_l)=\min\{|k-l|,n-|k-l|\}$, $k,l>0$ we call a circle or a circle of radius $n$ with centre $x_0$.
\end{definition}
In the following, we regard the centre $x_0$ as the base point in the pointed metric space $(C^0_n,d,x_0)$ and denote it $0$.
We are also going to use an uncentered circle, i.e. a subgraph $C_n=\{x_1,x_2,...,x_n\}$ with the induced metric. On $C_n$, we define orientation: We say point $x_l$ lies to the left of the point $x_k$, $k,l\in\{1,...,n\}$, if one of these situations happens:
\begin{enumerate}
\item $k>\frac{n-1}{2}$ and $l\in\{k,k-1,...,k-\lfloor\frac{n+1}{2}\rfloor+1\}$,
\item $k\leq \frac{n-1}{2}$ and $l\in\{k,k-1,...,1\}\cup\{n,n-1,...,n-\lfloor\frac{n+1}{2}\rfloor+k+1\}$.
\end{enumerate}
Analogously, we say $x_l$ lies to the right of $x_k$ if one of the following conditions is satisfied:
\begin{enumerate}
\item $k\leq\frac{n-1}{2}$ and $l\in\{k,k+1,...,k+\lfloor\frac{n+1}{2}\rfloor\}$,
\item $k>\frac{n-1}{2}$ and $l\in\{k,k+1,...,n\}\cup\{1,2,...,\lfloor\frac{n+1}{2}\rfloor-(n-k+1)\}$.
\end{enumerate}
We show that every retractional Schauder basis on $\mathcal F(C_n^0)$ has a basis constant which is increasing with $n$.
\begin{theorem}\label{circle}
Let $n\in\N$, $n\geq 10$ and let $\{\varphi_i\}_{i=0}^n$ be a system of retractions on a circle $C^0_n$ satisfying the conditions of Corollary \ref{one} . Then there is an $s\in\{1,...,n\}$ such that $$\operatorname{Lip}\varphi_s\geq\frac{\sqrt{8n+1}-1}{8}.$$
\end{theorem}
\begin{proof}
Let us fix $n\geq 10$ and denote $K=\frac{\sqrt{8n+1}-1}{8}$. We have $\mu_0=0$ and $\mu_1\in C_n$ with $\varphi_1(x)=\mu_1$ for all $x\in C_n$ and $\varphi_1(0)=0$. Indeed, if $\varphi_1(y)=0$ for some $y\in C_n$, then the sets $F_1(0)$ and $F_1(\mu_1)$ have distance $1$. Since they are finite, there exist $w\in F_1(0)$, $z\in F_1(\mu_1)$ such that $d(w,z)=1$ and clearly $d(\varphi_1(w),\varphi_1(z))=n$, which trivially yields the result, as $n>K$. We prove the theorem by contradiction and assume therefore, $\operatorname{Lip}\varphi_i< K$ for all $i\in\{1,...,n\}$.
For every point $x\in C_n$ there exists a $k\in\{1,...,n\}$ such that $\{x\}=\{\mu_k\}=\varphi_k(C_n)\setminus\varphi_{k-1}(C_n)$ and therefore there exists exactly one chain $S_x=(\mu_{k_1},\mu_{k_2},...,\mu_{k_l})$, such that $\mu_{k_1}=\mu_1$ and $\mu_{k_l}=x$ (equivalently $k_1=1$ and $k_l=k$).
Let us introduce sets
$$A=\{y|\ y\in C_n\setminus\{\mu_1\},d(y,\mu_1)\leq 3K,\text{$y$ lies to the left of $\mu_1$}\}$$
$$B=\{y|\ y\in C_n\setminus\{\mu_1\},d(y,\mu_1)\leq 3K,\text{$y$ lies to the right of $\mu_1$}\}$$
and a mapping $f:C_n\setminus\{\mu_1\}\to\{A,B\}$,
$$f(w)=\begin{cases}
A & \text{there is a $z\in S_w\cap A$ such that for every $y\in S_w$, $z\prec y$, we have $y\notin A\cup B$}\,, \\
B & \text{there is a $z\in S_w\cap B$ such that for every $y\in S_w$, $z\prec y$, we have $y\notin A\cup B$}\,. \\
\end{cases}$$
Note that the definitions of $A,B$ make perfect sense, as $3K<\frac{n}{2}$. Also, the mapping $f$ is well-defined, as for every $w\in C_n\setminus\{\mu_1\}$ the intersection $S_w\cap(A\cup B)$ is nonempty. Indeed, according to Step lemma \ref{step} applied on the $C_n$, the distance between any two adjacent points in a chain is smaller than $2K$ and therefore for the second element $z\in S_w$ (meaning $S_w=(\mu_1,z,...,w)$) we have $d(\mu_1,z)\leq 2K$ and thus $z\in A$ or $z\in B$.
Observe that $f(w)=A$ for every $w\in A$ and $f(w)=B$ for every $w\in B$. We prove there exist two points $a,b\in C_n\setminus\left(\{\mu_1\}\cup A\cup B\right)$ such that $d(a,b)=1$, $f(a)=A$ and $f(b)=B$.
Let us assume for contradiction that $f(w)=A$ for all points $w\in C_n\setminus\left(\{\mu_1\}\cup A\cup B\right)$. Denote $z$ the closest point to the right of the set $B$, i.e. the only point with $3K <d(z,\mu_1)\leq 3K+1$ and $d(z,B)=1$. We have $f(z)=A$, which means the chain $S_z=(\mu_1,\mu_{k_2},...,z)$ leaves the set $A$ and goes to the left around (meaning omitting the set $A\cup B$) the circle to the point $z$, with steps smaller than $2K$. Therefore there exists a point $\mu_l\in S_z$ such that $d(\mu_1,\mu_l)\geq\frac{n-2K}{2}$. But then we have $\varphi_{l}(\mu_1)=\mu_1$, $\varphi_{l}(z)=\mu_l$, which yields
$$\operatorname{Lip}\varphi_l\geq \frac{d(\mu_1,\mu_l)}{d(\mu_1,z)}\geq\frac{n-2K}{2(3K+1)}\geq K,$$
as $n\geq 10$, which contradicts our assumption.
Therefore, let there exist two points $a,b\in C_n\setminus\left(\{\mu_1\}\cup A\cup B\right)$ such that $d(a,b)=1$, $f(a)=A$ and $f(b)=B$. Consider the two chains $S_a=(\mu_1,\mu_{k_1},\mu_{k_2}...,a)$ and $S_b=(\mu_1,\mu_{l_1},\mu_{l_2}...,b)$ and let $i$ and $j$ be such that $\mu_{k_i}\in A$, $\mu_{l_j}\in B$ and we have $\mu,\nu\notin A\cup B\cup\{\mu_1\}$ for every $\mu\in S_a$, $\mu_{k_i}\prec \mu$ and every $\nu\in S_b$, $\mu_{l_j}\prec \nu$. Note that $d(\mu_1,\mu_{l_j})\geq K+1$ and $d(\mu_1,\mu_{k_i})\geq K+1$.
Without loss of generality suppose $k_i<l_j$. Then $\varphi_{l_j}(b)=\mu_{l_j}$ and $d(\varphi_{l_j}(a),\mu_{l_j})\leq K$. This implies $u_a:=\varphi_{l_j}(a)$ has distance at most $K$ from the set $B$, which yields $d(\mu_1,u_a)\leq 4K$ and the chain $S=(\mu_{k_i},...,u_a)$ must go from the set $A$ to the left around the circle closer to the set $B$. Thus there must exist a point $v=\mu_s\in S$ such that $d(v,\mu_1)\geq\frac{n-2K}{2}$. It follows that $$\operatorname{Lip} \varphi_s\geq \frac{d(\varphi_s(u_a),\varphi_s(\mu_1))}{d(u_a,\mu_1)}=\frac{d(v,\mu_1)}{d(u_a,\mu_1)}\geq\frac{n-2K}{8K}=K,$$ which is again a contradiction. We conclude there exists an $s\in\{1,...,n\}$ such that $\operatorname{Lip}\varphi_s\geq K=\frac{\sqrt{8n+1}-1}{8}$.
\end{proof}
\begin{corollary}\label{no basis} There exists a uniformly discrete set $N\subseteq\R^2$ such that the Free space $\mathcal F(N)$ has no retractional Schauder basis.
\end{corollary}
\begin{proof}
Let $N=\bigcup_{n=1}^\infty C^0_{4^n}$ be a union of circles with the same centre $0$ and with radii $4^n$, $n\in\N$. Suppose $d_n$ is the metric on $C^0_{4^n}$. Let us define a metric on $N$ in the following way:
$$d(x,y)=\begin{cases}
d_n(x,y) & \text{ if } x,y\in C^0_{4^n}\,,\\
\max\{4^i,4^j\} & \text{ if } x\in C_{4^i},y\in C_{4^j},i\neq j\,.\\
\end{cases}$$
It is clear that $d$ is indeed a metric on $N$ and one has no difficulties to embed $N$ into $\R^2$ in a bilipschitz way, actually with distortion not worse than $2\pi$.
We show that every sequence of retractions $\varphi_i:N\to N$ satisfying conditions $(i)$ and $(iv)$ from Corollary \ref{one} cannot satisfy the condition $(iii)$ of that corollary.
Let therefore $\varphi_i:N\to N$ be a commuting sequence of retractions such that $\varphi_0(0)=0$ and $|\varphi_i(N)|=i+1$. We show that for every $k\in\N$, $k\geq 4$, there exists an $n=n_k\in\N$ such that $\operatorname{Lip}\varphi_{n_k}\geq k.$ Pick therefore $k\in\N$, $k\geq 4$, and find the smallest $n$ such that $\mu_n\in C_{4^k}$. Then $\varphi_i(\mu_n)=\mu_n$ for every $i\geq n$. If there exist $j\geq n$ and $x\in C_{4^k}$ such that $\varphi_j(x)\notin C_{4^k}$, we have $\operatorname{Lip}\varphi_j\geq 4^k\geq k$ and the proof is finished. Indeed, if we take $x\in C_{4^k}$ such that $\varphi_j(x)\notin C_{4^k}$ and without loss of generality we assume $x$ is such that $d(x,\mu_n)$ is minimal among all $x\in C_{4^k}$ with $\varphi_j(x)\notin C_{4^k}$, we have $d\left(\varphi_j(y),\varphi_j(x)\right)\geq 4^k\geq k$ for one of $x$'s neighbours $y$ (i.e. $d(x,y)=1$). This means $\operatorname{Lip}\varphi_j\geq k$.
If, on the contrary, we have $\varphi_i(x)\in C_{4^k}$ for all $i\geq n$ and all $x\in C_{4^k}$, we find ourselves in the case of Theorem \ref{circle}. Indeed, if we view the circle $C^0_{4^k}$ as a set $C^0_{4^k}=\{0,\mu_{s_1},\mu_{s_2},...,\mu_{s_{4^k}}\}$ (for some eligible $s_1,s_2,...,s_{4^k}\in\N$) and look only at retractions $\varphi_0,\varphi_{s_1},\varphi_{s_2},...,\varphi_{s_{4^k}}$ restricted to the circle $C^0_{4^k}$, we apply \ref{circle} and conclude $\max\{\operatorname{Lip}\varphi_{s_1},\operatorname{Lip}\varphi_{s_2},...,\operatorname{Lip}\varphi_{s_{4^k}}\}\geq\frac{\sqrt{8\cdot 4^k+1}-1}{8}\geq k$.
\end{proof}
We see it is impossible to build a retractional Schauder basis on $\mathcal F(N)$. However, the space $\mathcal F(N)$ has an extensional Schauder basis as we are going to show in the next proposition:
\begin{proposition} Let $N=\bigcup_{n=1}^\infty C^0_{4^n}$ be the metric space from Corollary \ref{no basis}. Then $\mathcal F(N)$ has an extensional monotone Schauder basis.
\end{proposition}
\begin{proof} First, note that we have orientation of every $C_{4^n}$, $n\in\N$. For every $i\in\N$, define $k=k(i)$ as the unique integer such that $\frac{4^{k}-1}{3}\leq i< \frac{4^{k+1}-1}{3}$. Let $N=\{0,x_1,x_2,x_3,...\}$ be enumerated in such way that for every $i\in\N$ we have $x_i\in C_{4^{k}}$ and that the enumeration respects the orientation on every circle $C_{4^k}$. Namely, if $x_i,x_{i+1}\in C_{4^k}$, we have that $d(x_i,x_{i+1})=1$ and $x_{i+1}$ lies to the right of $x_i$. Denote $D_i=\{0,x_1,x_2,...x_{i}\}$.
We are going to define a sequence of extension operators $P_i:\operatorname{Lip}_0(D_i)\to\operatorname{Lip}_0(N)$ and prove they satisfy the assumptions of Theorem \ref{operator}. In order to do that, let us define some preparatory notions. Define the left and the right "$D_i$-neighbour" functions $\nu^l_i,\nu^r_i:\bigcup_{n=1}^{k(i)} C_{4^n}^0\to D_i$ as follows: For each $n\in\{1,2,...,k(i)\}$ and $x\in C_{4^{n}}$, let $\nu^l_i(x)\in D_i$ be the closest point to the left of $x$ and let $\nu^r_i(x)\in D_i$ be the closest point to the right of $x$. We set $\nu^l_i(0)=\nu^r_i(0)=0$. Note that $\nu^l_i(x)=\nu^{r}_i(x)=x$ if and only if $x\in D_i$. Further we need to define "right-" and "left-" metric function (not proper metrics) on every circle $C_{4^n}$. For points $x,y\in C_{4^n}$ we set the value $d^l(x,y)$ as the length of the path (in the graph $C_{4^n}$) going from $x$ to the left up to $y$. Analogously, we set $d^r(x,y)$ as the length of the path going from $x$ to the right up to $y$. It is clear that for $x,y\in C_{4^n}$ we have $d^l(x,y)=d^r(y,x)$ and $d(x,y)=\min\{d^r(x,y),d^l(x,y)\}$.
Further we define for every $i\in\N$ the $i$-th interpolation function $I_i:\operatorname{Lip}_0(D_i)\times \bigcup_{n=1}^{k(i)} C_{4^n}^0\to\R$ via
$$I_i(f,x)=\frac{d^r(x,\nu^r_i(x))f(\nu^l_i(x))+d^l(x,\nu^l_i(x))f(\nu^r_i(x))}{d^l(x,\nu^l_i(x))+d^r(x,\nu^r_i(x))}\ \ \ \text{if } x\neq \nu^l_i(x) \text{ or } x\neq \nu^r_i(x)$$
and $I_i(f,x)=f(x)$ for $x=\nu^l_i(x)=\nu^r_i(x)$. Clearly, $I_i(f,x)$ is the value of linear interpolation of the function $f$ between closest points of $x$ to the left and to the right from the set $D_i$, given we take $x$ itself to be the closest point to $x$ in any direction if $x\in D_i$. Let now $f\in\operatorname{Lip}_0(D_i)$. Then we define our (extension) operators $P_i$, $i\in\N$ simply as
$$P_if(x)=\begin{cases}
I_i(f,x) & x\in\bigcup_{n=1}^{k(i)} C_{4^n}^0\,,\\
0 & x\in\bigcup_{n=k(i)+1}^{\infty} C_{4^n}
\end{cases}$$
and of course, $P_0=0$. Clearly $P_i$ is a linear operator for every $i\in\N$ and the function $P_if$ is Lipschitz with the same constant as $f$. Indeed, if we take $x\in C_{4^{n}}$ and $y\in C_{4^{m}}$ with $m< n$, we see from the definition of $I_i$ that $\min_{z\in C_{4^{n}}}f(z)\leq P_if(x)\leq\max_{z\in C_{4^{n}}}f(z)$ and $\min_{w\in C_{4^{m}}}f(w)\leq P_if(y)\leq\max_{w\in C_{4^{m}}}f(w)$. From that and from the fact that $d(z,w)=d(x,y)=4^n$ holds for all $z\in C_{4^n}$ and $w\in C_{4^m}$, we get
$$|P_if(x)-P_if(y)|\leq \max_{\substack{
z\in C_{4^{n}}\\
w\in C_{4^{m}}}}
|f(z)-f(w)|\leq 4^n \| f\|=d(x,y)\| f\|.$$
For $x\in C_{4^{n}}$ and $0$ we have clearly $|P_if(x)-P_if(0)|\leq\max_{z\in C_{4^{n}}}|f(z)|\leq d(x,0)\| f\|$.
The only nontrivial case to prove is the case $x,y\in C_{4^{k(i)}}$. Let therefore $x,y\in C_{4^{k(i)}}$. There are three cases. If $x,y\in D_i$, then $P_if(x)=f(x)$ and $P_if(y)=f(y)$, which is trivial. Let $x,y\notin D_i$ and $\nu^r_i(x)=\nu^r_i(y)=a$, $\nu_i^l(x)=\nu_i^l(y)=b$. We can assume $d^r(b,x)\leq d^r(b,y)$, for the roles of $x$ and $y$ are symetrical. From that we have $d^r(y,a)\leq d^r(x,a)$. If $d(x,y)=d^r(x,y)$, we have
\begin{align*}
|P_if(x)-P_if(y)|&=\left|\frac{f(b)d^r(x,a)+f(a)d^r(b,x)}{d^r(b,a)}-\frac{f(b)d^r(y,a)+f(a)d^r(b,y)}{d^r(b,a)}\right|\\
&=\left|\frac{f(b)d^r(x,y)-f(a)d^r(x,y)}{d^r(b,a)}\right|\\
&\leq \frac{\| f\| d(a,b)}{d^r(b,a)}d^r(x,y)\leq \| f\| d(x,y).
\end{align*}
If $d(x,y)=d^l(x,y)$, then $d(x,y)=d^r(y,a)+d^r(a,b)+d^r(b,x)$ and then from $d^r(b,a)-d^r(x,y)=d^r(b,x)+d^r(y,a)$ we have by triangle inequality
\begin{align*}
|P_if(x)-P_if(y)|&=\left|\frac{f(b)d^r(x,y)-f(a)d^r(x,y)}{d^r(b,a)}\right|\\
&=\left|\frac{f(b)\left(d^r(x,y)-d^r(b,a)\right)+(f(b)-f(a))d^r(b,a)+f(a)\left(d^r(b,a)-d^r(x,y)\right)}{d^r(b,a)}\right|\\
&=\left|\frac{\left(d^r(b,x)+d^r(y,a)\right)\left(f(a)-f(b)\right)+(f(b)-f(a))d^r(b,a)}{d^r(b,a)}\right|\\
&\leq \| f\|\left(\frac{d(a,b)}{d^r(a,b)}\left(d^r(b,x)+d^r(y,a)\right)+d(a,b)\right)\leq\| f\| d(x,y)\\
\end{align*}
The case $x\in D_i$, $y\notin D_i$ is proved in a similar way.
We see that the functions $f_j=P_i\left(\chi_{\{x_j\}}\right)$, $1\leq j\leq i$ create a basis of each space $P_i(\operatorname{Lip}_0(N))$, hence $\dim P_i(\operatorname{Lip}_0(N))=i$ for every $i\in\N$.
To prove the commutativity it suffices to prove $P_{i+1}P_i=P_iP_{i+1}=P_i$ for every $i\in\N$. While $P_{i}P_{i+1}=P_i$ is clear, we prove for every $f\in\operatorname{Lip}_0(N)$ we have $P_{i+1}P_if=P_if$. Fix $f\in\operatorname{Lip}_0(N)$. If $k(i+1)>k(i)$, then $D_i=\bigcup_{n=1}^{k(i)} C_{4^n}^0$ and $P_{i+1}P_i f(x)=f(x)=P_i f(x)$ for all $x\in \bigcup_{n=1}^{k(i)} C_{4^n}^0$ and $P_{i+1}P_i f(x)=0=P_i f(x)$ for all $x\notin \bigcup_{n=1}^{k(i)} C_{4^n}^0$. Let therefore $k(i+1)=k(i)$.
Denote $a=x_i=\nu^l_{i}(x_{i+1})$ and $b=\nu^r_{i}(x_{i+1})$. All we need to check is $P_{i+1}P_i f(y)=P_i f(y)$ holds for all $y\in C_{4^{k(i)}}\setminus D_i$. Indeed, for all other points $x$ we have $P_if(x)=P_{i+1}f(x)$. Take therefore a point $y\neq x_{i+1}$ (otherwise it is trivial). Note that $\nu^l_{i}(y)=a$, $\nu^r_{i}(y)=b$ and that $d^r(a,x_{i+1})=1$. Then we have
\begin{align*}
P_{i+1}(P_i f)(y)&=\frac{d^r(x_{i+1},y)P_if(b)+d^r(y,b)P_if(x_{i+1})}{d^r(x_{i+1},b)}\\
&=\frac{d^r(x_{i+1},y)f(b)+d^r(y,b)\cdot\frac{f(b)+d^r(x_{i+1},b)f(a)}{d^r(a,b)}}{d^r(x_{i+1},b)}\\
&=\frac{d^r(x_{i+1},y)d^r(a,b)+d^r(y,b)}{d^r(x_{i+1},b)d^r(a,b)}\cdot f(b)+\frac{d^r(y,b)}{d^r(a,b)}\cdot f(a)\\
&=\frac{d^r(x_{i+1},y)d^r(x_{i+1},b)+d^r(x_{i+1},y)+d^r(y,b)}{d^r(x_{i+1},b)d^r(a,b)}\cdot f(b)+\frac{d^r(y,b)}{d^r(a,b)}\cdot f(a)\\
&=\frac{d^r(x_{i+1},b)\left(1+d^r(x_{i+1},y)\right)}{d^r(x_{i+1},b)d^r(a,b)}\cdot f(b)+\frac{d^r(a,y)}{d^r(a,b)}\cdot f(a)\\
&=\frac{d^r(a,y)}{d^r(a,b)}\cdot f(b)+\frac{d^r(a,y)}{d^r(a,b)}\cdot f(a)\\
&=P_i f(y)\\
\end{align*}
and the commutativity is proved.
Let $i\in\N$. If $f_{\alpha}\to f$ pointwise, then for every $x\in D_i$ we have $P_if_{\alpha}(x)=f_{\alpha}(x)\to f(x)=P_if(x)$ and for every $x\in\bigcup_{l=k(i)+1}^\infty C_{4^{l}}$ we have $P_if_{\alpha}(x)=0=P_if(x)$. Finally, for every $x\in C_{4^{k(i)}}\setminus D_i$ we have $P_if_{\alpha}(x)=\gamma_x f_{\alpha}(a_x)+(1-\gamma_x)f_{\alpha}(b_x)$, for some eligible $\gamma_x\in [0,1]$, $a_x,b_x\in D_i$ and the choice of these points depends only on $x$ (and $i$ of course). Therefore $P_if_{\alpha}\to P_if$ pointwise, which means that every operator $P_i$ is continuous with respect to topology of pointwise convergence.
Finally the sequence $P_if$ converges pointwise to $f$. Indeed, for every $y\in N$ there exists $i\in\N$ such that $y\in D_i\subseteq D_{i+1}\subseteq D_{i+2}\dots$, which yields $P_i f(y)=P_{j}f(y)=f(y)$ for all $j\geq i$. Hence $P_i f\to f$ pointwise.
Since the operators $P_i$ meet all assumptions from Theorem \ref{operator}, we get that there is a sequence of operators $T_i:\mathcal F(N)\to\mathcal F(N)$, $i\in\N_0$ with $T_i^*=P_i$ which build a monotone Schauder basis for $\mathcal F(N)$.
\end{proof}
\begin{remark*} It was not necessary for the construction of $P_i$'s to enumerate the set $N$ with respect to orientation on every circle $C_{4^k}$. Actually any enumeration which satisfies $x_i\in C_{4^{k}}$ for every $i\in\N$ works. Our choice only slightly simplifies the proof.
\end{remark*}
\section{Unconditionality of retractional Schauder bases}\label{unconditionality}
As we construct a Schauder basis on $\mathcal F(M)$ via sequence of retractions, as described in Corollary \ref{one}, properties of such a basis depend also on properties of the metric space $M$. Naturally it leads us to the question: What can $M$ be like such that there is an unconditional retractional Schauder basis on $\mathcal F(M)$? The next lemma sets a condition on the chains under which the acquired basis is conditional. It is further used in Theorem \ref{main}, which shows that retractional bases on Free spaces of nets in finite-dimensional spaces are conditional.
\begin{lemma}\label{alligned chains} Let $\alpha,\beta>0$ and let $N$ be an $\alpha$-separated metric space, such that there exist retractions $\varphi_i:N\to N$ satisfying the conditions from Corollary \ref{one}. Suppose there exists $n_0\in\N$ such that for every $n\in\N$, $n\geq n_0$ there exist chains $S=(\mu_{0},\mu_{k_1},...,\mu_{k_s})$ and $T=(\mu_0,\mu_{l_1},...,\mu_{l_m})$, $s,m\in\N$ with $d(\mu_{k_s},\mu_{l_m})\leq\beta$ and $|S\setminus T|\geq n$. Then the retractional Schauder basis on $\mathcal F(N)$ corresponding to the retractions $\varphi_i$ is conditional.
\end{lemma}
\begin{proof}
Let now $P_i$ be the associated Schauder projection to the mapping $\varphi_i$ for each $i\in\N_0$, i.e. the projection to the subspace $\operatorname{span}\{\delta_{\mu_0},\delta_{\mu_1},...,\delta_{\mu_i}\}$. Instead of working directly with $P_0,P_1,P_2,...$ we will use their adjoints $P_0^*,P_1^*,P_2^*,...$ and for every $n\in\N$, $n\geq n_0$ we construct a function $f_n\in\operatorname{Lip}_0(N)$ with $\| f_n\|\leq 1$ and find a sequence of signs $ \varepsilon_0, \varepsilon_1,..., \varepsilon_{k_s}$ for some $s\geq n$ such that the following inequality holds
$$\left\Vert\sum_{i=0}^{k_s} \varepsilon_i(P_{i+1}^*-P_{i}^*)f_n\right\Vert\geq \frac{\alpha (n-1)}{\beta}.$$
Fix $n\in\N$ and chains $S=(\mu_0,\mu_{k_1},...,\mu_{k_s})$, $T=(\mu_0,\mu_{l_1},...,\mu_{l_m})$ for which we have $d(\mu_{k_s},\mu_{l_m})<\beta$ and $|S\setminus T|\geq n$. Suppose now $t\in\{0,1,2,...,s-n\}$ is such that $\mu_{k_t}\in T$ and $\mu_{k_{t+1}}\notin T$ (we set $\mu_{k_0}=\mu_0$). We define the function $f_n$ on $N$ via the formula
$$f_n(x)=\begin{cases}
\frac{\alpha}{2} & x=\mu_{k_j}\text{ for } j \text{ odd},j>t\,,\\
\frac{-\alpha}{2} & x=\mu_{k_j}\text{ for } j \text{ even},j> t\,,\\
0 & \text{else}\,.
\end{cases}$$
Clearly, $f_n(\mu_0)=0$ and $\| f_n\|\leq 1$. For the following choice of sings $ \varepsilon_0=1$,
$$ \varepsilon_i=\begin{cases}
- \varepsilon_{i-1} & i=k_j \text{ for some }j\in\N\,,\\
\varepsilon_{i-1} & \text{else}\,,
\end{cases}$$
we have
$$\sum_{i=0}^{k_s} \varepsilon_i(P_{i+1}^*-P_{i}^*)=-P_0^{*}+2\sum_{j=1}^s(-1)^{j+1}P^*_{k_j}+(-1)^sP^{*}_{k_s+1}=:P$$
and then
\begin{align*}
\left\Vert P\right\Vert&\geq \left\Vert P f_n\right\Vert\geq \left\Vert \frac{Pf_n(\mu_{k_s})-Pf_n(\mu_{l_m})}{d(\mu_{k_s},\mu_{l_m})}\right\Vert\geq\frac{1}{\beta}\left\Vert Pf_n(\mu_{k_s})-Pf_n(\mu_{l_m})\right\Vert=\\
&=\frac{1}{\beta}\left\vert -f_n(0)+2\sum_{j=1}^s(-1)^{j+1}f_n(\mu_{k_j})+(-1)^sf_n(\mu_{k_s})+0\right\vert\\
&=\frac{1}{\beta}\left\vert 2\sum_{j=t+1}^s\frac{\alpha}{2}-\frac{\alpha}{2}\right\vert\geq\frac{\alpha(s-t-1)}{\beta}\geq\frac{\alpha (n-1)}{\beta}.\\
\end{align*}
\end{proof}
Recall that a subset $S$ of a metric space $M$ is called an $\alpha,\beta$-net whenever $S$ is $\alpha$-separated and $\beta$-dense in $M$, i.e. $\inf_{x\neq y}d(x,y)\geq \alpha$, $x,y\in S$ and $\operatorname{sup}_{x\in M} d(x,S)\leq \beta$.
In \cite{HN}, the authors constructed a system of retractions on the integer lattice in $c_0$ which satisfies the conditions of Corollary \ref{one}. Through suitable homomorphisms they further showed the existence of a basis on any Free space of a net in a separable $C(K)$ space or a net in $c_0^+$, the positive cone in $c_0$.
\begin{corollary} Let $N$ be a net in any of the following metric spaces: $C(K)$, $K$ metrizable compact, or
$c_0^+$ (the subset of $c_0$ consisting of elements with non-negative coordinates). The basis on $\mathcal F(N)$ constructed in \cite{HN} is conditional.
\end{corollary}
\begin{proof}
First we consider the case $N=\mathbb{Z}^{<\omega}\subseteq c_0$, the integer lattice in $c_0$. Following the proof of Lemma $14$ in \cite{HN} we see, there are chains which go parallelly along the first coordinate axis (or any other coordinate axis). Every such two chains hence satisfy the conditions of the previous lemma, which yields that a basis arising from these retractions cannot be unconditional. As the existence of bases in other cases than $N$ being the integer lattice in $c_0$ was proven only by isomorphisms, we conclude that none of them are unconditional.
\end{proof}
\begin{theorem}\label{main}
Let $N$ be an $\alpha,\beta$-net in a finite-dimensional normed space $X$ with $\dim X\geq 2$. Let $E=\{e_i\}_{i=1}^\infty$ be a retractional Schauder basis on $\mathcal F(N)$. Then $E$ is conditional.
\end{theorem}
In the following, $B_{ \varepsilon}(x)$ denotes closed ball of radius $ \varepsilon>0$ and centre $x\in X$, $B_{ \varepsilon}^{\circ}(x)$ denotes its interior. In the same way $B_{ \varepsilon}:=B_{ \varepsilon}(0)$ and $S_{ \varepsilon}$ denotes sphere of radius $ \varepsilon$ and centre $0$.
\begin{proof}
Let $\varphi_i:N\to N$ be the corresponding retractions to the basis $E$. We prove the theorem by showing that the assumptions of Lemma \ref{alligned chains} are met. Denote $\operatorname{sup}_{i\in\N}\operatorname{Lip}\varphi_i=K<\infty$. Pick $n\in\N$, such that $n>8K$. Define annulus with radii $r$ and $w$, $w<r$ as $A(r,w)=B_{r+w}(0)\setminus B^{\circ}_{r-w}(0)$. Our aim is to prove there exist chains $T,Z$ with final points $t,z\in A(3K\beta n+\beta,\beta)\cap N$ with $d(t,z)\leq 2\beta$ such that $x\in B_{K\beta n}$ holds for $x=x_{t,z}$, the final point of the chain $T\cap Z$. Then we have $d(t,x)\geq 3K\beta n-K\beta n=2K\beta n$ and Step lemma \ref{step} yields $|T\setminus Z|\geq n$, which by Lemma \ref{alligned chains} concludes the proof.
For the following, for every two points $x,y\in N$ with $x\prec y$ denote $T_x^y$ the chain with initial point $x$ and final point $y$. Assume now for contradiction, for every pair of points $t,z\in A(3K\beta n+\beta,\beta)\cap N=:A$ with $d(t,z)\leq 2\beta$ the final point $x_{t,z}$ of $T_0^t\cap T_0^z$ lies outside the ball $B_{K\beta n}$. That means there exists a point $\mu_m\in N$ for some $m\in\N$ with $d(0,\mu_m)>K\beta n$ such that $\varphi_m(t)=\mu_m$ for every $t\in A$. To prove this, note that $0\in\bigcap_{t\in A}T_0^t$ and as $\bigcap_{t\in A}T_0^t$ is a chain, it has a final point which we denote $\mu_m$ and prove that $d(0,\mu_m)>K\beta n$. We show that for every two points $t,z\in A$ the final point $x_{t,z}$ of the chain $T_0^t\cap T_0^z$ is of greater norm than $K\beta n$. Clearly, if $d(t,z)\leq 2\beta$, the statement holds as assumed. If $d(t,z)> 2\beta$, we can find a finite sequence of points $y_1,...,y_l\in A$, $l\in\N$ such that $d(y_i,y_{i+1})\leq 2\beta$ for every $i\in\{1,...,l-1\}$ and that $y_1=t$ and $y_l=z$. Then $x_{t,z}\in\{x_{y_i,y_{i+1}}|\ i\in\{1,...,l-1\}\}$, which means $\| x_{t,z}\|> K\beta n$. Note that for any three points $s,t,z\in A$ the final point $x_{s,t,z}$ of the chain $T_0^s\cap T_0^t\cap T_0^z$ is equal to one of the points $x_{s,t},x_{t,z},x_{s,z}$. Indeed, as $x_{s,t},x_{t,z}\in T_0^t$, we have that either $x_{s,t}\prec x_{t,z}$ or $x_{s,t}\succ x_{t,z}$. If $x_{s,t}\prec x_{t,z}$, then $x_{s,z}=x_{s,t}=x_{s,t,z}$ and the other case follows symmetrically. But from that we get inductively that for any finite number of points $t_1,...,t_v$, there are indices $i,j\in\{1,...,v\}$, such that the final point $x_{t_1,...,t_v}$ of the chain $\bigcap_{l=1}T_0^{t_l}$ equals $x_{t_i,t_j}$. Because for each two $t,z\in A$ we have $\| x_{t,z}\|>K\beta n$ and $A$ is finite, we have $\| \mu_m\|> K\beta n$.
Observe further, that $T_{\mu_m}^t\cap B_{\beta n}=\emptyset$ holds for every chain $T_{\mu_m}^t$ with initial point $\mu_m$ and final point $t\in A$. Indeed, if $\mu_p\in T_{\mu_m}^t$, $p\in\N$ is such that $\|\mu_p\|\leq \beta n$, we have $\operatorname{Lip}\varphi_m\geq \frac{\|\varphi_m(0)-\varphi_m(\mu_p)\|}{\| \mu_p\|}=\frac{\|\mu_m\|}{\|\mu_p\|}>\frac{K\beta n}{\beta n}=K$, which is not possible.
Let us denote $S=\bigcup_{t\in A}T_{\mu_m}^{t}$ the set of all chains from $\mu_m$ to points of $A$. Let $S=\{\mu_{k_1},...,\mu_{k_q}\}$ for some $k_1<k_2<...<k_q$, $q\in\N$. Note that $\mu_{k_1}=\mu_m$. For every chain $T=(t_1,...,t_l)$, $l\in\N$ define a trajectory of the chain $\operatorname{Tr}(T)$ as the union of the line segments $\bigcup_{i=1}^{l-1} [t_i,t_{i+1}]$. Denote $D=\bigcup_{t\in A}\operatorname{Tr}\left(T_{\mu_m}^{t}\right)$. Define now a function $F:[1,q]\times A\to D$ via
$$F(t,x)=(t-i)\varphi_{k_{i+1}}(x)+(1-(t-i))\varphi_{k_{i}}(x), x\in A, t\in [i,i+1), i\in\{1,...,q-1\}$$
and $F(q,x)=x$, $x\in A$. We see that for each $t\in [1,q]$, the function $F(t,\cdot)$ is $K$-Lipschitz and that we have $F(1,x)=\mu_m$ for all $x\in A$.
Let $ \varepsilon=3K\beta n+\beta$ and consider $B=\{B^{\mathrm{o}}_{2\beta}(x)\cap S_{ \varepsilon}\}_{x\in A}$ as an open cover of $S_{ \varepsilon}$ and find a partition of unity $\{\psi_a\}_{a\in A}$ subordinated to the cover $B$. Define a function $R:[1,q]\times S_{ \varepsilon}\to X$ by
$$R(t,x)=\sum_{a\in A}\psi_a(x)F(t,a),\ \ t\in [1,q],\ x\in S_{ \varepsilon}.$$
We see, that $R(1,x)=\mu_m$ for all $x\in S_{ \varepsilon}$ and that $$\operatorname{sup}_{x\in S_{ \varepsilon}}|R(q,x)-x|\leq 2\beta.$$ Of course, $R$ is continuous on $[1,q]\times S_{ \varepsilon}$. Our goal is to prove there is a continuous deformation of $S_{ \varepsilon}$ into one point $\mu_m$ avoiding the origin, which is a contradiction. For that we define a straight-line homotopy between identity and $R(q,\cdot)$ by $W:[0,1]\times S_{ \varepsilon}\to A( \varepsilon,2\beta)$, $W(t,x)=tR(q,x)+(1-t)x$. Joining mappings $W$ and $R$ we get a mapping $Z:[0,q]\times S_{ \varepsilon}\to X$ precisely defined by
$$Z(t,x)=\begin{cases}
W(t,x) & t\in[0,1), x\in S_{ \varepsilon}\,,\\
R\left(\frac{q}{t},x\right) & t\in[1,q], x\in S_{ \varepsilon}\,.\\
\end{cases}$$
All there is left to prove is that $R([1,q]\times S_{ \varepsilon})\cap \{0\}=\emptyset$. To see that, note that the value $R(t,x)$ is a convex combination of values $F(t,a)$, where $a\in A$ are such that $d(x,a)<2\beta$. Fix therefore $x\in S_{ \varepsilon}$ and let $\mu_{l_1},\mu_{l_2},...,\mu_{l_p}\in A$ be such that $d(x,\mu_{l_i})<2\beta$ for all $i$. From the preceding paragraphs it follows that the trajectory $\operatorname{Tr}(T_{\mu_m}^{\mu_{l_i}})$ of each chain from $\mu_m$ to $\mu_{l_i}$ has no intersection with $B_{\beta \frac{n}{2}}$. Indeed, as the chain $T_{\mu_{m}}^{\mu_{l_i}}$ avoids the ball $B_{\beta n}$ and the distance between two consecutive points in a chain is bounded by $2\beta K$ and $n>2K$, we get the result. From the fact that $d(\mu_{l_j},\mu_{l_i})\leq 4\beta$ for all $i,j$, we have that $\| F(t,\mu_{l_i})-F(t,\mu_{l_j})\|\leq 4K\beta$ for all $t\in [1,q]$. But as $n>8K$ we get $R(t,x)\neq 0$ for any $t\in [0,1]$. Altogether we obtain $Z([0,q]\times S_{ \varepsilon})\cap \{0\}=\emptyset$, which was to prove.
\end{proof}
One could ask in general what are the metric spaces $M$ such that $\mathcal F(M)$ has an unconditional Schauder basis. It is clear that if $M$ contains a line segment, then $ L_1$ is contained in $\mathcal F(M)$ and therefore $\mathcal F(M)$ cannot have an unconditional Schauder basis. The only interesting cases are then topologically discrete spaces $M$. Our guess is that if $\mathcal F(M)$ has an unconditional Schauder basis, it is isomorphic to $\ell_1$.
\\
\\\textbf{Open problem 1} \textit{Suppose $\mathcal F(M)$ has an unconditional Schauder basis. Is it isomorphic to $\ell_1$?}
In \cite{Gd}, one sees that $\mathcal F(M)$ is a complemented subspace of $L_1$ if and only if $M$ can be bi-Lipschitzly embedded into an $\R$-tree. A complemented subspace of $ L_1$ with unconditional basis is isomorphic to the space $\ell_1$ due to \cite{LiPe}. One can therefore restate the conjecture above into: Suppose $\mathcal F(M)$ has a Schauder basis $B$. If $M$ cannot be embedded into an $\R$-tree, is it true that $B$ is conditional?
\\
\\\textbf{Open problem 2} \textit{Is it true that for every uniformly discrete set $N\subseteq\R^2$ the space $\mathcal F(N)$ has a Schauder basis?}
It follows from Corollary \ref{no basis} the answer is no if we restrict ourselves only to retractional Schauder bases. However, we don't know if, supposed the answer is yes, we can find for every uniformly discrete set $N\subseteq\R^2$ an extensional Schauder basis on $\mathcal F(N)$.
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 4,067
|
\section{Introduction}
In this article we study an isoperimetric problem with an added long-range repulsive term in two space dimensions. The repulsive term can be seen as the interaction energy of a uniformly charged mass, when restricted to columnar states, i.e., for a given set $E\subset \R^2$, the charged mass is given as $\{(x_1,x_2,x_3)\subset \R^3 : (x_1,x_2)\in E, x_3\in\R\}$. This leads to a logarithmic interaction kernel.
The study of charged droplets is commonly referred to as Gamow's liquid drop model \cite{gamow1928quantentheorie}, originally devised for an explanation for the shape of nuclear cores due to a competition between short range attractive (e.g., perimeter type) and long range repulsive (e.g., Coulombic) potentials. In many cases, this leads to existence of minimizers up to a critical mass (which then are usually spherical), and nonexistence thereafter (since, when breakup into more than one piece is energetically expedient, these pieces can further reduce the interaction energy by increasing their distance) \cite{MR3509012,MR3055587,MR3272365,MR3226747,MR3218265,MR3794526}. Nonexistence for larger masses can of course be prevented by considering droplets confined to bounded domains \cite{MR3069960} or background potentials, where breakup or loss of existence may again depend on the relative strengths of the confining and repulsive potentials \cite{MR3947064, MR3251907}.
In our setting, due to the restriction to columnar sets and a full Coulombic interaction, we are faced with nonexistence of minimizers for any prescribed area of a two-dimensional slice $E$ when considering a standard perimeter since the extension to three dimensions always has infinite mass. Instead of introducing a background potential, however, we opt for a different avenue, also pursued in \cite{dayrens2019connected}: we replace the standard perimeter with a `connected perimeter', which can be briefly described by the relaxation of the perimeter of a connected, $L^1$-approximating set. For a precise statement on the setting, see Section \ref{section preliminaries}. To conform with the common language in the mathematics literature concerning such charged mass models, we will, in the following, refer to the prescribed area of a two-dimensional slice as the `mass' in the problem -- this is a slight abuse of nomenclature, as it is in fact a mass density when considering the associated three-dimensional problem. Furthermore, even though we are talking about a minimization problem which is effectively two-dimensional, we will refer to the sets $E$ as charged `droplets'.
This connected perimeter used here was introduced in \cite{dayrens2019connected}. A phase-field variant of the connected perimeter was developed in \cite{MR4011685}.
Our main analytic results are the following.
\begin{enumerate}
\item Minimizers exist for any mass. This part, in Section \ref{sec:existence}, follows closely the arguments in \cite{dayrens2019connected}.
\item A charged droplet of small mass aggregates in a disk. We call this the {\em perimeter-dominated} regime since minimization of surface tension drives the behavior. Our connectedness constraint does not influence the local behavior in this regime -- it does, however, remove the global minimizer of droplets disappearing at infinity in opposite directions. The analysis is conducted in Section \ref{section small mass} and the precise result is stated in Theorem \ref{prop2}. The main difficulty here is that the connected perimeter does not directly yield sufficient regularity for minimizers to study the Euler-Lagrange-equation of the energy.
\item Charged drops of large mass organize in long and thin objects. We call this the {\em repulsion-dominated} regime. This regime is considered in Section \ref{section large mass}. Precise statements are given in Theorems \ref{theorem long} and \ref{theorem thin}, together with an asymptotic expansion of the minimal energy in terms of problem parameters in Theorem \ref{theorem scaling}.
\end{enumerate}
To study the intermediate regime, we use an efficient numerical method to find shapes of minimizing configurations in numerical simulations using an Ohta-Kawasaki phase-field approximation of our problem, including the connectedness constraint. The phase-field simulations of course take place on bounded domains, so some aspects of confinement as well as further changes when requiring simple-connectedness are studied there as well.
The article is structured as follows. A rigoros introduction to the problem is given in Section \ref{section preliminaries}. We present analytic results concerning existence and shapes of minimizers of our functional in Section \ref{section analysis}, before developing the phase-field approach and discussing numerical results in Section \ref{numerics}.
\section{Preliminaries}\label{section preliminaries}
We study the variational problems associated with the energy functionals
\begin{align}\label{thefunc1}
{\mathcal F}^{\lambda}_{C}(\chi_{E}) \coloneqq \ \overline{P^{r}_{C}}(\{\chi_{E} =1\}) + \lambda \int\limits_{\mathbb{R}^{2}}\int\limits_{\mathbb{R}^{2}} \log\left(\frac{1}{|x-y|}\right)\chi_{E}(x)\chi_{E}(y) ~\mathrm{d}x\mathrm{d}y,
\end{align}
\begin{align}\label{thefunc2}
{\mathcal F}^{\lambda}_{S}(\chi_{E}) \coloneqq \overline{P^{r}_{S}}(\{\chi_{E} =1\}) + \lambda\int\limits_{\mathbb{R}^{2}}\int\limits_{\mathbb{R}^{2}} \log\left(\frac{1}{|x-y|}\right)\chi_{E}(x)\chi_{E}(y) ~\mathrm{d}x\mathrm{d}y,
\end{align}
where $\chi_{E}$ is the characteristic function of the subset $E\subset \mathbb{R}^{2}$ with finite perimeter and volume/mass $|E|= m>0$ and $\lambda > 0$ is a parameter. Here $\overline{P^{r}_{C}}$ and $\overline{P^{r}_{S}}$ describe the connected and the simply connected perimeter of the set $E$ defined by
\begin{align*}
\overline{P^{r}_{C}}(E)=\inf \left\{ \liminf_{n\rightarrow \infty} P(E_{n}) \ | \ E_{n}\rightarrow E \ \text{in} \ L^{1}, E_{n} \ \text{connected and} \ C^{\infty}-\text{smooth}\right\},
\end{align*}
and
\begin{align*}
\overline{P^{r}_{S}}(E)=\inf \left\{ \liminf_{n\rightarrow \infty} P(E_{n}) \ | \ E_{n}\rightarrow E \ \text{in} \ L^{1}, E_{n} \ \text{simply connected and} \ C^{\infty}-\text{smooth}\right\},
\end{align*}
where $P(\cdot)$ is the usual perimeter of a set.
It was shown recently \cite{dayrens2019connected}, that for essentially bounded sets $E\subset \mathbb{R}^{2}$ such that $\partial E =\partial_{*}E$ modulo sets of zero $\mathcal{H}^{1}$-measure the identity
\[
\overline{P^{r}_{C}}(E)=P(E)+2\mathcal{S}t(E)
\]
holds, where $\mathcal{S}t(E)$ is the length of the Steiner tree of $\bar{E}$, i.e.,
\[
\mathcal{S}t(E)=\inf \{ \mathcal{H}^{1}(K)| E\cup K \ \text{connected} \}.
\]
Above, $\mathcal{H}^{1}$ denotes the $1$-dimensional Hausdorff measure on $\mathbb{R}^{2}$ and $\partial_{*}E$ is the essential boundary of $\bar{E}$, see Definition 3.60 in~\cite{MR1857292}. For the existence of Steiner trees, their properties and regularity see~\cite{MR3018174}.
In the following, we consider the minimization problem
\begin{align}\label{min}
\min_{\substack{E\subset \mathbb{R}^{2}, \\ |E|=m}} {\mathcal F}^{\lambda}_{C/S}(\chi_{E}).
\end{align}
We prove that minimizers exist for all $ m > 0$ and all $\lambda > 0$ and describe the shape of such minimizers for small masses $m$/small parameters $\lambda$ and large masses $m$/large parameters $\lambda$, respectively.
\begin{remark}
We note that due to the unboundedness of the logarithmic potential, the functional $ P(\{\chi_{E} =1\}) + \lambda \int\limits_{\mathbb{R}^{2}}\int\limits_{\mathbb{R}^{2}} \log\left(\frac{1}{|x-y|}\right)\chi_{E}(x)\chi_{E}(y) ~\mathrm{d}x\mathrm{d}y$ on $\R^2$ does not admit minimizers for any $\lambda>0$ or any prescribed mass. Usage of the connected perimeter is therefore necessary for the arguments below.
\end{remark}
\section{Analytical Results}\label{section analysis}
\subsection{Existence of Minimizers} \label{sec:existence}
We prove the existence of solutions of the problem in~\eqref{min} for all masses $m>0$ and all $\lambda > 0$. This section follows the proof in \cite{dayrens2019connected}, where the nonlocal part of the energy was given by
\begin{align*}
\int\limits_{\mathbb{R}^{2}}\int \limits_{\mathbb{R}^{2}} \frac{1}{|x-y|^{\alpha}}\chi_{E}(x)\chi_{E}(y) ~\mathrm{d}x\mathrm{d}y
\end{align*}
with some $\alpha \in (0,2)$. In \cite{dayrens2019connected}, the singularity at the origin is stronger, leading to a stronger local repulsion. On the other hand, the power law interaction decays to zero at infinity while the logarithm of inverse distance approaches negative infinity. This leads to a stronger non-local ``attraction from infinity'' in our model. While both interaction models drive sets to be more `spread out', the precise mechanisms are different.
To adapt the proof from Theorem 5.2 in~\cite{dayrens2019connected} to our case we first state the following simple proposition.
\begin{proposition}\label{prop0}
For $m>0$, $R>0$ we have
\begin{align*}
\inf_{\substack {E \subset B_{R}(0), \\ |E|=m}}\lambda \int\limits_{\mathbb{R}^{2}} \int\limits_{\mathbb{R}^{2}} \log\left(\frac{1}{|x-y|}\right)\chi_{E}(x)\chi_{E}(y) ~\mathrm{d}x\mathrm{d}y \geq - m^{2}\lambda \log(\operatorname{diam} E) \geq - m^{2}\lambda \log(2R).
\end{align*}
\end{proposition}
\begin{proof}
The inequality follows from basic estimates on the logarithm and the diameter.
\end{proof}
\begin{remark}
Here and below we denote the diameter of a measurable set $E$ as
\[
\operatorname{diam}(E) = \sup\left\{|x-y|\::\: |E\cap B_r(x)|, \:|E\cap B_r(y)| >0\quad\forall\ r>0\right\}.
\]
As usual, $B_R(x)$ denotes the ball of radius $R$ around a point $x$, in our case always in $\R^2$.
\end{remark}
We also require a continuity result, analogous to \cite[Lemma 5.1]{dayrens2019connected}.
\begin{lemma}\label{lem3}
Let $R>0$ and let $E_n$ be a sequence of sets such that
\[
E_n\subseteq B_R(0), \qquad \chi_{E_n}\to \chi_E \quad\text{in }L^1(B_R(0)).
\]
Then
\[
\int\limits_{E_n}\int\limits_{E_n} \log\left(\frac{1}{|x-y|}\right) ~\mathrm{d}x\mathrm{d}y \to \int\limits_{E}\int\limits_{E} \log\left(\frac{1}{|x-y|}\right) ~\mathrm{d}x\mathrm{d}y.
\]
\end{lemma}
\begin{proof}
The logarithm of inverse distance is integrable on $B_R(0)\times B_R(0)$, so the result follows from the dominated convergence theorem.
\end{proof}
This allows to prove the statement ensuring existence of minimizers for any mass.
\begin{theorem}\label{theorem existence of minimizers}
For all $m > 0$ and all $\lambda > 0$ the minimization problems
\begin{align}\label{min1}
\min \left \{ \overline{P^{r}_{C}}(E) + \lambda \int\limits_{E}\int\limits_{E} \log\left(\frac{1}{|x-y|}\right) ~\mathrm{d}x\mathrm{d}y \ \bigg| \ E\subset \mathbb{R}^{2} \ \text{measurable},|E|=m\right\},
\end{align}
\begin{align}\label{min2}
\min \left \{ \overline{P^{r}_{S}}(E) + \lambda \int\limits_{E}\int\limits_{E} \log\left(\frac{1}{|x-y|}\right) ~\mathrm{d}x\mathrm{d}y \ \bigg| \ E\subset \mathbb{R}^{2} \ \text{measurable},|E|=m\right\}
\end{align}
for ${\mathcal F}_C^\lambda$ and ${\mathcal F}_S^\lambda$, respectively, admit solutions. Furthermore, there exists a constant $C>0$, depending only on $m$ and $\lambda$, so that any solution $E$ to the minimization problem above satisfies $\operatorname{diam}(E) < C$.
\end{theorem}
\begin{proof}
We consider the case of ${\mathcal F}_C^\lambda$, the proof for ${\mathcal F}_S^\lambda$ proceeds analogously.
Before proceeding we mention that for any connected set $E$ of finite perimeter, we have
\begin{align}\label{inequality}
2\operatorname{diam}(E) \leq |\partial E|
\end{align}
and thus obtain, using Proposition \ref{prop0},
\begin{align}\label{eq1}
\mathcal{F}^{\lambda}_{C}(\chi_E) \geq 2\operatorname{diam}(E) - \lambda m^{2} \log(\operatorname{diam}(E)) \geq \min_{r>0} (2r-\lambda m^{2} \log(r)) > -\infty.
\end{align}
Let now $E_{n}$ be a minimizing sequence for the problem in~\eqref{min1} with $|E_{n}|=m < \infty$. We immediately obtain from \eqref{eq1} that $\sup_n\operatorname{diam}(E_n) < C(m,\lambda)$. Using the translation invariance of ${\mathcal F}^{\lambda}_{C}$, we may thus assume that there exists $R>0$ such that $E_n\subset B_R(0)$ for all $n\in\N$, modulo Lebesgue null sets. The usual compactness of sets of finite perimeter, together with Lemma \ref{lem3}, yield the existence result.
\end{proof}
\begin{remark} \label{rem:scaling_bound}
Note that by approximation, estimate \eqref{eq1} carries over to the minimizer, denoted by $E_{m,\lambda}$, so that
\begin{equation}\label{eq scaling lower bound}
{\mathcal F}_C(\chi_{E_{m,\lambda}}) \geq 2\operatorname{diam}(E_{m,\lambda}) - \lambda m^{2} \log(\operatorname{diam}(E_{m,\lambda})).
\end{equation}
\end{remark}
\subsection{Shape of Minimizers for Small Mass}\label{section small mass}
Now we consider the shape of solutions of~\eqref{min1} and~\eqref{min2} for small masses $m$ or small values of $\lambda > 0$ respectively. The goal of this section is to show that for small values $\lambda >0$ or small masses $m > 0$ the unique solution of~\eqref{min1} and~\eqref{min2} is a disk.
We first note that, for a given set $E$ and $\mu>0$, we have
\[
|\mu E| = \mu^2\,|E|, \qquad \overline{P^r_C}(\mu E) = \mu\,\overline{P^r_C}(E)
\]
since $\overline{P^r_C}$ scales like the perimeter functional, and
\begin{align*}
\int_{\mu E} \int_{\mu E} \log\left(\frac1{|x-y|}\right) \,\mathrm{d}x \,\mathrm{d}y
&= \int_{E} \int_{E} \log\left(\frac1{|\mu x-\mu y|}\right) \mu^2\,\mathrm{d}x \,\mu^2\,\mathrm{d}y\\
&= \mu^4 \int_E\int_E \log\left(\frac1{|x- y|}\right) + \log \left(\frac1{\mu}\right)\,\mathrm{d}x\,\mathrm{d}y\\
&= \mu^4 \int_E\int_E \log\left(\frac1{|x- y|}\right)\,\mathrm{d}x\,\mathrm{d}y - \mu^4\log(\mu) \,|E|^2.
\end{align*}
The last term on the right hand side is independent of $E$ when $|E|=m$ is fixed. Thus the minimization problems
\[
\text{minimize}\quad \overline{P^r_C}(E) + \lambda \int_{E} \int_{E} \log\left(\frac1{|x-y|}\right) \,\mathrm{d}x \,\mathrm{d}y
\]
in the class of sets with mass $|E|=m$ and
\[
\text{minimize}\quad \sqrt{\frac m\pi} \cdot \left[\overline{P^r_C}(E) + \lambda\left(\frac m\pi\right)^{3/2} \int_{E} \int_{E} \log\left(\frac1{|x-y|}\right) \,\mathrm{d}x \,\mathrm{d}y\right]
\]
in the class of sets with mass $|E|= \pi$ are equivalent by rescaling with $\mu = \sqrt{\frac m\pi}$. We conclude that considering the small mass limit for fixed $\lambda$ and the small $\lambda$ limit for fixed mass are equivalent and thus confine ourselves to the case where the mass $|E|=m=\pi$ is fixed and $\lambda$ becomes small.
\begin{remark}
Of course, the scaling argument remains unchanged if $\overline{P^r_C}$ is replaced by the standard perimeter $P$.
\end{remark}
We now consider the functional
\begin{align}\label{thefunc_const}
{\mathcal F}^{\lambda}(\chi_{E})\coloneqq P(E) + \lambda \int\limits_{E}\int\limits_{E} \log\left(\frac{1}{|x-y|}\right) ~\mathrm{d}x\mathrm{d}y
\end{align}
and the constrained optimization problem
\begin{align}\label{min_const}
\min \left \{ {\mathcal F}^{\lambda}(\chi_{E}) \bigg| \ E\subset \mathbb{R}^{2} \ \text{measurable},|E|=\pi, E\subset B_\rho \right \},
\end{align}
with $\rho>2C(\pi,\lambda)$, the diameter bound from Theorem \ref{theorem existence of minimizers}. Existence of solutions for this problem immediately follows from standard existence theory of minimizers for lower semicontinuous functionals bounded from below. Let now $E$ be a minimizer of ${\mathcal F}^{\lambda}(\chi_{E})$ in the class above and $E'\subset B_\rho(0)$. We then obtain
\begin{align}\label{eq:quasi_min1}
\int\limits_{E}\int\limits_{E} \log\left(\frac{1}{|x-y|}\right)~\mathrm{d}x\mathrm{d}y &- \int\limits_{E'}\int\limits_{E'}\log\left(\frac{1}{|x-y|}\right)~\mathrm{d}x\mathrm{d}y \notag \\
&= \int\limits_{\mathbb{R}^{2}}\int\limits_{\mathbb{R}^{2}} \log\left(\frac{1}{|x-y|}\right) \chi_{E}(x)\chi_{E}(y)~\mathrm{d}x\mathrm{d}y \notag \\
&- \int\limits_{\mathbb{R}^{2}}\int\limits_{\mathbb{R}^{2}} \log\left(\frac{1}{|x-y|}\right) \chi_{E'}(x)\chi_{E'}(y)~\mathrm{d}x\mathrm{d}y \notag \\
&= \int\limits_{\mathbb{R}^{2}}\int\limits_{\mathbb{R}^{2}} \log\left(\frac{1}{|x-y|}\right) \chi_{E}(x)(\chi_{E}(y)-\chi_{E'}(y))~\mathrm{d}x\mathrm{d}y \notag \\
&+\int\limits_{\mathbb{R}^{2}}\int\limits_{\mathbb{R}^{2}} \log\left(\frac{1}{|x-y|}\right) \chi_{E'}(x)(\chi_{E}(y)-\chi_{E'}(y))~\mathrm{d}x\mathrm{d}y.
\end{align}
Taking now $\omega_{1} = \log\left(\frac{1}{|x-y|}\right) * \chi_{E}$ and $\omega_{2}= \log\left(\frac{1}{|x-y|}\right) * \chi_{E'}$ we can estimate
\begin{align}\label{eq:quasi_min2}
\int\limits_{E}\int\limits_{E} \log\left(\frac{1}{|x-y|}\right)~\mathrm{d}x\mathrm{d}y&- \int\limits_{E'}\int\limits_{E'}\log\left(\frac{1}{|x-y|}\right)~\mathrm{d}x\mathrm{d}y \notag \\
&\leq \int\limits_{\mathbb{R}^{2}}\omega_{1}(y)(\chi_{E}(y)-\chi_{E'}(y)) ~\mathrm{d}y + \int\limits_{\mathbb{R}^{2}} \omega_{2}(y)(\chi_{E}(y)-\chi_{E'}(y)) ~\mathrm{d}y \notag \\
&\leq \|\omega_{1}\|_{L^{\infty}(E\Delta E')}|E\Delta E'|+\|\omega_{2}\|_{L^{\infty}(E\Delta E')}|E\Delta E'|.
\end{align}
Finally using that $\|\omega_{1}\|_{L^{\infty}(E\Delta E')} \leq \|\omega_{1}\|_{L^{\infty}(B_\rho(0))}$ and $\|\omega_{2}\|_{L^{\infty}(E\Delta E')} \leq \|\omega_{2}\|_{L^{\infty}(B_\rho(0))}$ we have
\begin{align*}
P(E)\leq P(E') + \left(|\omega_{1}\|_{L^{\infty}(B_\rho(0))}+\|\omega_{2}\|_{L^{\infty}(B_\rho(0))}\right) |E\Delta E'| \leq P(E') + C |E\Delta E'|.
\end{align*}
Thus minimizers of ${\mathcal F}^{\lambda}(\chi_{E})$ are quasi-minimizers of the perimeter constrained to lie within a smooth set. It follows that for a solution $E$ of~\eqref{min_const} the boundary $\partial E$ is of class $C^{1,1}$ \cite{MR664576}, see also \cite{MR2976521}.
Thus, recalling the bound on the diameter,
we conclude that every minimizer has a well-defined curvature, and the boundary satisfies the Euler-Lagrange equation for~\eqref{thefunc_const}. Therefore, the procedure from~\cite{MR3055587} is applicable, and we obtain the following result.
\begin{proposition}\label{prop1}
There exists $\lambda_1$ such that for all $\lambda \leq \lambda_1$ the unique solution of~\eqref{min_const} is the unit disk.
\end{proposition}
\begin{proof}
Let $B_{1}=B_{1}(x_{0})$, where $x_{0}$ is the barycenter of $E$. Due to the regularity of $\partial E$ and the uniform boundedness constraint, $E\subset B_{\rho}(0)$, we can apply \cite[Lemma 7.2]{MR3055587}, \cite[Lemma 7.3]{MR3055587} and \cite[Lemma 7.4]{MR3055587} to the problem in \eqref{min_const}. Thus we deduce, that for small $\lambda$ the set $E$ is convex and fulfills
\begin{align}\label{eq5.0}
|E\Delta B_{1}(x_{0})|\leq C \sqrt{D(E)}
\end{align}
with a universal constant $C> 0$ and the isoperimetric deficit $D(E)$ given by
\[
D(E)\coloneqq \frac{|\partial E|}{2\pi}-1.
\]
Now we have ${\mathcal F}^{\lambda}(\chi_{E}) \leq {\mathcal F}^{\lambda}(\chi_{B_{1}})$ by the minimization property of $E$, which is equivalent to
\begin{align}
D(E) \leq \frac{\lambda}{2\pi}\left( \;\int\limits_{B_{1}}\int\limits_{B_{1}} \log\left(\frac{1}{|x-y|}\right)~\mathrm{d}x\mathrm{d}y- \int\limits_{E}\int\limits_{E}\log\left(\frac{1}{|x-y|}\right)~\mathrm{d}x\mathrm{d}y\right).
\end{align}
Transforming like in~\eqref{eq:quasi_min1} we get
\begin{align*}
\int\limits_{B_{1}}\int\limits_{B_{1}} \log\left(\frac{1}{|x-y|}\right)~\mathrm{d}x\mathrm{d}y&- \int\limits_{E}\int\limits_{E}\log\left(\frac{1}{|x-y|}\right)~\mathrm{d}x\mathrm{d}y \\
&\leq \int\limits_{\mathbb{R}^{2}}\omega_{1}(y)(\chi_{B_{1}}(y)-\chi_{E}(y)) ~\mathrm{d}y + \int\limits_{\mathbb{R}^{2}} \omega_{2}(y)(\chi_{B_{1}}(y)-\chi_{E}(y)) ~\mathrm{d}y \\
&\leq \|\omega_{1}\|_{L^{\infty}(B_{1}\Delta E)}|B_{1}\Delta E|+\|\omega_{2}\|_{L^{\infty}(B_{1}\Delta E)}|B_{1}\Delta E|
\end{align*}
with $\omega_{1} = \log\left(\frac{1}{|x-y|}\right) * \chi_{B_{1}}$ and $\omega_{2}= \log\left(\frac{1}{|x-y|}\right) * \chi_{E}$.
Using now that due to the convexity of $E$ and due to $\pi =|E|=|B_{1}|$ we have
\begin{align}\label{eq5.1}
\|\omega_{2}\|_{L^{\infty}(B_{1}\Delta E)}\leq C \|\omega_{1}\|_{L^{\infty}(B_{1}\Delta E)} \leq C |B_{1}\Delta E|
\end{align}
with a constant $C$ independent of $E$, see results from~\cite{MR2456887}, we can finally conclude
\begin{align}\label{eq5.2}
D(E) \leq C \lambda |B_{1}\Delta E|^{2}.
\end{align}
Combining \eqref{eq5.0} and \eqref{eq5.2}, we obtain
\begin{align}\label{eq5}
c |B_{1}\Delta E|^{2} \leq D(E) \leq C \lambda |B_{1}\Delta E|^{2}
\end{align}
for some constants $c$ and $C$, which are independent of $E$. This means that as long as $\lambda$ is small enough we have $D(E)=0$ and thus find $E=B_{1}(x_{0})$.
\end{proof}
We can now use the above result to reach a conclusion for the connected perimeter, but without constraint.
\begin{theorem}\label{prop2}
There exists $\lambda_{0}$ such that for all $\lambda \leq \lambda_{0}$ the unique minimizers of ${\mathcal F}_{C}^{\lambda}(\chi_{E})$ and ${\mathcal F}_{S}^{\lambda}(\chi_{E})$ are the unit disk.
\end{theorem}
\begin{proof}
We restrict ourselves to ${\mathcal F}_{C}^{\lambda}(\chi_{E})$ as the result for ${\mathcal F}_{S}^{\lambda}(\chi_{E})$ follows in the same manner and consider only $\lambda < 1$. Let again $B_{1}=B_{1}(x_{0})$ with the barycenter $x_{0}$ of $E$.
As derived in Theorem \ref{theorem existence of minimizers}, minimizers $E$ of ${\mathcal F}_{C}^{\lambda}(\chi_{E})$ satisfy $\operatorname{diam}(E)\le C$ with a uniform bound, so we may assume that up to translation we have $E\subset B_{2C}(0)$. Now that
\[
P(E)\leq \overline{P^{r}_{C}}(E)
\]
for all $E\subset B_{2C}(0)$ we have
\[
{\mathcal F}^{\lambda}(B_{1})\leq{\mathcal F}^{\lambda}(E)\leq {\mathcal F}_{C}^{\lambda}(E)
\]
for all $E\subset B_{2C}(0)$ by Proposition~\ref{prop1}. The assertion then follows from $P(B_{1})=\overline{P^{r}_{C}}(B_{1})$.
\end{proof}
\subsection{Shape of Minimizers for Large Mass}\label{section large mass}
In this section, we consider the large mass limit as the opposite extreme. We obtain the first two contributions to the energy expansion in the large length limit. The shape of minimizers is described only coarsely, showing that their diameter scales weakly like $\lambda$ and that they do not concentrate mass close to any point on scales significantly smaller than $O(\lambda)$. It remains open whether they are convex, and how minimizers look in the intermediate regime. Denote
\begin{align}
e_C(\lambda)&:= \min \left \{ {\mathcal F}_C^\lambda(\chi_E)\:\big|\: E\subseteq \R^2\text{ measurable, }|E| = \pi\right\},\\
e_S(\lambda)&:= \min \left \{ {\mathcal F}_S^\lambda(\chi_E)\:\big|\: E\subseteq \R^2\text{ measurable, }|E| = \pi\right\}.
\end{align}
\begin{theorem}\label{theorem scaling}
For large $\lambda$, the expansions
\begin{align*}
e_C(\lambda) &= -\pi^2\,\lambda\,\log\left(\frac{\pi^2\lambda}2\right) + \tilde e_C(\lambda)\,\lambda + O(1)\\
e_S(\lambda) &= -\pi^2\,\lambda\,\log\left(\frac{\pi^2\lambda}2\right) + \tilde e_S(\lambda)\,\lambda + O(1)
\end{align*}
hold for coefficient functions satisfying
\[
\pi^2 \:\leq\: \tilde e_C, \tilde e_S \:\leq\: 3\pi^2.
\]
\end{theorem}
\begin{proof}
{\bf Lower bound.} We deduce from \eqref{eq scaling lower bound} that
\[
e_C(\lambda) \geq \inf_{r>0} \big[2r - \pi^2\lambda\,\log(r)\big].
\]
The right hand side is large for $r$ close to zero or very large, so a minimizing $r$ exists and satisfies
\[
0 = \frac{d}{dr}\big[2r - \pi^2\lambda\,\log(r)\big] = 2 - \frac{\pi^2\lambda}r\qquad\Ra\quad r = \frac{\pi^2\lambda}2.
\]
It follows that
\[
e_C(\lambda) \geq 2\,\frac{\pi^2\lambda}2 - \pi^2\lambda\,\log\left(\frac{\pi^2\lambda}2\right) \geq \pi^2\lambda\left[1 - \log\left(\frac{\pi^2\lambda}2\right)\right].
\]
{\bf Upper bound.} Denote $E^r = [0,r]\times [0,\pi r^{-1}]$. We compute
\[
\overline{P_C^r}(E^r) = \overline{P_S^r}(E_r) = P(E^r) = 2r + 2\pi\,r^{-1}
\]
and
\begin{align*}
\int_{E^r}\int_{E^r} \log\left(\frac1{|x-y|}\right)\,\mathrm{d}x\,\mathrm{d}y &\leq \int_{E^r}\int_{E^r} \log\left(\frac1{|x_1-y_1|}\right)\,\mathrm{d}x\,\mathrm{d}y\\
&= \frac{\pi^2}{r^2} \int_0^r\int_0^r \log\left(\frac1{|x_1-y_1|}\right)\,\mathrm{d}x\,\mathrm{d}y\\
&\leq \frac{\pi^2}{r^2} \int_0^r \int_0^r \log\left(\frac1{|x_1-r/2|}\right)\,\mathrm{d}x_1\,\mathrm{d}y_1\\
&= \frac{2\pi^2}r \int_0^{r/2}\log\left(\frac1s\right)\,\mathrm{d}s\\
&= - \frac{2\pi^2}r\,\int_0^{r/2}\log (s)\,\mathrm{d}s\\
&= - \frac{2\pi^2}r \left[\frac{r}2\log\left(\frac r2\right) - \frac r2 +0\right]\\
&= \pi^2\left[1-\log\left(\frac r2\right)\right].
\end{align*}
Taking $r = \pi^2\lambda$, we obtain
\[
e_C(\lambda) \leq {\mathcal E}_C^\lambda(E^\lambda) \leq 2\pi^2\lambda+ \frac{2}{\pi\lambda} + \pi^2\lambda\left[1-\log\left(\frac {\pi^2\lambda}{2}\right)\right].
\]
{\bf Conclusion.} We have shown that
\[
\pi^2\lambda\left[1 - \log\left(\frac{\pi^2\lambda}2\right)\right]
\: \leq\: e_C(\lambda) \: \leq \: 2\pi^2\lambda + \frac{2\pi}\lambda + \pi^2\lambda\left[1-\log\left(\frac {\pi^2\lambda}{2}\right)\right].
\]
The upper and lower bound differ by $2\pi^2\lambda + \frac{2\pi}\lambda$.
\end{proof}
The energy competitors we constructed were long, thin squares. To leading order, the only important property of the sequence was that most mass in the system has a distance of order $\lambda$ to the point $x$ for any $x\in E$. The precise distance is irrelevant since $\log(c\lambda) - \log\lambda = \log c \ll \log\lambda$ for large $\lambda$. The same scaling is expected for any sequence of sets with similar properties, for example annular regions with very similar (large) radii, or a union of several fattened line segments meeting at the origin. This zeroth order analysis therefore cannot provide more precise information on the shape of minimizers in the large mass regime.
We can, however, show that minimizers must be long and thin in a suitable sense. First, we show that the length of minimizers scales roughly like $\lambda$.
\begin{theorem}\label{theorem long}
\begin{enumerate}
\item Let $E^\lambda$ be a sequence of sets such that
\[
\limsup_{\lambda\to \infty} \frac{{\mathcal F}_C^\lambda(E^\lambda)}{\lambda\,\log\lambda} \leq 0.
\]
Then
\[
\limsup_{\lambda\to \infty} \frac{\log(\operatorname{diam}(E^\lambda))}{\log\lambda} \leq 1.
\]
\item If
\[
\limsup_{\lambda\to \infty} \frac{{\mathcal F}_C^\lambda(E^\lambda)}{\lambda\,\log\lambda} = -\pi^2,
\]
then
\[
\lim_{\lambda\to \infty} \frac{\log(\operatorname{diam}(E^\lambda))}{\log\lambda} =1.
\]
\end{enumerate}
\end{theorem}
\begin{proof}
Denote the diameter of $E^\lambda$ by $R^\lambda$. The intuition is as follows: If $R_\lambda\gg \lambda$, then the perimeter term becomes more expensive than the repulsion term can compensate for. On the other hand, if $R_\lambda\ll \lambda$, then we do not exploit the repulsion term fully.
{\bf Step 1.} In this step we show that if ${\mathcal F}_C^\lambda(E^\lambda) \leq 0$ for all large enough $\lambda$, then
\[
\limsup_{\lambda\to \infty} \frac{\log(R_\lambda)}{\log\lambda} \leq 1.
\]
We pass to a subsequence in $\lambda$ which realizes the upper limit.
Assume for the sake of contradiction that
\[
1 < 1+2\sigma = \lim_{\lambda\to \infty} \frac{\log(R_\lambda)}{\log\lambda} \leq C <\infty.
\]
Then
\[
R_\lambda = e^{\log(R_\lambda)} \geq e^{(1+\sigma)\,\log\lambda} = \lambda^{1+\sigma}
\]
for all sufficiently large $\lambda$, and thus by \eqref{eq scaling lower bound}
\[
{\mathcal F}^\lambda_C(E^\lambda) \geq 2R_\lambda - \pi^2\lambda\,\log(R_\lambda) \geq 2\,\lambda^{1+\sigma} - C\,\lambda\,\log\lambda>0
\]
for all sufficiently large $\lambda$. The assumption that the upper limit is finite can be removed by considering the splitting
\[
R_\lambda = R_\lambda^\frac1{1+\sigma/2} R_\lambda^\frac{\sigma}{2+\sigma} \geq \lambda^\frac{1+\sigma}{1+\sigma/2} R_\lambda^\frac{\sigma}{2+\sigma} \gg \lambda\,\log(R_\lambda).
\]
{\bf Step 2.} Assume now that
\[
\liminf_{\lambda\to\infty} \frac{\log(R_\lambda)}{\log\lambda} \leq 1-2\sigma <1.
\]
Again, we pass to a subsequence along the lower limit is realized. Since $E^\lambda$ is contained in a ball of radius $R_\lambda$, by Proposition \ref{prop0} we have
\[
\int_{E^\lambda}\int_{E^\lambda}\log\left(\frac1{|x-y|}\right)\,\mathrm{d}x\,\mathrm{d}y \geq - \pi^2\log(R_\lambda) \geq - \pi^2\log\big(\lambda^{1-\sigma}\big) = -\pi^2(1-\sigma)\,\log\lambda
\]
for all sufficiently large $\lambda$, so
\[
\liminf_{\lambda\to\infty}\frac{{\mathcal F}^\lambda_C(E^\lambda)}{\lambda\,\log\lambda} \geq \liminf_{\lambda\to \infty} \frac1\lambda \int_{E^\lambda}\int_{E^\lambda}\log\left(\frac1{|x-y|}\right)\,\mathrm{d}x\,\mathrm{d}y \geq -\pi^2(1-\sigma) > -\pi^2.
\]
\end{proof}
In the next theorem, we show that minimizing sets are thin in the sense that mass does not concentrate close to a single point on a scale significantly shorter than $\lambda$.
\begin{theorem}\label{theorem thin}
For $\lambda>0$, let $E^\lambda$ be a family of sets such that for every $\lambda$ there exists a point $x^\lambda$ such that
\[
\big|E\cap B_{\lambda^\alpha}(x^\lambda)\big|\geq \bar c
\]
where $\alpha\in[0,1)$ and $\bar c>0$ does not depend on $\lambda$. Then
\[
\liminf_{\lambda\to\infty} \frac{ {\mathcal F}^\lambda_C(E^\lambda)}{\lambda\,\log\lambda} > -\pi^2.
\]
\end{theorem}
\begin{proof}
Up to translation, we may assume that $x^\lambda\equiv 0$. We pass to a subsequence in $\lambda$ such that
\[
\lim_{\lambda\to\infty} \big|E^\lambda \cap B_{\lambda^\alpha}\big| = \bar c>0,
\]
where we denote $B_{\lambda^\alpha} = B_{\lambda^\alpha}(0)$.
We split
\begin{align*}
\int_{E^\lambda}\int_{E^\lambda}\log\left(\frac1{|x-y|}\right)\,\mathrm{d}x \,\mathrm{d}y &= \int_{E^\lambda \cap B_{\lambda^\alpha}}\int_{E^\lambda\cap B_{\lambda^\alpha}}\log\left(\frac1{|x-y|}\right)\,\mathrm{d}x \,\mathrm{d}y\\
&\qquad + 2\int_{E^\lambda\cap B_{\lambda^\alpha}}\int_{E^\lambda\setminus B_{\lambda^\alpha}}\log\left(\frac1{|x-y|}\right)\,\mathrm{d}x \,\mathrm{d}y \\
&\qquad+ \int_{E^\lambda\setminus B_{\lambda^\alpha}}\int_{E^\lambda\setminus B_{\lambda^\alpha}}\log\left(\frac1{|x-y|}\right)\,\mathrm{d}x \,\mathrm{d}y\\
&\geq -\big|E^\lambda \cap B_{\lambda^\alpha}\big|^2\,\log\left(2\lambda^\alpha \right)\\
&\qquad - 2\,|E^\lambda \cap B_{\lambda^\alpha}|\,|E^\lambda\setminus B_{\lambda^\alpha}|\,\log(R_\lambda)\\
&\qquad- |E^\lambda\setminus B_{\lambda^\alpha}|^2 \log(R_\lambda)
\end{align*}
using Proposition \ref{prop0} on the first term. Assume for the sake of contradiction that
\[
\lim_{\lambda\to\infty} \frac{ {\mathcal F}^\lambda_C(E^\lambda)}{\lambda\,\log\lambda} = -\pi^2.
\]
Using Theorem \ref{theorem long}, we find that
\[
\lim_{\lambda\to\infty}\frac{\log (R_\lambda)}{\log\lambda} = 1,
\]
so
\begin{align*}
\liminf_{\lambda\to\infty}\frac1{\log\lambda} \int_{E^\lambda}\int_{E^\lambda}\log\left(\frac1{|x-y|}\right)\,\mathrm{d}x \,\mathrm{d}y
&\geq - \bar c^2\,\alpha - 2(\pi - \bar c)\bar c - (\pi - \bar c)^2 > - \pi^2.
\end{align*}
We have thus reached a contradiction.
\end{proof}
So a minimizing sequence for ${\mathcal F}_C^\lambda$ has to be increasingly `spread out' and cannot concentrate positive mass close to a single point $x^\lambda$ on any scale $\lambda^\alpha$ for $\alpha<1$.
Note that the arguments above are specific to the plane, and that the analysis changes entirely if the sets $E$ are confined to a bounded domain $\Omega$ or a compact manifold, e.g., a sphere or a flat torus. On such domains, the Green's function for the Laplacian is bounded from below and `spreading out' is no longer an option. Understanding minimizers analytically no longer seems possible in this regime.
In the following, we discuss a numerical approach to finding minimizers in the intermediate regime where $\lambda$ is neither small nor large, or where $E$ is confined to a set of finite diameter. In many cases, confinement to a domain is a feature of the problem. To approximate minimization in the plane, we can minimize $E$ among sets confined to a a large set $\Omega$. If the confinement is to be neglected, the diameter of $\Omega$ has to scale linearly with $\lambda$.
\section{Numerical Implementation}\label{numerics}
\subsection{Variational Problem and Gradient Flow}
To describe the functionals from~\eqref{thefunc1} and~\eqref{thefunc2} in a diffuse interface approach suitable for numerical treatment, we consider the Ohta-Kawasaki free energy functional, first mentioned in~\cite{ohta1986equilibrium},
\begin{align}\label{functional}
{\mathcal F}_\varepsilon^{\lambda}(u)=\frac{1}{c_{0}}\int\limits_{\Omega} \frac{\epsilon}{2}|\nabla u|^{2} + \frac{1}{\epsilon} W(u) ~\mathrm{d}x\mathrm{d}y + \frac{\lambda}{2} \int\limits_{\Omega} (u-\bar{m})(-\Delta) ^{-1} (u-\bar{m}) ~\mathrm{d}x\mathrm{d}y,
\end{align}
where we set
\begin{align*}
\bar{m}= \frac{1}{|\Omega|} \int\limits_{\Omega} u ~ \mathrm{d}x\mathrm{d}y, \quad W(s) = \frac{1}{4}s^{2}(s-1)^{2}, \quad\text{and}\quad c_{0}=\frac{1}{6\sqrt{2}}.
\end{align*}
As usual, the small parameter $\varepsilon>0$ takes the role of diffuse interface width and $\Omega$ is a bounded domain. At least formally, ${\mathcal F}_\varepsilon^{\lambda}$ is an approximation of ${\mathcal F}^\lambda$ from Section \ref{section small mass}, when one neglects the influence of the boundary on the electrostatic potential -- and therefore simply obtains a logarithmic potential. We note that by the results in \cite{MR3101793,MR3176350}, some of this correspondence can be made rigorous in appropriate scaling regimes. The study of the Ohta-Kawasaki functional, however, also has independent merit.
To give the inverse of the Laplacian a proper meaning we incorporate Neumann boundary conditions and define the operator $\Delta_{N}^{-1}$ such that the $H^{-1}(\Omega)$-inner product can be described in one of the equivalent forms
\[
\left<w,v\right>_{H^{-1}(\Omega)}\coloneqq \left\{\begin{array}{ll} (-\Delta_{N}^{-1}w,v) \\
\big((-\Delta_{N})^{-\frac{1}{2}}w,(-\Delta_{N})^{{-\frac{1}{2}}}v\big) \ \ \ \ \ \forall \ v,w \in H_{*}^{1}(\Omega), \\
(w,-\Delta_{N}^{-1}v)
\end{array}\right.
\]
where $-\Delta_{N}^{-1}v=g$ means that $-\Delta g=v$ with $g \in H_{*}^{1}(\Omega)$ and $\frac{\partial g}{\partial \eta}_{|\partial \Omega}=0$ with the outer unit normal $\eta$ on $\partial \Omega$. The set $H^{1}_{*}(\Omega)$ is given by
\[
H^{1}_{*}(\Omega)= \left\{ u \in H^{1}(\Omega) \ \bigg| \ \int\limits_{\Omega} u~\mathrm{d}x\mathrm{d}y =0 \right\}.
\]
Thus we may rewrite the functional in~\eqref{functional} and consider
\begin{align*}
{\mathcal F}_\varepsilon^{\lambda}(u) = \frac{1}{c_{0}}\int\limits_{\Omega} \frac{\epsilon}{2}|\nabla u|^{2} + \frac{1}{\epsilon} W(u)~\mathrm{d}x\mathrm{d}y + \frac{\lambda}{2} \|u-\bar{m}\|_{H^{-1}(\Omega)}^{2}.
\end{align*}
Doing so, we can formulate the gradient flow of the functional in~\eqref{functional} as
\begin{align}\label{gradientflow}
\left<\partial_{t}u,\phi\right>_{H^{-1}(\Omega)}=- \delta_{u;\phi}{\mathcal F}_\varepsilon^{\lambda}(u) \ \forall \ \phi \in H_{*}^{1}(\Omega)
\end{align}
with the first variation $ \delta_{u;\phi}{\mathcal F}_\varepsilon^{\lambda}(u)$ in $u$ in the direction of $\phi$. This yields
\begin{align*}
\left<\partial_{t}u,\phi\right>_{H^{-1}(\Omega)} &= \int\limits_{\Omega} \left\{ \frac{\epsilon}{c_{0}} \Delta u - \frac{1}{c_{0}\epsilon} W'(u)-\lambda (-\Delta_{N})^{-1}(u-\bar{m})\right\}\phi\,\mathrm{d}x\mathrm{d}y
\end{align*}
for all test functions $\phi \in H^{1}_{*}(\Omega)$.
Setting now $w= \Delta_{N}^{-1}\partial_{t}u+ \lambda \Delta_{N}^{-1}(u-\bar{m})$ and using the mass conservation of solutions of the following system, see, e.g., \cite{parsons2012numerical}, we are finally required to solve
\begin{align}\label{system}
\int\limits_{\Omega}\left\{ \partial_{t}u-\Delta w + \lambda (u-\bar{m})\right\} \phi\, \mathrm{d}x\mathrm{d}y &= 0 , \notag \\
\int\limits_{\Omega} \left\{ w+ \frac{\epsilon}{c_{0}} \Delta u -\frac{1}{c_{0}\epsilon} W'(u)\right\}\phi\,\mathrm{d}x\mathrm{d}y &=0
\end{align}
for all test functions $\phi \in H^{1}(\Omega)$.
\subsection{Phase Field Connectedness}
It remains to include the possibility of using connected and simply connected perimeters in the numerical treatment of the Ohta-Kawasaki energy. Our method to enforce such a connectedness constraint for diffuse interfaces is based on the functional $\mathcal{C}_{\epsilon}$, introduced in~\cite{MR3590663, MR4011685}, and given by
\begin{align}\label{pathPenfunc}
\mathcal{C}_{\epsilon}^{(1)}(u) = \int\limits_{\Omega}\int\limits_{\Omega} \beta_{\epsilon}(u(x))\beta_{\epsilon}(u(y)) \operatorname{d}^{\psi_\varepsilon(u)}(x,y) ~\mathrm{d}x\mathrm{d}y,
\end{align}
where $\beta_{\epsilon}, \psi_{\epsilon}$ are continuous functions such that
\begin{align*}
\beta_{\epsilon}, \psi_\varepsilon \geq 0, \ \ \beta_{\epsilon}(z)= 0 \Leftrightarrow z \in [0,1-\alpha_\varepsilon], \ \ \psi_\varepsilon(z) > 0 \Leftrightarrow z \in [0,1-\alpha_\varepsilon]
\end{align*}
with $\alpha_\varepsilon = \varepsilon^s$ for some $0<s<1/2$ and $\operatorname{d}^\psi$ is a geodesic distance with local weight $\psi$.
Adding the functional in~\eqref{pathPenfunc} to a given functional in a diffuse interface approach then ensures approximate connectedness of the phase $\{u\approx 1\}$. Connectedness of the phase $\{1-u\approx 1\}=\{u\approx 0\}$ on the other hand can be achieved by adding the functional
\begin{align*}
\mathcal{C}_{\epsilon}^{(2)}(u) = \int\limits_{\Omega}\int\limits_{\Omega} \beta_{\epsilon}(1-u(x))\beta_{\epsilon}(1-u(y)) \,\operatorname{d}^{\psi_\varepsilon(1-u)}(x,y) ~\mathrm{d}x\mathrm{d}y,
\end{align*}
thus adding both $\mathcal{C}_{\epsilon}^{(1)}(u)$ and $\mathcal{C}_{\epsilon}^{(2)}(u)$ to a given functional serves to keep the phase $\{u\approx 1\}$ simply connected in our two-dimensional setting.
Incorporating the connectedness constraint in the gradient flow dynamics in~\eqref{gradientflow} then leads to
\begin{align}\label{functional2}
\left<\partial_{t}u,\phi\right>_{H^{-1}(\Omega)}=- \left[\delta_{u;\phi}{\mathcal F}_\varepsilon^{\lambda}(u)+\frac{\zeta_{1}}{\epsilon^{\kappa}}\delta_{u;\phi}\mathcal{C}_{\epsilon}^{(1)}(u) +\frac{\zeta_{2}}{\epsilon^{\kappa}}\delta_{u;\phi}\mathcal{C}_{\epsilon}^{(2)}(u)\right] \ \ \forall \ \phi \in H^{1}(\Omega)
\end{align}
for parameters $\kappa>0$, $\zeta_{1},\zeta_{2} \geq 0$. Considering now the system of equations in~\eqref{system} we are finally faced with solving
\begin{align}\label{system1}
\int\limits_{\Omega}\left\{ \partial_{t}u-\Delta w + \lambda (u-\bar{m})\right\} \phi ~\mathrm{d}x\mathrm{d}y &= 0 , \notag \\
\int\limits_{\Omega} \left\{ w+ \frac{\epsilon}{c_{0}} \Delta u -\frac{1}{c_{0}\epsilon} W'(u)\right\}\phi ~\mathrm{d}x\mathrm{d}y - \left(\frac{\zeta_{1}}{\epsilon^{\kappa}}\delta_{u;\phi}\mathcal{C}_{\epsilon}^{(1)}(u)+\frac{\zeta_{2}}{\epsilon^{\kappa}}\delta_{u;\phi}\mathcal{C}_{\epsilon}^{(2)}(u)\right) &=0
\end{align}
for all test functions $\phi \in H^{1}(\Omega)$.
\subsection{Discretization}
To compute approximate solutions of the system in~\eqref{system1} numerically, we use P1-finite elements and obtain the system of equations
\begin{align*}
\left(\frac{u_{h}^{n}-u_{h}^{n-1}}{\Delta t},v_{h}\right) &= - (\nabla w_{h}^{n},\nabla v_{h})- \lambda (u_{h}^{n}-\bar{m},v_{h}) \\
(w_{h}^{n},v_{h}) &= \frac{\epsilon}{c_{0}} (\nabla u_{h}^{n},\nabla v_{h}) + \frac{1}{c_{0}\epsilon}\big(W'(u_{h}^{n},u^{n-1}_{h}),v_{h}\big) \\
& \quad \quad \quad + \zeta_{1} \epsilon^{-\kappa}\delta_{u^{n-1}_{h};v_{h}}\mathcal{C}_{\epsilon}^{(1)}(u^{n-1}_{h})\\
& \quad \quad \quad +\zeta_{2} \epsilon^{-\kappa}\delta_{u^{n-1}_{h};v_{h}}\mathcal{C}_{\epsilon}^{(2)}(u^{n-1}_{h}),
\end{align*}
which uses a linearized version of the double well potential $W(u)$. Specifically, we use the approximation
\[
W'(u^{n})\approx \frac{u^{n}}{2}\left((u^{n-1}-1)^{2}+u^{n-1}(u^{n-1}-1)\right)= W'(u^{n},u^{n-1}).
\]
This linearization was used in a similar way in~\cite{parsons2012numerical} for the numerical approximation of local minimizers of the Ohta-Kawasaki Energy. There, further relevant issues regarding stability and boundedness for a similar linearization are treated.
The explicit treatment and discretization of the variation of the functionals $\mathcal{C}_{\epsilon}^{(1)}$ and $\mathcal{C}_{\epsilon}^{(2)}$ are discussed in detail in \cite{Dondl_18f}. As described there, we use a Dijkstra-type algorithm, based on ideas in \cite{MR2684290,MR3337998}, to compute the variation of a discretized geodesic distance.
\subsection{Numerical Results}\label{section numerical}
We now consider a fully discrete gradient flow of the functional in~\eqref{functional2}. For the numerical experiments, the functions $\beta_{\epsilon}$ and $\psi_\varepsilon$ are given as in~\cite{MR4011685}
\begin{align*}
\beta_\varepsilon(s) &= \begin{cases}
0 & s\le 1-\alpha \\
\frac{c_1}{2}(s-1+\alpha)^2 & s>1-\alpha
\end{cases} \\
\quad\text{and}\\
\psi_\varepsilon(s) &= \begin{cases}
\frac{1}{2}(s-1+\alpha)^2 & s<1-\alpha\\
0 & s \le 1-\alpha,
\end{cases}
\end{align*}
respectively. The parameter $c_{1}$ is chosen such that $\int_{\alpha}^{1} \beta_{\epsilon}(s)~\mathrm{d}s =1$ and $\kappa$ in~\eqref{functional2} is set to $\kappa =2$. The value of $\alpha = \alpha_\varepsilon$ changes slightly between experiments.
By incorporating Neumann boundary conditions as described above the mass of the initial condition is maintained during the evolution of the gradient flow.
\subsubsection{Experiment 1} In the first numerical experiment we choose an initial condition which is approximately given by the characteristic function of the set $\{r< 0.02+0.45\cos(2\,\theta)\}$ with $r= \sqrt{x^{2}+y^{2}} $ and $\theta = \arctan(x,y)$, see Figure~\ref{fig1}. We set $\epsilon= 8 \cdot 10^{-3}$, $\tau=9.5 \cdot 10^{-9}$ and $\lambda=10606$. The mean value $\bar{m}$ is given by the initial condition as $\bar{m}\approx 0.178$. The parameters $\alpha$ and $\zeta_{1}$ are set to $\alpha=0.35$ and $\zeta_{1}=3.0$. The parameter $\zeta_{2}$ is set to zero so we just ensure the phase $\{u\approx 1\}$ to be connected. The discretization is made up of approximately $4.6 \cdot 10^{4}$ P1 triangle elements on the square $\Omega = \big(-\frac{1}{2},\frac{1}{2}\big)$.
Without using a path-connectedness constraint two discs which repel each other form, see Figure~\ref{fig1}. They remain at a finite distance due to boundary effects. This represents a classical ``dynamically metastable'' solution to the minimization problem in~\eqref{functional2} without disconnectedness penalty, see, e.g., \cite{MR2854591}. Incorporating path-connectedness in the functional in~\eqref{functional2}, these balls cling to the Steiner-tree forming a dumbbell-like structure.
\begin{figure}[ht!]\begin{center}
\raisebox{-0.5\height}{\includegraphics[height=3.25cm]{initial1.png}}
\raisebox{-0.5\height}{\includegraphics[height=3.25cm]{no_pen_big1.png}}
\raisebox{-0.5\height}{\includegraphics[height=3.25cm]{pen_big1.png}}
\raisebox{-0.5\height}{\includegraphics[height=2cm]{colorbar_u.png}}
\caption{Results for a numerical example. From left to right: Initial condition for $u$, ``dynamically metastable" state $u$ without disconnectedness penalty, stationary state with disconnectedness penalty. We use $\epsilon = 8 \cdot 10^{-3}$, $\lambda=10606$.}
\label{fig1}
\end{center}
\end{figure}
\begin{figure}[H]
\centering
\qquad
\subfigure[Without disconnectedness penalty.] {\includegraphics[width=0.46\textwidth]{graph1.png}}\hspace{0.05em}
\subfigure[With disconnectedness penalty.] {\includegraphics[width=0.46\textwidth]{graph2.png}}
\captionsetup{width=0.9\linewidth}
\caption[]{Time evolution of the components of the free energy functional for experiment 1.}
\label{graph1}
\end{figure}
\subsubsection{Experiment 2} In the second experiment we set $\epsilon = 4\cdot 10^{-3}$, $\tau = 4.7 \cdot 10^{-9}$ and $\lambda =14849$. Further we decrease the mass $m$ and thus the initial condition is approximately given by the characteristic function of the set $\{r< 0.01+0.35\cos(2\,\theta)\}$ with the same notation as before, see Figure~\ref{fig2}. The mean value $\bar{m}$ is given by the initial condition as $\bar{m}\approx 0.1$. The parameters $\alpha$ and $\zeta_{1}$ are set to $\alpha=0.35$ and $\zeta_{1}=1.0$. The parameter $\zeta_{2}$ is set to zero so we just ensure the phase $\{u\approx 1\}$ to be connected. The discretization is again made up of approximately $4.6 \cdot 10^{4}$ P1 triangle elements on the square $\Omega = [-\frac{1}{2},\frac{1}{2}]$.
The results of the second experiment are similar to the results from the first experiment, whereas the commingling of the two monomers is less pronounced and sharper interfaces are developed.
\begin{figure}[ht!]\begin{center}
\raisebox{-0.5\height}{\includegraphics[height=3.25cm]{initial2.png}}
\raisebox{-0.5\height}{\includegraphics[height=3.25cm]{no_pen_small.png}}
\raisebox{-0.5\height}{\includegraphics[height=3.25cm]{pen_small.png}}
\raisebox{-0.5\height}{\includegraphics[height=2cm]{colorbar_u.png}}
\caption{Results for a numerical example. From left to right: Initial condition for $u$, ``dynamically metastable" state $u$ without disconnectedness penalty, stationary state with disconnectedness penalty. We use $\epsilon = 4 \cdot 10^{-3}$, $\lambda=14849$.}
\label{fig2}
\end{center}
\end{figure}
\begin{figure}[H]
\centering
\qquad
\subfigure[Without disconnectedness penalty.] {\includegraphics[width=0.46\textwidth]{graph3.png}}\hspace{0.05em}
\subfigure[With disconnectedness penalty.] {\includegraphics[width=0.46\textwidth]{graph4.png}}
\captionsetup{width=0.9\linewidth}
\caption[]{Time evolution of the components of the free energy functional for experiment 2.}
\label{graph2}
\end{figure}
\begin{remark}
It should be mentioned that the steady states in the experiments with disconnectedness penalty indeed seem to be local minimizers of the energy in ~\eqref{functional2}. This effect can be explained by the observation that, in contrast to the case without disconnectedness penalty, every increase in the distance of the two droplets would also increase the perimeter of the phase $\{u\approx 1\}$. This is different to the ``dynamically metastable'' state occurring when abandoning the disconnectedness penalty, as every increase in the distance of the two droplets would decrease the whole energy in~\eqref{functional2}.
\end{remark}
\subsubsection{Experiment 3} In a final third experiment we illustrated the effect when penalizing simple-connectedness of the phase $\{u\approx 1\}$. This is achieved by setting $\zeta_{1}=\zeta_{2}=0.01$ in~\eqref{functional2}. We now take the initial condition for $u$ as an approximation of the characteristic function of the set $\{r< 0.4+0.2\cos(2\,\theta)\}$, see Figure~\ref{fig3}. We further set $\epsilon = 3 \cdot 10^{-3}$, $\tau = 3 \cdot 10^{-9}$ and $\lambda =20000$. The parameter $\alpha$ is now set to $\alpha= 0.068$ and the discretization is made up of approximately $1.4 \cdot 10^{5}$ P1 triangle elements on the square $\Omega = [-1,1]$. The mean value $\bar{m}$ is thus given by the initial condition as $\bar{u}\approx 0.141$.
Due to the chosen initial condition and the value of $\lambda$, tubular structures occur in the simulation without disconnectedness penalty. These multiply-connected tubular structures are further typical ``dynamically metastable'' states of the Ohta-Kawasaki functional, see, e.g., \cite{MR2854591}. When we incorporate the simple-connectedness penalty, the tube tears open forming a simply connected structure for $\{u\approx 1\}$, see Figure~\ref{fig3}. As the impact of the boundedness of the reference domain is more visible than in the experiments before, the relevance of this experiment is more justified by effects inherited by the phase field model. An appropriate connection to the results in Section~\ref{section large mass} may not exist.
\begin{figure}[ht!]\begin{center}
\raisebox{-0.5\height}{\includegraphics[width = 3.25cm]{initial3.png}}
\raisebox{-0.5\height}{\includegraphics[width = 3.25cm]{simplyconnected.png}}
\raisebox{-0.5\height}{\includegraphics[width = 3.25cm]{simply_connected_pen.png}}
\raisebox{-0.5\height}{\includegraphics[height=2cm]{colorbar_u.png}}
\caption{Results for a numerical example. From left to right: Initial condition for $u$, ``dynamically metastable" state $u$ without disconnectedness penalty, ``dynamically metastable" state using simple-connectedness constraint. We use $\epsilon = 3 \cdot 10^{-8}$, $\lambda=20000$.}
\label{fig3}
\end{center}
\end{figure}
\begin{figure}[H]
\centering
\qquad
\subfigure[Without disconnectedness penalty.] {\includegraphics[width=0.46\textwidth]{graph5.png}}\hspace{0.05em}
\subfigure[With disconnectedness penalty.] {\includegraphics[width=0.46\textwidth]{graph6.png}}
\captionsetup{width=0.9\linewidth}
\caption[]{Time evolution of the components of the free energy functional for experiment 3.}
\label{graph3}
\end{figure}
\bibliographystyle{alphaabbr}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 8,822
|
Home statements
We are under siege because of our human rights work for the rural poor
Our organization is under siege. We are experiencing relentless systematic surveillance, harassments and threats because of the work that we do for the rural poor of Northern Mindanao.
'Do not be surprised, brothers, that the world hates you.' — 1 John 3:13
On March 7, 2014 at around 3 o'clock in the afternoon, Rural Missionaries of the Philippines-Northern Mindanao Sub-Region (RMP-NMR) alternate coordinator Jonah Cossma Jumagbas was followed by an unidentified man as she left our sub-regional office in Villaverde, Iligan City.
Jumagbas suspected that she was being tailed by a man in his mid-30s when she was at the Palao Market intending to buy some fruits. Trying to ward-off the pursuer, Jumagbas took a fast-paced walk along Quezon Avenue and circled back to Palao Market via Aguinaldo Avenue. But still, the man pursued, maintaining a 10-15 meter distance.
Deflecting, Jumagbas took a jeepney ride going to Tambo Bus Terminal and then boarded a bus bound for Cagayan de Oro City. But while waiting for the bus to depart, Jonah saw the same man at the bus terminal, seeming to look for someone. To evade the pursuer, Jumagbas stepped out from the bus and hurriedly took a jeepney ride back to the City Proper where to find a safer place.
Tenioso Balangiao Jr., member of the Sub-Regional Coordinating Body of RMP-NMR, continues to experience surveillance, harassment and intimidation as of this moment. The threat to Balangiao was confirmed on February 20, 2014, when he received a suspicious text message from an unidentified number. The sender indicated in the said message that he knows Balangiao and his family. The sender also told Balangiao that he knows his address, and that he also knows Balangiao fears for his security due to his work. The unknown sender also tried to reassure Balangiao that he must not worry for his life because he can protect him and his family.
This incident prompted Balangiao to change his mobile phone number. However, Balangiao continued to receive text messages from the same unidentified number. The message said, "Ayaw pagpuli sim Jun kay makabalo gyapon ko sa imo namber…" (Don't change your SIM card for I can still know your number…) With this, Balangiao engaged the unknown sender and from the exchange of messages, the sender identified himself as one 'John Meraflor'. He told Balangiao that he has good intentions and wants to make an acquaintance with him. From that date forward, the certain "John Meraflor" sends text messages to Balangiao telling him that he knows what Balangiao was doing for his work and tried to incriminate him as a supporter of the CPP-NPA (Communist Party of the Philippines/New Peoples' Army). The said texter also tried to implicate Balangiao as having plans to join the rebel group.
As a peasant community organizer of RMP-NMR, Balangiao works closely with the Kilusang Magbubukid ng Pilipinas (KMP or Philippine Peasant Movement) in order to bring RMP's projects into far-flung peasant communities. Due to these messages, he does not feel safe and this has prompted him to keep away from his home and his work in RMP-NMR.
'Do not fear what you are about to suffer. Behold, the devil is about
to throw some of you into prison, that you may be tested,
and for ten days you will have tribulation. Be faithful unto death,
and I will give you the crown of life.' — Revelation 2:10
There's an obvious pattern of harassment and surveillance perpetrated against our organization since last year.
In September of 2013, our long-time lay co-worker, Joel Q. Yagao, was slapped with trumped-up charges – baseless charges of double murder and multiple murder. Despite interventions from international human rights organizations, Yagao is still in jail up to now for the crime he did not commit. With the snail-paced judicial process we have in the country, he might stay in jail for a minimum of 5 years — even if proven not guilty.
Also last year, we have complained on the series of harassments against our sub-regional coordinator, Sr. Ma. Famita N. Somgod, MSM, and the surveillance on our sub-regional headquarters. And on March 18, 2014, one of our literacy and numeracy schools in Agusan del Sur was also harassed. Members of the 26th IB of the Philippine Army arrived at Sitio Tabanganan, Brgy. Binicalan in San Luis, Agusan del Sur. The teachers of the learning center and the parents of its students were then planning for their recognition exercises which they had set for March 20. Suddenly, they heard a series of gunshots coming from the area where the military was, not 100 meters away, directly in front of the school. The children who were at the playground scattered fearing that they were the targets of the bullets.
'With respect to this they are surprised when you do not join them
in the same flood of debauchery, and they malign you.' — 1 Peter 4:4
In a bigger context, it is important to note that extra-judicial killings and violations of civil and political rights of the rural poor has become a phenomenon in Northern Mindanao since 2012.
Earlier this year, farmer-leader Julito Lauron of Kasama-Bukidnon (Kahugpungan sa mga Mag-uuma sa Bukidnon or Peasant Association of Bukidnon) was gunned down on February 05. This happened after Datu Rolando Ambungan of indigenous peoples' community-based organization, Pig-akuman, was also killed by a paramilitary group in Guinabsan, Buenavista Agusan del Norte on January 31.
Rolen Langala, an indigenous leader of indigenous group Pangalasag in Opol town in Misamis Oriental was murdered on December 1, 2013 days before the International Human Rights Week. Langala and his community's resistance against palm oil cultivation encroaching their ancestral lands cost him his life, and of their chairperson, Gilbert Paborada, who was also gunned down in October 2012.
It is also important to note the killings of Jimmy Liguyon, Margarito Cabal and Genesis Ambason, all human rights defenders working for land rights and the environment, all killed in 2012 in various dates and places. Despite interventions from various international human rights organizations and foreign consulates in the country, including the European Union, these killings were left unresolved.
Judicial harassment has also become a tactic against human rights defenders. Aside from Joel Yagao and a number of farmer activists slapped with legal cases, peasant organizer Estelita Tacalan, 61, was abducted and was later surfaced with trumped-up charges in March 2013. Estelita is still in prison right now, immobilized to continue her work for the Misamis Oriental Farmers' Association-KMP.
In the face of all these forms of repression, RMP-NMR brought to the attention of the national and international human rights community the human rights violations committed with impunity done against our network of peasant organizations. We were never cowed. In all of these cases, we point our fingers at Pres. Benignon Aquino III and his state security forces for all of these crimes.
We believe that our organization is being targeted because we speak against all of these violations, and because of our sustained human rights work for the peasant communities in Northern Mindanao Region who stand against the militarization of their villages to pave way for the entry of companies engaged in resource-extractive activities such as mining, energy and plantations. We have condemned all of these systematic assaults against the rural poor's civil and political rights committed in the framework of International Peace and Security Plan (IPSP), or more popularly called 'Oplan Bayanihan.'
We condemn these systematic harassment and surveillance, and all forms of human rights violations perpetrated against RMP-NMR and the rural poor communities we are serving.
As advocates from the church working on land rights and access to resources of the rural poor—farmers, fisherfolks, agricultural workers and indigenous peoples—our work falls under the definition of 'human rights defenders' defined in the United Nation's 'Declaration on the Right and Responsibility of Individuals, Groups and Organs of Society to Promote and Protect Universally Recognized Human Rights and Fundamental Freedoms' or the 'Declaration on Human Rights Defenders.' Yet, we have been subjected to surveillance, harassment and arbitrary arrests, and the rural poor communities we are serving are physically attacked.
Needless to say, the assaults against church advocates and human rights defenders are magnifying the terror in a bigger extent, and gives a chilling effect to the grassroots communities aspiring for genuine land reform, right to ancestral domain, and the fullness of life.
'But even if you should suffer for righteousness' sake,
you will be blessed. Have no fear of them, nor be troubled.' — 1 Peter 3:14
Time and again, we have already called the attention of the state to cease the political violence they are inflicting on the people. To no avail. A lot of our work and staff have been displaced, and our regular operations have been affected by these relentless attacks against us.
But we will continue to carry forward our commitment of living and working with the rural poor for the realization of their just aspirations for land rights and access to resources, and together we will continue to demand justice for the thousands of victims of human rights violations—no matter how long it takes.
RURAL MISSIONARIES OF THE PHILIPPINES
Northern Midnanao Sub-Region (RMP-NMR), Inc
Room 1, Kalinaw Lanao Center for Interfaith Resources
0016 Bougainvilla Puti, Villaverde
9200 Iligan City
T/F: +63 (63) 223 5179
E: info@rmp-nmr.org
W: http://www.rmp-nmr.org/
Boyen
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 8
|
\section{Introduction}
Different solutions and technologies have been developed for
focusing transmitted beams on users' receivers, in order to achieve
high bit rate communication or tracking capabilities. The
technological challenge is twofold: design antenna systems that
support narrow beams for large coverage area, and allow to locate
users with tight delay constraints for either scheduling or target
tracking. The considerable regain of interest in focusing antennas
is related to 5G systems which are in the process of definition in
different research frameworks and fora. It is expected that 5G
spectrum evolutions will benefit from higher frequency bands
\cite{METIS_IEEE_Magazine} making it possible to reduce the size of
large antenna arrays.
Different techniques have been developed to focus energy close to
the receiver. In an environment rich of multipaths which is
typically encountered in dense urban or indoor environment, \ac{TR},
also known as the Transmit Matched Filter, is receiving increasing
interest, particularly for the internet of things
\cite{chen2014InternetOfThings}. \ac{TR} is a pre-filtering
technique for \ac{MIMO} wireless systems
\cite{TimeReveral2004Paulraj}. The channel state information at
several transmit antennas is used to precode transmitted symbols
with the time reversed version of their respective channel impulse
responses. These "time reversed" waves propagate in the channel,
resulting in power focusing in space and time at the receiver.
\ac{TR} can be efficiently used for low complexity receivers such as
those expected in future connected objects \cite{DThuy2013dumb}, and
even for high mobility scenarios \cite{DThuy2013fastVehicles}. The
drawback of this technique is that it requires \ac{TDD} and full
\ac{CSI} at the transmitter side.
The problem of focusing the beam on moving targets has been addressed for decades
in the context of radar applications, and more specifically, in
millimeter wave phase array technology. Recently, the use of
millimeter adaptive antenna array, operating at the 70/80 GHz bands,
has been proposed for serving a high data rate moving user
\cite{SamsungPaper2010hybrid}. The antenna array consists of analog
sub-arrays behind a digital beamformer that estimates the \ac{AoA}
for the moving user.
Multilevel beamforming has been proposed in \cite{multileveBF2011backhaul} for millimeter wave backhaul
serving urban pico-cells. To ensure the link quality, an efficient search algorithm is performed to maintain
the alignment of the transmit and receive beams. The search is performed on a multilevel codebook thus reducing
considerably the number of beam couples to be tested. The channel gain matrix is not required, making this
technology cheaper and suitable for \ac{FDD} systems.
Recently, the concepts of \ac{VSC}
\cite{AnaMaria_virtual_smallcell_2015} and \ac{ViS}
\cite{tall_virtualsectorizationdesign_2015} have been proposed, with
the aim of creating a small cell or a sector using an antenna array
located at the base station. To manage interference between the
macro cell and \ac{ViS}, a self-optimizing frequency splitting
algorithm has been proposed that dynamically shares the frequency
bandwidth between the two cells. The main technological challenge
for both \ac{VSC} and \ac{ViS} is how to optimally focus the beam at
the area where traffic is present. This issue is implicitly solved
by the multilevel beamforming proposed in this paper.
The present work adapts the concept of multilevel beamforming
to the context of multi-user communication. In terms of
implementation complexity, the proposed approach is particularly
attractive. It can be implemented in a \ac{FDD} system where the
beam selection only depends on the mobile feedback, namely on the
\ac{CQI}. Different scenarios can be envisaged for the multilevel
beamforming, such as cellular coverage (in the sense of service
provisioning) in a low level or multipath propagation environment or
the coverage of mass events and crowded area. Unlike the backhaul
problem described above, the multilevel beamforming in this paper is generated at
the transmitter only. Cell coverage should be guaranteed with low
level inter-cell interference. The projection of beams (particularly
high gain narrow beams) may strongly spread out and overshoot
neighboring cells. Hence the generation of the set of multi-level
beams (or codebook) should take into account geometrical parameters
of the cell (e.g. cell size, antenna height) and can be performed
off-line.
The contributions of the paper can be summarized as follows:
\begin{itemize}
\item An antenna optimization framework for generating beams with reduced interference from side-lobes for large angular domain.
\item A beamforming codebook design strategy which avoids overshooting at neighboring cells.
\item A beam selection algorithm for efficient search through the multilevel beamforming codebook.
\item Performance analysis of the multilevel beamforming for two \ac{LTE} use cases taking into account different channel and traffic models.
\end{itemize}
The rest of the paper is organized as follows. Section \ref{sec:antenna_design} presents the antenna array design
and optimization for the multilevel beamforming. Section \ref{sec:multilevel_beamforming}
describes the multilevel beam construction and their selection algorithm. The performance of the
proposed multilevel beamforming for different channel models is analyzed in Section \ref{sec:results} for a mass event
and a rural scenario using an event-based \ac{LTE} network simulator.
Section \ref{sec:conclusion} concludes the paper.
\section{Antenna Array Design} \label{sec:antenna_design}
This Section presents the guidelines for the antenna array design supporting multilevel beamforming.
The antenna array modeling is first introduced and then the design of the beam diagrams is formulated
as an optimization problem.
\subsection{Antenna model}
Consider a $N_x \times N_z$ (sub) antenna array of vertical dipoles, at a distance of $\frac{\lambda}{4}$
from a square metallic conductor, with $\lambda$ being the wavelength. The full antenna array generates the
highest level (narrowest) beams, whereas lower level beams correspond to smaller (rectangular) sub arrays size (see Figure \ref{fig:beam_hierarchy}).
If another type of radiating element is chosen, only its radiation pattern should be modified. To simplify the model,
we approximate hereafter the reflector as an infinite \ac{PEC}. The $N_x$ and $N_z$ elements in each row and column are equally
spaced with distances $d_x$ and $d_z$, respectively (Figure \ref{fig:ant_array}).
\begin{figure}[!ht]
\centering
\includegraphics[width=3.5in]{vsc_antenna_array.png}
\caption{Antenna array with dipole radiating elements.}
\label{fig:ant_array}
\end{figure}
The direction of a beam is determined by the angle $(\theta_e,\phi_e)$ in the spherical coordinates
$\theta$ and $\phi$. The antenna gain for a given beam defined by $(\theta_e,\phi_e)$ in a given direction $(\theta, \phi)$ is written as
\begin{equation}
G(\theta,\phi,\theta_e,\phi_e) = G_0 f(\theta,\phi,\theta_e,\phi_e )
\end{equation}
where $f$ is a normalized gain function and $G_0$ the maximum
gain in the $(\theta_e,\phi_e)$ direction. A separable excitation in
the $x$ and $z$ directions is assumed, resulting in the following
separable form of $f$:
\begin{equation}
\begin{split}
f(\theta,\phi,\theta_e,\phi_e ) = | & AF_x^2 (\theta,\phi,\theta_e,\phi_e ) \cdot AF_y^2 (\theta,\phi) \\
& \cdot AF_z^2 (\theta,\theta_e )| \cdot G_d (\theta)
\end{split}
\end{equation}
$AF_x (\theta,\theta_e,\phi,\phi_e)$ and $AF_z(\theta,\theta_e)$ are the array factors in the $x$ and $z$ directions and are given by
\begin{equation}
AF_x (\theta,\theta_e,\phi,\phi_e )=\frac{1}{\sum_{m=1}^{N_x} w_m} \sum_{m=1}^{N_x} w_m \cdot a_m
\end{equation}
and
\begin{equation}
AF_z (\theta,\theta_e )=\frac{1}{\sum_{n=1}^{N_z} v_n} \sum_{n=1}^{N_z} v_n \cdot b_n .
\end{equation}
$a_m$ and $b_n$ are complex amplitude contributions of the radiating element
located at $(m-1) d_x$ and $(n-1) d_z$, respectively:
\begin{equation}
a_m = \exp\left(-j 2 \pi \frac{(m-1)d_x}{\lambda} (\sin\theta\sin\phi-\sin\theta_e\sin\phi_e)\right),
\end{equation}
\begin{equation}
b_n=\exp \left(-j 2 \pi \frac{(n-1)d_z}{\lambda} (\cos\theta-\cos\theta_e) \right).
\end{equation}
The weights $w_m$ and $v_n$ for radiating elements in the $m$-th row and $n$-th columns define a Gaussian tapering
function used to control the sidelobe level of the gain pattern
\begin{equation}
w_m = \exp{\left(-\left(\frac{(m-1) L_x - \frac{L_x}{2}}{\sigma_x} \right)^2 \right)},
\end{equation}
\begin{equation}
v_n = \exp{\left(-\left(\frac{(n-1) L_z - \frac{L_z}{2}}{\sigma_z} \right)^2 \right)},
\end{equation}
where $L_x$ and $L_z$ are the array size in the $x$ and $z$ directions respectively, with $L_x = (N_x-1) d_x$ and $L_z=(N_z-1) d_z$.
The values for $\sigma_s, s=x,z$, are defined by fixing the ratio between the extreme and center dipole amplitudes respectively to a given value of $\alpha_s$:
\begin{equation}
\sigma_s^2=- \left( \frac{L_s}{2} \right) \frac{1}{\log(\alpha_s )} ; s=x,z
\end{equation}
The impact of the \ac{PEC} can be modeled by replacing it with the images of the radiating elements it
creates. The term $AF_y(\theta,\phi)$ takes into account the images and is written as:
\begin{equation}
AF_y (\theta,\phi) = \sin\left(\frac{\pi}{2} \sin\theta \cos\phi \right)
\end{equation}
The normalized gain pattern of the dipoles, $G_d(\theta)$, is approximated as
\begin{equation}
G_d(\theta) = \sin^3\theta .
\end{equation}
The term $G_0$ is obtained from the power conservation equation:
\begin{equation}
G_0 = \frac{4\pi}{\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \int_0^\pi f(\theta,\phi) \sin\theta \, d\theta d\phi}.
\end{equation}
A beam is defined by the (rectangular) sub-array size, and the couple $(\theta_e,\phi_e)$ defines its direction.
The generation of the beams is discussed in Section \ref{sec:multilevel_beamforming}. The antenna modeling for all the
beams remains unchanged.
\subsection{Antenna pattern optimization}
The (sub) antenna array design constitutes an optimization problem with two objectives: maximizing the antenna gain
(or conversely, minimizing the width of the main lobe) and minimizing the side-lobes' level, as a function of the
parameters $d_s$ and $\alpha_s$, $s=x,z$. The problem is written as a constrained optimization problem:
\begin{subequations} \label{eq:ant_opt}
\begin{align}
\underset{d_x,d_z,\alpha_x,\alpha_z}{\text{maximize}} \, & G_0(N_{x,\max},N_{z,max},d_x,d_z,\theta_e,\phi_e) \\
\text{s.t. } & \\
& \max_{N_x,N_z}\{\emph{SL}(N_x,N_z,d_x,d_z,\theta_e,\phi_e)\} \leq Th; \label{eq:sl_th} \\
& \,\, N_{s,\min} \leq N_s \leq N_{s,\max}; \, s=x,z; \\
& \,\, 0 < \alpha_s \leq 1 ; \, s=x,z; \\
& \,\, 0 < d_s \leq \frac{\lambda}{2} ; \, s=x,z ;\\
& \,\, \theta_\text{min} \leq \theta_e \leq \theta_\text{max} ; \\
& \,\, - \phi_\text{max} \leq \phi_e \leq \phi_\text{max};
\end{align}
\end{subequations}
where $N_{s,\min}$ and $N_{s,\max}$ are respectively the minimum and
maximum number of antenna elements in the $s$ direction,
$\theta_\text{min}, \theta_\text{max}, \phi_\text{min},
\phi_\text{max}$ are respectively the minimum and maximum electrical
elevation and azimuth angles of the antenna array. The constraint
\eqref{eq:sl_th} reads: the maximum side-lobe level for the whole
range of sub array size should be below a predefined threshold $Th$.
It is noted that for small elevation electrical tilt values, the projection of the beams on the plane is likely to spread out.
Special care should be taken when setting the $\theta_\text{min}, \phi_\text{min}, \phi_\text{max}$ angles in order to avoid overshooting
on neighboring cells. These angles will depend on the geometrical characteristics of the cell (original coverage area of the considered \ac{BS} before deploying the antenna array), such as the cell shape, size, and antenna height.
One can consider optimizing the antenna for a wide range of elevation and azimuth angles, and then, according to the cell geometry, construct
a codebook of beams for a desired angular range. Furthermore, a database with a set of codebooks can be pre-optimized for a set of cell geometries and
then, according to the specific cell deployment, the most suitable codebook can be selected.
\section{Multilevel beamforming} \label{sec:multilevel_beamforming}
\subsection{Beams structure}
Consider a multilevel codebook as shown in Figure \ref{fig:beam_hierarchy}, with $L$ levels and $J_l$ beams
at the level \emph{l}, $l=0,...,L$. The $j$th beam at level $l$ is written as $B_{l,j}
(\theta,\theta_{l,j},\phi,\phi_{l,j})$, $j=1,...,J_l$, and for brevity of notation - as $B_l(j)$.
It is noted that the angles $(\theta_{l,j},\phi_{l,j})$ correspond to ($\theta_e,\phi_e$) defined
in section \ref{sec:antenna_design}.
\begin{figure}[!ht]
\centering
\includegraphics[width=2in]{beam_hierarchy.png}
\caption{Example of beam hierarchy}
\label{fig:beam_hierarchy}
\end{figure}
The beam of the first level, namely level $0$ in Figure \ref{fig:beam_hierarchy}, $B_0(1)$, covers the entire cell.
Beams at level $l$ are generated by the same sub-array, i.e.
with the same number of array elements, and differ from each
other by the angles $(\theta_{l,j},\phi_{l,j})$. Denote by $\hat{C}$
a \emph{coverage operator} which receives as argument a beam, and
outputs its coverage area (often denoted as the best server area),
where the beam provides the strongest signal with respect to other
cell or beam coverage. By construction we assume that for a
given level $l$, the beams' coverage do not overlap:
\begin{equation} \label{eq:coverage_overlap}
\hat{C}(B_l(i)) \wedge \hat{C}(B_l(j)) = \emptyset \, , \forall i \neq j.
\end{equation}
The multilevel structure of the beams in the codebook means that a given beam $B_l(j)$ at level $l$ where $l < L$
has two children beams $B_{l+1}(2j-1)$ and $B_{l+1}(2j)$ with
\begin{equation} \label{eq:coverage_inclusion}
\hat{C}(B_{l+1}(2j-1)) \cup \hat{C}(B_{l+1}(2j)) \subset \hat{C}(B_{l}(j))
\end{equation}
The beams at level $L$ are the narrowest that can be obtained given the $N_{x,max} \times N_{z,max}$ antenna array.
\subsection{Beam selection algorithm}
The beam selection algorithm consists in finding the best beam available by navigating through the multilevel codebook.
It starts with $B_0(1)$ which covers the entire cell and keeps track of the overall best beam up till now ($B^*$).
Assuming the beam selection algorithm is at level $l$ with $l < L$, the best beam is updated as follows
\begin{align} \label{eq:beam_select}
B^* &= \argmax{B \in \{ B^*, B_{l+1}(j), j = (2j_{l+1}-1,2j_{l+1}) \}} \, S(B,u)
\end{align}
where $S(B,u)$ is the \ac{SINR} of user $u$ served by the beam $B$, and $j_l$ denotes
index of the beam at level $l$.
The algorithm stops when the best beam does not change in a
given iteration, i.e. the parent beam provides better \ac{SINR}
than the children beams, or the highest level of beams $L$ is
reached. The complexity of such an algorithm is of the order of
$log(N)$, $N$ being the total number of beams, hence
convergence is obtained in a very small number of iterations.
It is noted that condition \eqref{eq:coverage_inclusion} can be relaxed so that narrower beams
can cover regions not covered by their parent beams. In this case the beam selection algorithm
should continue until level $L$. The multilevel beam structure presented in this section is just
one illustration of how a multilevel codebook structure can be designed. Other approaches can be adopted regarding
the relation between parent and children beams in terms of coverage. The only requirement is to be
able to easily navigate through the codebook in an iterative manner.
The beam selection algorithm runs in parallel with the scheduling algorithm. A user is first
scheduled based on its \ac{SINR} obtained with the level 0 beam.
During the scheduling period, the user's best beam is updated based on the received feedback using equation \eqref{eq:beam_select}.
If the scheduling period is long enough, the beam selection algorithm can converge. Otherwise the beam selection
resumes at the next scheduling period based on the \ac{SINR} of the best beam tested so
far. It is noted that other scheduling strategies can be considered.
\subsection{Implementation issues}
The beam codebook can be precalculated for a given cell and stored in a database of a
self-configuration server at the management plane. Upon deployment of the multilevel beamforming feature,
the multilevel codebook is downloaded from the server to the
\ac{BS}. As mentioned previously, the codebook selection can be
based on geometrical characteristics of the cell.
The antenna array can be dynamically configured using different approaches. The classical approach would be to feed
each antenna element by a distinct amplifier which receives the appropriate input
signal necessary to excite the selected beam from the codebook.
More recently, the \emph{load modulated massive MIMO} approach has been reported
\cite{modulated_MIMO} in which the base band input signal is used to adapt a load behind each antenna
element which controls its complex input impedance. This approach which utilizes a single amplifier
aims at further reducing the antenna size and cost, and could be a
candidate technology for the multilayer beamforming (further studies are still necessary).
The size of the antenna array depends on the number of antenna elements and the spacing
between them. In Section \ref{sec:mass_event}, we use $N_{x,max} = 12$ and $N_{z,max} = 32$
antenna elements with spacings of $d_x = 0.5\lambda$ and $d_z =
0.7\lambda$. For the \ac{LTE} technology with a 2.6 GHz
carrier, the antenna size is of 0.69 m $\times$ 2.58 m.
Multilevel beamforming will be particularly attractive in 5G technology where higher frequency bands will be available, allowing moderate size of antenna array with a large number of radiating elements.
\section{Numerical results} \label{sec:results}
We present in this section numerical results for the multilevel beamforming.
Two scenarios are considered: a mass event type of scenario in an urban environment
with a crowded open area, e.g. an esplanade, and a rural environment in which
the users have a \ac{LoS} path component from the \ac{BS}. The multilevel beamforming is applied to one cell
which is interfered by two rings of neighboring \acp{BS}.
A \ac{LTE} event-based simulator coded in Matlab is used. Users (data sessions) arrive according to a Poisson process,
download a file of exponential size with mean of 4 Mbits, and leave the network as soon as their download is complete. We focus on the case where there is no mobility.
The channel coherence time of several milliseconds is assumed
(which is typically the case for low mobility), and so the beam selection algorithm converges within this coherence time.
Hence beam selection errors due to fast-fading are not considered.
The main simulation parameters used for the two scenarios are summarized in Table \ref{tab:paramsg}.
\begin{table}[!t]
\small
\renewcommand{\arraystretch}{1.3}
\caption{Network and Traffic characteristics}
\label{tab:paramsg}
\centering
\begin{tabular}{|M{4cm}|M{3cm}|
\hline
\multicolumn{2}{|c|}{Network parameters} \\
\hline
Number of sectors with multilevel beamforming & 1 \\
\hline
Number of interfering macros & 2 rings, 20 sectors \\
\hline
Macro Cell layout & hexagonal trisector \\
\hline
Antenna height & 30 m \\
\hline
Bandwidth & 10MHz \\
\hline
Scheduling Type & Proportional Fair \\
\hline
\multicolumn{2}{|c|}{Channel characteristics} \\
\hline
Thermal noise & -174 dBm/Hz \\
\hline
Path loss ($d$ in km) & 128.1 + 37.6 $\log_{10}(d)$ dB \\
\hline
Shadowing & Log-normal (6dB) \\
\hline
\multicolumn{2}{|c|}{Traffic characteristics} \\
\hline
Service type & FTP \\
\hline
Average file size & 4 Mbits \\
\hline
\end{tabular}
\end{table}
\subsection{Mass event scenario} \label{sec:mass_event}
Consider a cell with a very large hotspot described by a spatial Gaussian traffic distribution which is superimposed
on a uniform traffic over the whole cell area as shown in Figure \ref{fig:traff_map}. This distribution
represents the traffic intensity map in arrivals per second per km$^2$. The hotspot can represent a crowd watching a live concert
held on an esplanade for example.
It is assumed that the users have a significant direct (\ac{LoS}) path with the \ac{BS}.
It is recalled that in a rich scattering environment, other \ac{MIMO}
techniques are more appropriate. In order to take into account the residual multipaths due to
reflections on neighboring buildings, we use the Nakagami-m distribution for the fast fading.
\begin{figure}[!ht]
\centering
\includegraphics[width=3in]{traffic_intensity_map.png}
\caption{Traffic intensity map (in users/s/km$^2$).}
\label{fig:traff_map}
\end{figure}
\subsubsection{Illustration of the multilevel beamforming}
Figures \ref{fig:beams_u}, \ref{fig:zooms} and \ref{fig:ant_diags}
represent the coverage maps of the beams in each level, the best beam chosen at each level for a user located at the center of the hotspot area
(yellow square in Figure \ref{fig:zooms}) and the corresponding antenna diagrams, respectively, as described below.
\begin{figure}
\centering
\subfloat[Original Cell]{\includegraphics[width=3in]{beam0}
\label{fig:beam0u}}
\hfil
\subfloat[Level 1 beams ($N_x,N_z$)=(6,16)]{\includegraphics[width=3in]{beam1}
\label{fig:beam1u}}
\hfil
\subfloat[Level 2 beams ($N_x,N_z$)=(12,16)]{\includegraphics[width=3in]{beam2}
\label{fig:beam2u}}
\hfil
\subfloat[Level 3 beams ($N_x,N_z$)=(12,32)]{\includegraphics[width=3in]{beam3}
\label{fig:beam3u}}
\caption{Multilevel beam coverage maps for the mass event scenario}\label{fig:beams_u}
\end{figure}
The multilevel beam structure presented in Section \ref{sec:multilevel_beamforming} is illustrated in Figure \ref{fig:beams_u}.
Here, the condition \eqref{eq:coverage_overlap} is met by definition
of the coverage areas. However, condition \eqref{eq:coverage_inclusion}
is relaxed in order to allow narrower beams (level 3 in Figure \ref{fig:beam3u}) to cover blank spaces left by wider beams (level 2
in Figure \ref{fig:beam2u}).
\begin{figure}
\centering
\subfloat[Level 0 beam (\ac{SINR} = 7.75dB)]{\includegraphics[width=3in]{zoom0}
\label{fig:zoom0}}
\hfil
\subfloat[Level 1 beam (\ac{SINR} = 12.52dB)]{\includegraphics[width=3in]{zoom1}
\label{fig:zoom1}}
\hfil
\subfloat[Level 2 beam (\ac{SINR} = 14.24dB)]{\includegraphics[width=3in]{zoom2}
\label{fig:zoom2}}
\hfil
\subfloat[Level 3 beam (\ac{SINR} = 17.38dB)]{\includegraphics[width=3in]{zoom3}
\label{fig:zoom3}}
\caption{Successive narrowing of the beam for a given user}\label{fig:zooms}
\end{figure}
Figure \ref{fig:zooms} presents the beam selection algorithm performed according to \eqref{eq:beam_select} for a given user.
The \ac{SINR} of the selected user gradually increases from 7.75dB to 17.38dB at three iterations, i.e. by a factor of 9.
It is noted that the \ac{SINR} gains are expected to be even higher for cell edge users.
\begin{figure}
\centering
\subfloat[Level 1 beam diagrams]{\includegraphics[width=3in]{ant_diag1}
\label{fig:ant_diag1}}
\hfil
\subfloat[Level 2 beam diagrams]{\includegraphics[width=3in]{ant_diag2}
\label{fig:ant_diag2}}
\hfil
\subfloat[Level 3 beam diagrams]{\includegraphics[width=3in]{ant_diag3}
\label{fig:ant_diag3}}
\caption{Antenna diagrams for a given user's best beam in each level.}\label{fig:ant_diags}
\end{figure}
The antenna diagrams corresponding to the selected beams in each level in Figure \ref{fig:zooms} are presented in Figure \ref{fig:ant_diags}.
These diagrams were designed according to the optimization problem \eqref{eq:ant_opt}, with the side-lobe level constraint
\eqref{eq:sl_th} of $Th = 30dB$. One can see that the beam width of the main lobe gets narrower in elevation or azimuth plane and the maximum gain increases (from 23.76dB to 30.2dB) with the beam level. The antenna diagram for level 0 which correspond to the full cell coverage is omitted.
\subsubsection{Performance results} \label{sec:urban_perf}
We next evaluate the performance of the multilevel beamforming for the mass event urban scenario.
We use the Nakagami-m distribution which models fast-fading in environments with strong \ac{LoS} component
and many weaker reflection components. The \emph{shape parameter} m dictates
the contribution of the \ac{LoS} component in the overall signal. For m $=1$, there is no \ac{LoS} component
and the fast fading reduces to a Rayleigh distribution. As m grows to infinity, the \ac{LoS} component gradually becomes
preponderant. We consider various Nakagami-m fading scenarios with m = 2, 5 and 10,
and the no-fading case (corresponding to m $=+\infty$). We do not consider the m $=1$ case
due to the open environment considered in the scenario. The simulation parameters for the scenario are summarized in Table \ref{tab:paramsu}.
\begin{table}[!t]
\small
\renewcommand{\arraystretch}{1.3}
\caption{Network and traffic characteristics for the mass event scenario} \label{tab:paramsu}
\centering
\begin{tabular}{|M{4cm}|M{4cm}|}
\hline
Intersite distance & 500 m \\
\hline
Nakagami-m shape parameter & 2, 5 or 10 \\
\hline
Traffic spatial distribution & Gaussian Hotspot + Uniform (see Figure \ref{fig:traff_map}) \\
\hline
\end{tabular}
\end{table}
Figure \ref{fig:sel_beam_prob} presents the frequencies of selected beams throughout the simulation.
As expected, beam 17 which covers most of the hotspot region (see Figures \ref{fig:traff_map} and \ref{fig:beam3u})
is the most frequently selected. So the beam selection algorithm successfully locates the traffic in the direction of the hotspot and
adjusts the beam width without any prior knowledge of the hotspot location and size.
\begin{figure}[!ht]
\centering
\includegraphics[width=3.5in]{bsp}
\caption{Histogram of selected beams throughout the simulation: X is the beam number (see Figure \ref{fig:beams_u}) and Y - its selection probability.}
\label{fig:sel_beam_prob}
\end{figure}
Table \ref{tab:kpisu} presents the \ac{MUT}, the \ac{CET} and the \ac{PC} obtained for the various shape parameters of
the Nakagami-m fading distribution, with and without (denoted respectively as 'w.' and 'wo.' in Table \ref{tab:kpisu}) the multilevel beamforming.
For example, in Table \ref{tab:kpisu}, '2 wo.' means m=2 without multilevel beamforming. The \ac{PC} is evaluated using the approximate
linear \ac{PC} model given in \cite[Eq. (4-3)]{imran_energyefficiencyanalysis_2011}
\begin{equation}\label{eq:pc_model}
P_c = P_0 + \alpha P
\end{equation}
where $P_0 = 260$W is the \ac{PC} for zero-load, $\alpha =
2\times4.7$ is the scaling factor term for an antenna with
two-transmission chains and $P$ is the total transmit power when
serving a user with the entire bandwidth.
\begin{table}[!t]
\small
\renewcommand{\arraystretch}{1.3}
\caption{Performance gain using multilevel beamforming for the mass
event scenario} \label{tab:kpisu} \centering
\begin{tabular}{|c|c|c|c|}
\hline
m & MUT (Mbps) & CET (Mbps) & PC (W) \\ \hline
2 wo. & 7.64 & 1.78 & 397\\\hline
2 w. & 21.49 (181\%) & 5.52 (210\%) & 334 (-15.92\%)\\\hline
5 wo. & 7.21 & 1.35 & 400\\\hline
5 w. & 22.33 (210\%) & 5.59 (312\%) & 331 (-17.24\%)\\\hline
10 wo. & 6.97 & 1.18 & 402\\\hline
10 w. & 22.43 (222\%) & 5.31 (349\%) & 331 (-17.51\%)\\\hline
$+\infty$ wo. & 4.99 & 0.51 & 417 \\\hline
$+\infty$ w. & 21.85 (337\%) & 4.75 (822\%) & 334 (-19.98\%) \\\hline
\end{tabular}
\end{table}
The performance results show particularly high gain brought about by multilevel beamforming.
The \ac{MUT} is improved by a factor varying from 2.81 to 4.38, the \ac{CET} - from 3.1 to 9.22,
and the \ac{PC} is reduced by 15.9 to 20 percent for m varying from 2
to $+\infty$ respectively.
The difference in performance gain between \ac{MUT} and \ac{CET} is due to the fact that
cell edge users have initially low \ac{SINR} and their \ac{SINR} gain with beam focusing is larger.
The \ac{PC} is reduced due to the significant reduction in the sojourn time of the users so
the \ac{BS} transmits less often.
The performance gains increase with the value of m, namely with
the importance of the \ac{LoS} component relative to the multipaths' components.
It is recalled that in an environment rich of scatterers, the initial
level of beams (i.e. level 0 in Figure \ref{fig:beam_hierarchy}) will benefit
from higher diversity gain by using an opportunistic scheduler (e.g.
\ac{PF}) and therefore the gain obtained by the multilevel
beamforming is smaller. This observation further supports the claim that
the the multilayer beamforming is of particular interest for
open type of environment having a significant \ac{LoS}
propagation.
\subsection{Rural scenario}
The simulation parameters for the rural scenario are summarized in Table \ref{tab:paramsr}.
Unlike the mass event urban scenario, the bigger dimensions of
the cell make vertical beam separation complex.
A modification of the beam direction in elevation by a fraction of
a degree results in significant difference in its coverage. For
this reason, we consider multilevel beamforming in the
horizontal (azimuth) plane, as shown in Figure \ref{fig:beams_r}.
For the sake of brevity, fast-fading is not considered here. However, similar results as those presented for the mass event urban scenario
(see Section \ref{sec:urban_perf}) are expected, with performance gains increasing with the shape parameter m of the Nakagami-m fading.
\begin{figure}
\centering
\subfloat[Original Cell]{\includegraphics[width=3in]{rural/beam0}
\label{fig:beam0r}}
\hfil
\subfloat[Level 1 beams ($N_x,N_z$)=(5,14)]{\includegraphics[width=3in]{rural/beam1}
\label{fig:beam1r}}
\hfil
\subfloat[Level 2 beams ($N_x,N_z$)=(10,14)]{\includegraphics[width=3in]{rural/beam2}
\label{fig:beam2r}}
\hfil
\subfloat[Level 3 beams ($N_x,N_z$)=(20,14)]{\includegraphics[width=3in]{rural/beam3}
\label{fig:beam3r}}
\caption{Coverage maps for different beamforming levels for the rural scenario}\label{fig:beams_r}
\end{figure}
\begin{table}[!t]
\small
\renewcommand{\arraystretch}{1.3}
\caption{Network and traffic characteristics for the rural scenario} \label{tab:paramsr}
\centering
\begin{tabular}{|c|c|}
\hline
Intersite distance & 1732 m \\
\hline
Fast-fading & None \\
\hline
Traffic spatial distribution & uniform \\
\hline
Arrival rate & 2.5 users/s/km$^2$ \\
\hline
\end{tabular}
\end{table}
Table \ref{tab:kpis} compares performance results for \ac{MUT}, \ac{CET}, and \ac{PC} using different numbers of beamforming levels.
The performance of level k corresponds to the case where equation \eqref{eq:beam_select} is applied to a highest beam level set to k.
The performance gain are very high also in the rural scenario.
For example, for three levels of beams, \ac{MUT} and \ac{CET}
are increased by 238 and 501 percent. It is noted that the
gain achieved is lower than that obtained in the mass event urban scenario.
The reason for this is the smaller number of antenna elements
used in the rural scenario which results in lower antenna gains. For example, in the third (highest) level,
the number of antenna elements are $(N_{x,max},N_{z,max})$=(20,14) and $(N_{x,max},N_{z,max})$
=(12,32) in the rural and the mass event scenarios,
respectively.
\begin{table}[!t]
\small
\renewcommand{\arraystretch}{1.3}
\caption{Performance gain using multilevel beamforming for the rural
scenario for different beam levels} \label{tab:kpis}
\centering
\begin{tabular}{|c|c|c|c|}
\cline{2-4}
\multicolumn{1}{c|}{} & MUT (Mbps) & CET (Mbps) & PC (W) \\ \hline
Level 0 & 4.66 & 0.43 & 421 \\ \hline
Level 1 & 9.9 (112\%) & 1.15 (168\%) & 388 (-7.93\%) \\ \hline
Level 2 & 13.23 (184\%) & 1.96 (360\%) & 369 (-12.3\%) \\ \hline
Level 3 & 15.78 (238\%) & 2.57 (501\%) & 356 (-15.42\%) \\ \hline
\end{tabular}
\end{table}
\section{Conclusion} \label{sec:conclusion}
A design framework for beam focusing using antenna arrays has been presented in this paper.
In order to reduce the search complexity among all possible beams when a user is scheduled,
a multilevel beamforming strategy has been adopted in which the best beam is iteratively selected for each level
based on the user \ac{CQI}. The multilevel beams' codebook can be constructed offline, as an optimization problem, taking into account
coverage and interference constraints in each level. A higher level beam covers a fraction (e.g. half)
of its lower level parent beam. The numerical results show very high performance gains brought about by the multilevel beamforming, both in terms of
throughput and power consumption. Two scenarios have been evaluated: a mass event urban scenario and a rural scenario.
The multilevel beamforming solution is well adapted to the
\ac{FDD} technology, and provides highest gains in environment
with significant \ac{LoS} component and low level of multipath
propagation. To achieve highly focused beams, antenna arrays
with a large number of radiating elements is required. Hence higher
frequency envisaged in 5G spectrum evolution will make this
technology particularly attractive.
\bibliographystyle{IEEEtran}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 8,518
|
{"url":"https:\/\/www.rdocumentation.org\/packages\/stats\/versions\/3.6.2\/topics\/formula","text":"# formula\n\n0th\n\nPercentile\n\n##### Model Formulae\n\nThe generic function formula and its specific methods provide a way of extracting formulae which have been included in other objects.\n\nas.formula is almost identical, additionally preserving attributes when object already inherits from \"formula\".\n\nKeywords\nmodels\n##### Usage\nformula(x, \u2026)\nDF2formula(x, env = parent.frame())\nas.formula(object, env = parent.frame())# S3 method for formula\nprint(x, showEnv = !identical(e, .GlobalEnv), \u2026)\n##### Arguments\nx, object\n\nR object, for DF2formula() a data.frame.\n\nfurther arguments passed to or from other methods.\n\nenv\n\nthe environment to associate with the result, if not already a formula.\n\nshowEnv\n\nlogical indicating if the environment should be printed as well.\n\n##### Details\n\nThe models fit by, e.g., the lm and glm functions are specified in a compact symbolic form. The ~ operator is basic in the formation of such models. An expression of the form y ~ model is interpreted as a specification that the response y is modelled by a linear predictor specified symbolically by model. Such a model consists of a series of terms separated by + operators. The terms themselves consist of variable and factor names separated by : operators. Such a term is interpreted as the interaction of all the variables and factors appearing in the term.\n\nIn addition to + and :, a number of other operators are useful in model formulae. The * operator denotes factor crossing: a*b interpreted as a+b+a:b. The ^ operator indicates crossing to the specified degree. For example (a+b+c)^2 is identical to (a+b+c)*(a+b+c) which in turn expands to a formula containing the main effects for a, b and c together with their second-order interactions. The %in% operator indicates that the terms on its left are nested within those on the right. For example a + b %in% a expands to the formula a + a:b. The - operator removes the specified terms, so that (a+b+c)^2 - a:b is identical to a + b + c + b:c + a:c. It can also used to remove the intercept term: when fitting a linear model y ~ x - 1 specifies a line through the origin. A model with no intercept can be also specified as y ~ x + 0 or y ~ 0 + x.\n\nWhile formulae usually involve just variable and factor names, they can also involve arithmetic expressions. The formula log(y) ~ a + log(x) is quite legal. When such arithmetic expressions involve operators which are also used symbolically in model formulae, there can be confusion between arithmetic and symbolic operator use.\n\nTo avoid this confusion, the function I() can be used to bracket those portions of a model formula where the operators are used in their arithmetic sense. For example, in the formula y ~ a + I(b+c), the term b+c is to be interpreted as the sum of b and c.\n\nVariable names can be quoted by backticks like this in formulae, although there is no guarantee that all code using formulae will accept such non-syntactic names.\n\nMost model-fitting functions accept formulae with right-hand-side including the function offset to indicate terms with a fixed coefficient of one. Some functions accept other \u2018specials\u2019 such as strata or cluster (see the specials argument of terms.formula).\n\nThere are two special interpretations of . in a formula. The usual one is in the context of a data argument of model fitting functions and means \u2018all columns not otherwise in the formula\u2019: see terms.formula. In the context of update.formula, only, it means \u2018what was previously in this part of the formula\u2019.\n\nWhen formula is called on a fitted model object, either a specific method is used (such as that for class \"nls\") or the default method. The default first looks for a \"formula\" component of the object (and evaluates it), then a \"terms\" component, then a formula parameter of the call (and evaluates its value) and finally a \"formula\" attribute.\n\nThere is a formula method for data frames. When there's \"terms\" attribute with a formula, e.g., for a model.frame(), that formula is returned. If you'd like the previous (R $\\le$ 3.5.x) behavior, use the auxiliary DF2formula() which does not consider a \"terms\" attribute. Otherwise, if there is only one column this forms the RHS with an empty LHS. For more columns, the first column is the LHS of the formula and the remaining columns separated by + form the RHS.\n\n##### Value\n\nAll the functions above produce an object of class \"formula\" which contains a symbolic model formula.\n\n##### Environments\n\nA formula object has an associated environment, and this environment (rather than the parent environment) is used by model.frame to evaluate variables that are not found in the supplied data argument.\n\nFormulas created with the ~ operator use the environment in which they were created. Formulas created with as.formula will use the env argument for their environment.\n\n##### References\n\nChambers, J. M. and Hastie, T. J. (1992) Statistical models. Chapter 2 of Statistical Models in S eds J. M. Chambers and T. J. Hastie, Wadsworth & Brooks\/Cole.\n\nI, offset.\n\nFor formula manipulation: terms, and all.vars; for typical use: lm, glm, and coplot.\n\n##### Aliases\n\u2022 formula\n\u2022 formula.default\n\u2022 formula.formula\n\u2022 formula.terms\n\u2022 formula.data.frame\n\u2022 DF2formula\n\u2022 as.formula\n\u2022 print.formula\n\u2022 [.formula\n##### Examples\nlibrary(stats) # NOT RUN { class(fo <- y ~ x1*x2) # \"formula\" fo typeof(fo) # R internal : \"language\" terms(fo) environment(fo) environment(as.formula(\"y ~ x\")) environment(as.formula(\"y ~ x\", env = new.env())) ## Create a formula for a model with a large number of variables: xnam <- paste0(\"x\", 1:25) (fmla <- as.formula(paste(\"y ~ \", paste(xnam, collapse= \"+\")))) # } \nDocumentation reproduced from package stats, version 3.6.2, License: Part of R 3.6.2\n\n### Community examples\n\nalphail2z3T8 at Sep 12, 2018 stats v3.5.1\n\n #example of usage of y ~ ., to explain the statement: #\"The usual one is in the context of a data argument of model #fitting functions and means \u2018all columns not otherwise in the formula\u2019: see terms.formula.\" #create mydata mydata<-data.frame(matrix(c( 1,5501,8.1,9552,1923, 2,5945,7.0,9680,1961, 3,6629,7.3,9731,1979, 4,7556,7.5,11666,2030, 5,8716,7.0,14675,2112, 6,9369,6.4,15265,2192, 7,9920,6.5,15484,2235, 8,10167,6.4,15723,2351, 9,11084,6.3,16501,2411, 10,12504,7.7,16890,2475) , nrow = 10, ncol = 5, byrow=TRUE)) colnames(mydata) <- c(\"gene\",\"cna\",\"common\",\"PC1\",\"PC2\") #generate linear regression fit for mydata. gene ~ . is equivalent to gene ~ cna+common+PC1+PC2, ie. #the righthand side of ~ is a function of all the variables other than gene (which is on the left hand side). mymodel=lm(gene ~ .,data=mydata) #generates the fit \n\ndivyanshu86@gmail.com at Aug 31, 2018 stats v3.5.1\n\n##New example Get the ouput of formula by inserting variables readinteger<-function() + { + n<-readline(prompt=\"Enter an integer:\") + n<-as.integer(n) + x=((((n+2)*3)-6)\/2) + return(as.integer(x)) + } > print(readinteger())\n\ndivyanshu86@gmail.com at Aug 31, 2018 stats v3.5.1\n\n##New example Get the ouput of formula by inserting variables readinteger<-function() + { + n<-readline(prompt=\"Enter an integer:\") + n<-as.integer(n) + x=((((n+2)*3)-6)\/2) + return(as.integer(x)) + } > print(readinteger())\n\nrichie@datacamp.com at Jan 17, 2017 stats v3.3.1\n\ny is the response; x1, x2 and x3 are independent variables; terms with colons are the interactions between those variables. {r} y ~ x1 + x2 + x3 + x1:x2 + x1:x3 + x2:x3 + x1:x2:x3 A more compact form of the above. {r} y ~ x1 * x2 * x3 You can specify interactions up to a certain level using the power operator. {r} y ~ (x1 + x2 + x3) ^ 2 # same as y ~ x1 + x2 + x3 + x1:x2 + x1:x3 + x2:x3 Minus removes terms from the formula. {r} y ~ x1 * x2 * x3 - x1:x2:x3 # same as the previous formula To include powers of variables, use the [I()](https:\/\/www.rdocumentation.org\/packages\/base\/topics\/AsIs) function. {r} y ~ I(x1 ^ 2) Other functions can be included as is. {r} log(y) ~ log(x1) Some functions allow formulae with no left-hand side. {r} ~ x1 * x2 * x3 Modelling functions use the syntax plus zero to specify a model with no intercept. {r} y ~ x1 + 0 You can also use minus one to specify a model with no intercept. {r} y ~ x1 - 1 # same as the previous formula Some functions accept grouping formulae using pipes. {r} y ~ x1 + x2 | x3 Groups can sometimes also be nested using forward slashes. {r} y ~ x1 + x2 | x3 \/ x4 %in% is rarely used, and works like a colon {r} y ~ x1 %in% x2 # same as y ~ x1:x2 Sometimes it is convenient to use [paste()](https:\/\/www.rdocumentation.org\/packages\/base\/topics\/paste) to construct the formula as a string, then use as.formula(). {r} x_names <- paste0(\"x\", 1:25) as.formula(paste(\"y ~ \", paste(x_names, collapse= \" + \"))) Non-standard variable names can be included by using backticks, though functions are not guaranteed to be able correctly interpret them {r} y ~ x 1 Formulae (along with expressions, calls and names) are language objects. {r} is.language(y ~ x) formulae have an associated environment. This tells functions like [lm()](https:\/\/www.rdocumentation.org\/packages\/stats\/topics\/lm) where to look for variables that aren't included in the data argument. {r} environment(y ~ x) In advanced usage, you can specify the associated environment. {r} environment(as.formula(\"y ~ x\")) environment(as.formula(\"y ~ x\", env = new.env()))","date":"2020-05-29 11:13:16","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 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\": 0.7350867390632629, \"perplexity\": 2952.8149823277654}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2020-24\/segments\/1590347402885.41\/warc\/CC-MAIN-20200529085930-20200529115930-00367.warc.gz\"}"}
| null | null |
Q: Force headers on all Rails 404/500 responses I am trying to set the 'X-Frame-Options' header on all responses returned by my Rails application. It seems like this header is not set on 404 or 500 type responses. How can I configure Rails to always include this header?
It appears I somehow need to hook into Rails to ensure these headers are always set.
A: I am having success using the below middleware as my 'exceptions_app'.
class XSecurityHandler
def initialize(app)
@app = app
end
def call(env)
_status, headers, response = @app.call(env)
headers['X-Frame-Options'] = "SAMEORIGIN"
headers['X-Content-Type-Options'] = "nosniff"
[status(env), headers, response]
end
private
def status(env)
path = env["ORIGINAL_FULLPATH"]
if path == "/404"
404
elsif path == "/422"
422
else
500
end
end
end
A: Set default headers in config/application.rb:
config.action_dispatch.default_headers['X-Frame-Options'] = 'SAMEORIGIN'
but it wont work, if you have configured reverse proxy (like nginx) to serve static assets which does not exists (404), but i think you know about this :)
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 1,658
|
#if NET461 || NETCOREAPP2_0 || NETCOREAPP3_0 || NET5_0_OR_GREATER
using Audit.Elasticsearch.Providers;
using Nest;
using NUnit.Framework;
using System;
using System.Collections.Generic;
using System.Linq;
using Audit.Core;
using Moq;
using System.Threading;
using System.Threading.Tasks;
using Elasticsearch.Net;
using System.Text;
namespace Audit.IntegrationTest
{
public class ElasticsearchTests
{
private ElasticsearchDataProvider GetElasticsearchDataProvider(List<Core.AuditEvent> ins, List<Core.AuditEvent> repl)
{
var client = new ElasticClient(new Uri("http://127.0.0.1:9200"));
return new ElasticsearchDataProviderForTest(ins, repl, client);
}
[Test]
[Category("Elasticsearch")]
public void Test_Elasticsearch_HappyPath()
{
var ins = new List<Core.AuditEvent>();
var repl = new List<Core.AuditEvent>();
var ela = GetElasticsearchDataProvider(ins, repl);
var indexName = "auditevent_order";
var guids = new List<string>();
ela.IndexBuilder = ev => indexName;
ela.IdBuilder = ev => { var g = Guid.NewGuid().ToString().Replace("-", "/"); guids.Add(g); return g; };
Audit.Core.Configuration.Setup()
.UseCustomProvider(ela)
.WithCreationPolicy(Core.EventCreationPolicy.InsertOnStartReplaceOnEnd)
.ResetActions();
var order = new Order()
{
Id = 1,
Status = "Created"
};
using (var scope = new AuditScopeFactory().Create("eventType", () => order, new { MyCustomField = "value" }, null, null))
{
order.Status = "Updated";
}
ela.Client.Indices.Refresh(indexName);
var evLoad = ela.GetEvent(new ElasticsearchAuditEventId() { Id = guids[0], Index = indexName });
var orderOldValue = Configuration.JsonAdapter.Deserialize<Order>(repl[0].Target.Old.ToString());
var orderNewValue = Configuration.JsonAdapter.Deserialize<Order>(repl[0].Target.New.ToString());
var oldDictionary = evLoad.Target.Old as Dictionary<string, object>;
var newDictionary = evLoad.Target.New as Dictionary<string, object>;
Assert.IsNotNull(evLoad);
Assert.IsNotNull(oldDictionary);
Assert.IsNotNull(newDictionary);
Assert.AreEqual(1, guids.Count);
Assert.AreEqual(1, ins.Count);
Assert.AreEqual(1, repl.Count);
Assert.AreEqual("Created", orderOldValue.Status);
Assert.AreEqual("Created", oldDictionary["status"].ToString());
Assert.AreEqual("Updated", orderNewValue.Status);
Assert.AreEqual("Updated", newDictionary["status"].ToString());
Assert.AreEqual("value", evLoad.CustomFields["MyCustomField"]);
Assert.AreEqual(null, ins[0].Target.New);
}
[Test]
[Category("Elasticsearch")]
public async Task Test_Elasticsearch_HappyPath_Async()
{
var ins = new List<Core.AuditEvent>();
var repl = new List<Core.AuditEvent>();
var ela = GetElasticsearchDataProvider(ins, repl);
var indexName = "auditevent_order";
var guids = new List<string>();
ela.IndexBuilder = ev => indexName;
ela.IdBuilder = ev => { var g = Guid.NewGuid().ToString().Replace("-", "/"); guids.Add(g); return g; };
Audit.Core.Configuration.Setup()
.UseCustomProvider(ela)
.WithCreationPolicy(Core.EventCreationPolicy.InsertOnStartReplaceOnEnd)
.ResetActions();
var order = new Order()
{
Id = 1,
Status = "Created"
};
using (var scope = await new AuditScopeFactory().CreateAsync("eventType", () => order, new { MyCustomField = "value" }, null, null))
{
order.Status = "Updated";
}
await ela.Client.Indices.RefreshAsync(indexName);
var evLoad = await ela.GetEventAsync(new ElasticsearchAuditEventId() { Id = guids[0], Index = indexName });
var orderOldValue = Configuration.JsonAdapter.Deserialize<Order>(repl[0].Target.Old.ToString());
var orderNewValue = Configuration.JsonAdapter.Deserialize<Order>(repl[0].Target.New.ToString());
var oldDictionary = evLoad.Target.Old as Dictionary<string, object>;
var newDictionary = evLoad.Target.New as Dictionary<string, object>;
Assert.IsNotNull(evLoad);
Assert.IsNotNull(oldDictionary);
Assert.IsNotNull(newDictionary);
Assert.AreEqual(1, guids.Count);
Assert.AreEqual(1, ins.Count);
Assert.AreEqual(1, repl.Count);
Assert.AreEqual("Created", orderOldValue.Status);
Assert.AreEqual("Created", oldDictionary["status"].ToString());
Assert.AreEqual("Updated", orderNewValue.Status);
Assert.AreEqual("Updated", newDictionary["status"].ToString());
Assert.AreEqual("value", evLoad.CustomFields["MyCustomField"]);
Assert.AreEqual(null, ins[0].Target.New);
}
[Test]
[Category("Elasticsearch")]
public void Test_Elasticsearch_AutoGeneratedId()
{
var ins = new List<Core.AuditEvent>();
var repl = new List<Core.AuditEvent>();
var ela = GetElasticsearchDataProvider(ins, repl);
var indexName = "auto_" + new Random().Next(10000, 99999);
ela.IndexBuilder = ev => indexName;
ela.IdBuilder = ev => null;
Audit.Core.Configuration.Setup()
.UseCustomProvider(ela)
.WithCreationPolicy(Core.EventCreationPolicy.InsertOnStartReplaceOnEnd)
.ResetActions();
var sb = "init";
using (var scope = new AuditScopeFactory().Create("eventType", () => sb, new { MyCustomField = "value" }, null, null))
{
sb += "-end";
}
ela.Client.Indices.Refresh(indexName);
var results = ela.Client.Search<Core.AuditEvent>(new SearchRequest(indexName));
var evResult = results.Documents.FirstOrDefault();
if (evResult != null)
{
ela.Client.Delete(new DeleteRequest(results.Hits.First().Index, results.Hits.First().Id));
}
Assert.IsNotNull(evResult);
Assert.AreEqual(1, results.Documents.Count);
Assert.AreEqual(1, ins.Count);
Assert.AreEqual(1, repl.Count);
Assert.AreEqual("init", evResult.Target.Old.ToString());
Assert.AreEqual("init", ins[0].Target.Old.ToString());
Assert.AreEqual(null, ins[0].Target.New);
Assert.AreEqual("init", repl[0].Target.Old.ToString());
Assert.AreEqual("init-end", repl[0].Target.New.ToString());
Assert.AreEqual("init-end", evResult.Target.New.ToString());
Assert.AreEqual("value", evResult.CustomFields["MyCustomField"]?.ToString());
}
[Test]
[Category("Elasticsearch")]
public async Task Test_Elasticsearch_AutoGeneratedId_Async()
{
var ins = new List<Core.AuditEvent>();
var repl = new List<Core.AuditEvent>();
var ela = GetElasticsearchDataProvider(ins, repl);
var indexName = "auto_" + new Random().Next(10000, 99999);
ela.IndexBuilder = ev => indexName;
ela.IdBuilder = ev => null;
Audit.Core.Configuration.Setup()
.UseCustomProvider(ela)
.WithCreationPolicy(Core.EventCreationPolicy.InsertOnStartReplaceOnEnd)
.ResetActions();
var sb = "init";
using (var scope = await new AuditScopeFactory().CreateAsync("eventType", () => sb, new { MyCustomField = "value" }, null, null))
{
sb += "-end";
}
await ela.Client.Indices.RefreshAsync(indexName);
var results = await ela.Client.SearchAsync<Core.AuditEvent>(new SearchRequest(indexName));
var evResult = results.Documents.FirstOrDefault();
if (evResult != null)
{
await ela.Client.DeleteAsync(new DeleteRequest(results.Hits.First().Index, results.Hits.First().Id));
}
Assert.IsNotNull(evResult);
Assert.AreEqual(1, results.Documents.Count);
Assert.AreEqual(1, ins.Count);
Assert.AreEqual(1, repl.Count);
Assert.AreEqual("init", evResult.Target.Old.ToString());
Assert.AreEqual("init", ins[0].Target.Old.ToString());
Assert.AreEqual(null, ins[0].Target.New);
Assert.AreEqual("init", repl[0].Target.Old.ToString());
Assert.AreEqual("init-end", repl[0].Target.New.ToString());
Assert.AreEqual("init-end", evResult.Target.New.ToString());
Assert.AreEqual("value", evResult.CustomFields["MyCustomField"]?.ToString());
}
}
public class ElasticsearchDataProviderForTest : ElasticsearchDataProvider
{
private List<Core.AuditEvent> _inserted;
private List<Core.AuditEvent> _replaced;
public ElasticsearchDataProviderForTest(List<Core.AuditEvent> ins, List<Core.AuditEvent> repl, IElasticClient cli) : base(cli)
{
_inserted = ins;
_replaced = repl;
}
public override object InsertEvent(Core.AuditEvent auditEvent)
{
_inserted.Add(Audit.Core.AuditEvent.FromJson(auditEvent.ToJson()));
return base.InsertEvent(auditEvent);
}
public override Task<object> InsertEventAsync(Core.AuditEvent auditEvent)
{
_inserted.Add(Audit.Core.AuditEvent.FromJson(auditEvent.ToJson()));
return base.InsertEventAsync(auditEvent);
}
public override void ReplaceEvent(object eventId, Core.AuditEvent auditEvent)
{
_replaced.Add(Audit.Core.AuditEvent.FromJson(auditEvent.ToJson()));
base.ReplaceEvent(eventId, auditEvent);
}
public override Task ReplaceEventAsync(object eventId, Core.AuditEvent auditEvent)
{
_replaced.Add(Audit.Core.AuditEvent.FromJson(auditEvent.ToJson()));
return base.ReplaceEventAsync(eventId, auditEvent);
}
}
}
#endif
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 3,146
|
<mods xmlns="http://www.loc.gov/mods/v3" xmlns:exslt="http://exslt.org/common" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:xlink="http://www.w3.org/1999/xlink" xsi:schemaLocation="http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-3.xsd" version="3.3" ID="P0b002ee18d612a79">
<name type="corporate">
<namePart>United States Government Publishing Office</namePart>
<role>
<roleTerm type="text" authority="marcrelator">publisher</roleTerm>
<roleTerm type="code" authority="marcrelator">pbl</roleTerm>
</role>
<role>
<roleTerm type="text" authority="marcrelator">distributor</roleTerm>
<roleTerm type="code" authority="marcrelator">dst</roleTerm>
</role>
</name>
<name type="corporate">
<namePart>United States</namePart>
<namePart>United States District Court Eastern District of California</namePart>
<role>
<roleTerm type="text" authority="marcrelator">author</roleTerm>
<roleTerm type="code" authority="marcrelator">aut</roleTerm>
</role>
<description>Government Organization</description>
</name>
<typeOfResource>text</typeOfResource>
<genre authority="marcgt">government publication</genre>
<language>
<languageTerm authority="iso639-2b" type="code">eng</languageTerm>
</language>
<extension>
<collectionCode>USCOURTS</collectionCode>
<category>Judicial Publications</category>
<branch>judicial</branch>
<dateIngested>2015-08-26</dateIngested>
</extension>
<originInfo>
<publisher>Administrative Office of the United States Courts</publisher>
<dateIssued encoding="w3cdtf">2015-08-25</dateIssued>
<issuance>monographic</issuance>
</originInfo>
<physicalDescription>
<note type="source content type">deposited</note>
<digitalOrigin>born digital</digitalOrigin>
</physicalDescription>
<classification authority="sudocs">JU 4.15</classification>
<identifier type="uri">http://www.gpo.gov/fdsys/pkg/USCOURTS-caed-1_11-cv-01884</identifier>
<identifier type="local">P0b002ee18d612a79</identifier>
<recordInfo>
<recordContentSource authority="marcorg">DGPO</recordContentSource>
<recordCreationDate encoding="w3cdtf">2015-08-26</recordCreationDate>
<recordChangeDate encoding="w3cdtf">2015-08-26</recordChangeDate>
<recordIdentifier source="DGPO">USCOURTS-caed-1_11-cv-01884</recordIdentifier>
<recordOrigin>machine generated</recordOrigin>
<languageOfCataloging>
<languageTerm authority="iso639-2b" type="code">eng</languageTerm>
</languageOfCataloging>
</recordInfo>
<accessCondition type="GPO scope determination">fdlp</accessCondition>
<extension>
<docClass>USCOURTS</docClass>
<accessId>USCOURTS-caed-1_11-cv-01884</accessId>
<courtType>District</courtType>
<courtCode>caed</courtCode>
<courtCircuit>9th</courtCircuit>
<courtState>California</courtState>
<courtSortOrder>2061</courtSortOrder>
<caseNumber>1:11-cv-01884</caseNumber>
<caseOffice>Fresno</caseOffice>
<caseType>civil</caseType>
<natureSuitCode>550</natureSuitCode>
<natureSuit>Prisoner - Civil Rights (U.S. defendant)</natureSuit>
<cause>42:1983 Prisoner Civil Rights</cause>
<party firstName="Robin" fullName="Robin Dasenbrock" lastName="Dasenbrock" role="Plaintiff"></party>
<party firstName="A." fullName="A. Enenmoh" lastName="Enenmoh" role="Defendant"></party>
<party firstName="J." fullName="J. Clark Kelso" lastName="Kelso" middleName="Clark" role="Defendant"></party>
<party fullName="Kings County" lastName="Kings County" role="Defendant"></party>
<party fullName="Page" lastName="Page" role="Defendant"></party>
<party firstName="Zafar" fullName="Zafar Parvez" lastName="Parvez" role="Defendant"></party>
<party fullName="Perez" lastName="Perez" role="Defendant"></party>
<party firstName="J." fullName="J. Walker" lastName="Walker" role="Defendant"></party>
<party firstName="D." fullName="D. Ybarra" lastName="Ybarra" role="Defendant"></party>
</extension>
<titleInfo>
<title>(PC) Dasenbrock v. Kings County et al</title>
<partNumber>1:11-cv-01884</partNumber>
</titleInfo>
<location>
<url access="object in context" displayLabel="Content Detail">http://www.gpo.gov/fdsys/pkg/USCOURTS-caed-1_11-cv-01884/content-detail.html</url>
</location>
<classification authority="sudocs">JU 4.15</classification>
<identifier type="preferred citation">1:11-cv-01884;11-1884</identifier>
<name type="corporate">
<namePart>United States District Court Eastern District of California</namePart>
<namePart>9th Circuit</namePart>
<namePart>Fresno</namePart>
<affiliation>U.S. Courts</affiliation>
<role>
<roleTerm authority="marcrelator" type="text">author</roleTerm>
<roleTerm authority="marcrelator" type="code">aut</roleTerm>
</role>
</name>
<name type="personal">
<displayForm>Robin Dasenbrock</displayForm>
<namePart type="family">Dasenbrock</namePart>
<namePart type="given">Robin</namePart>
<namePart type="termsOfAddress"></namePart>
<description>Plaintiff</description>
</name>
<name type="personal">
<displayForm>A. Enenmoh</displayForm>
<namePart type="family">Enenmoh</namePart>
<namePart type="given">A.</namePart>
<namePart type="termsOfAddress"></namePart>
<description>Defendant</description>
</name>
<name type="personal">
<displayForm>J. Clark Kelso</displayForm>
<namePart type="family">Kelso</namePart>
<namePart type="given">J.</namePart>
<namePart type="termsOfAddress"></namePart>
<description>Defendant</description>
</name>
<name type="personal">
<displayForm>Kings County</displayForm>
<namePart type="family">Kings County</namePart>
<namePart type="given"></namePart>
<namePart type="termsOfAddress"></namePart>
<description>Defendant</description>
</name>
<name type="personal">
<displayForm>Page</displayForm>
<namePart type="family">Page</namePart>
<namePart type="given"></namePart>
<namePart type="termsOfAddress"></namePart>
<description>Defendant</description>
</name>
<name type="personal">
<displayForm>Zafar Parvez</displayForm>
<namePart type="family">Parvez</namePart>
<namePart type="given">Zafar</namePart>
<namePart type="termsOfAddress"></namePart>
<description>Defendant</description>
</name>
<name type="personal">
<displayForm>Perez</displayForm>
<namePart type="family">Perez</namePart>
<namePart type="given"></namePart>
<namePart type="termsOfAddress"></namePart>
<description>Defendant</description>
</name>
<name type="personal">
<displayForm>J. Walker</displayForm>
<namePart type="family">Walker</namePart>
<namePart type="given">J.</namePart>
<namePart type="termsOfAddress"></namePart>
<description>Defendant</description>
</name>
<name type="personal">
<displayForm>D. Ybarra</displayForm>
<namePart type="family">Ybarra</namePart>
<namePart type="given">D.</namePart>
<namePart type="termsOfAddress"></namePart>
<description>Defendant</description>
</name>
<extension>
<docClass>USCOURTS</docClass>
<accessId>USCOURTS-caed-1_11-cv-01884</accessId>
<courtType>District</courtType>
<courtCode>caed</courtCode>
<courtCircuit>9th</courtCircuit>
<courtState>California</courtState>
<courtSortOrder>2061</courtSortOrder>
<caseNumber>1:11-cv-01884</caseNumber>
<caseOffice>Fresno</caseOffice>
<caseType>civil</caseType>
<natureSuitCode>550</natureSuitCode>
<natureSuit>Prisoner - Civil Rights (U.S. defendant)</natureSuit>
<cause>42:1983 Prisoner Civil Rights</cause>
<party firstName="Robin" fullName="Robin Dasenbrock" lastName="Dasenbrock" role="Plaintiff"></party>
<party firstName="A." fullName="A. Enenmoh" lastName="Enenmoh" role="Defendant"></party>
<party firstName="J." fullName="J. Clark Kelso" lastName="Kelso" middleName="Clark" role="Defendant"></party>
<party fullName="Kings County" lastName="Kings County" role="Defendant"></party>
<party fullName="Page" lastName="Page" role="Defendant"></party>
<party firstName="Zafar" fullName="Zafar Parvez" lastName="Parvez" role="Defendant"></party>
<party fullName="Perez" lastName="Perez" role="Defendant"></party>
<party firstName="J." fullName="J. Walker" lastName="Walker" role="Defendant"></party>
<party firstName="D." fullName="D. Ybarra" lastName="Ybarra" role="Defendant"></party>
<state>California</state>
</extension>
<relatedItem type="constituent" ID="id-USCOURTS-caed-1_11-cv-01884-0" xlink:href="http://www.gpo.gov/fdsys/granule/USCOURTS-caed-1_11-cv-01884/USCOURTS-caed-1_11-cv-01884-0/mods.xml">
<titleInfo>
<title>(PC) Dasenbrock v. Kings County et al</title>
<subTitle>ORDER DENYING Motion for Appointment of Counsel 3, signed by Magistrate Judge Dennis L. Beck on 11/18/11: Motion is DENIED, without prejudice. (Hellings, J)</subTitle>
<partNumber>0</partNumber>
</titleInfo>
<originInfo>
<dateIssued>2011-11-18</dateIssued>
</originInfo>
<relatedItem type="otherFormat" xlink:href="http://www.gpo.gov/fdsys/pkg/USCOURTS-caed-1_11-cv-01884/pdf/USCOURTS-caed-1_11-cv-01884-0.pdf">
<identifier type="FDsys Unique ID">D09002ee18d627dfb</identifier>
</relatedItem>
<identifier type="uri">http://www.gpo.gov/fdsys/granule/USCOURTS-caed-1_11-cv-01884/USCOURTS-caed-1_11-cv-01884-0</identifier>
<identifier type="former granule identifier">caed-1_11-cv-01884_0.pdf</identifier>
<location>
<url access="object in context" displayLabel="Content Detail">http://www.gpo.gov/fdsys/granule/USCOURTS-caed-1_11-cv-01884/USCOURTS-caed-1_11-cv-01884-0/content-detail.html</url>
<url access="raw object" displayLabel="PDF rendition">http://www.gpo.gov/fdsys/pkg/USCOURTS-caed-1_11-cv-01884/pdf/USCOURTS-caed-1_11-cv-01884-0.pdf</url>
</location>
<extension>
<searchTitle>USCOURTS 1:11-cv-01884; (PC) Dasenbrock v. Kings County et al; </searchTitle>
<courtName>United States District Court Eastern District of California</courtName>
<state>California</state>
<accessId>USCOURTS-caed-1_11-cv-01884-0</accessId>
<sequenceNumber>0</sequenceNumber>
<dateIssued>2011-11-18</dateIssued>
<docketText>ORDER DENYING Motion for Appointment of Counsel 3, signed by Magistrate Judge Dennis L. Beck on 11/18/11: Motion is DENIED, without prejudice. (Hellings, J)</docketText>
</extension>
</relatedItem>
<relatedItem type="constituent" ID="id-USCOURTS-caed-1_11-cv-01884-1" xlink:href="http://www.gpo.gov/fdsys/granule/USCOURTS-caed-1_11-cv-01884/USCOURTS-caed-1_11-cv-01884-1/mods.xml">
<titleInfo>
<title>(PC) Dasenbrock v. Kings County et al</title>
<subTitle>ORDER dismissing case 1:11-cv-1917-GSA-pc as duplicative of this case signed by Magistrate Judge Gary S. Austin on 12/8/2011. (Lundstrom, T)</subTitle>
<partNumber>1</partNumber>
</titleInfo>
<originInfo>
<dateIssued>2011-12-08</dateIssued>
</originInfo>
<relatedItem type="otherFormat" xlink:href="http://www.gpo.gov/fdsys/pkg/USCOURTS-caed-1_11-cv-01884/pdf/USCOURTS-caed-1_11-cv-01884-1.pdf">
<identifier type="FDsys Unique ID">D09002ee18d627df9</identifier>
</relatedItem>
<identifier type="uri">http://www.gpo.gov/fdsys/granule/USCOURTS-caed-1_11-cv-01884/USCOURTS-caed-1_11-cv-01884-1</identifier>
<identifier type="former granule identifier">caed-1_11-cv-01884_1.pdf</identifier>
<location>
<url access="object in context" displayLabel="Content Detail">http://www.gpo.gov/fdsys/granule/USCOURTS-caed-1_11-cv-01884/USCOURTS-caed-1_11-cv-01884-1/content-detail.html</url>
<url access="raw object" displayLabel="PDF rendition">http://www.gpo.gov/fdsys/pkg/USCOURTS-caed-1_11-cv-01884/pdf/USCOURTS-caed-1_11-cv-01884-1.pdf</url>
</location>
<extension>
<searchTitle>USCOURTS 1:11-cv-01884; (PC) Dasenbrock v. Kings County et al; </searchTitle>
<courtName>United States District Court Eastern District of California</courtName>
<state>California</state>
<accessId>USCOURTS-caed-1_11-cv-01884-1</accessId>
<sequenceNumber>1</sequenceNumber>
<dateIssued>2011-12-08</dateIssued>
<docketText>ORDER dismissing case 1:11-cv-1917-GSA-pc as duplicative of this case signed by Magistrate Judge Gary S. Austin on 12/8/2011. (Lundstrom, T)</docketText>
</extension>
</relatedItem>
<relatedItem type="constituent" ID="id-USCOURTS-caed-1_11-cv-01884-2" xlink:href="http://www.gpo.gov/fdsys/granule/USCOURTS-caed-1_11-cv-01884/USCOURTS-caed-1_11-cv-01884-2/mods.xml">
<titleInfo>
<title>(PC) Dasenbrock v. Kings County et al</title>
<subTitle>ORDER REQUIRING PLAINTIFF EITHER TO FILE AMENDED COMPLAINT OR NOTIFY COURT OF WILLINGNESS TO PROCEED ONLY ON CLAIMS FOUND TO BE COGNIZABLE,signed by Magistrate Judge Dennis L. Beck on 9/24/2012. (30)Day Deadline (Attachments: # (1) Amended Complaint Form)(Martin-Gill, S)</subTitle>
<partNumber>2</partNumber>
</titleInfo>
<originInfo>
<dateIssued>2012-09-24</dateIssued>
</originInfo>
<relatedItem type="otherFormat" xlink:href="http://www.gpo.gov/fdsys/pkg/USCOURTS-caed-1_11-cv-01884/pdf/USCOURTS-caed-1_11-cv-01884-2.pdf">
<identifier type="FDsys Unique ID">D09002ee18d627d6a</identifier>
</relatedItem>
<identifier type="uri">http://www.gpo.gov/fdsys/granule/USCOURTS-caed-1_11-cv-01884/USCOURTS-caed-1_11-cv-01884-2</identifier>
<identifier type="former granule identifier">caed-1_11-cv-01884_2.pdf</identifier>
<location>
<url access="object in context" displayLabel="Content Detail">http://www.gpo.gov/fdsys/granule/USCOURTS-caed-1_11-cv-01884/USCOURTS-caed-1_11-cv-01884-2/content-detail.html</url>
<url access="raw object" displayLabel="PDF rendition">http://www.gpo.gov/fdsys/pkg/USCOURTS-caed-1_11-cv-01884/pdf/USCOURTS-caed-1_11-cv-01884-2.pdf</url>
</location>
<extension>
<searchTitle>USCOURTS 1:11-cv-01884; (PC) Dasenbrock v. Kings County et al; </searchTitle>
<courtName>United States District Court Eastern District of California</courtName>
<state>California</state>
<accessId>USCOURTS-caed-1_11-cv-01884-2</accessId>
<sequenceNumber>2</sequenceNumber>
<dateIssued>2012-09-24</dateIssued>
<docketText>ORDER REQUIRING PLAINTIFF EITHER TO FILE AMENDED COMPLAINT OR NOTIFY COURT OF WILLINGNESS TO PROCEED ONLY ON CLAIMS FOUND TO BE COGNIZABLE,signed by Magistrate Judge Dennis L. Beck on 9/24/2012. (30)Day Deadline (Attachments: # (1) Amended Complaint Form)(Martin-Gill, S)</docketText>
</extension>
</relatedItem>
<relatedItem type="constituent" ID="id-USCOURTS-caed-1_11-cv-01884-3" xlink:href="http://www.gpo.gov/fdsys/granule/USCOURTS-caed-1_11-cv-01884/USCOURTS-caed-1_11-cv-01884-3/mods.xml">
<titleInfo>
<title>(PC) Dasenbrock v. Kings County et al</title>
<subTitle>ORDER Denying Plaintiff's 12 Motion for Reconsideration, signed by Magistrate Judge Dennis L. Beck on 10/30/12. (Gonzalez, R)</subTitle>
<partNumber>3</partNumber>
</titleInfo>
<originInfo>
<dateIssued>2012-10-31</dateIssued>
</originInfo>
<relatedItem type="otherFormat" xlink:href="http://www.gpo.gov/fdsys/pkg/USCOURTS-caed-1_11-cv-01884/pdf/USCOURTS-caed-1_11-cv-01884-3.pdf">
<identifier type="FDsys Unique ID">D09002ee18d627db2</identifier>
</relatedItem>
<identifier type="uri">http://www.gpo.gov/fdsys/granule/USCOURTS-caed-1_11-cv-01884/USCOURTS-caed-1_11-cv-01884-3</identifier>
<identifier type="former granule identifier">caed-1_11-cv-01884_3.pdf</identifier>
<location>
<url access="object in context" displayLabel="Content Detail">http://www.gpo.gov/fdsys/granule/USCOURTS-caed-1_11-cv-01884/USCOURTS-caed-1_11-cv-01884-3/content-detail.html</url>
<url access="raw object" displayLabel="PDF rendition">http://www.gpo.gov/fdsys/pkg/USCOURTS-caed-1_11-cv-01884/pdf/USCOURTS-caed-1_11-cv-01884-3.pdf</url>
</location>
<extension>
<searchTitle>USCOURTS 1:11-cv-01884; (PC) Dasenbrock v. Kings County et al; </searchTitle>
<courtName>United States District Court Eastern District of California</courtName>
<state>California</state>
<accessId>USCOURTS-caed-1_11-cv-01884-3</accessId>
<sequenceNumber>3</sequenceNumber>
<dateIssued>2012-10-31</dateIssued>
<docketText>ORDER Denying Plaintiff's 12 Motion for Reconsideration, signed by Magistrate Judge Dennis L. Beck on 10/30/12. (Gonzalez, R)</docketText>
</extension>
</relatedItem>
<relatedItem type="constituent" ID="id-USCOURTS-caed-1_11-cv-01884-4" xlink:href="http://www.gpo.gov/fdsys/granule/USCOURTS-caed-1_11-cv-01884/USCOURTS-caed-1_11-cv-01884-4/mods.xml">
<titleInfo>
<title>(PC) Dasenbrock v. Kings County et al</title>
<subTitle>ORDER Denying 25 Motion to Appoint Counsel, signed by Magistrate Judge Dennis L. Beck on 10/4/13. (Verduzco, M)</subTitle>
<partNumber>4</partNumber>
</titleInfo>
<originInfo>
<dateIssued>2013-10-04</dateIssued>
</originInfo>
<relatedItem type="otherFormat" xlink:href="http://www.gpo.gov/fdsys/pkg/USCOURTS-caed-1_11-cv-01884/pdf/USCOURTS-caed-1_11-cv-01884-4.pdf">
<identifier type="FDsys Unique ID">D09002ee18d627db3</identifier>
</relatedItem>
<identifier type="uri">http://www.gpo.gov/fdsys/granule/USCOURTS-caed-1_11-cv-01884/USCOURTS-caed-1_11-cv-01884-4</identifier>
<identifier type="former granule identifier">caed-1_11-cv-01884_4.pdf</identifier>
<location>
<url access="object in context" displayLabel="Content Detail">http://www.gpo.gov/fdsys/granule/USCOURTS-caed-1_11-cv-01884/USCOURTS-caed-1_11-cv-01884-4/content-detail.html</url>
<url access="raw object" displayLabel="PDF rendition">http://www.gpo.gov/fdsys/pkg/USCOURTS-caed-1_11-cv-01884/pdf/USCOURTS-caed-1_11-cv-01884-4.pdf</url>
</location>
<extension>
<searchTitle>USCOURTS 1:11-cv-01884; (PC) Dasenbrock v. Kings County et al; </searchTitle>
<courtName>United States District Court Eastern District of California</courtName>
<state>California</state>
<accessId>USCOURTS-caed-1_11-cv-01884-4</accessId>
<sequenceNumber>4</sequenceNumber>
<dateIssued>2013-10-04</dateIssued>
<docketText>ORDER Denying 25 Motion to Appoint Counsel, signed by Magistrate Judge Dennis L. Beck on 10/4/13. (Verduzco, M)</docketText>
</extension>
</relatedItem>
<relatedItem type="constituent" ID="id-USCOURTS-caed-1_11-cv-01884-5" xlink:href="http://www.gpo.gov/fdsys/granule/USCOURTS-caed-1_11-cv-01884/USCOURTS-caed-1_11-cv-01884-5/mods.xml">
<titleInfo>
<title>(PC) Dasenbrock v. Kings County et al</title>
<subTitle>ORDER signed by Magistrate Judge Dennis L. Beck on 11/20/2013 denying Motion for Extension of Time as moot re 30, 35. (Lundstrom, T)</subTitle>
<partNumber>5</partNumber>
</titleInfo>
<originInfo>
<dateIssued>2013-11-21</dateIssued>
</originInfo>
<relatedItem type="otherFormat" xlink:href="http://www.gpo.gov/fdsys/pkg/USCOURTS-caed-1_11-cv-01884/pdf/USCOURTS-caed-1_11-cv-01884-5.pdf">
<identifier type="FDsys Unique ID">D09002ee18d627dae</identifier>
</relatedItem>
<identifier type="uri">http://www.gpo.gov/fdsys/granule/USCOURTS-caed-1_11-cv-01884/USCOURTS-caed-1_11-cv-01884-5</identifier>
<identifier type="former granule identifier">caed-1_11-cv-01884_5.pdf</identifier>
<location>
<url access="object in context" displayLabel="Content Detail">http://www.gpo.gov/fdsys/granule/USCOURTS-caed-1_11-cv-01884/USCOURTS-caed-1_11-cv-01884-5/content-detail.html</url>
<url access="raw object" displayLabel="PDF rendition">http://www.gpo.gov/fdsys/pkg/USCOURTS-caed-1_11-cv-01884/pdf/USCOURTS-caed-1_11-cv-01884-5.pdf</url>
</location>
<extension>
<searchTitle>USCOURTS 1:11-cv-01884; (PC) Dasenbrock v. Kings County et al; </searchTitle>
<courtName>United States District Court Eastern District of California</courtName>
<state>California</state>
<accessId>USCOURTS-caed-1_11-cv-01884-5</accessId>
<sequenceNumber>5</sequenceNumber>
<dateIssued>2013-11-21</dateIssued>
<docketText>ORDER signed by Magistrate Judge Dennis L. Beck on 11/20/2013 denying Motion for Extension of Time as moot re 30, 35. (Lundstrom, T)</docketText>
</extension>
</relatedItem>
<relatedItem type="constituent" ID="id-USCOURTS-caed-1_11-cv-01884-6" xlink:href="http://www.gpo.gov/fdsys/granule/USCOURTS-caed-1_11-cv-01884/USCOURTS-caed-1_11-cv-01884-6/mods.xml">
<titleInfo>
<title>(PC) Dasenbrock v. Kings County et al</title>
<subTitle>ORDER Granting Defendants' Motion To Modify The Discovery And Scheduling Order To Extend The Dispositive Motion Deadline (ECF No.56), signed by Magistrate Judge Dennis L. Beck on 4/11/2014. (Fahrney, E)</subTitle>
<partNumber>6</partNumber>
</titleInfo>
<originInfo>
<dateIssued>2014-04-11</dateIssued>
</originInfo>
<relatedItem type="otherFormat" xlink:href="http://www.gpo.gov/fdsys/pkg/USCOURTS-caed-1_11-cv-01884/pdf/USCOURTS-caed-1_11-cv-01884-6.pdf">
<identifier type="FDsys Unique ID">D09002ee18d627dac</identifier>
</relatedItem>
<identifier type="uri">http://www.gpo.gov/fdsys/granule/USCOURTS-caed-1_11-cv-01884/USCOURTS-caed-1_11-cv-01884-6</identifier>
<identifier type="former granule identifier">caed-1_11-cv-01884_6.pdf</identifier>
<location>
<url access="object in context" displayLabel="Content Detail">http://www.gpo.gov/fdsys/granule/USCOURTS-caed-1_11-cv-01884/USCOURTS-caed-1_11-cv-01884-6/content-detail.html</url>
<url access="raw object" displayLabel="PDF rendition">http://www.gpo.gov/fdsys/pkg/USCOURTS-caed-1_11-cv-01884/pdf/USCOURTS-caed-1_11-cv-01884-6.pdf</url>
</location>
<extension>
<searchTitle>USCOURTS 1:11-cv-01884; (PC) Dasenbrock v. Kings County et al; </searchTitle>
<courtName>United States District Court Eastern District of California</courtName>
<state>California</state>
<accessId>USCOURTS-caed-1_11-cv-01884-6</accessId>
<sequenceNumber>6</sequenceNumber>
<dateIssued>2014-04-11</dateIssued>
<docketText>ORDER Granting Defendants' Motion To Modify The Discovery And Scheduling Order To Extend The Dispositive Motion Deadline (ECF No.56), signed by Magistrate Judge Dennis L. Beck on 4/11/2014. (Fahrney, E)</docketText>
</extension>
</relatedItem>
<relatedItem type="constituent" ID="id-USCOURTS-caed-1_11-cv-01884-7" xlink:href="http://www.gpo.gov/fdsys/granule/USCOURTS-caed-1_11-cv-01884/USCOURTS-caed-1_11-cv-01884-7/mods.xml">
<titleInfo>
<title>(PC) Dasenbrock v. Kings County et al</title>
<subTitle>ORDER Regarding Plaintiff's Motions (ECF Nos.39,45,47,48,53,62,64,74,75,82,83,84), 87,91), ORDER Regarding Defendants' Motion To Take Deposition As Moot (ECF No.41), ORDER Denying Motion For Summary Judgment Without Prejudice To Refiling (ECF No.68), signed by Magistrate Judge Dennis L. Beck on 9/17/2014. Plaintiffs motions (ECF Nos. 39, 45, 47, 48, 53, 62, 64, 74, 75, 82, 83, 84, 87, 91) are DENIED. Defendants motion to take Plaintiffs deposition by videoconference is DENIED as moot. Defendants motion for summary judgment is DENIED WITHOUT PREJUDICE to refiling at the conclusion of discovery. (Fahrney, E)</subTitle>
<partNumber>7</partNumber>
</titleInfo>
<originInfo>
<dateIssued>2014-09-17</dateIssued>
</originInfo>
<relatedItem type="otherFormat" xlink:href="http://www.gpo.gov/fdsys/pkg/USCOURTS-caed-1_11-cv-01884/pdf/USCOURTS-caed-1_11-cv-01884-7.pdf">
<identifier type="FDsys Unique ID">D09002ee18d627dad</identifier>
</relatedItem>
<identifier type="uri">http://www.gpo.gov/fdsys/granule/USCOURTS-caed-1_11-cv-01884/USCOURTS-caed-1_11-cv-01884-7</identifier>
<identifier type="former granule identifier">caed-1_11-cv-01884_7.pdf</identifier>
<location>
<url access="object in context" displayLabel="Content Detail">http://www.gpo.gov/fdsys/granule/USCOURTS-caed-1_11-cv-01884/USCOURTS-caed-1_11-cv-01884-7/content-detail.html</url>
<url access="raw object" displayLabel="PDF rendition">http://www.gpo.gov/fdsys/pkg/USCOURTS-caed-1_11-cv-01884/pdf/USCOURTS-caed-1_11-cv-01884-7.pdf</url>
</location>
<extension>
<searchTitle>USCOURTS 1:11-cv-01884; (PC) Dasenbrock v. Kings County et al; </searchTitle>
<courtName>United States District Court Eastern District of California</courtName>
<state>California</state>
<accessId>USCOURTS-caed-1_11-cv-01884-7</accessId>
<sequenceNumber>7</sequenceNumber>
<dateIssued>2014-09-17</dateIssued>
<docketText>ORDER Regarding Plaintiff's Motions (ECF Nos.39,45,47,48,53,62,64,74,75,82,83,84), 87,91), ORDER Regarding Defendants' Motion To Take Deposition As Moot (ECF No.41), ORDER Denying Motion For Summary Judgment Without Prejudice To Refiling (ECF No.68), signed by Magistrate Judge Dennis L. Beck on 9/17/2014. Plaintiffs motions (ECF Nos. 39, 45, 47, 48, 53, 62, 64, 74, 75, 82, 83, 84, 87, 91) are DENIED. Defendants motion to take Plaintiffs deposition by videoconference is DENIED as moot. Defendants motion for summary judgment is DENIED WITHOUT PREJUDICE to refiling at the conclusion of discovery. (Fahrney, E)</docketText>
</extension>
</relatedItem>
<relatedItem type="constituent" ID="id-USCOURTS-caed-1_11-cv-01884-8" xlink:href="http://www.gpo.gov/fdsys/granule/USCOURTS-caed-1_11-cv-01884/USCOURTS-caed-1_11-cv-01884-8/mods.xml">
<titleInfo>
<title>(PC) Dasenbrock v. Kings County et al</title>
<subTitle>ORDER REGARDING PLAINTIFF'S MOTIONS TO COMPEL AND/OR REOPEN DISCOVERY 49, 57, 63, 65, 67 AND MOTION FOR ENLARGEMENT OF TIME TO COMPLETE DISCOVERY 55; ORDER AND NOTICE AUTHORIZING ISSUANCE OF SUBPOENA DUCES TECUM DIRECTING PRODUCTION OF DOCUMENTS BY STU SHERMAN, WARDEN OF CORCORAN SUBSTANCE ABUSE AND TREATMENT FACILITY; ORDER DIRECTING CLERKS OFFICE TO SERVE COPY OF SUBPOENA WITH ORDER AND ORDER REOPENING DISCOVERY AS TO DEFENDANT PAGE signed by Magistrate Judge Dennis L. Beck on 10/15/2014. (Attachments: # (1) Subpoena).(Lundstrom, T)</subTitle>
<partNumber>8</partNumber>
</titleInfo>
<originInfo>
<dateIssued>2014-10-15</dateIssued>
</originInfo>
<relatedItem type="otherFormat" xlink:href="http://www.gpo.gov/fdsys/pkg/USCOURTS-caed-1_11-cv-01884/pdf/USCOURTS-caed-1_11-cv-01884-8.pdf">
<identifier type="FDsys Unique ID">D09002ee18d627db0</identifier>
</relatedItem>
<identifier type="uri">http://www.gpo.gov/fdsys/granule/USCOURTS-caed-1_11-cv-01884/USCOURTS-caed-1_11-cv-01884-8</identifier>
<identifier type="former granule identifier">caed-1_11-cv-01884_8.pdf</identifier>
<location>
<url access="object in context" displayLabel="Content Detail">http://www.gpo.gov/fdsys/granule/USCOURTS-caed-1_11-cv-01884/USCOURTS-caed-1_11-cv-01884-8/content-detail.html</url>
<url access="raw object" displayLabel="PDF rendition">http://www.gpo.gov/fdsys/pkg/USCOURTS-caed-1_11-cv-01884/pdf/USCOURTS-caed-1_11-cv-01884-8.pdf</url>
</location>
<extension>
<searchTitle>USCOURTS 1:11-cv-01884; (PC) Dasenbrock v. Kings County et al; </searchTitle>
<courtName>United States District Court Eastern District of California</courtName>
<state>California</state>
<accessId>USCOURTS-caed-1_11-cv-01884-8</accessId>
<sequenceNumber>8</sequenceNumber>
<dateIssued>2014-10-15</dateIssued>
<docketText>ORDER REGARDING PLAINTIFF'S MOTIONS TO COMPEL AND/OR REOPEN DISCOVERY 49, 57, 63, 65, 67 AND MOTION FOR ENLARGEMENT OF TIME TO COMPLETE DISCOVERY 55; ORDER AND NOTICE AUTHORIZING ISSUANCE OF SUBPOENA DUCES TECUM DIRECTING PRODUCTION OF DOCUMENTS BY STU SHERMAN, WARDEN OF CORCORAN SUBSTANCE ABUSE AND TREATMENT FACILITY; ORDER DIRECTING CLERKS OFFICE TO SERVE COPY OF SUBPOENA WITH ORDER AND ORDER REOPENING DISCOVERY AS TO DEFENDANT PAGE signed by Magistrate Judge Dennis L. Beck on 10/15/2014. (Attachments: # (1) Subpoena).(Lundstrom, T)</docketText>
</extension>
</relatedItem>
<relatedItem type="constituent" ID="id-USCOURTS-caed-1_11-cv-01884-9" xlink:href="http://www.gpo.gov/fdsys/granule/USCOURTS-caed-1_11-cv-01884/USCOURTS-caed-1_11-cv-01884-9/mods.xml">
<titleInfo>
<title>(PC) Dasenbrock v. Kings County et al</title>
<subTitle>ORDER DISMISSING 94 Motion for Issuance of Subpoenas and 99 & 100 Motions for Clarification; ORDER DISMISSING 97 Request for Ruling; ORDER DENYING Plaintiff's 95 Motion for Reconsideration, signed by Magistrate Judge Dennis L. Beck on 11/6/2014. (Marrujo, C)</subTitle>
<partNumber>9</partNumber>
</titleInfo>
<originInfo>
<dateIssued>2014-11-07</dateIssued>
</originInfo>
<relatedItem type="otherFormat" xlink:href="http://www.gpo.gov/fdsys/pkg/USCOURTS-caed-1_11-cv-01884/pdf/USCOURTS-caed-1_11-cv-01884-9.pdf">
<identifier type="FDsys Unique ID">D09002ee18d627dfa</identifier>
</relatedItem>
<identifier type="uri">http://www.gpo.gov/fdsys/granule/USCOURTS-caed-1_11-cv-01884/USCOURTS-caed-1_11-cv-01884-9</identifier>
<identifier type="former granule identifier">caed-1_11-cv-01884_9.pdf</identifier>
<location>
<url access="object in context" displayLabel="Content Detail">http://www.gpo.gov/fdsys/granule/USCOURTS-caed-1_11-cv-01884/USCOURTS-caed-1_11-cv-01884-9/content-detail.html</url>
<url access="raw object" displayLabel="PDF rendition">http://www.gpo.gov/fdsys/pkg/USCOURTS-caed-1_11-cv-01884/pdf/USCOURTS-caed-1_11-cv-01884-9.pdf</url>
</location>
<extension>
<searchTitle>USCOURTS 1:11-cv-01884; (PC) Dasenbrock v. Kings County et al; </searchTitle>
<courtName>United States District Court Eastern District of California</courtName>
<state>California</state>
<accessId>USCOURTS-caed-1_11-cv-01884-9</accessId>
<sequenceNumber>9</sequenceNumber>
<dateIssued>2014-11-07</dateIssued>
<docketText>ORDER DISMISSING 94 Motion for Issuance of Subpoenas and 99 & 100 Motions for Clarification; ORDER DISMISSING 97 Request for Ruling; ORDER DENYING Plaintiff's 95 Motion for Reconsideration, signed by Magistrate Judge Dennis L. Beck on 11/6/2014. (Marrujo, C)</docketText>
</extension>
</relatedItem>
<relatedItem type="constituent" ID="id-USCOURTS-caed-1_11-cv-01884-10" xlink:href="http://www.gpo.gov/fdsys/granule/USCOURTS-caed-1_11-cv-01884/USCOURTS-caed-1_11-cv-01884-10/mods.xml">
<titleInfo>
<title>(PC) Dasenbrock v. Kings County et al</title>
<subTitle>ORDER DIRECTING Personal Service of Subpoena Duces Tecum Within Seven Days by United States Marshal Without Prepayment of Costs, signed by Magistrate Judge Dennis L. Beck on 11/6/2014. (Marrujo, C)</subTitle>
<partNumber>10</partNumber>
</titleInfo>
<originInfo>
<dateIssued>2014-11-07</dateIssued>
</originInfo>
<relatedItem type="otherFormat" xlink:href="http://www.gpo.gov/fdsys/pkg/USCOURTS-caed-1_11-cv-01884/pdf/USCOURTS-caed-1_11-cv-01884-10.pdf">
<identifier type="FDsys Unique ID">D09002ee18d627db4</identifier>
</relatedItem>
<identifier type="uri">http://www.gpo.gov/fdsys/granule/USCOURTS-caed-1_11-cv-01884/USCOURTS-caed-1_11-cv-01884-10</identifier>
<identifier type="former granule identifier">caed-1_11-cv-01884_10.pdf</identifier>
<location>
<url access="object in context" displayLabel="Content Detail">http://www.gpo.gov/fdsys/granule/USCOURTS-caed-1_11-cv-01884/USCOURTS-caed-1_11-cv-01884-10/content-detail.html</url>
<url access="raw object" displayLabel="PDF rendition">http://www.gpo.gov/fdsys/pkg/USCOURTS-caed-1_11-cv-01884/pdf/USCOURTS-caed-1_11-cv-01884-10.pdf</url>
</location>
<extension>
<searchTitle>USCOURTS 1:11-cv-01884; (PC) Dasenbrock v. Kings County et al; </searchTitle>
<courtName>United States District Court Eastern District of California</courtName>
<state>California</state>
<accessId>USCOURTS-caed-1_11-cv-01884-10</accessId>
<sequenceNumber>10</sequenceNumber>
<dateIssued>2014-11-07</dateIssued>
<docketText>ORDER DIRECTING Personal Service of Subpoena Duces Tecum Within Seven Days by United States Marshal Without Prepayment of Costs, signed by Magistrate Judge Dennis L. Beck on 11/6/2014. (Marrujo, C)</docketText>
</extension>
</relatedItem>
<relatedItem type="constituent" ID="id-USCOURTS-caed-1_11-cv-01884-11" xlink:href="http://www.gpo.gov/fdsys/granule/USCOURTS-caed-1_11-cv-01884/USCOURTS-caed-1_11-cv-01884-11/mods.xml">
<titleInfo>
<title>(PC) Dasenbrock v. Kings County et al</title>
<subTitle>ORDER Dismissing 96 Motion Directing Personal Service; ORDER Denying 106 Motion for Third Part Discovery, signed by Magistrate Judge Dennis L. Beck on 12/25/14. (Gonzalez, R)</subTitle>
<partNumber>11</partNumber>
</titleInfo>
<originInfo>
<dateIssued>2014-12-29</dateIssued>
</originInfo>
<relatedItem type="otherFormat" xlink:href="http://www.gpo.gov/fdsys/pkg/USCOURTS-caed-1_11-cv-01884/pdf/USCOURTS-caed-1_11-cv-01884-11.pdf">
<identifier type="FDsys Unique ID">D09002ee18d627dfd</identifier>
</relatedItem>
<identifier type="uri">http://www.gpo.gov/fdsys/granule/USCOURTS-caed-1_11-cv-01884/USCOURTS-caed-1_11-cv-01884-11</identifier>
<identifier type="former granule identifier">caed-1_11-cv-01884_11.pdf</identifier>
<location>
<url access="object in context" displayLabel="Content Detail">http://www.gpo.gov/fdsys/granule/USCOURTS-caed-1_11-cv-01884/USCOURTS-caed-1_11-cv-01884-11/content-detail.html</url>
<url access="raw object" displayLabel="PDF rendition">http://www.gpo.gov/fdsys/pkg/USCOURTS-caed-1_11-cv-01884/pdf/USCOURTS-caed-1_11-cv-01884-11.pdf</url>
</location>
<extension>
<searchTitle>USCOURTS 1:11-cv-01884; (PC) Dasenbrock v. Kings County et al; </searchTitle>
<courtName>United States District Court Eastern District of California</courtName>
<state>California</state>
<accessId>USCOURTS-caed-1_11-cv-01884-11</accessId>
<sequenceNumber>11</sequenceNumber>
<dateIssued>2014-12-29</dateIssued>
<docketText>ORDER Dismissing 96 Motion Directing Personal Service; ORDER Denying 106 Motion for Third Part Discovery, signed by Magistrate Judge Dennis L. Beck on 12/25/14. (Gonzalez, R)</docketText>
</extension>
</relatedItem>
<relatedItem type="constituent" ID="id-USCOURTS-caed-1_11-cv-01884-12" xlink:href="http://www.gpo.gov/fdsys/granule/USCOURTS-caed-1_11-cv-01884/USCOURTS-caed-1_11-cv-01884-12/mods.xml">
<titleInfo>
<title>(PC) Dasenbrock v. Kings County et al</title>
<subTitle>ORDER DENYING Motion for Appointment of Counsel 113, signed by Magistrate Judge Dennis L. Beck on 1/5/15: Motion is DENIED without prejudice. (Hellings, J)</subTitle>
<partNumber>12</partNumber>
</titleInfo>
<originInfo>
<dateIssued>2015-01-05</dateIssued>
</originInfo>
<relatedItem type="otherFormat" xlink:href="http://www.gpo.gov/fdsys/pkg/USCOURTS-caed-1_11-cv-01884/pdf/USCOURTS-caed-1_11-cv-01884-12.pdf">
<identifier type="FDsys Unique ID">D09002ee18d627dfc</identifier>
</relatedItem>
<identifier type="uri">http://www.gpo.gov/fdsys/granule/USCOURTS-caed-1_11-cv-01884/USCOURTS-caed-1_11-cv-01884-12</identifier>
<identifier type="former granule identifier">caed-1_11-cv-01884_12.pdf</identifier>
<location>
<url access="object in context" displayLabel="Content Detail">http://www.gpo.gov/fdsys/granule/USCOURTS-caed-1_11-cv-01884/USCOURTS-caed-1_11-cv-01884-12/content-detail.html</url>
<url access="raw object" displayLabel="PDF rendition">http://www.gpo.gov/fdsys/pkg/USCOURTS-caed-1_11-cv-01884/pdf/USCOURTS-caed-1_11-cv-01884-12.pdf</url>
</location>
<extension>
<searchTitle>USCOURTS 1:11-cv-01884; (PC) Dasenbrock v. Kings County et al; </searchTitle>
<courtName>United States District Court Eastern District of California</courtName>
<state>California</state>
<accessId>USCOURTS-caed-1_11-cv-01884-12</accessId>
<sequenceNumber>12</sequenceNumber>
<dateIssued>2015-01-05</dateIssued>
<docketText>ORDER DENYING Motion for Appointment of Counsel 113, signed by Magistrate Judge Dennis L. Beck on 1/5/15: Motion is DENIED without prejudice. (Hellings, J)</docketText>
</extension>
</relatedItem>
<relatedItem type="constituent" ID="id-USCOURTS-caed-1_11-cv-01884-13" xlink:href="http://www.gpo.gov/fdsys/granule/USCOURTS-caed-1_11-cv-01884/USCOURTS-caed-1_11-cv-01884-13/mods.xml">
<titleInfo>
<title>(PC) Dasenbrock v. Kings County et al</title>
<subTitle>ORDER REGARDING Plaintiff's 109 Motion to Compel and Request for Addtional Subpoena Duces Tecum, Plaintiff's 110 Motion to Lodge Depositions, Plaintiff's 111 Motion for Third Party Discovery, Plaintiff's 114 Motion for Deposition Subpoenas, Plaintiff's 117 Motion for Third Party Discovery and Request to Reopen Discovery, Plaintiff's 118 Motion for Reconsideration, Plaintiff's 120 Motion to Compel, and Plaintiff's 121 Motion for Third Party Discovery; ORDER DIRECTING Defendant Page to SHOW CAUSE; ORDER and NOTICE AUTHORIZING Issuance of Subpoena Duces Tecum Directing Production of Documents by Stu Sherman, Warden of Corcoran Substance Abuse and Treatment Facility; ORDER DIRECTING Clerk's Office to Serve Copy of Subpoena With Order, signed by Magistrate Judge Dennis L. Beck on 4/22/2015. (Attachments: # (1) Not Issued Subpoena)(Marrujo, C)</subTitle>
<partNumber>13</partNumber>
</titleInfo>
<originInfo>
<dateIssued>2015-04-24</dateIssued>
</originInfo>
<relatedItem type="otherFormat" xlink:href="http://www.gpo.gov/fdsys/pkg/USCOURTS-caed-1_11-cv-01884/pdf/USCOURTS-caed-1_11-cv-01884-13.pdf">
<identifier type="FDsys Unique ID">D09002ee18d627daf</identifier>
</relatedItem>
<identifier type="uri">http://www.gpo.gov/fdsys/granule/USCOURTS-caed-1_11-cv-01884/USCOURTS-caed-1_11-cv-01884-13</identifier>
<identifier type="former granule identifier">caed-1_11-cv-01884_13.pdf</identifier>
<location>
<url access="object in context" displayLabel="Content Detail">http://www.gpo.gov/fdsys/granule/USCOURTS-caed-1_11-cv-01884/USCOURTS-caed-1_11-cv-01884-13/content-detail.html</url>
<url access="raw object" displayLabel="PDF rendition">http://www.gpo.gov/fdsys/pkg/USCOURTS-caed-1_11-cv-01884/pdf/USCOURTS-caed-1_11-cv-01884-13.pdf</url>
</location>
<extension>
<searchTitle>USCOURTS 1:11-cv-01884; (PC) Dasenbrock v. Kings County et al; </searchTitle>
<courtName>United States District Court Eastern District of California</courtName>
<state>California</state>
<accessId>USCOURTS-caed-1_11-cv-01884-13</accessId>
<sequenceNumber>13</sequenceNumber>
<dateIssued>2015-04-24</dateIssued>
<docketText>ORDER REGARDING Plaintiff's 109 Motion to Compel and Request for Addtional Subpoena Duces Tecum, Plaintiff's 110 Motion to Lodge Depositions, Plaintiff's 111 Motion for Third Party Discovery, Plaintiff's 114 Motion for Deposition Subpoenas, Plaintiff's 117 Motion for Third Party Discovery and Request to Reopen Discovery, Plaintiff's 118 Motion for Reconsideration, Plaintiff's 120 Motion to Compel, and Plaintiff's 121 Motion for Third Party Discovery; ORDER DIRECTING Defendant Page to SHOW CAUSE; ORDER and NOTICE AUTHORIZING Issuance of Subpoena Duces Tecum Directing Production of Documents by Stu Sherman, Warden of Corcoran Substance Abuse and Treatment Facility; ORDER DIRECTING Clerk's Office to Serve Copy of Subpoena With Order, signed by Magistrate Judge Dennis L. Beck on 4/22/2015. (Attachments: # (1) Not Issued Subpoena)(Marrujo, C)</docketText>
</extension>
</relatedItem>
<relatedItem type="constituent" ID="id-USCOURTS-caed-1_11-cv-01884-14" xlink:href="http://www.gpo.gov/fdsys/granule/USCOURTS-caed-1_11-cv-01884/USCOURTS-caed-1_11-cv-01884-14/mods.xml">
<titleInfo>
<title>(PC) Dasenbrock v. Kings County et al</title>
<subTitle>ORDER DIRECTING Personal Service of Subpoena Duces Tecum Within Seven Days by United States Marshal Without Prepayment of Costs, signed by Magistrate Judge Dennis L. Beck on 5/28/15. (Attachments: # (1) Issued Subpoena) (Marrujo, C)</subTitle>
<partNumber>14</partNumber>
</titleInfo>
<originInfo>
<dateIssued>2015-05-29</dateIssued>
</originInfo>
<relatedItem type="otherFormat" xlink:href="http://www.gpo.gov/fdsys/pkg/USCOURTS-caed-1_11-cv-01884/pdf/USCOURTS-caed-1_11-cv-01884-14.pdf">
<identifier type="FDsys Unique ID">D09002ee18d627d6b</identifier>
</relatedItem>
<identifier type="uri">http://www.gpo.gov/fdsys/granule/USCOURTS-caed-1_11-cv-01884/USCOURTS-caed-1_11-cv-01884-14</identifier>
<identifier type="former granule identifier">caed-1_11-cv-01884_14.pdf</identifier>
<location>
<url access="object in context" displayLabel="Content Detail">http://www.gpo.gov/fdsys/granule/USCOURTS-caed-1_11-cv-01884/USCOURTS-caed-1_11-cv-01884-14/content-detail.html</url>
<url access="raw object" displayLabel="PDF rendition">http://www.gpo.gov/fdsys/pkg/USCOURTS-caed-1_11-cv-01884/pdf/USCOURTS-caed-1_11-cv-01884-14.pdf</url>
</location>
<extension>
<searchTitle>USCOURTS 1:11-cv-01884; (PC) Dasenbrock v. Kings County et al; </searchTitle>
<courtName>United States District Court Eastern District of California</courtName>
<state>California</state>
<accessId>USCOURTS-caed-1_11-cv-01884-14</accessId>
<sequenceNumber>14</sequenceNumber>
<dateIssued>2015-05-29</dateIssued>
<docketText>ORDER DIRECTING Personal Service of Subpoena Duces Tecum Within Seven Days by United States Marshal Without Prepayment of Costs, signed by Magistrate Judge Dennis L. Beck on 5/28/15. (Attachments: # (1) Issued Subpoena) (Marrujo, C)</docketText>
</extension>
</relatedItem>
<relatedItem type="constituent" ID="id-USCOURTS-caed-1_11-cv-01884-15" xlink:href="http://www.gpo.gov/fdsys/granule/USCOURTS-caed-1_11-cv-01884/USCOURTS-caed-1_11-cv-01884-15/mods.xml">
<titleInfo>
<title>(PC) Dasenbrock v. Kings County et al</title>
<subTitle>ORDER DISCHARGING 122 Order to Show Cause; ORDER GRANTING Defendant Page Thirty Days to Respond to Initial Discovery Requests, signed by Magistrate Judge Dennis L. Beck on 5/29/2015. (Marrujo, C)</subTitle>
<partNumber>15</partNumber>
</titleInfo>
<originInfo>
<dateIssued>2015-05-29</dateIssued>
</originInfo>
<relatedItem type="otherFormat" xlink:href="http://www.gpo.gov/fdsys/pkg/USCOURTS-caed-1_11-cv-01884/pdf/USCOURTS-caed-1_11-cv-01884-15.pdf">
<identifier type="FDsys Unique ID">D09002ee18d627db1</identifier>
</relatedItem>
<identifier type="uri">http://www.gpo.gov/fdsys/granule/USCOURTS-caed-1_11-cv-01884/USCOURTS-caed-1_11-cv-01884-15</identifier>
<identifier type="former granule identifier">caed-1_11-cv-01884_15.pdf</identifier>
<location>
<url access="object in context" displayLabel="Content Detail">http://www.gpo.gov/fdsys/granule/USCOURTS-caed-1_11-cv-01884/USCOURTS-caed-1_11-cv-01884-15/content-detail.html</url>
<url access="raw object" displayLabel="PDF rendition">http://www.gpo.gov/fdsys/pkg/USCOURTS-caed-1_11-cv-01884/pdf/USCOURTS-caed-1_11-cv-01884-15.pdf</url>
</location>
<extension>
<searchTitle>USCOURTS 1:11-cv-01884; (PC) Dasenbrock v. Kings County et al; </searchTitle>
<courtName>United States District Court Eastern District of California</courtName>
<state>California</state>
<accessId>USCOURTS-caed-1_11-cv-01884-15</accessId>
<sequenceNumber>15</sequenceNumber>
<dateIssued>2015-05-29</dateIssued>
<docketText>ORDER DISCHARGING 122 Order to Show Cause; ORDER GRANTING Defendant Page Thirty Days to Respond to Initial Discovery Requests, signed by Magistrate Judge Dennis L. Beck on 5/29/2015. (Marrujo, C)</docketText>
</extension>
</relatedItem>
<relatedItem type="constituent" ID="id-USCOURTS-caed-1_11-cv-01884-16" xlink:href="http://www.gpo.gov/fdsys/granule/USCOURTS-caed-1_11-cv-01884/USCOURTS-caed-1_11-cv-01884-16/mods.xml">
<titleInfo>
<title>(PC) Dasenbrock v. Kings County et al</title>
<subTitle>ORDER Regarding Plaintiff's Request for Summons Package and GRANTING Plaintiff Leave to File Amended Complaint Naming Doe Defendant 133, signed by Magistrate Judge Dennis L. Beck on 8/25/15: Thirty-Day Deadline. (Hellings, J)</subTitle>
<partNumber>16</partNumber>
</titleInfo>
<originInfo>
<dateIssued>2015-08-25</dateIssued>
</originInfo>
<relatedItem type="otherFormat" xlink:href="http://www.gpo.gov/fdsys/pkg/USCOURTS-caed-1_11-cv-01884/pdf/USCOURTS-caed-1_11-cv-01884-16.pdf">
<identifier type="FDsys Unique ID">D09002ee18d627db5</identifier>
</relatedItem>
<identifier type="uri">http://www.gpo.gov/fdsys/granule/USCOURTS-caed-1_11-cv-01884/USCOURTS-caed-1_11-cv-01884-16</identifier>
<identifier type="former granule identifier">caed-1_11-cv-01884_16.pdf</identifier>
<location>
<url access="object in context" displayLabel="Content Detail">http://www.gpo.gov/fdsys/granule/USCOURTS-caed-1_11-cv-01884/USCOURTS-caed-1_11-cv-01884-16/content-detail.html</url>
<url access="raw object" displayLabel="PDF rendition">http://www.gpo.gov/fdsys/pkg/USCOURTS-caed-1_11-cv-01884/pdf/USCOURTS-caed-1_11-cv-01884-16.pdf</url>
</location>
<extension>
<searchTitle>USCOURTS 1:11-cv-01884; (PC) Dasenbrock v. Kings County et al; </searchTitle>
<courtName>United States District Court Eastern District of California</courtName>
<state>California</state>
<accessId>USCOURTS-caed-1_11-cv-01884-16</accessId>
<sequenceNumber>16</sequenceNumber>
<dateIssued>2015-08-25</dateIssued>
<docketText>ORDER Regarding Plaintiff's Request for Summons Package and GRANTING Plaintiff Leave to File Amended Complaint Naming Doe Defendant 133, signed by Magistrate Judge Dennis L. Beck on 8/25/15: Thirty-Day Deadline. (Hellings, J)</docketText>
</extension>
</relatedItem>
</mods>
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 483
|
package io.dropwizard.auth.basic;
import com.codahale.metrics.MetricRegistry;
import com.google.common.collect.ImmutableList;
import io.dropwizard.auth.AuthDynamicFeature;
import io.dropwizard.auth.AuthResource;
import io.dropwizard.auth.util.AuthUtil;
import io.dropwizard.jersey.DropwizardResourceConfig;
import io.dropwizard.logging.BootstrapLogging;
import org.glassfish.jersey.server.filter.RolesAllowedDynamicFeature;
import org.glassfish.jersey.servlet.ServletProperties;
import org.glassfish.jersey.test.DeploymentContext;
import org.glassfish.jersey.test.JerseyTest;
import org.glassfish.jersey.test.ServletDeploymentContext;
import org.glassfish.jersey.test.TestProperties;
import org.glassfish.jersey.test.grizzly.GrizzlyWebTestContainerFactory;
import org.glassfish.jersey.test.spi.TestContainerException;
import org.glassfish.jersey.test.spi.TestContainerFactory;
import org.junit.Test;
import javax.ws.rs.WebApplicationException;
import javax.ws.rs.container.ContainerRequestFilter;
import javax.ws.rs.core.HttpHeaders;
import java.security.Principal;
import static org.assertj.core.api.Assertions.assertThat;
import static org.assertj.core.api.Assertions.failBecauseExceptionWasNotThrown;
public class BasicAuthProviderTest extends JerseyTest {
private final static String ADMIN_ROLE = "ADMIN";
static {
BootstrapLogging.bootstrap();
}
@Override
protected TestContainerFactory getTestContainerFactory()
throws TestContainerException {
return new GrizzlyWebTestContainerFactory();
}
@Override
protected DeploymentContext configureDeployment() {
forceSet(TestProperties.CONTAINER_PORT, "0");
return ServletDeploymentContext.builder(new BasicAuthTestResourceConfig())
.initParam(ServletProperties.JAXRS_APPLICATION_CLASS, BasicAuthTestResourceConfig.class.getName())
.build();
}
@Test
public void respondsToMissingCredentialsWith401() throws Exception {
try {
target("/test/admin").request().get(String.class);
failBecauseExceptionWasNotThrown(WebApplicationException.class);
} catch (WebApplicationException e) {
assertThat(e.getResponse().getStatus()).isEqualTo(401);
assertThat(e.getResponse().getHeaders().get(HttpHeaders.WWW_AUTHENTICATE))
.containsOnly("Basic realm=\"realm\"");
}
}
@Test
public void resourceWithoutAuth200() {
assertThat(target("/test/noauth").request()
.get(String.class))
.isEqualTo("hello");
}
@Test
public void resourceWithAuthenticationWithoutAuthorizationWithCorrectCredentials200() {
assertThat(target("/test/profile").request()
.header(HttpHeaders.AUTHORIZATION, "Basic b3JkaW5hcnktZ3V5OnNlY3JldA==")
.get(String.class))
.isEqualTo("'ordinary-guy' has user privileges");
}
@Test
public void resourceWithAuthenticationWithoutAuthorizationNoCredentials401() {
try {
target("/test/profile").request().get(String.class);
failBecauseExceptionWasNotThrown(WebApplicationException.class);
} catch (WebApplicationException e) {
assertThat(e.getResponse().getStatus()).isEqualTo(401);
assertThat(e.getResponse().getHeaders().get(HttpHeaders.WWW_AUTHENTICATE))
.containsOnly("Basic realm=\"realm\"");
}
}
@Test
public void resourceWithAuthorizationPrincipalIsNotAuthorized403() {
try {
target("/test/admin").request()
.header(HttpHeaders.AUTHORIZATION, "Basic b3JkaW5hcnktZ3V5OnNlY3JldA==")
.get(String.class);
failBecauseExceptionWasNotThrown(WebApplicationException.class);
} catch (WebApplicationException e) {
assertThat(e.getResponse().getStatus()).isEqualTo(403);
}
}
@Test
public void resourceWithDenyAllAndNoAuth401() {
try {
target("/test/denied").request().get(String.class);
failBecauseExceptionWasNotThrown(WebApplicationException.class);
} catch (WebApplicationException e) {
assertThat(e.getResponse().getStatus()).isEqualTo(401);
}
}
@Test
public void resourceWithDenyAllAndAuth403() {
try {
target("/test/denied").request()
.header(HttpHeaders.AUTHORIZATION, "Basic Z29vZC1ndXk6c2VjcmV0")
.get(String.class);
failBecauseExceptionWasNotThrown(WebApplicationException.class);
} catch (WebApplicationException e) {
assertThat(e.getResponse().getStatus()).isEqualTo(403);
}
}
@Test
public void transformsCredentialsToPrincipals() throws Exception {
assertThat(target("/test/admin").request()
.header(HttpHeaders.AUTHORIZATION, "Basic Z29vZC1ndXk6c2VjcmV0")
.get(String.class))
.isEqualTo("'good-guy' has admin privileges");
}
@Test
public void respondsToNonBasicCredentialsWith401() throws Exception {
try {
target("/test/admin").request()
.header(HttpHeaders.AUTHORIZATION, "Derp Z29vZC1ndXk6c2VjcmV0")
.get(String.class);
failBecauseExceptionWasNotThrown(WebApplicationException.class);
} catch (WebApplicationException e) {
assertThat(e.getResponse().getStatus()).isEqualTo(401);
assertThat(e.getResponse().getHeaders().get(HttpHeaders.WWW_AUTHENTICATE))
.containsOnly("Basic realm=\"realm\"");
}
}
@Test
public void respondsToExceptionsWith500() throws Exception {
try {
target("/test/admin").request()
.header(HttpHeaders.AUTHORIZATION, "Basic YmFkLWd1eTpzZWNyZXQ=")
.get(String.class);
failBecauseExceptionWasNotThrown(WebApplicationException.class);
} catch (WebApplicationException e) {
assertThat(e.getResponse().getStatus()).isEqualTo(500);
}
}
public static class BasicAuthTestResourceConfig extends DropwizardResourceConfig {
public BasicAuthTestResourceConfig() {
super(true, new MetricRegistry());
register(new AuthDynamicFeature(getAuthFilter()));
register(RolesAllowedDynamicFeature.class);
register(AuthResource.class);
}
private ContainerRequestFilter getAuthFilter() {
final String adminUser = "good-guy";
final String ordinaryUser = "ordinary-guy";
BasicCredentialAuthFilter.Builder<Principal> builder = new BasicCredentialAuthFilter.Builder<>();
builder.setAuthorizer(AuthUtil.getTestAuthorizer(adminUser, ADMIN_ROLE));
builder.setAuthenticator(AuthUtil.getBasicAuthenticator(ImmutableList.of(adminUser, ordinaryUser)));
return builder.buildAuthFilter();
}
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 3,520
|
Q: как запустить react приложение после того как собрал и минимизировал все webpack'ом после сборки проекта появляется файл html в который подключен bandle.js со всем проектом, вопрос заключается в том как запустить этот html чтобы все работало как в create-react- app когда пишешь npm run start
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 9,077
|
Ghoul Roger Stone to Appear as "Head Ghoul" at Utah LP Halloween Event
In celebration of the 45th anniversary of the founding of the Libertarian Party of Utah; in honor of its first chair, tax protester (and one of the several key national party co-founders) Karl Bray and in ghoulish alignment with this year's union of Halloween and Utah's Special Election (Nov 7) the Utah LP announces:
"A Dark Night of Political Horror with THE "Dark Knight" of Political Horror, Roger Stone"
to be held at the Peace Coliseum, Nucleus Room, Saturday October 28 from 5 to 9.
Frightful Festivities Feature:
5:00 PM Book signing and screening of the documentary GET ME ROGER STONE, tickets HERE
6:35 PM Post-screening Q&A with Roger Stone
7:00 PM Karl Bray Fundraising dinner, tickets HERE
Roger Stone keynote
Civil Liberty Activist of the Year Award – Christine Stenquist of TRUCE (Together for
Responsible Use and Cannabis Education).
Financial Transparency Activist of the Year Award – John Dougall, Auditor, State of Utah.
Karl Bray Memorial Utah Libertarian Activist of the Year Award – TBA.
"Anyone who is an ally of drug policy reform, especially in regards to cannabis, is a welcome friend in my book. Here's to building a coalition of unexpected allies!!!" – Christine Stenquist.
"I will not seek, nor would I accept his endorsement, unless he, um . . . insisted." – Joe Buchman, 2017 Special Election Candidate, and current state chair.
"I was told this was a masquerade but I don't see anything mentioning attire." – Anon.
"Isn't everything a masquerade when you're dealing with Roger Stone?"
Tickets are available at the links above.
All lifetime members of the national party who are also current UT LP members, are welcome to attend at no cost (with up to one guest).
The first 10 Lifetime members of the national party living outside of Utah are likewise invited to attend at no cost (email us for the eventbrite code).
The Libertarian Party of Utah website states:
"The scariest man in politics is coming to Utah for one night only!
Come see the man, the myth, the legend, the ghoul . . . the one and only ROGER STONE!
The Libertarian Party of Utah is celebrating 45 years as a party this Halloween season with the scariest man in politics. With skeletons, ghosts, jokers . . . and Roger Stone.
From www.FindAGrave.com –
Karl J. Bray was a political activist and co-founder of the national Libertarian Party. A charismatic libertarian leader and outspoken tax rebel, he served as an early member of the Libertarian National Committee, then in 1974 was the Libertarian candidate for U.S. Senate in his home state of Utah, running against opponent Jake Garn.
It was Karl's sincere conviction that the federal income tax was unconstitutional. He had done considerable research, published pamphlets and given speeches centered around this topic.
After losing the election he was arrested and convicted by the IRS over tax issues. He took the case all the way to the Supreme Court.
He died soon after contracting an aggressive form of cancer in federal prison.
Karl Bray's headstone in the Provo City Cemetery is inscribed "THE LIBERTARIAN TAX REBEL".
This entry was posted in Libertarian Party and tagged Halloween, roger stone, Utah on October 16, 2017 by Joseph Buchman.
← CANCELLED Libertarian Party: Bylaws Committee 10/14 at 11pm Eastern (proposal to radically re-structure the LNC) North Carolina Ballot Access Bill Enacted into Law →
10 thoughts on "Ghoul Roger Stone to Appear as "Head Ghoul" at Utah LP Halloween Event"
paulie October 17, 2017 at 10:58
From a reader on IPR FB: "You lay down with the dogs, you get up with the fleas"
wredlich October 20, 2017 at 14:09
The LP continues to discredit itself.
Thane Eichenauer October 20, 2017 at 23:26
Warren,
The LP of Utah is having an event. Only insiders like you or I even have an clue about the history of Roger Stone. If it advances the state party I say good for them.
I don't think it advances them to associate with him in any way or give him any more LP credibility, as it seems to be a case of the scorpion and the frog.
itdoesntmatter October 22, 2017 at 02:26
Roger Stone regularly appears in the media as one of Donald Trumps biggest supporters, today in 2017. I would say that is enough to keep our distance, without knowing any of his history.
Starchild October 22, 2017 at 05:59
Sadly, I think Paulie is probably right, but if the Utah LP's planned this and are already selling tickets, they might not feel willing or able to cancel. So here's a possible way to salvage/redeem the event in terms of minimizing the damage to the LP of associating with Roger Stone (are you listening Joe Buchman?):
Get three people to dress up as Donald Trump, Al Sharpton, and Richard Nixon (Stone has worked for all three!) at the event, to shadow Stone, treat him as an old pal, photo-bomb the pictures he takes with guests, tell everyone about his history and what a great guy he is to have on your side when you need somebody willing to hit below the belt, etc.
Having these three other "guests" who the LP is clearly not trying to endorse or support appear along with Stone could put his presence in the proper context.
Joseph Buchman Post author October 25, 2017 at 23:22
We've canceled the dinner due to logistics issues involved with catering at the venue. New schedule is as follows:
An evening with Roger Stone
A dark night of political horror, with The "Dark Knight" of American Politics
Roger Stone, advisor to Presidents from Nixon to Trump, author of THE MAKING OF A PRESIDENT 2016: HOW DONALD TRUMP ORCHESTRATED A REVOLUTION, and "Father of Dirty Tricks" is presenting a keynote speech Saturday, 28 October 2017, at the Overstock.com Peace Coliseum, 799 Coliseum Way, Midvale, UT 84047.
Schedule is as follows:
4:30 Book sales and signing with Roger Stone
5:00 Remarks by Patrick Byrne, Jonathan Johnson and UT LP Chair, Joe Buchman
5:15 Screening of GET ME ROGER STONE
6:45 Award presentations (media welcome)
7:00 Keynote, Roger Stone
7:15 Q&A with Roger Stone
7:30 Closing Remarks
A VIP reception with Roger will be held concurrent with the screening of the documentary. Tickets are $100.
Awards will be presented by the Libertarian Party of Utah to State Auditor John Dougall for Financial Transparency and Executive Director of TRUCE Christine Stenquist for the advancement of Civil Liberty.
https://www.eventbrite.com/e/get-me-roger-stone-documentary-screening-and-qa-with-roger-stone-tickets-38994412337
That's even worse.
itdoesntmatterttomuch October 28, 2017 at 03:12
Go to Twitter, see Trending: Roger Stone. Read. Maybe they will arrest him at your event. Great publicity for LP!
http://www.independent.co.uk/news/world/americas/us-politics/trump-roger-stone-cnn-journalists-white-house-latest-twitter-a8024566.html
Adviser Roger Stone launches tirade of foul-mouthed abuse against CNN journalists critical of Donald Trump
Roger Stone described Don Lemon, Jake Tapper and Ana Navarro as "human excrement"
One of Donald Trump's close advisers has called for the firing of journalists critical of the US president.
Roger Stone launched a tirade against CNN calling for journalists Don Lemon, Jake Tapper and Ana Navarro to be fired and describing them as "human excrement".
In a tweet about the merger between AT&T and Time Warner, CNN's parent company, Mr Stone wrote: "When AT&T aquires [sic] Time Warner the house cleaning at CNN of human excrement like @donlemon @jaketapper & dumbf*** @ananavarro will be swift".
Yes, because firing journalists for criticizing Dear Leader is so libertarian…being a dirty tricks henchman for the likes of Nixon and Trump is so libertarian…and corporate owners micromanaging news departments and firing people for criticizing the Caudillo is…well, you know. As par for the course for the Drumpf gang (the story notes that other Drumpf crime family lieutenants also call for silencing any critical journalists) we are seeing behavior more commonly associated with regimes in places like Turkey, Uzbekistan or Zimbabwe. Not quite to North Korean levels yet but give it time. Go team Libertarian!
#SoProud
PS: Bill Maher doesn't even pretend to be a libertarian anymore, but…well, see for yourself:
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 1,347
|
Percy Jackson and the Greek Gods- A Beginner's Guide to Greek Mythology
BooksBiographies
The Percy Jackson series made quite a buzz in the literature world. Written by American author Rick Riordan come on the series attempts to acquaint the young generations with Greek and Roman mythology by portraying them in a contemporary light.
Mythology is not the first genre that comes to mind while discussing books. Most of us who label ourselves as bookworms choose novels or stories that help us evade the grey reality of our everyday lives. So most of the stories on our shelves would be science fiction, romance, and such.
Mythology if you think about it is not that far from fiction though. That is exactly what Rick Riordan's books attempt to make the young readers realize. Rick blends old mythological stories with the adventures of a young boy and his squad, thereby putting in all the ingredients that a young teen would like in a story.
The Percy Jackson series follows the adventures of a young boy named Percy, short for Perseus Jackson. This boy is a Demi-God. This means that the boy has a parent who is a God and another parent who is a human. In the case of Percy, he turns out to be the son of the mighty God of the sea, Poseidon.
The series follows the journey of the young lad as he struggles to maintain as normal a life as is possible for a demigod in a world of humans. As soon as this covers the fact that he is a demigod his troubles start to rise. At first, he is prophesied to be the boy who would bring down the empire of the gods. Many times it so happens that gods who do not have that much of a good equation with his father, Poseidon, try and take out their anger on the boy. He and his gang go through adventures of all sorts, fighting demons, escaping the wrath of the gods at times, and all in all just trying to stay alive.
The review you are about to read through is that of "Percy Jackson and the Greek Gods". This book is not directly a part of the entire Percy Jackson series but has the boy as its narrator, as in all the other episodes of the series. This particular book is different from the others in the series in its plot as well. In the other books, Rick does not directly attempt to acquaint his readers with Greek mythology, giving subtle hints and remarks about the gods and goddesses here and there. However, with this book, he traces the entire Greek mythology, in a fun and contemporary tone and lingo.
The book opens with how the world was created from utter Chaos. At first, there was nothing but Chaos. Chaos then created Earth, Gaea. Gaea soon got lonely and asked for a companion. Chaos then created the Sky, Ouranos. Even though the other primordial gods that Chaos had created tried to get cozy with Gaia now and then, Ouranos and Gaea had a pretty neat time courting each other. However, things started to go downhill as soon as Gaea gave birth to her first set of children. Gaia gave birth to a batch of 12 children- 6 girls and six boys. These kids looked kind of like humans but were way taller and stronger. They were called the Titans.
Ouranos started spending lesser and lesser time with Gaia. Like any other average marriage, they guessed that things would probably get better if they had more children. Needless to say that it was quite the contrary. Gaia gave birth to triplets – these triplets were big on strong but brutish and hulking too. They were named the elder cyclops. Ouranos could not handle the sight of them and soon came back with James and through the elder cyclops into Tartarus, a bit like the sky, but at the bottom of the earth.
A new set of kids followed after that, but they were more monstrous than the elder cyclops. They had 100 arms, and they were all around the chests. And they also had 50 tiny heads clustered on their shoulders. They also suffered the same fate as the elder cyclops.
This was too much for Gaia to absorb. She summoned the hardest substance that she could find from her earthly domain and created the first-ever weapon – a scythe. This was her weapon for revenge. She asked all of her children as to who would be brave enough to overthrow their father and be the new ruler of the universe.
Kronos, the God of Time, stood up. He was the youngest out of all his siblings and never quite taken that seriously. That was to forever change though. He took the weapon, devised a master plan, and got rid of Ouranos once and for all. Kronos was the new Lord of the Universe and the Scythe was his weapon.
Kronos assigned various locations of the world to all of his siblings and assigned them their fields that they were to overlook for the better functioning of the world. He went on to marry Rhea, one of his siblings (yes, gross, but it is what it is). Gaia felt she had found a good leader who could correctly rule the universe. She thought she could retire and take a break.
Everything was going fine, except for inside the head of Kronos. It was prophesied that the children of Kronos would be the reason for his downfall, in a similar pattern as that of the death of Ouranos. However, Kronos had moved past that prophecy and wanted to give domestic life a short. However, things got pretty ugly once Rhea and Kronos started having babies. The babies were much taller and stronger than their Titan parents. This was more than enough to get Kronos to go crazy. He swallowed the kids one by one as Rhea kept presenting them to him, except for the last one, Zeus. Gaia guided her to Cretes and gave her directions on how she could save him and how he would return and save his other siblings.
Fair enough Zeus grew up to be a handsome young man. He heard all about how his father treated his mother and how he swallowed his siblings from Rhea. He then devised a plan that would let him get close to Kronos, without him suspecting a thing, and on the first chance, he would kill his father and rescue his siblings from his gut. The plan was a success and that is how the Greek gods as we know them today came into being. They all were assigned different fields and corners of the world that they would look after thereafter.
A long war between the Titans and the gods had followed after that. The palace of the Titans on Mount Othrys got destroyed in the war, making Olympus the highest mountain in Greece. Mount Olympus became the residence of the Gods thereafter.
The book traces the stories of these gods vividly. It talks about how Atlas ended up holding up the entire world, how Persephone came to marry Hades, why Poseidon and Athena just cannot stand each other, and so on.
The best part about the book is its informal tone. While most mythologies attempt to stall the gods and goddesses, putting them way about us, Rick shows these gods in a more human light. They commit mistakes that humans would, indulge in personal and childish bickering, and at times are even irresponsible with the jobs that they are assigned.
The book overall has been a good experience. It educates you but keeps the fun alive. At an age when people are increasingly resorting to visual forms of media, attempts such as Rick Riordan's "Percy Jackson and the Greek Gods" serve as good initiatives to bring back the millennial audience to the pages. If you are looking for a fun read that would also give you some actual information then this would be a perfect choice.
A little tip, new readers would enjoy it much more if they read through the other Percy Jackson stories first and then came to this one. The other Percy Jackson stories are more fun to read and have discreet plotlines. This one is enjoyable only if you have a thing for exploring Greek mythology and want to know a bit more about it. The first books of the series that deal with the adventures of Percy Jackson would give you a reason to start liking Greek mythology.
"Percy Jackson and the Greek Gods" is quite engaging in its development, writing style, and matter. If you're looking for a fun read then this is it.
The Push- A Psychological Thriller
greek mythology books
percy jackson and the greek gods
percy jackson book series
percy jackson's greek gods
rick riordan books
Percy Jackson and the Greek Gods- A Beginner's Guide to Greek MythologyThe Percy Jackson series made quite a buzz in the literature world. Written by American author Rick Riordan come on the series attempts to acquaint the young generations with Greek and Roman mythology by portraying them in a contemporary light. Mythology is not the first...
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 4,418
|
Q: To check if List> is empty or not The answer from a library (DBpediaLookupClient.variableBindings()) results in
List<Map<String, String>>
I am trying to check is if the list if empty or not.
What I have tried so far is
if (dbpedialookup.variableBindings() != null && !dbpedialookup.variableBindings().isEmpty()) {
System.out.println("Results Present);
} else {
System.out.println("No Results");
}
But, on items where the resultant List is []. Its throwing,
Exception in thread "main" java.lang.NullPointerException
How do we check for null in such a situation?
A: Look like the top object is null so
if (dbpedialookup != null &&
dbpedialookup.variableBindings() != null &&
!dbpedialookup.variableBindings().isEmpty()) {
A: The following is the pattern:
if (myList != null && !myList.isEmpty()) {
System.out.println("Isn't empty");
} else {
System.out.println("Is empty");
}
If you want to check variables in the list use the following:
if (myList != null) {
for (Map<String, String> map : myList) {
if (map != null) {
//perform on map
}
}
}
A: Use Optional to tidy things up:
if (Optional.ofNullable(dbpedialookup).map(DBpediaLookupClient::variableBindings).map(List::isEmpty).orElse(true))
// it's empty / null
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 9,489
|
<?xml version="1.0" encoding="UTF-8"?>
<!--
Copyright 2015 Software Evolution and Architecture Lab, University of Zurich
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
-->
<beans xmlns="http://www.springframework.org/schema/beans"
xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:context="http://www.springframework.org/schema/context"
xmlns:mvc="http://www.springframework.org/schema/mvc"
xsi:schemaLocation="http://www.springframework.org/schema/beans
http://www.springframework.org/schema/beans/spring-beans.xsd
http://www.springframework.org/schema/context
http://www.springframework.org/schema/context/spring-context-3.1.xsd
http://www.springframework.org/schema/mvc
http://www.springframework.org/schema/mvc/spring-mvc.xsd">
<context:component-scan base-package="eu.cloudwave.wp5.feedbackhandler" />
<mvc:annotation-driven />
<bean class="eu.cloudwave.wp5.feedbackhandler.DatabaseConfiguration" />
<bean id="viewResolver"
class="org.springframework.web.servlet.view.InternalResourceViewResolver">
<property name="viewClass" value="org.springframework.web.servlet.view.JstlView" />
<property name="prefix" value="/WEB-INF/templates/" />
<property name="suffix" value=".jsp" />
</bean>
<mvc:resources mapping="/static/**" location="/WEB-INF/static/" />
</beans>
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 9,384
|
Study Provides Guidance for Transfusion Practices in Patients With Leukemia Who Experience ICH
Intracranial hemorrhage (ICH) is a common complication in patients with acute leukemia and is associated with significant morbidity and mortality. Information on platelet transfusion practice in patients following ICH is limited, so researchers assessed clinical features and outcomes to better guide transfusion practices after ICH. Shannon Nixon, NP, of the Princess Margaret Cancer Centre at the University of Toronto, discussed the findings at the ASH Annual Meeting on December 3, 2018.
The retrospective study included adult patients diagnosed with acute leukemia who had documented ICH at a large, quaternary, academic cancer center between January 1, 2009, and December 31, 2016. Researchers assessed demographics, medications, infection and bleeding history in the week prior to ICH, characteristics of ICH, acute management, transfusion practice in the first 90 days, and clinical outcomes. They also assessed radiologic scans to determine whether ICH was stable or if new or progressive bleeding had developed.
Of the 2,576 identified patients, 101 had an ICH. Most patients (n = 94) had AML, including acute promyelocytic leukemia (n = 9), acute lymphocytic leukemia (n = 6), and mixed phenotype acute leukemia (n = 1). At the time of ICH, 61 patients were newly diagnosed or receiving induction chemotherapy, 33 had relapsed disease, and seven were in complete remission. Many patients (n = 76) experienced spontaneous ICH. In the week preceding ICH, seven patients received medications that are known to increase bleeding risk and 39 received tranexamic acid. Researchers observed clinical evidence of bleeding elsewhere in 64 patients and evidence of infection in 22 patients.
On the day of the ICH event, most patients had active disease. The median platelet count was 16 × 109/L (range = 0–433 × 109/L). Almost a third of patients (n = 31) had a platelet count less than 10 × 109/L, and 10 patients received a platelet transfusion prior to the bleed. Of the 70 patients who had a platelet count ≥ 10 × 109/L, 17 received a platelet transfusion prior to the bleed. Six patients (6%) were refractory to platelet transfusion.
In the 90 days following ICH, platelet transfusions were administered for platelet counts of:
Less than 10 × 109/L (21%)
Between 10 × 109/L and 29 × 109/L (55%)
30 × 109/L or greater (24%)
Twenty-eight patients experienced new or progressive ICH.
The median platelet transfusion threshold was 19 × 109/L (range = 0–114 × 109/L) for those without new or progressive ICH and 21×109/L (range = 0–93 × 109/L for those with progression (p = 0.04).
Seventy-nine patients died, although most (n = 65; 82%) deaths were attributed to non-ICH causes. The median overall survival was 5.6 months for those without new or progressive ICH compared to 2.9 months for those with progression (p = 0.002).
"Platelet transfusion practice was variable, and the median threshold was higher in those who subsequently developed new or progressive bleeding," the researchers noted. Although the reasons were unclear, the investigators hypothesized additional risk factors, such as fever or infection, may have contributed.
American Society of Hematology Annual Meeting
Patients With CLL Report Worse QoL and Other Factors
Experimental Three-Drug Treatment May Be Used for Childhood Leukemia
FDA Approves Tisagenlecleucel for B-cell ALL, Tocilizumab for Cytokine Release Syndrome
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 4,934
|
CSS3 framework.
This CSS3 framework can use every front-end-developer and UI/UX designer.
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 8,892
|
\section{Introduction}
\label{S1}
Graphene-based electronics has been the subject of an intensive theoretical and experimental research since the discovery of
this striking two-dimensional material in 2004 \cite{NG2004}.
Particularly promising are device architectures that mimic the ordinary semiconductor heterojunctions between positively and negatively doped regions (``n'' and ``p'' regions,
respectively).
In graphene, such junctions can be obtained by suitable gates configurations, since the electron/hole density can be locally tuned by local electrostatic fields
\cite{CF2006,Fang07,Huard2007,YK2009}.
Thus, a sharp potential variation corresponds to a transition between two differently doped regions, so that we speak of ``p-n'' or ``n-p'' heterojunctions.
In correspondence of such junctions very interesting phenomena occur, such as the so-called Klein paradox \cite{KNG2006,YK2009} and the negative refraction
(Veselago) electron lensing \cite{CFA2007,LeeParkLee2015}, which could be exploited to create innovative devices.
\par
The aim of this paper is to apply the theory of diffusive quantum transmission conditions, developed in Ref.\ \cite{BN2018},
to the mathematical modelling of a device of this kind.
\par
The concept of quantum interface conditions goes back to the work of Ben Abdallah and coworkers \cite{NBA98,NBA02},
and was initially developed in the framework of kinetic equations.
The corresponding diffusion theory has been obtained in Refs.\ \cite{DS98,DEA02}, where a boundary layer analysis leads to diffusive transmission conditions.
Such conditions permit to link two ``classical regions'', described by classical (or semiclassical) drift-diffusion equations, separated by a
localized quantum interface (e.g.\ a sharp potential variation), which scatters electrons according to the laws of
quantum mechanics.
In particular, the transmission conditions contain a parameter, dubbed ``interpolation coefficient'' (by analogy with the ``extrapolation coefficient'' occurring in neutron transport theory \cite{BBS1984}), that depends on the scattering coefficients, thus containing the quantum information of the dynamics at the interface.
\par
The theory has been recently revisited in the case of graphene in Ref.\ \cite{BN2018}.
The main novelty in such a case comes from the fact that electrons in graphene feature a conical intersection between the conduction band
and the valence band and, therefore, the behaviour of charge carriers is well described by a Dirac-like equation \cite{CastroNeto09}.
This fact, with respect to traditional semiconductors, not only changes the dispersion relation from quadratic to linear but also introduces a stronger coupling between
positive-energy and negative-energy electrons (the latter to be described as holes)
As we shall see, the populations of electrons and holes are independent in the classical regions but become (in general) coupled by the
quantum interface, so that the interpolation coefficient becomes an interpolation matrix.
\par
Clearly, the theory of quantum interfaces is very attractive when dealing with graphene heterojunctions since,
as we have remarked at the beginning of this introduction, they originate the most interesting quantum effects.
For heterojunction devices, therefore, quantum transmission conditions may represent a useful tool for modelling purposes.
The present paper is exactly aimed at illustrating the potentiality of this approach in the case of a prototypical n-p-n graphene device \cite{Huard2007,Osyilmaz2007,YK2009}.
\par
Let us present now the outline of this paper.
In Section \ref{S2} we review the main results of Ref.\ \cite{BN2018}.
In particular, we show how the densities at both sides of a quantum interface are connected by diffusive transmission conditions (Theorem \ref{T2}).
Such conditions depend on ``asymptotic densities'' associated to the solution of a four-fold Milne (half-space) kinetic problem which, in turn, arises from a boundary layer
analysis involving quantum reflection and transmission coefficients.
A result about existence and other properties of such asymptotic densities is summarized in Theorem \ref{T1}.
\par
The solution of the Milne problem represents a surviving kinetic step, that one would like to avoid when working in a diffusion framework.
Then, it is natural to look for some approximations that allow to write down explicitly the solution to the Milne problem and compute the related
asymptotic densities. This point, which was only briefly mentioned in Ref. \cite{BN2018} , is fully developed in the Section \ref{S3} of the present paper.
We obtain in this way an explicit expression of the interpolation coefficient for the specific case we are interested in, that is the case
of a potential barrier and of purely electron transport.
The Maxwell-Boltzmann approximation is also discussed in Section \ref{S3}, which is a further simplification that can be introduced in regimes of low densities or high
temperatures.
\par
Finally, in Section \ref{S4} we set up a model of a graphene n-p-n heterojunction and perform some numerical experiments by assuming
purely electronic transport and sharp potential barrier profile.
We show that our model is able to reproduce, at least in a suitable range of physical parameters, important features that have been highlighted in laboratory experiments.
\section{Quantum transmission conditions}
\label{S2}
In this section we briefly review the transport model across quantum interfaces in graphene, model that has been developed in Ref.\ \cite{BN2018}.
\par
Assume that a graphene sheet is described by the coordinates ${\boldsymbol{x}} = (x,y)$ and that a ``quantum active region'' (e.g. a potential barrier) is
localized into a tiny strip around $x=0$.
More precisely, we assume that the electric potential is the sum of two distinct parts, namely
$$
V(x) + U(x,y),
$$
where $V(x)$ represents the step/barrier profile, which is assumed to have variations localized around $x=0$ and to be constant outside the active region,
taking the values
$$
V_0 \qquad \text{and} \qquad V_0 + {\delta V}
$$
at the left and at the right, respectively (see Figure \ref{figura0}).
\begin{figure}[h]
\begin{center}
\includegraphics[width=.6\linewidth]{figure0.eps}
\caption{Schematic geometry of our model: the rectangle represents the graphene sheet and the central strip represents the quantum active region, i.e.\ the zone where
the variations of $V = V(x)$ are localized.
Outside the strip, in the two classical regions, the potential $V$ has constant values $V_0$ and $V_0+{\delta V}$.}
\label{figura0}
\end{center}
\end{figure}
Note that $V_0$ is a ``background'' potential and ${\delta V}$ is the total potential variation across the quantum strip.
The ``smooth'' part of the potential, $U(x,y)$ is assumed to vary on a much larger (macroscopic) space scale
and can be used to describe, e.g., a bias voltage.
\par
Our the graphene sheet is then modelled as two ``classical'' regions ($x<0$ and $x>0$), where the charge transport is assumed to be diffusive,
separated by a ``quantum interface'', localized at $x=0$.
Mathematically, the quantum interface is seen as a boundary where transmission conditions have to be determined by solving a scattering
problem for the potential $V$.
The derivation of the final macroscopic model passes firstly through a kinetic step and then a diffusion step, steps briefly described below.
\subsection{Kinetic model}
\label{S2.1}
Let us consider the scattering problem for the electric potential $V$ (the electron potential energy is $-qV$,
where $q$ is the elementary charge):
\begin{equation}
\label{SE}
\left( -i\hbar v_F \nabla \cdot \boldsymbol{\sigma} - qV\sigma_0 \right) \psi_{{\boldsymbol{p}},s} = E\psi_{{\boldsymbol{p}},s} .
\end{equation}
Here, $v_F$ is the Fermi velocity, $\nabla = (\partial_x,\partial_y)$, $\boldsymbol{\sigma} = (\sigma_1,\sigma_2)$ are the $x$- and $y$- Pauli matrices,
${\boldsymbol{p}} = (p_x,p_y)$ is the electron (pseudo)momentum and $E$ is a given energy (which can be either positive or negative).
Moreover, $s = \pm 1$ is the chirality index, denoting electron states of positive and negative chirality \cite{CastroNeto09}.
Solving this equation provides the scattering states $\psi_{{\boldsymbol{p}},s}$ and the reflection/transmission coefficients $T_s^i({\boldsymbol{p}})$, $R_s^i({\boldsymbol{p}})$
corresponding to the energy
$$
E = sv_F\abs{{\boldsymbol{p}}}.
$$
Note that states with positive chirality are also states of positive energy (upper Dirac cone) and states with negative chirality are also
states of negative energy band (Dirac cone).
\par
The upper index $i$ appearing in the coefficients $T_s^i({\boldsymbol{p}})$, $R_s^i({\boldsymbol{p}})$ takes the values 1 and 2, and refers to a left ($i=1$)
or right ($i = 2$) incoming wave.
Throughout this paper, an upper index $i = 1,2$ will always denote left and right, respectively.
The scattering coefficients satisfy some basic properties:
\begin{enumerate}
\item[\it i)]
$T_s^i({\boldsymbol{p}}) \geq 0$ and $R_s^i({\boldsymbol{p}}) \geq 0$, with $T_s^i({\boldsymbol{p}}) + R_s^i({\boldsymbol{p}}) = 1$ (unitarity);
\item[\it ii)]
$T_s^i({\boldsymbol{p}})$ and $R_s^i({\boldsymbol{p}})$ are symmetric with respect to $p_x$ and $p_y$ (symmetry);
\item[\it iii)]
$T_s^1({\boldsymbol{p}}) = T_{s'}^2({\boldsymbol{p}}')$ if the conservation of energy
\begin{equation}
\label{CoE}
s v_F \abs{{\boldsymbol{p}}} = s' v_F \abs{{\boldsymbol{p}}'} - q\,{\delta V},
\end{equation}
holds (reciprocity).
\end{enumerate}
The key remark is that, away from the quantum interface, the scattering states are superpositions of incoming/reflected/transmitted
plane-wave-like solutions of the form
\begin{equation}
\label{planew}
\psi_{{\boldsymbol{p}},s}({\boldsymbol{x}}) =
\begin{pmatrix} 1 \\ s\,\mathrm{e}^{i\, \phi} \end{pmatrix} \mathrm{e}^{\frac{i}{\hbar}{\boldsymbol{p}}\cdot{\boldsymbol{x}}},
\end{equation}
which have definite values of chirality and momentum.
Such waves are semi-classically interpreted as inflowing and outflowing particles in the classical regions \cite{NBA98,NBA02}.
More precisely, if the phase-space distributions
$$
w^i_s({\boldsymbol{x}},{\boldsymbol{p}}), \qquad s = \pm 1, \quad
$$
describe the electron populations with positive energy ($s = +$) and negative energy ($s = -$) in the two classical regions, $x<0$ ($i = 1$) and $x>0$ (i = 2), we assume that at $x = 0$ the following kinetic transmission condition (KTC) hold:
\begin{equation}
\label{KTC}
\left\{
\begin{aligned}
&w_s^1({\boldsymbol{p}}) = R_s^1({\boldsymbol{p}}) w_s^1( {\sim}{\boldsymbol{p}}) + T_{s'}^2({\boldsymbol{p}}') w^2_{s'}({\boldsymbol{p}}'),&\quad &sp_x,\, s'p'_x < 0,
\\[8pt]
&w_{s'}^2({\boldsymbol{p}}') = R_{s'}^2({\boldsymbol{p}}') w_{s'}^2({\sim}{\boldsymbol{p}}') + T_s^1({\boldsymbol{p}}) w^1_s({\boldsymbol{p}}),& &s'p'_x,\, sp_x > 0,
\end{aligned}
\right.
\end{equation}
where $s$, $s'$, ${\boldsymbol{p}}$ and ${\boldsymbol{p}}'$ satisfy the conservation of energy \eqref{CoE} and the conservation of momentum
in the $y$ direction:
\begin{equation}
\label{pycons}
p_y = p'_y .
\end{equation}
In \eqref{KTC} we have denoted by a tilde the reflection transformation
\begin{equation}
\label{refldef}
{\sim}{\boldsymbol{p}} := (-p_x,p_y)
\end{equation}
and, in order to avoid cumbersome expressions, we have only indicated the dependence on the relevant variable ${\boldsymbol{p}}$, omitting the variables $y$ (which is just a parameter) and
$x$, which is of course equal to $0$ at interface.
The meaning of Eq.\ \eqref{KTC} is clear: the first equation says that the inflow in the left classical region through the interface is partly
due to reflected particles from the left and partly due to transmitted particles from the right, and the second equation describes the analogous balance
of particles inflowing in the right region.
Note that, since negative-chirality electrons travel in the direction opposed to momentum \cite{CastroNeto09}, the conditions $sp_x < 0$
and $s'p'_x < 0$ describe leftward particles, while $sp_x > 0$ and $s'p'_x > 0$ describe rightward particles.
\par
Since we shall study the diffusive limit of the kinetic model and, therefore, statistical considerations will come into play, it is convenient
to switch from positive/negative-energy electrons to electron/holes, by means of the transformation
\begin{equation}
\label{fdef}
f^i_+({\boldsymbol{x}},{\boldsymbol{p}}) = w^i_+({\boldsymbol{x}},{\boldsymbol{p}}), \qquad
f^i_-({\boldsymbol{x}},{\boldsymbol{p}}) = 1 - w^i_-({\boldsymbol{x}},-{\boldsymbol{p}}).
\end{equation}
Now, $f^i_+$ and $f^i_-$ represent, respectively, the phase-space populations of electrons and holes (both with positive energy).
Note that both electrons and holes move in the same direction of the momentum.
\par
In the classical regions, the dynamics of each population is assumed to be described by the stationary BGK (relaxation time)
transport equation
\cite{Barletti14,LF18}
\begin{equation}
\label{TE}
\boldsymbol{v}\cdot\nabla_{\boldsymbol{x}} f^i_s - s q \nabla_{\boldsymbol{x}} U\cdot\nabla_{\boldsymbol{p}} f^i_s =
\frac{1}{\tau}\left(F^i_s - f_s\right)
\end{equation}
where $U$ is the smooth part of the potential, as discussed above, and
\begin{equation}
\label{vdef}
\boldsymbol{v} = v_F\,\frac{{\boldsymbol{p}}}{\abs{{\boldsymbol{p}}}}
\end{equation}
is the semiclassical velocity.
The right-hand side of Eq.\ \eqref{TE} describes the separate relaxation of electrons and holes to the local Fermi-Dirac
distributions
\begin{equation}
\label{FD}
F^i_s({\boldsymbol{x}},{\boldsymbol{p}}) = \frac{1}{\mathrm{e}^{\beta \left[v_F \abs{{\boldsymbol{p}}}-A^i_s({\boldsymbol{x}})\right]}+1},
\end{equation}
where $\beta = (k_BT)^{-1}$, $T$ being the phonon bath temperature and $k_B$ the Boltzmann constant.
The functions $A^i_s({\boldsymbol{x}})$ are defined as
\begin{equation}
A^i_s({\boldsymbol{x}}) = s q V_0 + \mu^i_s({\boldsymbol{x}}),
\end{equation}
where $V_0$ is the background potential and $\mu^i_s$ are the chemical potentials of left and right electrons and holes
(however, in the following we will refer to the functions $A^i_s$ as to ``chemical potentials'').
Since the collisions conserve the number of particles, the chemical potentials are constrained by the relation
\begin{equation}
\label{constr}
n_s^i({\boldsymbol{x}}) := \bk{f_s^i}({\boldsymbol{x}}) = \bk{F_s^i}({\boldsymbol{x}}),
\end{equation}
where
\begin{equation}
\label{bkdef}
\bk{\cdot} = \frac{1}{h^2} \int_{\mathbb{R}^2} \cdot \, d{\boldsymbol{p}},
\end{equation}
where $h$ is the Planck constant.
The normalization constant is needed to retrieve the correct spatial density from phase-space density \cite{Barletti14}.
Integration of $F^i_s$ yields the following relation between density and chemical potential:
\begin{equation}
\label{AvsN}
\beta A^i_s = \phi_2^{-1} \Big( \frac{n^i_s}{n_0} \Big),
\end{equation}
where
$$
\qquad n_0 = \frac{2\pi}{(\beta h v_F)^2}
$$
and
\begin{equation}
\label{phidef}
\phi_k(z) := \frac{1}{\Gamma(k)} \int_0^\infty \frac{t^{k-1}}{\mathrm{e}^{t-z} + 1}\,dt
\end{equation}
is the Fermi integral of order $k$.
\par
The transport equations \eqref{TE}, which hold separately in $x>0$ ($i=1$) and $x<0$ ($i = 2$), are connected through the quantum interface by assuming that at $x = 0$
the KTC \eqref{KTC} holds.\footnote{%
The electron/hole version of \eqref{KTC} is readily obtained by means of the transformation \eqref{fdef}.%
}
It is proven in Ref.\ \cite{BN2018} that the boundary conditions \eqref{KTC} conserve the total charge flux across the interface, namely
\begin{equation}
\label{Jcons}
j^1_{+,x} - j^1_{-,x} = j^2_{+,x} - j^2_{-,x}, \qquad \text{at $x = 0$,}
\end{equation}
where
\begin{equation}
\label{Jdef}
(j^i_{s,x}, j^i_{s,y}) = \boldsymbol{j}^i_s := \bk{\boldsymbol{v} f^i_s}
\end{equation}
is the current.
In addition, if ${\delta V} = 0$, then the conservation of the flux holds separately for each population
\begin{equation}
\label{Jcons2}
j^1_{+,x} = j^2_{+,x}, \qquad j^1_{-,x} = j^2_{-,x}, \qquad \text{at $x = 0$.}
\end{equation}
\subsection{Diffusion model}
\label{S2.2}
The diffusive limit of Eq.\ \eqref{TE} can be obtained by means of the standard machinery of kinetic theory (namely, the Chapman-Enskog expansion) and, in the bulk classical regions,
yields the following fermionic drift-diffusion equations \cite{JSP12,BN2018} for the surface densities $n^i_s$:
\begin{equation}
\label{SDD}
\DIV \boldsymbol{j}^i_s = 0, \qquad \boldsymbol{j}^i_s = -\frac{\tau v_F^2}{2}\left[\nabla n^i_s - s \beta n_0\, \phi_1(\beta A^i_s) q \nabla U \right],
\end{equation}
where we recall that $A^i_s$ are related to $n^i_s$ by \eqref{AvsN} and $\phi_k$ is given by \eqref{phidef}.
Of course, one can alternatively use the chemical potential as unknown, in which case the drift-diffusion equations take the form
\begin{equation}
\label{SDDA}
\DIV \boldsymbol{j}^i_s = 0, \qquad \boldsymbol{j}^i_s = -\frac{\pi \tau}{\beta h^2}\, \phi_1(\beta A^i_s) \nabla \left( A^i_s - s q U \right).
\end{equation}
Of course our relaxation-time approach is a poor approximation of the electron-phonon scattering and, as a consequence, of the electron mobility.
This can be at least partially fixed by tuning the parameter $\tau$ at a given temperature.
\par
\smallskip
A more difficult task is to obtain the diffusive limit of the transmission conditions \eqref{KTC}.
This requires a boundary layer analysis, leading to Milne (half-space) kinetic problem.
The result of such analysis, contained in Ref.\ \cite{BN2018}, can be summarized as follows.
\par
After the introduction of the ``magnified'' boundary-layer variable $\xi = x/\tau$, the analysis
leads to the introduction of a boundary corrector $\theta_s^i(\xi,y,{\boldsymbol{p}})$ at order $\tau$ in the Hilbert expansion.
Up to an error of order $\tau^2$ the corrector satisfies the equation
\begin{equation}
\label{MilnEq}
v_x \frac{\partial \theta_s^i}{\partial \xi} = L^i_s \bk{\theta_s^i} - \theta^i_s,\quad (-1)^i\xi>0, \quad {\boldsymbol{p}} \in \mathbb{R}^2,
\end{equation}
where $L^i_s$ is the linearized Fermi-Dirac distribution \eqref{FD} around a given density $n_s^i$, i.e.
\begin{equation}
\label{Ldef}
L^i_s = \frac{d F^i_s}{dn^i_s} = \frac{ (F^i_s)^2 \,\mathrm{e}^{\beta ( v_F \abs{{\boldsymbol{p}}} - A^i_s)}}{n_0 \, \phi_1(\beta A^i_s)}.
\end{equation}
As it is shown in Ref.\ \cite{BN2018}, the four equations \eqref{MilnEq} are coupled at $\xi = 0$ by the following nonhomogeneous version
of the KTC:
\begin{equation}
\label{MilneTC}
\left\{
\begin{aligned}
&\theta_s^1({\boldsymbol{p}}) - G^1_s({\boldsymbol{p}}) = R^1_s({\boldsymbol{p}})\left[\theta_s^1({\sim}{\boldsymbol{p}}) - G_s^1({\sim}{\boldsymbol{p}}) \right]
+ss' T^2_{s'}({\boldsymbol{p}}')\left[ \theta^2_{s'}({\boldsymbol{p}}') - G^2_{s'}({\boldsymbol{p}}') \right] \ &p_x,\, p'_x < 0,
\\[8pt]
&\theta_{s'}^2({\boldsymbol{p}}') - G_{s'}^2({\boldsymbol{p}}') = R^2_{s'} ({\boldsymbol{p}})\left[ \theta_{s'}^2({\sim}{\boldsymbol{p}}') - G_{s'}^2({\sim}{\boldsymbol{p}}') \right]
+ ss' T_s^1({\boldsymbol{p}})\left[ \theta^1_{s}({\boldsymbol{p}}) - G^1_{s}({\boldsymbol{p}})\right],\ &p'_x,\, p_x > 0,
\end{aligned}
\right.
\end{equation}
where
\begin{equation}
\label{Gdef}
G^i_s(y,{\boldsymbol{p}}) := \frac{2}{\tau v_F^2}\,L^i_s({\boldsymbol{x}},{\boldsymbol{p}})\, \boldsymbol{v}({\boldsymbol{p}}) \cdot \boldsymbol{j}^i_s ({\boldsymbol{x}})_{\mid x = 0}.
\end{equation}
We remark that in Eq.\ \eqref{MilneTC} only the dependence on the relevant variable ${\boldsymbol{p}}$ has been explicitly indicated and, as usual, $s$, $s'$, ${\boldsymbol{p}}$ and
${\boldsymbol{p}}'$ are related by the conservation of energy \eqref{CoE}.
We remark that \eqref{MilnEq}-\eqref{MilneTC} is a system of four Milne (half-space, half-range) problems coupled at $\xi = 0$ by
nonhomogeneous transmission conditions.
in Ref.\ \cite{BN2018}, the following result is proven, which is a generalization to the multicomponent case of analogous results (obtained, e.g., in
Refs.\ \cite{BBS1984,DEA02,DS98}).
\begin{theorem}
\label{T1}
For any given $n^i_s \geq 0$ (with $s = \pm1$, $i = 1,2$), problem \eqref{MilnEq}-\eqref{MilneTC}
admits a solution $(\theta_+^1,\theta_+^2,\theta_-^1,\theta_-^2)$, such that
$$
\theta_s^i \in \mathrm{L}^\infty\big( (-1)^i[0,+\infty)\times \mathbb{R}^2, (L^i_s)^{-1}d\xi d{\boldsymbol{p}} \big),
$$
if and only if the flux conservation \eqref{Jcons} (or \eqref{Jcons2}, if ${\delta V} = 0$) holds.
This solution is unique up to the addition of any homogeneous solution (i.e., with $G^i_s = 0$).
Moreover, four constants $n^{i,\infty}_s$ exist s.t.
$$
\theta_s^i \to n_s^{i,\infty} L^i_s \quad \text{{\color{black} as\ } $\xi \to (-1)^i\infty$,}
$$
and the convergence is exponentially fast in $\xi$.
\end{theorem}
We remark that the four constants $n^i_s$ appear in the definition of $L^i_s$, which is the linearization of the Fermi-Dirac distribution around $n^i_s$.
We also remark that the coordinate $y$ is an overall parameter in the problem (in particular, $n^i_s$ and $n^{i,\infty}_s$ may depend on the parameter $y$).
\par
The second main result contained in Ref.\ \cite{BN2018} links the solution to the Milne problem \eqref{MilnEq}-\eqref{MilneTC}
with the diffusion limit at the interface.
\begin{theorem}
\label{T2}
Let $n^1_s$ and $n^2_s$ be the left and right densities at $x=0$ and let
$$
A[n] = \frac{1}{\beta}\,\phi_2^{-1} \left( \frac{n}{n_0} \right)
$$
denote the chemical potential $A$ corresponding to the density $n$, according to \eqref{AvsN}.
Then, up to $\mathcal{O}(\tau^2)$, the condition
\begin{equation}
\label{DTC}
sA[n^1_s + \tau n_s^{1,\infty}] = s'A[n^2_{s'} + \tau n_{s'}^{2,\infty}] - q \,{\delta V},
\end{equation}
hold for all couples $(s,s')$ satisfying the conservation of energy \eqref{CoE} for some ${\boldsymbol{p}}$ and ${\boldsymbol{p}}'$ in a nonzero measure set,
where $n_{s}^{i,\infty}$ are the asymptotic densities of the solution to the Milne problem \eqref{MilnEq}-\eqref{MilneTC} (see Theorem \ref{T1}).
Moreover, condition \eqref{DTC} is not affected by the particular choice of the solution to \eqref{MilnEq}-\eqref{MilneTC}.
\end{theorem}
By expanding Eq.\ \eqref{DTC} at first order in $\tau$, and using the property $\phi_k' = \phi_{k-1}$ of Fermi functions,
we obtain another version of Eq.\ \eqref{DTC}:
\begin{equation}
\label{DTC1}
sA^1_s - s'A^2_{s'} + q\,{\delta V} = \frac{\tau}{\beta n_0} \left( s'\alpha^2_{s'} n_{s'}^{2,\infty} - s\alpha^1_s n_s^{1,\infty} \right)
\end{equation}
where
\begin{equation}
\label{alphadef}
\alpha^i_s := \frac{1}{\phi_1(\beta A^i_s)},
\end{equation}
which is a more explicit condition on the left and right chemical potentials $A^i_s = A[n^i_s]$.
Equation \eqref{DTC1} gives the diffusive transmission conditions (DTC) that connect the two classical regions at the two sides of $x=0$.
They contain the quantum information coming from the scattering problem \eqref{SE}, which is enclosed in the four asymptotic densities $n_{s}^{i,\infty}$.
Note that at leading order in $\tau$ we obtain the semiclassical condition
\begin{equation}
\label{DTC0}
sA^1_s - s'A^2_{s'} = - q\,{\delta V},
\end{equation}
in which case the quantum dynamics occurring at the interface is completely lost.
\par
\section{Evaluation of the asymptotic densities}
\label{S3}
Solving the Milne problem \eqref{MilnEq}-\eqref{MilneTC}, which is needed in order to obtain the asymptotic densities $n_{s}^{i,\infty}$,
implies that a ``kinetic'' stage is still present in our diffusive model.
This is not very appealing, when looking for a simple and numerically treatable model.
Then, we should resort to some kind of approximation of the solution of the Milne problem.
\subsection{Albedo approximation}
\label{S3.1}
A typical approach \cite{DEA02,DS98} consists in finding some approximation of the ``albedo operator'', i.e., the map that connects the inflow,
$\theta^i_s(0,y,{\boldsymbol{p}})$, $(-1)^i p_x > 0$, to the outflow $\theta^i_s(0,y,{\boldsymbol{p}})$, $(-1)^i p_x < 0$, where $\theta^i_s(\xi,y,{\boldsymbol{p}})$ is a solution
to Eq.\ \eqref{MilnEq}.
In particular, assuming that the collisions are very fast, one can look for an approximate outflow of the equilibrium form
\begin{equation}
\label{AA1}
\theta^i_s(0,y,{\boldsymbol{p}}) = L^i_s(y,{\boldsymbol{p}}) \rho^i_s(y), \qquad (-1)^i p_x < 0,
\end{equation}
where $\rho^i_s(y)$ are outflow densities subject to the constraint of vanishing flux at $\xi = 0$:
\begin{equation}
\label{AA2}
\int_{\mathbb{R}^2} \theta^i_s(0,y,{\boldsymbol{p}}) \,v_x({\boldsymbol{p}})\, d{\boldsymbol{p}} = 0.
\end{equation}
To avoid cumbersome notations, in the following we will omit the explicit indication of the variables $\xi = 0$, $y$ and $p_y$, when not necessary.
By using the properties of the scattering coefficients we can rewrite the first of equations \eqref{MilneTC} in the following way:
\begin{multline}
\label{MilneTC2}
\theta_s^1({\boldsymbol{p}}) - \theta_s^1({\sim}{\boldsymbol{p}}) + sT^1_s({\boldsymbol{p}})\left[s\theta_s^1({\sim}{\boldsymbol{p}}) - s'\theta^2_{s'}({\boldsymbol{p}}')\right]
\\
= G_s^1({\boldsymbol{p}}) - G_s^1({\sim}{\boldsymbol{p}}) + sT^1_s({\boldsymbol{p}})\left[sG_s^1({\sim}{\boldsymbol{p}}) - s'G^2_{s'}({\boldsymbol{p}}')\right], \qquad p_x,\, p'_x < 0,
\end{multline}
Let us multiply this equation by $v_x$ and integrate over the inflow range $\{ {\boldsymbol{p}} \in \mathbb{R}^2 \mid p_x<0\}$ (simply denoted by ``$p_x<0$'').
This yields
\begin{multline}
\label{AUX1}
\int \theta_s^1({\boldsymbol{p}})\, v_x\, d{\boldsymbol{p}} + \int_{p_x<0} sT^1_s({\boldsymbol{p}})\left[s\theta_s^1({\sim}{\boldsymbol{p}}) - s'\theta^2_{s'}({\boldsymbol{p}}')\right] v_x \,d{\boldsymbol{p}}
\\
= \int G_s^1({\boldsymbol{p}})\, v_x\,d{\boldsymbol{p}} + \int_{p_x<0} sT^1_s({\boldsymbol{p}})\left[sG_s^1({\sim}{\boldsymbol{p}}) - s'G^2_{s'}({\boldsymbol{p}}')\right] v_x \,d{\boldsymbol{p}},
\end{multline}
We now recall that $ \theta_s^i$ is approximated by \eqref{AA1} and that the null-flux condition \eqref{AA2} holds.
We recall, moreover, that $G_s^i$ is given by \eqref{Gdef}.
Then,
\begin{multline}
\label{AUX2}
\int_{p_x<0} s T^1_s({\boldsymbol{p}})\left[sL_s^1({\boldsymbol{p}})\rho^1_s - s'L^2_{s'}({\boldsymbol{p}}')\rho^2_{s'}\right] v_x \,d{\boldsymbol{p}} =
\boldsymbol{j}^1_s \cdot \frac{2}{\tauv_F^2} \int L^1_s({\boldsymbol{p}}) \boldsymbol{v} v_x\,d{\boldsymbol{p}}
\\
+ \frac{2}{\tauv_F^2} \int_{p_x<0} sT^1_s({\boldsymbol{p}})\left[sL_s^1({\boldsymbol{p}}){\sim}\boldsymbol{v}\cdot\boldsymbol{j}^1_s - s'L^2_{s'}({\boldsymbol{p}}')\boldsymbol{v}'\cdot\boldsymbol{j}^2_{s'}\right] v_x \,d{\boldsymbol{p}},
\end{multline}
We shall now use the identity
\begin{equation}
\label{aLLa}
\alpha^2_{s'}L^1_s({\boldsymbol{p}}) = \alpha^1_s L^2_{s'}({\boldsymbol{p}}'),
\end{equation}
which holds assuming $sA^1_s - s'A^2_{s'} = -q\,{\delta V}$, i.e., at leading order in $\tau$ (see Ref.\ \cite{BN2018}).
Using this relation to compute $n^{i,\infty}_s$ will produce an error of order two in \eqref{DTC1}.
In Ref.\ \cite{BN2018} it is also proven that
\begin{equation}
\label{Lvar}
\int L^i_s({\boldsymbol{p}}) \boldsymbol{v} \otimes\boldsymbol{v}\,d{\boldsymbol{p}} = \frac{h^2 v_F^2}{2} I .
\end{equation}
From \eqref{AUX2}, \eqref{aLLa} and \eqref{alphadef}, we obtain
\begin{multline}
\label{SY1}
\int_{p_x>0} \frac{sT^1_s({\boldsymbol{p}})L_s^1({\boldsymbol{p}})}{\alpha^1_s} X_{ss'} v_x \,d{\boldsymbol{p}} = \frac{h^2}{\tau}\,j^1_{s,x}
\\
- \frac{2}{\tauv_F^2} \int_{p_x>0} \frac{sT^1_s({\boldsymbol{p}})L_s^1({\boldsymbol{p}})}{\alpha^1_s}
\left[s\alpha^1_s (v_x)^2 j^1_{s,x} + s'\alpha^2_{s'} v'_x v_x j^2_{s',x}\right] d{\boldsymbol{p}},
\end{multline}
where
\begin{equation}
\label{Xdef}
X_{ss'} := s'\alpha^2_{s'} \rho^2_{s'} - s\alpha^1_s \rho^1_s \, .
\end{equation}
and the signs where chosen such that both $v_x$ and $v'_x$ are positive.
\par
With an analogous procedure, from the second of equations \eqref{MilneTC} we obtain
\begin{multline}
\label{SY2}
\int_{p'_x>0} \frac{s'T^2_{s'}({\boldsymbol{p}}')L_{s'}^2({\boldsymbol{p}}')}{\alpha^2_{s'}} X_{ss'} v'_x \,d{\boldsymbol{p}} = \frac{h^2}{\tau}\,j^2_{s',x}
\\
+ \frac{2}{\tauv_F^2} \int_{p'_x>0} \frac{s'T^2_{s'}({\boldsymbol{p}}')L_{s'}^2({\boldsymbol{p}}')}{\alpha^2_{s'}}
\left[s'\alpha^2_{s'} (v'_x)^2 j^2_{s',x} + s\alpha^1_s v_x v'_x j^1_{s,x}\right] d{\boldsymbol{p}}',
\end{multline}
where, again, signs have been chosen such that both $v_x$ and $v'_x$ are positive.
Note that in \eqref{SY1} $s'$ and ${\boldsymbol{p}}'$ depend on ${\boldsymbol{p}}$ and $s$ while, conversely, in \eqref{SY2} $ss$ and ${\boldsymbol{p}}$ depend on ${\boldsymbol{p}}'$
and $s'$ (through the conservation of energy \eqref{CoE}).
However, once the integrals are split in the zones where $s'$ and, respectively, $s$ are constant, equations \eqref{SY1} and \eqref{SY2}
become a linear system for the unknowns $X_{ss'}$.
For example, assuming ${\delta V} < 0$ one obtains
\begin{equation}
\label{SY}
\left\{
\begin{aligned}
&D_{++} X_{++} + D_{+-} X_{+-} &= H^1_+
\\
-&D_{--} X_{--} &= H^1_-
\\
&D_{++} X_{++} &= H^2_+
\\
-&D_{--} X_{--} - D_{+-} X_{+-} &= H^2_-
\end{aligned}
\right.
\end{equation}
where
$$
\begin{aligned}
&D_{++} = \int\limits_{p_x > 0 \atop v_F\abs{{\boldsymbol{p}}} > \abs{{\delta V}}} \frac{T^1_+ ({\boldsymbol{p}}) L^1_+ ({\boldsymbol{p}})}{\alpha^1_+} \,v_x \,d{\boldsymbol{p}}
= \int\limits_{p'_x > 0} \frac{T^2_+ ({\boldsymbol{p}}') L^2_+ ({\boldsymbol{p}}')}{\alpha^2_+} \,v'_x \,d{\boldsymbol{p}}',
\\[4pt]
&D_{+-} = \int\limits_{p_x > 0 \atop v_F\abs{{\boldsymbol{p}}} < \abs{{\delta V}}} \frac{T^1_+ ({\boldsymbol{p}}) L^1_+ ({\boldsymbol{p}})}{\alpha^1_+}\,v_x \,d{\boldsymbol{p}}
= \int\limits_{p'_x > 0 \atop v_F\abs{{\boldsymbol{p}}'} < \abs{{\delta V}}} \frac{T^2_+ ({\boldsymbol{p}}') L^2_+ ({\boldsymbol{p}}')}{\alpha^2_+} \,v'_x \,d{\boldsymbol{p}}',
\\[4pt]
&D_{--} = \int\limits_{p_x > 0} \frac{T^1_- ({\boldsymbol{p}}) L^1_- ({\boldsymbol{p}})}{\alpha^1_-}\,v_x \,d{\boldsymbol{p}}
= \int\limits_{p'_x > 0 \atop v_F\abs{{\boldsymbol{p}}'} > \abs{{\delta V}}} \frac{T^2_- ({\boldsymbol{p}}') L^2_- ({\boldsymbol{p}}')}{\alpha^2_-} \,v'_x \,d{\boldsymbol{p}}',
\\[4pt]
&H^1_s = \frac{h^2}{\tau}\,j^1_{s,x} - \frac{2}{\tauv_F^2}\int_{p_x>0} \frac{T^1_s({\boldsymbol{p}})L_s^1({\boldsymbol{p}})}{\alpha^1_s}
\left[\alpha^1_s v_x^2 j^1_{s,x} + ss'\alpha^2_{s'} v'_x v_x j^2_{s',x}\right] d{\boldsymbol{p}},
\\[4pt]
&H^2_{s'} = \frac{h^2}{\tau}\,j^2_{s',x} + \frac{2}{\tauv_F^2} \int_{p'_x>0} \frac{T^2_{s'}({\boldsymbol{p}}')L_{s'}^2({\boldsymbol{p}}')}{\alpha^2_{s'}}
\left[\alpha^2_{s'} {v'_x}^2 j^2_{s',x} + ss'\alpha^1_s v_x v'_x j^1_{s,x}\right] d{\boldsymbol{p}}'.
\end{aligned}
$$
Note that the four equations in \eqref{SY} are not independent because the difference of the first two is equal to the difference of
the second two, which can be verified directly by using $v_xd{\boldsymbol{p}} = v'_xd{\boldsymbol{p}}'$ and the flux conservation $j^1_{+,x} - j^1_{-,x} = j^2_{+,x} - j^2_{-,x}$
(or derived from general considerations on the structure of KTC, see the proof of Proposition 3.1 in Ref.\ \cite{BN2018}).
Hence, \eqref{SY} is a rank-3 system for the unknowns $X_{++}$, $X_{+-}$ and $X_{--}$.
The case ${\delta V} = 0$ will be examined in the next subsection.
\par
System \eqref{SY} allows to compute the $X_{ss'}$'s as functions of the currents $j^1_{s,x}$ and the densities $n^1_s$ at the interface
(the latter are ``hidden'' in the terms $L^i_s$ and $\alpha^i_s$).
We now need to relate the asymptotic densities $n^{i,\infty}_s$ to the quantities $X_{ss'}$.
In order to do this, let us consider any function $\theta_s^i$ that satisfies the half-space equation \eqref{MilnEq}.
Integrating in ${\boldsymbol{p}}$ yields
$$
\frac{\partial \bk{v_x\theta_s^i}}{\partial \xi} = 0,
$$
which implies that the current is constant.
Using the fact that $\theta_s^i \to n_s^{i,\infty} L^i_s$ as $\xi \to (-1)^i\infty$ (see Theorem \ref{T1}) we obtain that such constant is zero:
$$
\bk{v_x\theta_s^i} = 0.
$$
Then, multiplying Eq.\ \eqref{MilnEq} by $v_x$ and integrating in ${\boldsymbol{p}}$ yields
$$
\frac{\partial \bk{v_x^2\theta_s^i}}{\partial \xi} = 0,
$$
which means that any solution to \eqref{MilnEq} has constant\footnote{Possibly depending on $y$.} variance.
To evaluate this constant we use again the asymptotics $\theta_s^i \to n_s^{i,\infty} L^i_s$ and the identity \eqref{Lvar},
and finally obtain
\begin{equation}
\label{asyvar}
\bk{v^2_x\theta_s^i} = \frac{1}{h^2} \int v^2_x\theta_s^i\, d{\boldsymbol{p}}= \frac{v_F^2}{2}\,n_s^{i,\infty}.
\end{equation}
Then, let us multiply by $v_x^2$ the first of the two equations \eqref{MilneTC}, written in the form \eqref{MilneTC2},
and integrate with respect to ${\boldsymbol{p}}$ over the inflow range $p_x<0$.
When doing so, note that
$$
\int_{p_x<0} \left[ \theta_s^1({\boldsymbol{p}}) - \theta_s^1({\sim}{\boldsymbol{p}}) \right] v_x^2 \,d{\boldsymbol{p}} =
\int \theta_s^1({\boldsymbol{p}})\, v_x^2 \,d{\boldsymbol{p}} - 2\rho^i_s \int_{p_x>0} L^i_s({\boldsymbol{p}}) \, v_x^2 \,d{\boldsymbol{p}}
$$ $$
\int \theta_s^1({\boldsymbol{p}})\, v_x^2 \,d{\boldsymbol{p}} - \rho^i_s \int L^i_s({\boldsymbol{p}}) \, v_x^2 \,d{\boldsymbol{p}} =
\frac{h^2 v_F^2}{2}\left( n_s^{i,\infty} - \rho^i_s \right).
$$
We obtain in this way
\begin{multline}
\label{SYaux1}
\frac{h^2 v_F^2}{2}\left( n_s^{1,\infty} - \rho^1_s \right) - \int_{p_x>0} \frac{sT^1_s({\boldsymbol{p}})L_s^1({\boldsymbol{p}})}{\alpha^1_s} X_{ss'}\,v_x^2 \,d{\boldsymbol{p}} =
-\frac{4}{\tau v_F^2}\,j^1_{s,x} \int_{p_x>0} L_s^1({\boldsymbol{p}})\,v_x^3 \, d{\boldsymbol{p}}
\\
+ \frac{2}{\tau v_F^2} \int_{p_x>0} \frac{sT^1_s({\boldsymbol{p}})L_s^1({\boldsymbol{p}})}{\alpha^1_s}
\left[s\alpha^1_s v_x^3 j^1_{s,x} + s'\alpha^2_{s'} v'_x v_x^2 j^2_{s',x}\right] d{\boldsymbol{p}}
\end{multline}
(with positive $v'_x$).
Analogously,
\begin{multline}
\label{SYaux2}
\frac{h^2 v_F^2}{2}\left( n_{s'}^{2,\infty} - \rho^2_{s'} \right) + \int_{p'_x>0} \frac{s'T^2_{s'}({\boldsymbol{p}}')L^2_{s'}({\boldsymbol{p}}')}{\alpha^2_{s'}} X_{ss'}\,{v'_x}^2 \,d{\boldsymbol{p}}' =
\frac{4}{\tau v_F^2}\,j^2_{s',x} \int_{p'_x>0} L^2_{s'}({\boldsymbol{p}}')\,{v'_x}^3\, d{\boldsymbol{p}}'
\\
- \frac{2}{\tau v_F^2}\int_{p'_x>0} \frac{s'T^2_{s'}({\boldsymbol{p}}')L^2_{s'}({\boldsymbol{p}})}{\alpha^2_{s'}}
\left[s'\alpha^2_{s'} {v'_x}^3 j^2_{s',x} + s\alpha^1_s v_x {v'_x}^2 j^1_{s,x}\right] d{\boldsymbol{p}}'
\end{multline}
(with positive $v_x$).
Multiplying \eqref{SYaux1} by $\frac{2s\alpha^1_s}{h^2v_F^2}$ and \eqref{SYaux2} by $\frac{2s'\alpha^2_{s'}}{h^2v_F^2}$, and subtracting the former from the latter, we finally obtain
\begin{multline}
\label{Albedo1}
s'\alpha^2_{s'} n_{s'}^{2,\infty} - s\alpha^1_s n_s^{2,\infty}
= X_{ss'}
- \frac{2}{h^2v_F^2} \int_{p_x>0}T^1_s({\boldsymbol{p}})L_s^1({\boldsymbol{p}}) X_{ss'({\boldsymbol{p}})}\,v_x^2 \,d{\boldsymbol{p}}
\\
- \frac{2}{h^2v_F^2} \int_{p'_x>0}T^2_{s'}({\boldsymbol{p}}')L^2_{s'}({\boldsymbol{p}}') X_{s({\boldsymbol{p}}')s'}\,{v'_x}^2 \,d{\boldsymbol{p}}'
+ E_{ss'},
\end{multline}
where
\begin{multline}
\label{Albedo2}
E_{ss'} = \frac{8s\alpha^1_s j^1_{s,x}}{\tau h^2v_F^4} \int_{p_x>0} L_s^1({\boldsymbol{p}})\,v_x^3 \, d{\boldsymbol{p}}
+ \frac{8s' \alpha^2_{s'} j^2_{s',x}}{\tau h^2v_F^4} \int_{p'_x>0} L^2_{s'}({\boldsymbol{p}}')\,{v'_x}^3\, d{\boldsymbol{p}}'
\\
- \frac{4}{\tau h^2 v_F^4} \int_{p_x>0} T^1_s({\boldsymbol{p}})L_s^1({\boldsymbol{p}})
\left[s\alpha^1_s v_x^3 j^1_{s,x} + s'\alpha^2_{s'({\boldsymbol{p}})} v'_x v_x^2 j^2_{s'({\boldsymbol{p}}),x}\right] d{\boldsymbol{p}}
\\
- \frac{4}{\tau h^2 v_F^4} \int_{p'_x>0} T^2_{s'}({\boldsymbol{p}}')L^2_{s'}({\boldsymbol{p}})
\left[s'\alpha^2_{s'} {v'_x}^3 j^2_{s',x} + s\alpha^1_{s({\boldsymbol{p}}')} v_x {v'_x}^2 j^1_{s({\boldsymbol{p}}'),x}\right] d{\boldsymbol{p}}'.
\end{multline}
Note that in the integrals above, in order to avoid possible confusion, we explicitly denoted the dependence of $s'$ on ${\boldsymbol{p}}$ and of $s$ on ${\boldsymbol{p}}'$.
\par
Expressions \eqref{Albedo1} and \eqref{Albedo2} give the term $s'\alpha^2_{s'} n_{s'}^{2,\infty} - s\alpha^1_s n_s^{2,\infty}$ as a function of $j^i_s$, $n^i_s$ and $X_{ss'}$, the latter being given by system \eqref{SY}.
This is exactly the term occurring in the DTC \eqref{DTC1}.
\begin{remark} \rm
A simplified approach, sometimes referred to as the Marshack approximation, consists in stopping the above procedure at the level of Eq.\ \eqref{SY}, and
taking
$$
s'\alpha^2_{s'} n_{s'}^{2,\infty} - s\alpha^1_s n_s^{2,\infty} \approx X_{ss'} \ .
$$
This, of course amounts to approximating $\rho^i_s \approx n_s^{i,\infty}$, which in turn means that the collisions are assumed to be so fast that the distribution attains the asymptotic state very close to $x=0$.
The Marshak approximation can also be considered the first step of a systematic iteration procedure proposed by Golse and Klar \cite{GK95}.
However, numerical experiments suggest that the Marshack approximation can be a very reliable alternative to the more complex
approaches \cite{DEA02}.
\end{remark}
\subsection{The case ${\delta V} = 0$}
\label{S3.2}
If ${\delta V} = 0$, then we only have the cases $s = s' = +1$ and $s = s' = -1$.
Then, the DTC \eqref{DTC} hold in the form $A[n^1_s + \tau n_s^{1,\infty}] = A[n^2_s + \tau n_s^{2,\infty}]$, $s = \pm 1$,
which simply implies
\begin{equation}
\label{DTCV0}
n^1_s -n^2_s = \tau \left( n_s^{2,\infty} - n_s^{1,\infty} \right), \qquad s = \pm 1.
\end{equation}
Note that electrons and holes are completely decoupled by such DTC.
Of course, the electron-hole coupling is still present in the Schr\"odinger equation \eqref{SE} and strongly affects
the scattering coefficients.
\par
When applying the albedo approximation to this case, we have that $D^1_{+-} = 0$ and $H^i_+ = H^i_-$, $i = 1,2$.
Hence, \eqref{SY} is a rank-2 system for the unknowns $X_{++}$ and $X_{--}$, where the first two equations are decoupled
and are equivalent to the second two.
This is readily solved and yields, explicitly,
\begin{equation}
\label{XdV0}
X_{ss} = \frac{2s \alpha^1_s j^1_{s,x} }{v_F} \, \frac{ \displaystyle \frac{h^2}{2} - 2\int_{p_x>0} T^1_{s}({\boldsymbol{p}})L^1_s({\boldsymbol{p}}) \Big(\frac{p_x}{\abs{{\boldsymbol{p}}}}\Big)^2 d{\boldsymbol{p}} }
{\displaystyle \int_{p_x>0} T^1_{s}({\boldsymbol{p}})L^1_s({\boldsymbol{p}}) \frac{p_x}{\abs{{\boldsymbol{p}}}}\,d{\boldsymbol{p}} }
\end{equation}
where we used the fact that ${\boldsymbol{p}}' = {\boldsymbol{p}}$, $\boldsymbol{j}^1_s = \boldsymbol{j}^2_s$ (see \eqref{Jcons2}) and the fact that, at leading order, $A^1_s = A^2_s$,
which in turn implies $\alpha^1_s = \alpha^2_s$.
Note that the above expression is written for the upper index 1 but it is actually equal to the same expression written for the upper index 2.
In the Marshak approximation, \eqref{XdV0} is already the expression for $\alpha^2_s n_s^{2,\infty} - \alpha^1_s n_s^{1,\infty}$ and,
comparing with \eqref{DTCV0}, we obtain therefore
\begin{equation}
\label{MarshakDTC}
n^1_s - n^2_s = s j_{s,x} \vartheta_s,
\qquad s = \pm 1.
\end{equation}
where $j_{s,x} := j^1_{s,x} = j^2_{s,x}$ is the common value of the left and right $x$-current, and
\begin{equation}
\label{qFD}
\vartheta_s := \frac{2}{v_F} \,
\frac{ \displaystyle \frac{h^2}{2} - 2\int_{p_x>0} T^1_{s}({\boldsymbol{p}})L^1_s({\boldsymbol{p}}) \Big(\frac{p_x}{\abs{{\boldsymbol{p}}}}\Big)^2 d{\boldsymbol{p}} }
{\displaystyle\int_{p_x>0} T^1_{s}({\boldsymbol{p}})L^1_s({\boldsymbol{p}}) \frac{p_x}{\abs{{\boldsymbol{p}}}}\,d{\boldsymbol{p}} } .
\end{equation}
The quantity $\vartheta_s$, having the dimensions of an inverse velocity, is the analogous of the ``extrapolation coefficient'' typically arising from kinetic boundary layers
\cite{BBS1984,DEA02,DS98}.
Since, in our case, the boundary layer connects two regions, we shall rather call our $q_s$ an ''interpolation coefficient''.
Let us also remark that the disappearance of $\tau$ in Eq.\ \eqref{MarshakDTC} is not contradictory, since the current $ j^1_{s,x}$ already contains the factor $\tau$ (see
Eq.\ \eqref{SDD}).
\par
The reformulation of the complete albedo approximation \eqref{Albedo1}-\eqref{Albedo2} in the case ${\delta V} = 0$
is just matter of straightforward computations which are not worth to be reported here.
Instead, it can be interesting to examine the form of the DTC in the Maxwell-Boltzmann (M-B) limit, i.e., for high temperatures or low carrier densities.
We first note that such limit is relevant only in the case of negligible ${\delta V}$.
This can be readily seen by considering the leading-order conditions \eqref{DTC0}, which for (e.g.) ${\delta V} < 0$ are
$$
A^1_+ = A^2_+ - q\,{\delta V}, \qquad A^1_+ = - A^2_- - q\,{\delta V}, \qquad A^1_- = A^2_- + q\,{\delta V}.
$$
These three conditions are clearly incompatible with the requirement $A^i_s < 0$, ($s = \pm 1$, $i = 1,2$) which is needed for the
M-B approximation to be valid for both populations on both sides.
The same problem does not arise in the case ${\delta V} = 0$, since the leading-order conditions are
$$
A^1_+ = A^2_+ \qquad A^1_- = A^2_-,
$$
which are compatible with the M-B regime.
\par
From the mathematical point of view the M-B asymptotic regime corresponds to the limit $\beta A^i_s \to -\infty$.
In this limit we have
$$
F^i_s({\boldsymbol{x}},{\boldsymbol{p}}) \approx \mathrm{e}^{-\beta \left[v_F \abs{{\boldsymbol{p}}}-A^i_s({\boldsymbol{x}})\right]}
\qquad \text{and} \qquad
\phi_k(\beta A^i_s) \approx \mathrm{e}^{\beta A^i_s} \approx \frac{n^i_s}{n_0}
$$
(independently on $k$), so that,
\begin{equation}
\label{MBlimit}
F^i_s({\boldsymbol{x}},{\boldsymbol{p}}) \approx n^i_s({\boldsymbol{x}}) M({\boldsymbol{p}})
\qquad \text{and} \qquad
L^i_s ({\boldsymbol{x}},{\boldsymbol{p}}) \approx M({\boldsymbol{p}})
\end{equation}
where
\begin{equation}
M({\boldsymbol{p}}) := \frac{1}{n_0}\,\mathrm{e}^{-\betav_F \abs{{\boldsymbol{p}}}}
\end{equation}
is the ``Maxwellian'' normalized with respect to $\bk{\cdot}$.
Then, the M-B approximations of the drift-diffusion equations \eqref{SDD} and \eqref{SDDA} are, respectively,
\begin{equation}
\label{SDDM}
\DIV \boldsymbol{j}^i_s = 0, \qquad \boldsymbol{j}^i_s = -\frac{\tau v_F^2}{2}\left(\nabla n^i_s - s \beta n^i_s q \nabla U \right)
\end{equation}
and
\begin{equation}
\label{SDDAM}
\DIV \boldsymbol{j}^i_s = 0, \qquad \boldsymbol{j}^i_s = -\frac{\pi \tau}{\beta h^2}\, \mathrm{e}^{\beta A^i_s} \nabla \left( A^i_s - s q U \right),
\end{equation}
while the form of the DTC remains \eqref{DTCV0}.
Moreover, in the Marshak approximation, the DTC still take the form \eqref{MarshakDTC}, but the
interpolation coefficient is now given by
\begin{equation}
\label{qMB}
\vartheta_s = \frac{2}{v_F} \,
\frac{ \displaystyle \frac{h^2}{2} - 2\int_{p_x>0} T^1_{s}({\boldsymbol{p}}) M({\boldsymbol{p}}) \Big(\frac{p_x}{\abs{{\boldsymbol{p}}}}\Big)^2 d{\boldsymbol{p}} }
{\displaystyle\int_{p_x>0} T^1_{s}({\boldsymbol{p}}) M({\boldsymbol{p}}) \frac{p_x}{\abs{{\boldsymbol{p}}}}\,d{\boldsymbol{p}} } .
\end{equation}
\par
A simple way to understand the physical meaning of the interpolation constant is the following.
From \eqref{MarshakDTC} and \eqref{AvsN} we can write
$$
n_0 \phi_2(\beta A^1_s) - n_0 \phi_2(\beta A^2_s) = s j_{s,x} \vartheta_s .
$$
Then, assuming that $A^i_s$ is not too far from the background potential $seV_0$, we can approximate
$$
\phi_2(\beta A^1_s) - \phi_2(\beta A^2_s) \approx \beta \phi_1(s \beta e V_0) ( A^1_s - A^2_s )
$$
(recall that $\phi_1$ is the derivative of $\phi_2$), obtaining therefore
$$
\frac{A^1_s - A^2_s}{j_{s,x}} \approx \frac{s \vartheta_s}{\beta \phi_1(s \beta eV_0)\, n_0}.
$$
We see therefore that $\vartheta_s$ is proportional to the ratio between the potential variation across the barrier
and the current, and so it is a quantity related to the``quantum resistance'' of the barrier.
Let us finally remark that, for small transmission coefficients, the denominator in expression \eqref{qFD} dominates, yielding a Landauer-like (but
corrected with statistics) expression of the conductance \cite{CF2006}.
In general, however, the variance-like term at the numerator of \eqref{qFD} is not negligible.
Such term can be interpreted as a diffusion correction to the Landauer (ballistic) picture.
\section{Device modelling}
\label{S4}
We give an example of application of the above-developed theory to the modelling of a graphene device.
The architecture that we have in mind is that of a ``n-p-n graphene heterojunction'', which is of primary importance for theoretical investigations
as well as for possible technological applications \cite{Huard2007,Osyilmaz2007,YK2009}.
In such devices, a relatively thin potential barrier (the p-region) is obtained as the combined effect of the electrostatic potentials
of a local top gate ({\it tg}) and a background gate ({\it bg}); additional gates correspond to contacts where a potential bias is applied
(see the schematic device pictured in Figure \ref{figura1}).
\begin{figure}
\begin{center}
\includegraphics[width=.6\linewidth]{figure1.eps}
\caption{A schematic picture of a n-p-n graphene device:
the graphene sheet is represented as the black honeycomb (not in scale), the grey regions represent gates and contacts,
and the blue box represents some substrate layer (typically an oxide).}
\label{figura1}
\end{center}
\end{figure}
Let us remark that, since $V$ is a potential barrier, then ${\delta V} = 0$.
We shall make the following assumptions:
\begin{enumerate}
\item
the system is homogeneous in the $y$-direction;
\item
the background potential is high enough so that only the population of electrons contribute significantly to the current;
\item
the electron statistics can be described in the Maxwell-Boltzmann approximation.
\end{enumerate}
These assumptions imply that the drift-diffusion equation for electrons in the classical regions (i.e.\ the n-regions) takes the form
\begin{equation}
\label{DD}
-\frac{\tau v_F^2}{2}\left(\partial_x n^i + \beta n^i \mathcal{E} \right) = j,
\end{equation}
where $j$ is the $x$-component of the current (which is constant all along the device) and, assuming that $U$
is the linear potential determined by the applied bias, $\mathcal{E} = -q\, \partial_x U$ is the corresponding constant electric force.
Note that we have dropped the index $s$, which is equal to $+1$, since holes can be neglected.
\par
Assuming the device length to be $2L$, and the barrier to be located at $x =0$, we have to set boundary conditions at $x = \pm L$
and transmission conditions at $x = 0$.
The boundary conditions are the usual Dirichlet type conditions
\begin{equation}
\label{BC}
n^1(-L) = n_l, \qquad n^1(L) = n_r,
\end{equation}
where $n_l$ and $n_r$ are the electron densities at the left and right contacts, while for the transmission condition we use the Marshak form
\eqref{MarshakDTC}, which, in the simplified notation introduced in this section, reads as follows:
\begin{equation}
\label{STC}
n^1- n^2 = j \vartheta,
\end{equation}
where $\vartheta \equiv \vartheta_+$ is the interpolation coefficient given by Eq.\ \eqref{qMB}.
\par
As a final ingredient we need to choose a model for the barrier and the transmission coefficient.
We assume a, perfectly sharp and flat, rectangular barrier of width $D$ and energy height
\begin{equation}
\label{Ehdef}
E_h = - qc_{\mathit{bg}} V_{\mathit{bg}} -q c_{\mathit{tg}} V_{\mathit{tg}},
\end{equation}
where $V_{\mathit{bg}}$, $V_{\mathit{tg}}$ are the back gate and local gate voltages, and $c_{\mathit{bg}}$, $c_{\mathit{tg}}$,
are suitable constants that relate the gate voltages to the effective electric potential on the graphene surface
(so that the background potential $V_0$ introduced in Sect.\ \ref{S1} is given by $V_0 = c_{\mathit{bg}} V_{\mathit{bg}}$).
Such constants furnish a simplified description of the (more complicated) capacitive coupling between gates, substrates and graphene,
which is widely used in literature, see e.g.\ Refs. \cite{Fang07,TSS2010,YK2009}.
\par
For a such perfectly sharp barrier the transmission coefficient is given by \cite{CastroNeto09,KNG2006}
\begin{equation}
\label{Texpr}
T_s({\boldsymbol{p}}) = \Re\left\{\frac{\cos^2\phi \, \cos^2\phi^*}
{[\cos(Dq_x)\, \cos\phi\, \cos\phi^*]^2 + \sin^2(Dq_x) (1 - ss'\sin\phi\, \sin\phi^*)}
\right\}.
\end{equation}
Here, $\phi$ is the incidence angle, so that $(p_x,p_y) = \abs{{\boldsymbol{p}}} (\cos \phi, \sin\phi)$,
$s' = \mathop{\mathrm{sgn}}(sv_F\abs{{\boldsymbol{p}}} - E_h)$
is the chirality of the electron inside the barrier,
$$
q_x = \sqrt{ \left( \frac{sv_F\abs{{\boldsymbol{p}}} - E_h}{\hbarv_F} \right)^2 -
\left( \frac{p_y}{\hbar}\right)^2}
$$
is the $x$-component of the refracted momentum inside the barrier and
$$
\phi^* = \tan^{-1} \left(\frac{p_y}{\hbar q_x}\right).
$$
is the refraction angle.
Note that $T_s({\boldsymbol{p}})$ is independent on the side-index $i$, for obvious symmetry reasons.
The transmission coefficient \eqref{Texpr} (with $s = +1$) will be used in the expression \eqref{qMB} for $q$.
\par
In Figure \ref{figura2} we represent $T_+({\boldsymbol{p}})$, as a function of the energy $E = v_F\abs{{\boldsymbol{p}}}$ and the incidence angle $\phi$, for
different values of the energy height $E_h$ of the barrier, together with the region which is significant for the integrals in \eqref{qMB}.
It is evident from the figure that changing the value of $E_h$ produces significant variations of the integrals, resulting in variations
of the interpolation coefficient.
\begin{figure}
\begin{center}
\includegraphics[width=.9\linewidth]{figure2.eps}
\caption{Gray-scale plots of $T_+({\boldsymbol{p}})$, as a function of the energy $E = v_F\abs{{\boldsymbol{p}}}$ and of the incidence angle $\phi$, for
different values of the energy height $E_h$. White corresponds to perfect transmission ($T_+ = 1$) and black to total reflection ($T_+ = 0$).
Note that for $\phi = 0$ the barrier is always completely transparent, regardless to $E_h$, which is the
so-called Klein paradox \cite{KNG2006}.
The dashed red line is a contour line of $M({\boldsymbol{p}}) \cos\phi$, corresponding to a region that encompasses approximately
90\% of its integral; such region is therefore where the main contribution to the integrals in \eqref{qMB} comes from
(the same region for $M({\boldsymbol{p}}) \cos^2\phi$ is just slightly narrower). In this figure the barrier width is $50\,\mathrm{nm}$
and the temperature is $40\,\mathrm{K}$. For lower values of the temperature, the Maxwellian will be narrower, resulting in a higher
sensitivity to the variations of $T_+$.}
\label{figura2}
\end{center}
\end{figure}
\subsection{Numerical results}
\label{S4.1}
In order to numerically solve the problem \eqref{DD}-\eqref{BC}-\eqref{STC} we adopt a simple finite-difference scheme that can be
outlined as follows.
Each of the two spatial domains, $[-L,0]$ and $[0,L]$, is decomposed in $N$ cells of length $\Delta x$, labeled with an index $k$, increasing
in the $x$-direction.
The corresponding discretized values of the density are $n^1, n^2, \ldots, n^N$ and in the left region and
$n^{N+1}, n^{N+2}, \ldots, n^{2N}$ in the right region.
The drift-diffusion equation for the is therefore discretized as
\begin{equation}
\frac{n^{k-1}-2n^{k}+n^{k+1}}{\Delta x^2} - \beta \mathcal{E} \frac{n^{k+1}-n^{k-1}}{2\Delta x}=0,
\end{equation}
with $k = 2, \ldots, N-1$, and $k = N+1, \ldots, 2N-1$.
At $x=\pm L$ we impose the Dirichlet boundary conditions \eqref{BC}
\begin{equation}
n^1 = n_l, \qquad n^{2N}=n_r.
\end{equation}
At the interface $x=0$ we need to impose the relation \eqref{STC}.
By approximating the left and right values of the current with, respectively, backward and forward second order finite differences, i.e.
$$
\begin{aligned}
&j^1\approx \frac{n^{N-2}-4n^{N-1}+3n^{N}}{2\Delta x} - \beta\mathcal{E} n^{N} ,
\\[4pt]
&j^2\approx \frac{-3n^{N+1}+4n^{N+2}-n^{N+3}}{2\Delta x} - \beta\mathcal{E} n^{N+1} ,
\end{aligned}
$$
we first write the flux conservation $j^1 = j^2$ as follows:
\begin{equation}
\frac{n^{N-2}-4n^{N-1}+3n^{N}}{2\Delta x} - \beta \mathcal{E} n^{N}
- \frac{-3n^{N+1}+4n^{N+2}-n^{N+3}}{2\Delta x} + \beta\mathcal{E} n^{N+1} =0.
\end{equation}
Then, the transmission condition \eqref{STC} can be written (by using, e.g., $j^2$ for $j$)
\begin{equation}
n^{N}-n^{N+1} - \vartheta \left( \frac{-3n^{N+1}+4n^{N+2}-n^{N+3}}{2\Delta x} - \beta\mathcal{E} n^{N+1} \right) = 0.
\end{equation}
The interpolation constant $\vartheta$ is computed numerically from \eqref{qMB}, as described above,
by means of standard integration routines.
\par
Using the above described model we have computed the conductance as a function of the top gate voltage $V_\mathit{tg}$
for different values of the back gate voltage $V_\mathit{bg}$ and for different values of temperature.
The values of the physical parameters used in our simulations are similar to those of the device described in
Ref.\ \cite{YK2009}, namely $L = 4\,\mu\mathrm{m}$, $D = 0.05\,\mu\mathrm{m}$, $\tau = 0.075\,\mathrm{ps}$.
The bias voltage applied at the contacts is $V_\mathit{bias} = 0.001\,\mathrm{V}$ and the contact width is $1\,\mu\mathrm{m}$
The constant $c_{\mathit{tg}}$ (see Eq.\ \eqref{Ehdef}) has been used as a tuning parameter and has been set to $0.05$.
Then, the value of $c_{\mathit{bg}}$ has been set to $12.8\, c_{\mathit{tg}}$, so to maintain the same ratio between the
corresponding capacitive constants as in Ref.\ \cite{YK2009}.
The values of the densities at the contacts, $n_l$ and $n_r$, has been simply set equal to the background density,
that is
$$
n_l = n_r = n_0\,\phi_2(\beta q c_{\mathit{bg}}V_\mathit{bg})
$$
(however, more refined models for the boundary densities could also be considered, see e.g.\ Ref.\ \cite{LJG2014}).
Finally, the conductance, that is the ratio between the total electric current flowing through the device and the bias voltage,
is expressed in our graphs in units of the ``quantum of conductance'' $q^2/h$.
The total current, is computed from the current density $j$ by assuming a device effective width of $1\,\mu\mathrm{m}$.
\begin{figure}
\begin{center}
\includegraphics[width=\linewidth]{figure3.eps}
\caption{Conductance as a function of the top gate voltage $V_\mathit{tg}$ for different
values of the back gate (left column) and for different values of the temperature (right column).
In the left plots, the temperature is fixed at $T = 10\,\mathrm{K}$ while, in the right plots, the back gate voltage
is fixed at $V_\mathit{tg} = 23\, \mathrm{V}$.
}
\label{figura3}
\end{center}
\end{figure}
\par
The results of the numerical simulations are reported in Figure \ref{figura3}.
In the left column we show plots of the conductance as a function of the top gate voltage $V_\mathit{tg}$ for different
values of the back gate, at a fixed temperature $T = 10\,\mathrm{K}$.
We see that, as long as
$E_h = -qc_{\mathit{bg}} V_{\mathit{bg}} -qc_{\mathit{tg}} V_{\mathit{tg}} > 0$ (correponding to the ``n-p-n'' case),
the conductance shows Fabry-Perot-like oscillations whose amplitude and period of the same order of those
reported in the experimental literature \cite{YK2009}.
The oscillations are followed by sudden rise as $E_h$ approaches 0 (which is also observed in the experiments \cite{Huard2007,YK2009}).
The shift towards the left of the point $E_h = 0$ for increasing $V_{\mathit{bg}}$
is also typical of experimental observation and is an obvious consequence of the relation between
$E_h$, $V_{\mathit{bg}}$ and $V_{\mathit{tg}}$.
Moreover, still in accordance with experimental measurements, the conductance oscillates around around a mean value that increases, approximately linearly, with $V_\mathit{bg}$.
\par
In the right column are shown plots of the conductance as a function of the top gate voltage $V_\mathit{tg}$ for different
values of the temperature, at a fixed back gate voltage $V_{\mathit{bg}} = 23\,\mathrm{V}$.
We see that the amplitude of the Fabry-Perot oscillations strongly decreases by increasing temperature,
as reported from experiments \cite{YK2009}.
A simple explanation of the latter phenomenon is apparent from Fig.\ \ref{figura2}: decreasing the temperature makes the Maxwellian
narrower thus making the interpolation constant $\vartheta$ more sensitive to the variations of the transmission coefficient.
\section{Conclusions}
\label{S5}
In this paper we have shown how the theory of diffusive transmission boundary conditions at a quantum interface,
developed in Ref.\ \cite{BN2018} and summarised in Section \ref{S2} of the present paper,
can be applied for the numerical simulation of a heterojunction graphene device.
To this aim, we also had to expand the theoretical part in order to simplify the kinetic step, represented by the solution of a four-fold Milne problem.
In fact, the asymptotic densities associated to the solution of such Milne problem provide the interpolation constant, which is the key ingredient in the
formulation of the transmission conditions.
This has been done in Sec.\ \ref{S3}, where explicit expressions of the asymptotic densities have been obtained assuming of very short collision times.
\par
The material developed in Secs.\ \ref{S2} and \ref{S3} is then used in Sec.\ \ref{S4} to set up a mathematical model of a generic ``n-p-n'' graphene device,
with some additional simplifying assumptions (above all the fact that the devices works in a regime where only the electron population is relevant and where
the Maxwell-Boltzmann statistics can be used instead of the Fermi-Dirac one).
Indeed, our simulations are intended to illustrate the method and its potentialities, rather than to faithfully reproduce a specific device in a specific regime.
\par
In spite of all these simplifications, the numerical simulations reported in Sec.\ \ref{S4.1} show that the model is able to reproduce some important features
of the electron transport in n-p-n graphene heterojunctions (see Figure \ref{figura3}).
In particular, we observe the Fabry-Perot oscillations of the conductance, which are the signature of quantum interference inside the barrier and of the chiral
nature of the electrons in graphene.
Such oscillations have the expected behaviour with respect to the variations of the gate voltages as well as to the variations of temperature.
Still in accordance with laboratory observations, the conductance has a sudden increase when the barrier height
$E_h$ approaches zero.
\par
A feature that our simulations are unable to describe is the behaviour of the conductance when the barrier height
$E_h$ enters the negative range (the ``n-n-n'' case).
In fact, when $E_h$ becomes negative, experiments show that the conductance, after the sudden jump described above,
keeps on increasing
(more slowly) and oscillations disappear.
Instead, our simulations predict a new decrease of the conductance
and new oscillations (not shown in the figure).
We believe that this fault is due to the ideal model of perfectly sharp barrier that we adopted.
On the other hand, the theoretical models adopted in Refs.\ \cite{Huard2007,YK2009} are also unable to describe such behaviour
(neither are the other models in literature we are aware of).
Probably, more refined descriptions of the barrier, requiring however a numerical solution of the scattering problem \eqref{SE}, could permit
to reproduce correctly the behaviour of the device across the entire range of $E_h$.
\par
Discrepancies of the overall values of the conductivity with respect to those observed in experiments
are mainly due to the oversimplified model for the mobility that we are using, which is not suited to accurately describe the great
variety of experimental devices.
However, as remarked above, since the aim of this paper is mainly to illustrate the mathematical method of quantum transmission conditions, rather
than to simulate a particular device, we preferred to use a simple model for the bulk transport and to focus on the treatment
of the quantum interface.
Of course, a more detailed description of the electron scattering \cite{CocoEtAl19,Morandi11,MajoranaNastasiRomano19},
more refined expressions for the mobility \cite{NastasiRomano19,NR20b}, a self-consistent potential model \cite{NR20a,NR20b}
or even quantum drift-diffusion equations \cite{LucaRomano19,Romano07,ZB11},
could be used to improve the model (see also Ref.\ \cite{CMR2020} for a general reference).
\section*{Acknowledgements}
All authors acknowledge support from French-Italian University "Galileo" project
{\it Classical and quantum kinetic models and their hydrodynamic limits: theoretical and applied aspects} (Ref. G18\_296).
G.N. acknowledges support from ``Progetto Giovani'' of the italian National Group for Mathematical Physics - GNFM 2019 {\it Modelli matematici, numerici e simulazione del trasporto di cariche e fononi nel grafene}.
Support is also acknowledged from Universit\`a degli Studi di Catania, "Piano della Ricerca 2016/2018 Linea di intervento 2".
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 952
|
\section*{Acknowledgements}
The experiments were supported by the JSPS Fellowship for Research in Japan Program, Grants-in-Aid for Scientific Research of the JSPS and the International Science Linkages (ISL) Program of the Australian Academy of Science. M.O. received support from Progetto di Ricerca d'Ateneo CSTO160004 and the ``Departments of Excellence 2018--2022'' Grant awarded by the Italian Ministry of Education, University and Research (MIUR, L.232/2016). A.A. and A.T. acknowledge support from the Air-Sea-Ice Lab Project. M.O. is grateful Dr. B. Giulinico for discussions.
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 5,960
|
Livin' Lovin' Rockin' Rollin': The 25th Anniversary Collection is a three-disc box set chronicling the career of country music band Alabama. It contains 51 tracks, dating from their earliest days as a recording act in 1973 through September 2000.
The box set was issued to commemorate Alabama's 25 years of national fame, even though their first national hit was released in 1977 and their first major hit came in 1980. During that time, Alabama had sold millions of albums, won countless awards from the Country Music Association and Academy of Country Music, and had had a major influence in both bringing groups and bands into the country music mainstream and in the styles of later successful groups, including Lonestar and Rascal Flatts.
Many of the songs on this collection are of Alabama's biggest hits, including a majority of their 32 No. 1 songs (as determined by Billboard magazine'''s Hot Country Singles & Tracks chart). However, as Allmusic reviewer Stephen Thomas Erlewine pointed out, The 25th Anniversary Collection was intended "as an aural biography of a band". Several of the hit titles are presented here either as live concert recordings or taken from alternate takes.[]
In addition to the three compact discs, The 25th Anniversary Collection'' includes a booklet containing photographs, a biography by Nashville journalist Robert K. Oermann and comments from band members.
Track listing
Disc 1
"My Home's in Alabama" (Teddy Gentry, Randy Owen) — 8:20C
"40 Hour Week (For a Livin')" (Dave Loggins, Don Schlitz, Lisa Silver) — 3:24
"Medley: That Silver-Haired Daddy of Mine / Suppertime / Teach Your Children / Don't It Make You Want to Go Home" (Gene Autry, Jimmy Long / Ira Stanphill / Graham Nash / Joe South) — 7:09AC
"High Cotton" (Scott Anders, Roger Murrah) — 3:01
"Mountain Music" (Owen) — 4:13
"Dixieland Delight" (Ronnie Rogers) — 5:18C
"Caroline Mountain Dewe" (Owen) — 4:25
"Roll On (Eighteen Wheeler)" (Loggins) — 4:26
"If You're Gonna Play in Texas (You Gotta Have a Fiddle in the Band)" (Murry Kellum, Dan Mitchell) — 3:42C
"Christmas in Dixie" (Jeff Cook, Gentry, Mark Herndon, Owen) — 3:42
"I Write a Little" (Cook, Owen, Rogers) — 4:18
"Song of the South" (Bob McDill) — 3:11
"Pass It On Down" (Gentry, Owen, Will Robinson, Rogers) — 4:54
"Five O'Clock 500" (Gentry, Owen, Rogers) — 3:38
"Tar Top" (Owen) — 5:23AC
"Dancin', Shaggin' on the Boulevard" (Greg Fowler, Gentry, Owen) — 4:43
Disc 2
"Feels So Right" (Owen) — 3:37
"Old Flame" (Donny Lowery, Mac McAnally) — 3:12
"Lady Down on Love" (Owen) — 3:58
"Very Special Love" (Gentry, Owen) — 4:45
"Close Enough to Perfect" (Carl Chambers) — 3:34
"Take Me Down" (Mark Gray, J.P. Pennington) — 4:53
"Medley: Deep River Woman / When We Make Love" (Lionel Richie / Troy Seals, Mentor Williams) — 4:21AC
"Face to Face" (alternate take) (Owen) — 3:03A
"'You've Got' the Touch" (John Jarrard, Lisa Palas, Robinson) — 4:16
"You Turn Me On" (Gentry, Owen) — 3:10
"Forever's as Far as I'll Go" (Mike Reid) — 3:37
"How Do You Fall in Love" (Fowler, Gentry, Owen) — 3:00
"I Just Couldn't Say No" (Fowler, Gentry, Owen) — 4:35
"Too Much Love" (Fowler, Owen) — 3:57
"If I Had You" (Chater, Mayo) — 3:35
"The Woman He Loves" (Seals, Setser) — 3:55
"God Must Have Spent a Little More Time on You" (Rogers, Sturken) — 4:41
"Angels Among Us" (Vocal Remix) (Don Goodman, Becky Hobbs) — 4:07
Disc 3
"Tennessee River" (Owen) — 7:53C
"Vacation" (Owen) — 5:19AC
"She and I" (Loggins) — 5:17
"Sad Lookin' Moon" (Fowler, Gentry, Owen) — 3:33
"Give Me One More Shot" (Gentry, Owen, Rogers) — 3:32
"Fallin' Again" (Fowler, Gentry, Owen) — 4:00B
"I'm in a Hurry (And Don't Know Why)" (Murrah, Randy Van Warmer) — 2:49
"Can't Keep a Good Man Down" (Bob Corbin) — 3:45C
"If It Ain't Dixie (It Won't Do)" (Jarrard, Robbins) — 6:42AC
"The Cheap Seats" (Hummon, Sharp) — 3:54
"Gonna Have a Party" (Channel, Cochran, Kane) — 4:59AC
"When It All Goes South" (Carnes, Carnes, Jarvis) — 6:57
"Down Home" (Bowles, Leo) — 3:29
"Born Country" (Byron Hill, John Schweers) — 3:18
"Ripperly O' Tucke" (demo) (Owen) — 3:21A
"Hats Off" (Fowler, Gentry, Owen, Rogers) — 3:56
"The Fans" (Fowler, Gentry, Owen) — 4:53
A Previously unreleased.
B Single edit.
C Live recording.
Personnel
Alabama
Jeff Cook- fiddle, electric guitar, vocals
Teddy Gentry- bass guitar, vocals
Mark Herndon- drums, percussion
Randy Owen- lead vocals, background vocals
Additional Musicians
Mark Casstevens- acoustic guitar
Don Cook- background vocals
Debbie Datz Pyle- string contractor
Steve Dorff- conductor, string arrangements
Larry Franklin- fiddle
John Barlow Jarvis- Hammond B-3 organ, piano
Brent Mason- 6-string bass guitar, 12-string electric guitar, electric guitar, gut string guitar
The Music Team- string contractors
Steve Nathan- keyboards
Lonnie Wilson- drums, percussion
Chart performance
References
Alabama (band) compilation albums
2006 compilation albums
RCA Records compilation albums
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 8,417
|
{"url":"http:\/\/wordpress.mrreid.org\/tag\/mathematics\/","text":"# One Million Hats\n\nFrom the always-excellent\u00a0Futility Closet, a problem by Paul J. Nahin:\n\nEach of a million people puts his or her hat into a very large box. Each hat has its owner\u2019s name on it. The box is given a good shaking, and then each person, one after another, randomly draws a hat out of the box. What is the probability that at least one person gets their own hat back?\n\nMost people might think that the chance is very, very small, but it\u2019s not. It\u2019s actually more than\u00a060%. How can this be true?\n\nWe can view this problem as having only two possible solutions (events): either\u00a0nobody gets their hat back, or\u00a0at least one person gets their hat back. The sum of the probabilities of these events must\u00a0be equal to one and therefore if we can work out the probability that\u00a0nobody gets their own hat back, then the probability that at least one person does is one minus that.\n\nFor each person, there is only a one-in-a-million chance that they have picked their own hat, and thus a 999999 in 1000000 chance that they have\u00a0not got their own hat.\n\n$\\Pr \\left( \\textnormal{one incorrect hat} \\right) = \\frac{999999}{1000000}$\n\n$\\Pr \\left( \\textnormal{one million incorrect hats} \\right) = \\left( \\frac{999999}{1000000} \\right)^{1000000}$\n\n$\\Pr \\left( \\textnormal{one million incorrect hats} \\right) = 0.368$\n\nIf the probability of all one million people picking the incorrect hat in 0.368, then via our previous reasoning, the probability of at least one person picking the correct hat is 1-0.368, or 63.2%.\n\nThis is a very counterintuitive result, but the wording of the question is key. If we changed the wording to\u00a0exactly one person getting their hat back then our answer changes dramatically. Starting with our 63.2% chance, we would have to subtract the chance of two people getting their hats back, and of three people getting their hats back, and so on \u2026 until we reached the very small chance of one person, and one person only, getting their hat back.\n\n# Fixed Area, Infinite Perimeter\n\nThe Koch Snowflake (named after its inventor, the Swedish mathematician Helge von Koch) is a fractal with\u00a0a number of interesting properties.\n\nThe first four generations of the Koch Snowflake\n\nAs the number of generations increases, the area of the snowflake increases, but it increases towards a limit: eight-fifths of the size of the first (triangular) generation. This is because each additional generation adds three triangles which are one-ninth the size of the triangle added in the previous generation (for a total increase of one-third), and the additional of increasingly small triangles has a lesser and lesser effect on the overall area as the number of generations increases.\n\nBut as the number of generations increases, the perimeter of the shape continues to grow, without approaching a limit: each generation of the Snowflake has a perimeter which is four-thirds of the previous generation\u2019s perimeter. This is because the additional perimeter added each time is\u00a0four times one-third of the length of each side, for a total increase of four-thirds, as opposed to the one-third increase in area. Because four-thirds is greater than one, the perimeter\u00a0tends to infinity, whereas the area (which at one-third is less than one) does not.\n\nAs you can see from the graph above, the area approaches its limit very quickly, whereas the perimeter grows very quickly (which is why it has to be shown on a different axis).\n\n# Dot Product and Cross Product\n\nThere is more than one way to multiply two numbers together.\n\nNormal everyday multiplication (e.g. $3 \\times 4 = 12$) isn\u2019t always good enough for physics. If we want to multiply two vectors (quantities that have both size and direction) like force or velocity, then the direction of those vectors matters. The result of a 3 N force multiplied by a 4 N force will depend on their relative directions: if they are pointing in the same direction we will get a different answer to if they are at right angles to each other.\n\nWhen multiplying two vectors, physicists use one of two products: the dot product or\u00a0the cross product. Both the moment of a force (the torque) and the work done by a force are calculated by finding the product of a\u00a0force and a distance, but calculating work done uses the dot product and calculating the moment of a force uses the cross product.\n\nThe dot product yields a scalar answer, an answer that does not have a direction.\u00a0Work done is a scalar quantity, and\u00a0doesn\u2019t have a direction, hence the use of the dot product.\u00a0The cross product yields a vector answer, which does have a direction (if you\u2019ve ever used Fleming\u2019s Left Hand rule to find the\u00a0force acting on a current-carrying wire in a magnetic field you\u2019ve found\u00a0the cross product of those two vectors).\u00a0The moment of a force does have a direction, hence the use of the cross product.\n\nUnlike \u201cnormal\u201d multiplication and the dot product, the cross product is not commutative, i.e. it matters in which order you multiply quantities. If we\u00a0find the cross product of \u00a0two forces, $\\mathbf{A}$ and $\\mathbf{B}$ then we will get a different answer to than if we had found the cross product of $\\mathbf{B}$ and\u00a0$\\mathbf{A}$, i.e. $\\mathbf{A} \\times \\mathbf{B} \\ne \\mathbf{B} \\times \\mathbf{A}$. This makes sense when you consider the vector nature of the cross product: a vector to the right multiplied by a vector upwards shouldn\u2019t produce the same result as a vector upwards multiplied by a vector to the right: the result has the same magnitude, but points in a different (opposite) direction.\n\n# Ranking Things Properly\n\nI keep seeing things ranked improperly, so here is how to do it right.\n\nImagine that we have six candidates for an exam, and they score as follows. Ranking these candidates is very easy.\n\n Name Score Rank Abel 90% 1 Bohr 80% 2 Curie 70% 3 Dirac 60% 4 Einstein 50% 5 Feynman 40% 6\n\nBut what if two candidates have the same score? The correct way of ranking is to give both of these candidates the same rank, but then the next rank is one place lower. In the example below, Abel and Bohr both score 90% and are therefore ranked in first place; Curie then remains in third place, rather than being elevated to second.\n\n Name Score Rank Abel 90% 1 Bohr 90% 1 Curie 70% 3 Dirac 60% 4 Einstein 50% 5 Feynman 40% 6\n\nThis prevents a situation in which we have six participants, but the person with the lowest score is\u00a0ranked fifth. If more than two participants have the same score, or if this situation occurs more than once, the same rule is applied.\n\n Name Score Rank Abel 90% 1 Bohr 90% 1 Curie 90% 1 Dirac 60% 4 Einstein 60% 4 Feynman 40% 6\n\n# Integer Sequences\n\nNumber can be broken up into many groups. Some of these groups have specific uses (for example, prime numbers are very important in cryptography) and some are just interesting for existing in the first place.\n\nThe natural numbers\u00a0are what you might call \u201ccounting numbers\u201d: 1, 2, 3, 4,\u00a0\u2026\u00a0. Whether or not zero is included in the natural numbers is a matter of some discussion, and there doesn\u2019t seem to be a\u00a0consensus either way. The natural numbers does not include the negative integers, as it is not possible to have \u201cminus one apples\u201d or \u201cminus two cars\u201d.\n\nThe rational numbers are those that can be expressed as a simple fraction: $\\frac{p}{q}$. Because $latex q$ can equal one, the rational numbers necessarily include\u00a0the natural numbers, but also every possible other fraction:\u00a0$\\frac{1}{2}$$\\frac{3}{4}$, $\\frac{27}{31}$\u00a0and so on. The irrational numbers are those that cannot be expressed as fractions: $e$, $\\pi$, $\\sqrt{2}$, \u2026 and\u00a0repeat indefinitely after their decimal points.\n\nThe square numbers are those that are the square of an integer: 1, 4, 9, 16, \u2026 . The cube numbers are those that are the cube of an integer: 1, 8, 27, 64 \u2026 . This process continues with $x^4$, $x^5$, and so on.\n\nThe prime numbers are those that are divisible only by one and themselves: 2, 3, 5, 7, \u2026 . The Mersenne primes are those prime numbers that are expressible as $2^n - 1$, one less than a power of two: 3, 7, 31, 127, \u2026 . Sphenic numbers are the product of three primes: 30, 42, 66, 70, \u2026 . The semiprimes are natural numbers that can be expressed as the product of two prime numbers: 4, 6, 9, 10, \u2026 . There are also almost primes which are then the product of three primes, four primes, and so on. The composite numbers\u00a0are those numbers that have a divisor\u00a0other than one and itself, thus they are the set of numbers that are\u00a0not prime.\n\nPerfect\u00a0numbers\u00a0are numbers that are the sum of their divisors:\u00a06, 28, 496, 8128, \u2026 .\u00a06 is \u00a0a perfect number because the factors of 6 are 1, 2 and 3, and the sum of 1, 2 and 3 is 6, and so on. A number is semiperfect if it is equal to the sum of\u00a0some of its divisors: 6, 12, 18, 20, \u2026\u00a0, whereas an untouchable number is a number that cannot be expressed as the sum of the divisors of\u00a0any number: 2, 5, 52, 88, \u2026 . That is, there is no number whose divisors sum to 2, or to 5, or to 52, etc.\n\nAbundant numbers are numbers\u00a0whose divisors sum to a total greater than itself: 12, 18, 20, 24, \u2026 .\u00a0For example, 12 is abundant because the divisors of 12 are 1, 2, 3, 4 and 6 which sum to 16 (i.e. the abundance of 12 is 4 and its abundancy is 12\/4 or 3). Friendly numbers are\u00a0pairs of numbers with the same abundancy: for example the abundancy of both 30 and 140 is 12\/5 and therefore 30 and 140 form a friendly pair. Amicable numbers are pairs of numbers where the sum of the divisors of one number is equal to the other and vice versa. For example, 220 and 284 are amicable because the divisors of 220 add up to 284 and the divisors of 284 add up to 220. This concept can be expanded to the sociable numbers\u00a0where each is part of a \u201cloop\u201d that arrives back at the first number (i.e. amicable numbers are sociable numbers with a period\u00a0of two). \u00a0At the moment there are many\u00a0known sequences of\u00a0four amicable numbers, but far fewer with periods longer than this.\n\nWeird numbers are those that are abundant but not semiperfect: 70, 836, 4030, 5830, \u2026 . The sum of their divisors is greater than the number itself, but no subset of their divisors add up to the number itself.\n\nThere are many, many other groups of numbers. Wikipedia is a good place to start looking for them.","date":"2019-02-16 10:20:16","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 19, \"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\": 0.7897543907165527, \"perplexity\": 395.5665148266858}, \"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\/1550247480240.25\/warc\/CC-MAIN-20190216085312-20190216111312-00334.warc.gz\"}"}
| null | null |
Home » US News » Appalachian State University student confirmed with mumps
Appalachian State University student confirmed with mumps
On Friday, Appalachian District Health Department and Appalachian State University confirmed one case of mumps in an Appalachian State University student.
Mumps/THD
The individual diagnosed with the virus is being treated, and actions are in effect to minimize contact with this person, per guidelines established by the State of North Carolina and the Centers for Disease Control.
Appalachian State University, AppHealthCare and the North Carolina Division of Public Health are working together to investigate this case and prevent the spread of mumps.
Dr. Robert Ellison, director of Appalachian State Unversity's Student Health Service stated, "Appalachian State University is working in close partnership with AppHealthCare and the North Carolina Division of Public Health to investigate this case and prevent the spread of mumps. We want to reassure our campus and community that this virus is spread through close contact like kissing, drinking after someone else, coughing or sneezing. The ill student has been cooperative in staying home while ill as we have instructed."
Public Health Director for AppHealthCare Beth Lovette commented, "We appreciate the partnership with Appalachian State University in our collaborative efforts to help address this single mumps case and take necessary steps to reduce the potential spread of disease to others. It is a good reminder for all of us that the best prevention is to be fully immunized. While there is a vaccine to protect against this disease, usually given as part of the mumps, measles, and rubella (MMR) vaccine, its effectiveness can wane over time. The recommended two doses of the vaccine provide approximately 88 percent protection against infection. A single dose of the vaccine provides approximately 78 percent protection, according to the U.S. Centers for Disease Control and Prevention. Together, we are continuing to monitor this situation closely in consultation with the North Carolina Division of Public Health Communicable Disease team."
Below is information regarding mumps exposure, in order for community members to be informed about symptoms. Members of the community are encouraged to promptly report suspected mumps cases to their primary care physicians.
Those exhibiting any of the symptoms listed below should take precautionary steps to limit contact with others.
Typhoid outbreak plateaus? Family, church releases statement
Florida: Dead bat found in packaged salad prompts investigation, recall
Ho Chi Minh City reports 1st pertussis case
Sweden continues to reports high levels of Campylobacter
Meningitis C outbreak in Nigeria continues to rise rapidly
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 6,876
|
Q: Unity3d LoadFromCacheOrDownload downloads existing bundle For downloading bundles I'm using LoadFromCacheOrDownload. It's works fine, but when I'm trying load bundle from cache, it start downloads bundle with same version again.
I'm look at Unity cache folder and found cached bundle(by resources name), but it still want to downlaod bundle.
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 3
|
\section{Introduction}
Today the exponential growth rate of data poses new and difficult challenges for data storage, management, and analytics. Labels attached to files describing their relevance or category provide significant assistance with the later handling and use of the data, for instance to optimize storage systems and policies \cite{IEEEISCAS:cognitive}, or to derive further insights by using the labelled datasets to train machine-learning algorithms. The growth rate of the data, and the associated level of resources it consumes, allow neither manual classification of the files, nor further resource-consuming classification systems. The main challenge can therefore be formulated as finding an efficient data classification system for application in environments with limited resources.
\par Data is typically organized in files of various types (e.g. picture, text, etc.). Files are associated with metadata, available in terms of key-value pairs, consisting of metadata fields and their values. Here we consider file classification based on metadata, where by metadata we mean not only file-system information, but in general features that can be obtained by analyzing the content of a file \cite{IEEEISCAS:keyvalue_pairs}. Various models have been developed to find near-optimal solutions for data classification. The most powerful classification models today rely on neural networks. Artificial neural networks (ANNs) have achieved excellent results in many applications. However, ANNs that require high-precision arithmetic are in general inefficient in terms of power consumption. SNNs \cite{IEEEISCAS:SNNs}\cite{IEEEISCAS:SNNs_intro} rely on sequences of spikes (ones and zeros) rather than continuous values for neuronal communication and are thus significantly more efficient than other ANNs\cite{IEEEISCAS:SNN_efficiency}. Moreover, SNNs are particularly attractive when inputs are sparse and asynchronous, and when learning must be on-line and lifelong. This is the case in data management systems, as the files to be classified are often asynchronously ingested. Furthermore, efficient temporal encoding schemes could sparsify large streams of files, while in certain cases the learning must continue for the classification of new files.
\par In this paper, we propose a file classification system using SNNs, where the relevant information contained in key-value metadata pairs is mapped by a novel correlative temporal encoding scheme to spike patterns. The key-value pairs representation together with the proposed encoding scheme make this system well suited for handling the issue of different file types at the input. We investigate possible trade-offs between classification accuracy and implementation complexity. Firstly, we consider unsupervised or supervised training based on spike-timing-dependent plasticity (STDP), a biologically plausible rule that allows efficient learning. Then we focus on backpropagation-based supervised training, where the error signal is obtained by comparing the spike pattern at the output neurons with a target pattern representing the desired class. Furthermore, we introduce an efficient overall system architecture relying on memristive crossbar arrays for the realization of neuronal connectivity. Simulation results are presented for various publicly available data sets. The accuracy obtained with file classifier SNNs and synaptic weights realized by memristive crossbar arrays is compared with that achieved by other learning algorithms, including logistic regression and support-vector machines (SVM).
\section{System Architecture}
Figure 1 illustrates the proposed overall file classification system based on SNNs. We consider an input file set $\mathcal{D}$, where each element from $\mathcal{D}$ is described with \textit{K} feature values $[f_1, f_2, ... f_K]$, also referred to as key-value pairs, from a set $\mathcal{S}$. The objective is to classify each file in $\mathcal{D}$ to one of \textit{M} classes from a set $\mathcal{C} = \{c_1, c_2, ... c_M\}$.
In general, each feature can be either categorical or numerical, whereas classes are discrete and do not imply an order. The classification task consists in inferring the class of an element in $\mathcal{D}$ given its feature values.
\begin{figure*}[!t]
\centering
\subfloat{\includegraphics[width=18cm]{figures/image001.pdf}%
\label{fig_system}}
\caption{Architecture of the proposed file classification system based on SNNs. Information from the input files of the input set $\mathcal{D}$ is obtained in two steps: (a) mapping input files to the set of key-value pairs and (b) encoding of key-value pairs to spike patterns using a correlative time encoding (CTE) scheme. The encoded input spike pattern is then (c) sent to the input of an SNN which classifies the file to one of the \textit{M} classes in set $\mathcal{C}$.
}
\end{figure*}
\subsection{Correlative Time Encoding (CTE)}
The spike communication brings energy efficiency to SNNs, however it is necessary to encode input files into input spike patterns and to decode output spike patterns into classes (Figure \ref{fig_temporal_encoding}). The information from each input file can be encoded into the rate of neuron spiking (\textit{rate encoding}) or into the precise timing of action potential (\textit{temporal encoding}) \cite{IEEEISCAS:thesisEncoding} (Figure 2(a)). The SNN produces an output spike pattern (Figure 2(b)). In case the output of the SNN is \textit{rate encoded} the class is predicted from a neuron that spikes with highest rate. In case of \textit{time encoded} output, for each class the target output pattern is predetermined. During training we attempt to induce spikes at those precise instants. The class is predicted as target spike pattern which is closest to the output spike pattern, using the \textit{van Rossum} distance metric \cite{IEEEISCAS:vanRossum}.
\par In \cite{IEEEISCAS:gardner} the input spike pattern was generated using \textit{temporal encoding}, where every neuron generates spikes as a random Poisson process. It was demonstrated that with such input encoding, the trained SNNs are able to reliably classify around 200 input spike patterns with 10 output classes. Other temporal encoding schemes were presented in \cite{IEEEISCAS:CTEbackground}\cite{IEEEISCAS:CTEbackground1}\cite{IEEEISCAS:CTEbackground2}.
\par When generating temporally encoded input spike patterns, we would like to translate similarities among the input files into the correlation of input spike patterns. Under the assumption that similar input files are often sharing the same class, this should facilitate the learning task for a neural network and improve the classification accuracy for input data sets that are larger than a few hundred files.
\begin{figure}[!thbp]
\centering
\includegraphics[width=8.7cm]{figures/input_output.pdf}
\caption{An example of encoding in SNN: (a) input spike pattern for all input neurons and (b) output spike pattern for one output neuron.}
\label{fig_temporal_encoding}
\end{figure}
Therefore, we propose a correlative temporal encoding (CTE) scheme, described as follows:
\begin{itemize}
\item for a given input file, metadata keys and corresponding values
are identified;
\item each key $k$ is associated with a set of input neurons $n_k$ of the SNN; those neurons generate spikes at pseudo-random time instants, depending on the value the key assumes for the given input file;
\item the input spiking neurons are fixed for a given key and pseudo-random spike patterns are fixed for a given key-value pair.
\end{itemize}
\begin{figure}[!thbp]
\centering
\includegraphics[width=8.7cm]{figures/fig_cte_example.pdf}
\caption{An example of encoding two image input files using proposed CTE scheme. The two images are described with key-value pairs which are identical (both pictures are taken \textit{the same day}, of \textit{the same object}, etc.) except the one key-value pair describing the time of the day the picture was taken (\textit{day} or \textit{night}). Identical pseudo-random spike patterns correspond to the same key-value pairs (neurons 0-80). The neurons generating the input for the key describing the time of the day (neurons 81-100) are going to generate different pseudo-random spike patterns (red points).}
\label{fig_cte_example}
\end{figure} In CTE, same key-value pairs imply the same spike patterns. Therefore, the similarity among input files due to the same key-value pairs is translated into the correlation (inner product) between input spike patterns. An example of CTE for two input image files is given in Figure \ref{fig_cte_example}.
\subsection{Learning in SNNs}
We investigate three learning algorithms in conjunction with CTE to train file classifier SNNs: the STDP learning rule \cite{IEEEISCAS:STDP}\cite{IEEEISCAS:STDPhebb}\cite{IEEEISCAS:inhibition}\cite{IEEEISCAS:STDPdiehl} and two variants of the backpropagation algorithm \cite{IEEEISCAS:backpropagation}\cite{IEEEISCAS:SNN_deeplearning}\cite{IEEEISCAS:SNNs_backprop1}, one probabilistic and one deterministic.
For STDP we assume the leaky-integrate-and-fire (LIF) neuron model and rate encoded output, while both backpropagation algorithms rely on time encoded target spike patterns. \\
Probabilistic backpropagation proposed in \cite{IEEEISCAS:gardner} assumes a spike response neuron model (SRM) \cite{IEEEISCAS:SRM} (a generalization of the LIF model). A neuron fires with probability $\rho(u)=1/(1+e^{(-\beta u)})$, given membrane potential \textit{u} and parameter $\beta$. The membrane potential at time instant $t$ of a postsynaptic neuron $j$ that receives input signals from presynaptic neurons $n$ is:
\begin{equation}
u_j(t) = \sum_{n}{w_{jn}(\mathcal{Y}_n \ast \epsilon)(t) + (\mathcal{Z}_j \ast \kappa)(t)},
\end{equation}
where $w_{jn}$ is the synaptic weight between neurons $n$ and $j$, $(\mathcal{Y}_n \ast \epsilon)(t)$ and $(\mathcal{Z}_j \ast \kappa)(t)$ denote convolution between a spike sequence and a postsynaptic potential (PSP) kernel $\epsilon$ and reset kernel $\kappa$, respectively, and where a spike sequence is given by a sequence of delta functions, $\mathcal{Y}_n(t) = \sum_{f}{\delta(t - t_n^f)}$. During the training process, the log-likelihood of target output patterns given output spike patterns from the SNN is maximized.\\
Deterministic backpropagation is proposed in \cite{IEEEISCAS:snu}, where the neuron behavior is described by two discrete-time equations:
\begin{equation}
\label{eq:SNU_LIF_DISCR}
\begin{array}{l}
s_t = g(Wx_t + l(\tau)\odot s_{t-1}\odot (1-y_{t-1}))\\
y_t = h(s_t + b),
\end{array}
\end{equation}
where $x_t$ is the input, $s_t$ is the vector of internal state variables and $y_t$ is the output vector. Furthermore, $W$ is a synaptic weight matrix, $l(\tau)$ is a \textit{leaky} parameter, \textit{g} and \textit{h} are activation functions, $b$ is a bias implementing the spiking threshold and $\odot$ is the element-wise product. It is shown in \cite{IEEEISCAS:snu} that such spiking neural unit (SNU) is mimicking the behaviour of the LIF model. During the training at each time step $t$ the binary cross-entropy loss between the neuron output and the target signal representing the desired class is minimized.
\begin{figure*}[!thbp]
\centering
\subfloat{\includegraphics[width=16cm]{figures/conductance.pdf}%
\label{fig_crossbar}}
\caption{(a) Neuronal connectivity implemented using memristive crossbar array, and (b) the conductance noise as a function of the programmed conductance value based on experimental measurements from 10,000 PCM devices from a prototype chip; the solid line represents the least squares fitting second-order polynomial to the data.}
\end{figure*}
\subsection {Implemented Models}
To investigate system performance and possible trade-offs with complexity of implementation, we consider the following CTE-based SNN models and learning techniques:
\begin{itemize}
\item System 1: one-layer SNN with unsupervised or supervised STDP learning;
\item System 2: one and two-layer SNNs, with probabilistic backpropagation \cite{IEEEISCAS:gardner};
\item System 3: multi-layer SNNs, with determininstic backpropagation \cite{IEEEISCAS:snu}.
\end{itemize}
\subsection {Efficient Realization Using Memristive Synapses}
Recently, memristive devices \cite{Y2015wongNatureNano}\cite{Y2011chuaAPA} have been proposed as candidates for efficient realization of synaptic weights in ANNs and SNNs \cite{IEEEISCAS:memristive}\cite{IEEEISCAS:memristive1}. Memristive devices when organized in a crossbar array can be used to realize the neuronal connectivity in different layers of the SNNs, as shown in Figure 4(a). The devices represent the synaptic weights in terms of their conductance values and the synaptic efficacy can be emulated by exploiting the Ohm's and Kirchhoff's laws \cite{IEEEISCAS:memristive2}\cite{Y2013kuzumNanotechnology}. Typically, two devices organized in a differential configuration are used to represent the positive and negative synaptic weights \cite{Y2012bichlerTED}. Phase change memory (PCM) devices \cite{Y2016burrJETCAS} are arguably the most advanced memristive devices and are particularly well suited for synaptic realizations \cite{Y2018boybatNatComm}\cite{Y2016tumaEDL}, owing to their ease of programmability and low-power consumption. However, there are non negligible conductance variations associated with each programmed conductance value \cite{Y2019joshiArXiv}\cite{Y2019sebastianVLSI}. We experimentally characterized the achievable conductance values and the associated conductance variations for mushroom-type PCM devices fabricated in the 90nm technology node (see Figure 4(b)). In Section III, we will investigate the impact of these conductance variations on the performance of the file classification system.
\section{Simulation Results}
We select four data sets from the \textit{UCI Machine Learning Repository} for classification tasks \cite{IEEEISCAS:UCIcar}\cite{IEEEISCAS:UCInursery}\cite{IEEEISCAS:UCIincome}\cite{IEEEISCAS:UCIcf} to train and test the proposed system.
\subsection{Baseline Models}
As baseline models, we consider standard logistic regression and SVM with a non-linear radial basis function (RBF) kernel. The two machine learning algorithms receive a non-temporal data to the input. The key-value pairs are categorical features (keys) represented as a one-hot encoded feature vector.
\subsection{Comparative Study}
A comparison between the classification accuracy achieved by the three models introduced in Section 2 and the baseline algorithms is given in Table \ref{tab_software_results}.
\begin{figure}[!thbp]
\centering
\includegraphics[width=8.7cm]{figures/spiking_example.pdf}
\caption{(a) Target spike patterns for 3 classes and (b) output of the SNN for different input elements after training; classes are distinguished by color.}
\label{fig_snn_output}
\end{figure}
\begin{table}[!t]
\renewcommand{\arraystretch}{1.3}
\caption{Simulation Results for Different Data Sets.}
\label{tab_software_results}
\centering
\begin{tabular}{|c||c||c||c||c|}
\hline
Model&Adult&Nursery&Car&Connect\\
&Income&School&Evaluation&Four\\
\hline
Log. Reg. &85.2\%& 93\%& 86.3\%& 75.6\%\\
\hline
SVM (RBF) &85.3\%&98.8\%&92.2\%&77.7\%\\
\hline
STDP unsup. &&&&\\
rate encoded &77.5\%& 67.2\%& 50.5\%& 64.9\%\\
\hline
STDP unsup. &77.8\%& 70.3\%& 59.6\%& 65.8\%\\
\hline
STDP sup. &75.6\%& 73.7\%& 70.2\%& 65.8\%\\
\hline
Probab. BackProp. &&&&\\
one layer &72.9\%& 73.9\%& 65.5\%& 59.8\%\\
\hline
Probab. BackProp. &&&&\\
two layers &79.2\%& 88.4\%& 87.7\%&64.5\%\\
\hline
Determ. BackProp. &&&&\\
two layers &85.4\%& 99.6\%& 96.7\%&74.4\%\\
\hline
Determ. BackProp. &&&&\\
five layers &85.7\%& 99.3\%& 97\%&73.6\%\\
\hline
\end{tabular}
\end{table}
\fnbelowfloat
The high efficiency of the unsupervised or supervised STDP in \textit{System 1} may justify a trade-off in performance compared to the backpropagation-based algorithms. Moreover, the classification accuracy achieved even via unsupervised learning is respectable enough to envisage a continuously learning file classifier based on SNNs. For \textit{System 2}, the performance of a two-layer model is significantly better than the one-layer model, even though the derivation of the weight update rule involves larger approximations \cite{IEEEISCAS:gardner}. \textit{System 3} shows the best accuracy overall. This is thanks to the update rule obtained by the adopted backpropagation through time \cite{IEEEISCAS:snu}, which does not require the approximations of the probabilistic approach. Figure 5 shows the target spike patterns for \textit{System 3} and the achieved outputs. The results obtained for that system are close to or even surpassing logistic regression and non-linear SVM performance.
\par We remark that the ability to obtain high accuracy for data sets with tens of thousands of elements was only possible owing to the introduction of the CTE scheme.
\subsection{Simulation Results on Memristive Synaptic Realization}
In order to evaluate the performance of the proposed system in hardware we resort to a hardware simulator. In particular, we focus on the two-layer model trained with deterministic backpropagation, which gives good performance with relatively low complexity.
With reference to Figure 4, assuming the model has already been trained in software and stored, the implementation of the hardware simulator includes:
\begin{itemize}
\item scaling the weights to conductance range [0$\mu$S, 25$\mu$S]
\item scaling the output of a crossbar to 8-bits ([-127, 127])
\item scaling the 8-bit value back to the ranges that were obtained from the training data
\item adding the noise that originates from different sources to the conductance values (weights)
\end{itemize}
\par In Table \ref{tab_results_hardware} the results of inference on the hardware simulator are given, for various values of the conductance-dependent noise standard deviation. It can be seen that there is hardly any drop in classification accuracy when implemented using existing PCM devices. Moreover, these networks are found to be robust to even much higher levels of conductance variations.
\begin{table}[!thbp]
\renewcommand{\arraystretch}{1.3}
\caption{Inference Results with Hardware Simulator.}
\label{tab_results_hardware}
\centering
\begin{tabular}{|c||c||c||c||c|}
\hline
Model&Adult&Nursery&Car&Connect\\
&Income&School&Eval.&Four\\
\hline
Software &85.4\%& 99.6\%& 96.7\%&74.4\%\\
\hline
HW (st. dev. = $\sigma$) &85.1\%& 99.4\%& 97\%&73.5\%\\
\hline
HW (st. dev. = 5 * $\sigma$)&81.6\%& 93.8\%& 93.2\%&69.6\%\\
\hline
HW (st. dev. = 10 * $\sigma$) &70.6\%& 73.1\%& 80.9\%&44.4\%\\
\hline
\end{tabular}
\end{table}
\section{Conclusion}
This paper introduces an SNN-based system to perform file classification with limited resources. We investigated different learning algorithms, models and configurations and evaluated their classification accuracy. We proposed a novel CTE scheme to map input elements that share same key-value pairs in the original data set to correlated input patterns, which leads to significantly improved performance. The classification accuracy achieved by deterministic backpropagation together with CTE is found to be comparable to, and even surpassing, that of logistic regression and non-linear SVM. In addition, we simulated a full system including hardware synapses implemented as memristive devices. Simulation results indicate that the hardware implementation of the system using memristive arrays wouldn't significantly affect performance. The presented work suggests that real time classification of asynchronously injested files could be a promising application for SNNs, especially if implemented efficiently using memristive hardware.
\newpage
\bibliographystyle{IEEEtran}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 3,044
|
Harriet Sohmers Zwerling's 1950's Paris Love Affair with Susan Sontag
(A nude of Harriet Sohmers Zwerling, which is the cover of her book)
Harriet Sohmers Zwerling was born in New York City in 1928. At 17 she was a student at Washington Square College, NYU. After classes she started frequenting the San Remo Cafe on MacDougal Street, a hangout for writers, artists and bohemians, including the crime photographer Weegee, the author Anatole Broyard, and the poet Max Bodenheim.
Harriet transferred to avant-garde Black Mountain College where she had her first lesbian relationship with the painter Peggy Tolk-Watkins who convinced her to move out to San Francisco. Enrolling at Berkeley in 1949, she was working at the university bookstore when a beautiful olive-skinned girl walked in...16-year old Susan Sontag. Approaching young Susan with a copy of Djuna Barnes' "Nightwood", a lesbian classic, she asked, "Have you read this?" She had ,and Harriet became her first lover, an event chronicled in Susan's early diaries, "Reborn" published in 2008.
In 1950 Harriet moved to Paris where she had many lovers and adventures. She worked at the International Herald Tribune, published three stories in New Story magazine and translated the novel Les Infortunes de la Vertue by the Marquis de Sade for the famous Obelisk Press. In 1957 Susan Sontag was on a Fulbright in Oxford. By this time she had married her professor and had a son. Abandoning the Fulbright, she came to Paris and moved in with her ex-lover Harriet. Harriet was still reeling from the end of a passionate love affair with Maria Irene Fornes, a seductive Cuban-American and later a famous playwright.
The sexual affair that Harriet and Susan rekindled in Paris was ambiguous and tumultuous, and even occasionally violent. Susan returned to the States in August 1958. In 1959, Harriet went back to New York, initially living with Susan until Susan broke off the relationship because she had fallen in love with Fornes. It was Irene's betrayal that devastated Harriet and led her to give up homosexuality for good.
Harriet fled New York for Provincetown where she became involved with the poet Bill Ward, who was just launching his literary journal, The Provincetown Review. Harriet became an editor just in time for the controversial 1961 "tralala" issue, which contained a chapter from Hubert Selby Jr.'s novel, "Last Exit to Brooklyn." Ward was arrested on obscenity charges but they were overturned at trial with an all-star defense witness panel, including Norman Mailer.
During the early 60's Harriet worked as a nude model in New York and even as a "Beatnik for Rent". She met and got involved with a merchant seaman named Louis Zwerling, married him, and had her son, MiloZ, now a well-known musician.
For 28 years Harriet taught in a New York City public school in Greenpoint, Brooklyn. After she retired, she published "Notes of a Nude Model", (Spuyten Duyvil Press, 2003), autobiographical stories that chronicle her wild youth in New York City. This book put her back on the literary map. She has starred in the documentary "Still Doing It" in 2004, about older women and sex. In 2010, she appeared in the documentary, "Norman Mailer the American."
Here is part of an excerpt from Harriet Sohmers Zwerling's "Expatriate Diaries", originally published in the Brooklyn Rail, November 2006.
Brooklyn Rail
Memories of Sontag: From an Ex-Pat's Diary
by Harriet Sohmers Zwerling
Susan Sontag is coming to Paris next week—Will it be good to see her?
(Susan and I met in 1949 in Berkeley where she, a sixteen-year old prodigy, was auditing classes. I was in my junior year at the university, working at a bookstore to support myself and in love with Peggy Tolk-Watkins, my first lesbian lover, who owned a jazz bar in Sausalito called The Tin Angel. Susan and I connected and I initiated her into the world of women lovers, by which she was already fascinated. Before I left for Paris in 1950 she came to visit me in New York and we renewed our relationship. She went to the University of Chicago, married her professor and had a son, David. In 1957, she came to Oxford on a Fulbright fellowship and contacted me through the Herald Tribune where I worked. She relinquished her Fulbright and stayed with me in Paris for nearly a year.
Susan is here. What a beauty she is! But, sadly, I dislike so much about her—the way she sings, girlish and tuneless; the way she dances, phony-sexy and unrhythmic. I was annoyed with her (poor kid) for having an upset stomach at the Eiffel Tower and especially at the Cinematheque last night. Does she attract me at all? I really don't think so, but then, she says she loves me, and I certainly need to hear that!
Saw Han the other night with his German painter friend, Reinhard—a very attractive man.
Have had no word from Irene.[ed.'s note: Maria Irene Fornes, the playwright and later Sontag's lover.]
I may still love Romaine; think of her constantly.
Susan's vulnerability and insecurity annoy me. She seems so naive, so easily flattered. Is she too honest? No, no, I can't believe she really means what she says.
(Harriet, Pont Neuf, 1950)
Irene, Irene—my real and only love. Last night in bed with Susan I said, "Move up, move up, pupi," and shocked us both with my old pet name for her. And I wept but tried not to let S. see so she wouldn't comfort me, as she did, by throwing her big body over me protectively. How heavy, how brusque she is!
I haven't written about my visit to Dublin where my sister is living. I had sex there with an Irish actor named Charley Roberts, very male and charming, who kept his socks on in bed. (It's cold in Dublin). My sister's lover Paddy is an exciting man but so afraid of feeling; he won't be good for her in the end.
What shall I do about Susan? Just lie back and enjoy being loved? But my sick jealousy is already starting. Everyone wants her, men and women, and although I don't really care about her, my envy reflex is still there. We are moving to the Poitou, my old hotel. Probably a mistake.
I don't like her smell. Bobbie said, "That's more important than anything else."
Blessed solitude! Susan has gone back to England for a week. Yesterday I felt a bit lonely but today I am enjoying being by myself again. I am back here in Irene's room which is mine now. Moving into the Poitou with S. was painful. My pitiful brain rejoiced at the memories and balked at being there without Irene, with someone else. But here in this room I am happy, recalling our crazy afternoons of sex when we just at the last minute remembered to turn off a light or pull a curtain…
Here's a description of Charley Roberts whom I slept with in Dublin. Long greasy black hair, very Spanish, slicked back with occasional loose locks hanging down around his very white face. A big American Indian nose, small thin crooked spitty mouth, dark shifty wicked eyes. When dressed up, wears a rather grubby red wool vest, dandyish, and a dirty shirt with a removable celluloid collar…Never removes his socks; feet seriously stink! Best sex I've had in a long time—The stove is not working right—it's freezing!
I'm working hard on the translation, a way to gain my freedom, at least from the job. But how free can I be with this choice of burdens: loneliness or Susan! I am already dreading the thought of our travel plans, of being with her in cities where I don't know anyone. I don't think I have ever been in such an absurd situation. At least with Sven there was sometimes good sex and the security of being with a man in social situations. I've never before lived with someone I neither desired sexually nor felt strongly about. It's so decadent! I feel terrible about it all, brooding depression—
Just a few more days at the Herald Trib. Susan and I are living in a flat borrowed from Sam Wolfenstein. It's great to be in an apartment, but it also means that she never lets me out of her sight. What will happen when I am no longer working at night? Will she stop seeing other people and spend twenty-four hours a day with me? Our sexual relationship is really bad. When I do, infrequently, make love to her, I am either drunk and totally incompetent or technical, brutal, and cold. It's hideous of me but what can I do? I am simply not attracted to her. Even her tenderness repels me; her tentative touch, so unreal.
Today I had a date at the Flore with a Negro man who stood me up. Susan insisted on coming with me in the Metro; she's going to the Deux Magots. I guess it serves me right that he didn't show, but I had really been looking forward to getting fucked!
The bottom line is, I think, that I'm really fed up with women. Susan is more relaxed than she was but still so quick to take offense, so vulnerable. Those anxious eyes probing my slightest mood remind me annoyingly of my mother!
At the flea market today I was aware of how totally I dominate her. If I picked up some buttons, looked at a doll, pointed out a necklace; she immediately enthused. "Oh, I like that! Oh, they're the prettiest!" That over-eager desire to please is pathetic. I simply must do something about this relationship. It is hurtful to her and makes me feel guilty. Even as I write this, I worry that she might come in. What a coward I am! I should have simply sent her packing. Soon she will leave and then I'll suffer through my usual abandonment anxiety all over again.
April 3, Sevilla, Spain, Holy Week
We just got here after two days in Madrid. Now I sit on the bed in the typical dim Spanish electric light. Susan is under the covers with her eyes closed. Music comes up through the open patio doors from the fonda downstairs. We've just been to watch a Semana Santa procession. The crowds are noisy and detached, as if they were at a movie. But it is tremendously moving to me. To add to the pathos, a saeta (lament) rose up from a corner of the square. My eyes overflowed, watching the penitentes in their pointed hoods, their wind-stirred gowns, bare, bloody feet; some with chains clanking on their ankles; some carrying heavy wooden crosses or the gaudy candle-lit figures of saints in velvet and gold. Susan drives me mad with her long explanations of things one only needs the eyes and the sensitivity of someone like Irene to see. She discoursed on Bosch at the Prado and was just now explaining that women are the main support of the Church. She launches into these textbook dissertations, like footnotes, which I find unbearable.
(Susan Sontag in Sevilla)
Of course, being here, I can't get Irene out of my thoughts. That was inevitable, given this language, these streets and tapas bars, these beautiful small plump Spanish girls with their gorgeous round asses. I was wretched in Madrid, felt ill and off balance. It's better here. But God, when I remember the awful fights we used to have and realize how patient I am with S., who is a far greater nuisance! It's a measure of my weakness and dependency.
April 30, Paris
In the Jardins du Luxembourg on a bright warm day. The gardeners are spraying something onto the grass. The sun is so real; it is melting down all my terrors, longings, boredom.
Oh, I wish Susan would go away; she bores and depresses me. Strangely, Bobbie is becoming a good influence; she is so alive now, especially sexually; she inspires me.
Irene is living her new life in NY and forgetting me. I am forgetting her too. Not exactly forgetting, but the remembering is becoming a sort of option. I'm not forced to do it as I used to be.
(Harriet Sohmers and Irene Fornes in the 1950s)
It's her birthday and I haven't heard from her in weeks. In spite of what I wrote above, I can't really forget her and am terribly dragged with Susan. Yesterday, she said she was moving out. If only I had the strength and the money to let her go instead of weakly saying, "I'd rather you didn't," which she only too eagerly seized upon as an invitation to stay.
We're living in the Hotel Ste. Marie Gallia , a charming place. I love the dark wood floors and the patronne and the polite, gentle maids. Last night, because I had told her it was Irene's birthday, Susan came to me in the dark bed and we made sweet love. But I just don't love her.
June 7 Berlin
It is seven years since my first trip here and the city has changed enormously. This afternoon I lay in the sun by a stream in Tiergarten, now rich and fruitful, not like the wasteland it was in 1950. I've been really cold to S. for the past three days until sex this morning broke the deadlock. Why am I taking my frustrations out on her? Some of it is jealousy; she gets so much more attention than I do. Not her fault. But I pick on her annoying little mannerisms like, "As you know, VW's are very popular in the States,"
"As you know, of course, etc—" It's mean and petty of me to attack her awkward use of her hands when she speaks. I shouldn't be taking out my helpless furies on her!
June 23 Paris
Being on the whore street at night with Susan and Reinhard, alternating malaise and enjoyment. Mainly anxiety. Susan's terrible beauty eclipses me totally. How I wish she were not my only source of love—back here there's a letter from Barbara Bank (none from Irene). She says, "Irene has probably written you that I am coming to Europe, etc. Feel very warm and good towards you"—Sure, now that Irene has left me!
July 16 Athens
In the white room on Evripidou Street, late afternoon. I lie naked on the white bed. Out the window is the ruined roofscape, crumbling buildings with their innards exposed, a swatch of wallpaper, a corner of vanished floor. The trolley car goes roaring by. Much talking and shouting in the street. The heat gets me very sexed-up but there's nothing to do about it. At least, when she's not here I can enjoy my fantasies.
I am being awful to Susan as always. This morning, when she asked why I was "angry," I said, "I just can't stand seeing you twenty-four hours a day!" and she answered mildly, "It won't be much longer," which is true and made me feel even meaner. Now she's gone up to the Parthenon and I'm enjoying the cooling of the day. I like the food here—rice pudding for breakfast, fish and salad for lunch in the workmen's tavernas. Yesterday I had a plate with one stuffed zucchini, one stuffed pepper and one stuffed eggplant. Lovely subtle differences between them.
Just a thought; could I live here? I like the men.
July 25 Hydra
Another island in my life. I sit at the cafe on the windswept quay in bright sunshine.…Susan has gone to Athens to see about money. Our landlord just rushed out screaming for two hundred drachmas. What a fright! He probably saw Susan leaving and thought we were trying to pull a fast one. Or did he really need the money, as he shouted?
I stretched dinner out as long as I could. Now I'm at the cafe sitting not too close to the foreign in-crowd… I don't intend to be depressed. In fact, I feel better than I usually do when S. is here. She has a way of making me feel isolated, alone with her. God knows, though, this group is repulsive.
Susan is leaving soon. I suppose I will miss her, probably more than I did Irene, since we were already estranged before she left. Susan truly surrounds me with affection. Too bad I can't enjoy it and am always rejecting and criticizing. I should be grateful for these nine months with her. Maybe I will be some time. I often feel a certain tenderness towards her, like today, when she left. She really is such a child, and though she can be annoying, her warmth is a child's, her sulking and suffering too.
August 12 Athens
It's our last night here. Evripidou Street is quiet, except for the occasional rumble of a late tram…Barbara Bank is here and gave me a tiny bouquet of wonderful white perfumed jasmine. She insists on talking about Irene, causing me much anguish. Susan takes it well, after her first neurotic protest. Barbara kissed me, stroking my face, promising to write me in Paris. "Judas kiss", said Susan, correctly.
August 26 Paris
Susan left three days ago and, wonder of wonders, I am suddenly surrounded by men. Surprise! There is sex on every corner—the Negro on Saturday, the painter on Sunday, and this big handsome perverse man named Henri whose looks kill me! He is like a dark version of the actor Peter van Eyk, complete with scar on his lip.
Poor darling Susan; how little I miss you!
Harriet Sohmers Zwerling is the author of Notes of a Nude Model.
Labels: Harriet Sohmers Zwerling, Notes of a Nude Model, Paris 1950s, Susan Sontag
Harriet Sohmers Zwerling's 1950's Paris Love Affai...
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 4,299
|
public class threads_001 {
public static void main(String[] args) {
//double t0 = System.currentTimeMillis();
long acc = 0;
int L = 10000000;
int n = 2 * L;
for (int i = 0; i <= n; ++i) acc += i;
//double t1 = System.currentTimeMillis();
//System.out.println("Time elapsed single-thread version Java: " + (t1 - t0) / 1000);
System.out.println("Java");
System.out.println(acc);
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 8,003
|
# Copyright
William Collins
An imprint of HarperCollins _Publishers_
1 London Bridge Street
London SE1 9GF
www.WilliamCollinsBooks.com
This eBook first published in Great Britain by William Collins in 2018
Copyright © Adam Zamoyski 2018
Cover photograph © Getty Images
Adam Zamoyski asserts the moral right to be identified as the author of this work
Maps by Martin Brown
A catalogue record for this book is available from the British Library
All rights reserved under International and Pan-American Copyright Conventions. By payment of the required fees, you have been granted the non-exclusive, non-transferable right to access and read the text of this e-book on-screen. No part of this text may be reproduced, transmitted, down-loaded, decompiled, reverse engineered, or stored in or introduced into any information storage and retrieval system, in any form or by any means, whether electronic or mechanical, now known or hereinafter invented, without the express written permission of HarperCollins.
Source ISBN: 9780008116071
Ebook Edition © October 2018 ISBN: 9780008116088
Version: 2018-08-28
# Dedication
In memory
of
GILLON AITKEN
# Contents
_Cover_
_Title Page_
_Copyright_
_Dedication_
List of Illustrations
List of Maps
Family Tree
Map
Preface
1 A Reluctant Messiah
2 Insular Dreams
3 Boy Soldier
4 Freedom
5 Corsica
6 France or Corsica
7 The Jacobin
8 Adolescent Loves
9 General Vendémiaire
10 Italy
11 Lodi
12 Victory and Legend
13 Master of Italy
14 Eastern Promise
15 Egypt
16 Plague
17 The Saviour
18 Fog
19 The Consul
20 Consolidation
21 Marengo
22 Caesar
23 Peace
24 The Liberator of Europe
25 His Consular Majesty
26 Towards Empire
27 Napoleon I
28 Austerlitz
29 The Emperor of the West
30 Master of Europe
31 The Sun Emperor
32 The Emperor of the East
33 The Cost of Power
34 Apotheosis
35 Apogee
36 Blinding Power
37 The Rubicon
38 Nemesis
39 Hollow Victories
40 Last Chance
41 The Wounded Lion
42 Rejection
43 The Outlaw
44 A Crown of Thorns
Notes
Picture Section
Bibliography
Index
_Also by Adam Zamoyski_
_About the Author_
_About the Publisher_
# Illustrations
Napoleon's mother Letizia Bonaparte in 1800, by Jean-Baptiste Greuze. _(Granger Historical Picture Archive/Alamy Stock Photo)_
Two sketches of Bonaparte by Jacques-Louis David. _(Sketches of Napoleon Bonaparte, 1797 (pencil), David, Jacques-Louis (1748–1825)/Musée d'Art et d'Histoire, Palais Massena, Nice, France/Bridgeman Images)_
Bonaparte during the Italian campaign of 1796, by Giuseppe Longhi. _(Paul Fearn/Alamy Stock Photo)_
Bonaparte leading his troops across the bridge at Arcole, by Antoine-Jean Gros. _(Photo by Universal History Archive/Getty Images)_
Bonaparte in 1797, by Francesco Cossia. _(Photo by Fine Art Images/Heritage Images/Getty Images)_
Josephine Bonaparte in 1797, by Andrea Appiani. _(ART Collection/Alamy Stock Photo)_
Auguste Marmont, by Georges Rouget. _(Wikimedia Commons)_
Andoche Junot, by David. _(© President and Fellows of Harvard College)_
Joachim Murat. _(ART Collection/Alamy Stock Photo)_
Josephine's son Eugène de Beauharnais, by Gros. _(Hirarchivum Press/Alamy Stock Photo)_
Napoleon's younger sister Pauline, by Jean Jacques Thérésa de Lusse. _(flickr/lost gallery/Pauline Bonaparte, Princess Borghese/De Lusse/CC by 2.0)_
Bonaparte visiting plague victims at Jaffa during his Syrian campaign, by Gros. _(Photo by Archiv Gerstenberg/ullstein bild via Getty Images)_
Joseph Bonaparte. _(Photo by Stefano Bianchetti/CORBIS/Corbis via Getty Images)_
Jean-Baptiste Bernadotte, by Nicolas Joseph Jouy. _(Heritage Image Partnership Ltd/Alamy Stock Photo)_
Napoleon's younger brother Lucien, by François-Xavier Fabre, c.1808. _(ART Collection/Alamy Stock Photo)_
Bonaparte in 1800, by Louis Léopold Boilly. _(Napoleon Bonaparte (1769–1821) Premier Consul (oil on canvas), Boilly, Louis Léopold (1761–1845)/Private Collection/Archives Charmet/Bridgeman Images)_
The house in the rue de la Victoire. _(Photo 12/Alamy Stock Photo)_
The Tuileries, c.1860. _(Photo by LL/Roger Viollet/Getty Images)_
Jean-Jacques-Régis Cambacérès, by Greuze, 1805. _(Cambacérès/Photo © CCI/Bridgeman Images)_
Charles-Maurice de Talleyrand in 1804, by David. _(Photo Josse/Leemage/Corbis via Getty Images)_
Joseph Fouché. _(Portrait of Joseph Fouché (1759–1820) Duke of Otranto, 1813 (oil on canvas), French School, (19th century)/Château de Versailles, France/Bridgeman Images)_
Josephine's daughter Hortense de Beauharnais, by François Gérard. _(Paul Fearn/Alamy Stock Photo)_
The Château of Malmaison, by Henri Courvoisier-Voisin. _(Photo Josse/Leemage/Corbis via Getty Images)_
Napoleon's younger brother Louis in 1809, by Charles Howard Hodges. _(Photo by Fine Art Images/Heritage Images/Getty Images)_
Napoleon crossing the Alps in 1802, by David. _(Photo by GraphicaArtis/Getty Images)_
The Emperor Napoleon I in 1805, by David. _(Photo Josse/Leemage/Corbis via Getty Images)_
A fragment of David's painting of the coronation, showing Joseph, Louis, Napoleon's three sisters, Hortense and her son Napoléon-Charles. _(Photo Josse/Leemage/Corbis via Getty Images)_
Napoleon's youngest brother Jérôme, 1805. _(Courtesy of the Maryland Historical Society, xx.5.52)_
Napoleon at Eylau, by Gros _(Photo by Universal History Archive/Getty Images)_
Marshal Jean Lannes, by Gérard. _(Photo by Fine Art Images/Heritage Images/Getty Images)_
General Armand de Caulaincourt, sketched in 1805 by David. _(Portrait of Armand Augustin Louis. Marquis de Caulaincourt (1772–1827) (pencil on paper) (b/w photo), David, Jacques Louis (1748–1825)/Musée des Beaux-Arts, Besancon, France/Bridgeman Images)_
General Géraud-Christophe Duroc, by Anne-Louis Girodet-Trioson. _(Portrait of Duroc, Grand Marshal of the Palace (oil on canvas), Girodet de Roucy-Trioson, Anne Louis (1767–1824)/Musée Bonnat, Bayonne, France/Bridgeman Images)_
Napoleon I in 1806, by Jean-Auguste-Dominique Ingres. _(Photo Josse/Leemage/Corbis via Getty Images)_
View of the proposed palace for the King of Rome, by Pierre-François Fontaine. _(From Projets d'architecture, plan number 32, France, 19th century/De Agostini Picture Library/Bridgeman Images)_
Napoleon _en famille_ , by Alexandre Menjaud. _(Napoleon I (1769–1821), Marie Louise (1791–1847) and the King of Rome (1811–73) 1812 (oil on canvas), Menjaud, Alexandre (1773–1832)/Château de Versailles, France/Bridgeman Images)_
Napoleon in early 1812, by David. _(Photo by Ann Ronan Pictures/Print Collector/Getty Images)_
Napoleon on the bridge of HMS _Bellerophon_ , by Charles Lock Eastlake, 1815. _(Granger Historical Picture Archive/Alamy Stock Photo)_
The house at Longwood on St Helena, where Napoleon spent his last years. _(Photo by The Print Collector/Getty Images)_
Napoleon on St Helena, 1820. _(Paul Fearn/Alamy Stock Photo)_
# Maps
Europe in 1792
Toulon
The Italian theatre
Montenotte
Lodi
The pursuit
Castiglione
Würmser outmanoeuvred
Arcole
Rivoli
The march on Vienna
The settlement of Campo Formio
Egypt
Europe in 1800
Marengo
Ulm
Austerlitz
The campaigns of 1806–07
Europe in 1808
Aspern–Essling
Wagram
Europe in 1812
The invasion of Russia
Borodino
The Berezina
The Saxon campaign, 1813
The defence of France in 1814
The Waterloo campaign
# Family Tree
# Map
# Preface
A Polish home, English schools, and holidays with French cousins exposed me from an early age to violently conflicting visions of Napoleon – as godlike genius, Romantic avatar, evil monster or just nasty little dictator. In this crossfire of fantasy and prejudice I developed an empathy with each of these views without being able to agree with any of them.
Napoleon was a man, and while I understand how others have done, I can see nothing superhuman about him. Although he did exhibit some extraordinary qualities, he was in many ways a very ordinary man. I find it difficult to credit genius to someone who, for all his many triumphs, presided over the worst (and entirely self-inflicted) disaster in military history and single-handedly destroyed the great enterprise he and others had toiled so hard to construct. He was undoubtedly a brilliant tactician, as one would expect of a clever operator from a small-town background. But he was no strategist, as his miserable end attests.
Nor was Napoleon an evil monster. He could be as selfish and violent as the next man, but there is no evidence of him wishing to inflict suffering gratuitously. His motives were on the whole praiseworthy, and his ambition no greater than that of contemporaries such as Alexander I of Russia, Wellington, Nelson, Metternich, Blücher, Bernadotte and many more. What made his ambition so exceptional was the scope it was accorded by circumstance.
On hearing the news of his death, the Austrian dramatist Franz Grillparzer wrote a poem on the subject. He had been a student in Vienna when Napoleon bombarded the city in 1809, so he had no reason to like him, but in the poem he admits that while he cannot love him, he cannot bring himself to hate him; according to Grillparzer, Napoleon was but the visible symptom of the sickness of the times, and as such bore the blame for the sins of all. There is much truth in this view.
In the half-century before Napoleon came to power, a titanic struggle for dominion saw the British acquire Canada, large swathes of India, a string of colonies, and aspire to lay down the law at sea; Austria grab provinces in Italy and Poland; Prussia increase in size by two-thirds; and Russia push her frontier 600 kilometres into Europe and occupy large areas of Central Asia, Siberia and Alaska, laying claims as far afield as California. Yet George III, Maria Theresa, Frederick William II and Catherine II are not generally accused of being megalomaniac monsters and compulsive warmongers.
Napoleon is frequently condemned for his invasion of Egypt, while the British occupation which followed, designed to guarantee colonial monopoly over India, is not. He is regularly blamed for re-establishing slavery in Martinique, while Britain applied it in its colonies for a further thirty years, and every other colonial power for several decades after that. His use of police surveillance and censorship is also regularly reproved, even though every other state in Europe emulated him, with varying degrees of discretion or hypocrisy.
The tone was set by the victors of 1815, who arrogated the role of defenders of a supposedly righteous social order against evil, and writing on Napoleon has been bedevilled ever since by a moral dimension, which has entailed an imperative to slander or glorify. Beginning with Stendhal, who claimed he could only write of Napoleon in religious terms, and no doubt inspired by Goethe, who saw his life as 'that of a demi-god', French and other European historians have struggled to keep the numinous out of their work, and even today it is tinged by a sense of awe. Until very recently, Anglo-Saxon historians have shown reluctance to allow an understanding of the spirit of the times to help them see Napoleon as anything other than an alien monster. Rival national mythologies have added layers of prejudice which many find hard to overcome.
Napoleon was in every sense the product of his times; he was in many ways the embodiment of his epoch. If one wishes to gain an understanding of him and what he was about, one has to place him in context. This requires ruthless jettisoning of received opinion and nationalist prejudice, and dispassionate examination of what the seismic conditions of his times threatened and offered.
In the 1790s Napoleon entered a world at war, and one in which the very basis of human society was being questioned. It was a struggle for supremacy and survival in which every state on the Continent acted out of self-interest, breaking treaties and betraying allies shamelessly. Monarchs, statesmen and commanders on all sides displayed similar levels of fearful aggression, greed, callousness and brutality. To ascribe to any of the states involved a morally superior role is ahistorical humbug, and to condemn the lust for power is to deny human nature and political necessity.
For Aristotle power was, along with wealth and friendship, one of the essential components of individual happiness. For Hobbes, the urge to acquire it was not only innate but beneficent, as it led men to dominate and therefore organise communities, and no social organisation of any form could exist without the power of one or more individuals to order others.
Napoleon did not start the war that broke out in 1792 when he was a mere lieutenant and continued, with one brief interruption, until 1814. Which side was responsible for the outbreak and for the continuing hostilities is fruitlessly debatable, since responsibility cannot be laid squarely on one side or the other. The fighting cost lives, for which responsibility is often heaped on Napoleon, which is absurd, as all the belligerents must share the blame. And he was not as profligate with the lives of his own soldiers as some.
French losses in the seven years of revolutionary government (1792–99) are estimated at four to five hundred thousand; those during the fifteen years of Napoleon's rule at just under twice as high, at eight to nine hundred thousand. Given that these figures include not only dead, wounded and sick, but also those reported as missing, whose numbers went up dramatically as his ventures took the armies further afield, it is clear that battle losses were lower under Napoleon than during the revolutionary period – despite the increasing use of heavy artillery and the greater size of the armies. The majority of those classed as missing were deserters who either drifted back home or settled in other countries. This is not to diminish the suffering or the trauma of the war, but to put it in perspective.
My aim in this book is not to justify or condemn, but to piece together the life of the man born Napoleone Buonaparte, and to examine how he became 'Napoleon' and achieved what he did, and how it came about that he undid it.
In order to do so I have concentrated on verifiable primary sources, treating with caution the memoirs of those such as Bourrienne, Fouché, Barras and others who wrote principally to justify themselves or to tailor their own image, and have avoided using as evidence those of the duchesse d'Abrantès, which were written years after the events by her lover the novelist Balzac. I also ignore the various anecdotes regarding Napoleon's birth and childhood, believing that it is immaterial as well as unprovable that he cried or not when he was born, that he liked playing with swords and drums as a child, had a childhood crush on some little girl, or that a comet was sighted at his birth and death. There are quite enough solid facts to deal with.
I have devoted more space in relative terms to Napoleon's formative years than to his time in power, as I believe they hold the key to understanding his extraordinary trajectory. As I consider the military aspects only insofar as they produced an effect, on him and his career or the international situation, the reader will find my coverage very uneven. I give prominence to the first Italian campaign because it demonstrates the ways in which Napoleon was superior to his enemies and colleagues, and because it turned him into an exceptional being, both in his own eyes and those of others. Subsequent battles are of interest primarily for the use he made of them, while the Russian campaign is seminal to his decline and reveals the confusion in his mind which led to his political suicide. To those who would like to learn more about the battles I would recommend Andrew Roberts's masterful _Napoleon the Great_. The battle maps in the text are similarly spare, and do not pretend to accuracy; they are designed to illustrate the essence of the action.
The subject is so vast that anyone attempting a life of Napoleon must necessarily rely on the work of many who have trawled through archives and on published sources. I feel hugely indebted to all those involved in the Fondation Napoléon's new edition of Napoleon's correspondence. I also owe a great deal to the work done over the past two decades by French historians in debunking the myths that have gained the status of truth and excising the carbuncles that have overgrown the verifiable facts during the past two centuries. Thierry Lentz and Jean Tulard stand out in this respect, but Pierre Branda, Jean Defranceschi, Patrice Gueniffey, Annie Jourdan, Aurélien Lignereux and Michel Vergé-Franceschi have also helped to blow away cobwebs and enlighten. Among Anglo-Saxon historians, Philip Dwyer has my gratitude for his brilliant work on Napoleon as propagandist, and Munro Price for his invaluable archival research on the last phase of his reign. The work of Michael Broers and Steven Englund is also noteworthy.
I owe a debt of thanks to Olivier Varlan for bibliographic guidance, and particularly for having let me see Caulaincourt's manuscript on the Prussian and Russian campaigns of 1806–07; to Vincenz Hoppe for seeking out sources in Germany; to Hubert Czyżewski for assisting me in unearthing obscure sources in Polish libraries; to Laetitia Oppenheim for doing the same for me in France; to Carlo De Luca for alerting me to the existence of the diary of Giuseppe Mallardi; and to Angelika von Hase for helping me with German sources. I also owe thanks to Shervie Price for reading the typescript, and to the incomparable Robert Lacey for his sensitive editing.
Although at times I felt like cursing him, I would like to thank Detlef Felken for his implicit faith in suggesting I write this book, and Clare Alexander and Arabella Pike for their support. Finally, I must thank my wife Emma for putting up with me and encouraging me throughout what has been a challenging task.
_Adam Zamoyski_
## 1
# A Reluctant Messiah
At noon on 10 December 1797 a thunderous discharge from a battery of guns echoed across Paris, opening yet another of the many grandiose festivals for which the French Revolution was so notable.
Although the day was cold and grey, crowds had been gathering around the Luxembourg Palace, the seat of the Executive Directory which governed France, and according to the Prussian diplomat Daniel von Sandoz-Rollin, 'never had the cheering sounded more enthusiastic'. People lined the streets leading up to the palace in the hope of catching a glimpse of the hero of the day. But his reticence defeated them. At around ten o'clock that morning he had left his modest house on the rue Chantereine with one of the Directors who had come to fetch him in a cab. As it trundled through the streets, followed by several officers on horseback, he sat well back, seeming in the words of one English witness 'to shrink from those acclamations which were then the voluntary offering of the heart'.
They were indeed heartfelt. The people of France were tired after eight years of revolution and political struggle marked by violent lurches to the right or the left. They were sick of the war which had lasted for more than five years and which the Directory seemed unable to end. The man they were cheering, a twenty-eight-year-old general by the name of Bonaparte, had won a string of victories in Italy against France's principal enemy, Austria, and forced her emperor to come to terms. The relief felt at the prospect of peace and the political stability it was hoped would ensue was accompanied by a subliminal sense of deliverance.
The Revolution which began in 1789 had unleashed boundless hopes of a new era in human affairs. These had been whipped up and manipulated by successive political leaders in a self-perpetuating power struggle, and people longed for someone who could put an end to it. They had read the Bulletins recounting this general's deeds and his proclamations to the people of Italy, which contrasted sharply with the utterances of those ruling France. Many believed, or just hoped, that the longed-for man had come. The sense of exaltation engendered by the Revolution had been kept alive by overblown festivals, and this one was, according to one witness, as ' _magnifique_ ' as any.
The great court of the Luxembourg Palace had been transformed for the occasion. A dais had been erected opposite the entrance, on which stood the indispensable 'altar of the fatherland' surmounted by three statues, representing Liberty, Equality and Peace. These were flanked by panoplies of enemy standards captured during the recent campaign, beneath which were placed seats for the five members of the Directory, one for its secretary-general, and more below them for the ministers. Beneath were places for the diplomatic corps, and to either side stretched a great amphitheatre for the members of the two legislative chambers and for the 1,200-strong choir of the Conservatoire. The courtyard was decked with tricolour flags and covered by an awning, turning it into a monumental tent.
As the last echoes of the gun salute died away, the Directors emerged from a chamber in the depths of the palace, dressed in their ' _grand costume_ '. Designed by the painter Jacques-Louis David, this consisted of a blue velvet tunic heavily embroidered with gold thread and girded with a gold-tasselled white silk sash, white breeches and stockings, and shoes with blue bows. It was given a supposedly classical look by a voluminous red cloak with a white lace collar, a 'Roman' sword on a richly embroidered baldric, and a black felt hat adorned by a blue-white-red tricolour of three ostrich feathers.
The Directors took their place at the end of a cortège led by the commissioners of police, followed by magistrates, civil servants, the judiciary, teachers, members of the Institute of Arts and Sciences, officers, officials, the diplomatic representatives of foreign powers, and the ministers of the Directory. It was preceded by a band playing 'the airs beloved of the French Republic'.
The cortège snaked its way through the corridors of the palace and out into the courtyard, the various bodies taking their appointed seats. The members of the legislative chambers had already taken theirs. They wore costumes similar to that of the Directors, the 'Roman' look in their case sitting uneasily with their four-cornered caps, which were David's homage to the heroes of the Polish revolution of 1794.
Having taken their seats, the Directors despatched an official to usher in the principal actors of the day's festivities. The airs beloved of the French Republic had been superseded by a symphony performed by the orchestra of the Conservatoire, but this was rudely interrupted by shouts of ' _Vive Bonaparte!_ ', ' _Vive la Nation!_ ', ' _Vive le libérateur de l'Italie!_ ' and ' _Vive le pacificateur du continent!_ ' as a group of men entered the courtyard.
First came the ministers of war and foreign relations in their black ceremonial costumes. They were followed by a diminutive, gaunt figure in uniform, his lank hair dressed in the already unfashionable 'dog's ears' flopping on either side of his face. His gauche movements 'charmed every heart', according to one onlooker. He was accompanied by three aides-de-camp, 'all taller than him, but almost bowed by the respect they showed him'. There was a religious silence as the group entered the courtyard. Everyone present stood and uncovered themselves. Then the cheering broke out again. 'The present elite of France applauded the victorious general, for he was the hope of everyone: republicans, royalists, all saw their present and future salvation in the support of his powerful arm.' The dazzling military victories and diplomatic triumph he had achieved contrasted so strikingly with his puny stature, dishevelled appearance and unassuming manner that it was difficult not to believe he was inspired and guided by some higher power. The philosopher Wilhelm von Humboldt was so impressed when he saw him, he thought he was contemplating an ideal of modern humanity.
When the group reached the foot of the altar of the fatherland, the orchestra and choir of the Conservatoire struck up a 'Hymn to Liberty' composed by François-Joseph Gossec to the tune of the Catholic Eucharistic hymn _O Salutaris Hostia_ , and the crowd joined in an emotionally charged rendition of what the official account of the proceedings described as 'this religious couplet'. The Directors and assembled dignitaries took their seats, with the exception of the general himself. 'I saw him decline placing himself in the chair of state which had been prepared for him, and seem as if he wished to escape from the general bursts of applause,' recalled the English lady, who was full of admiration for the 'modesty in his demeanour'. He had in fact requested that the ceremony be cancelled when he heard what was in store. But there was no escape.
The Republic's minister for foreign relations, Charles-Maurice de Talleyrand, limped forward in his orthopaedic shoe, his ceremonial sword and the plumes in his hat performing curious motions as he went. The President of the Directory had chosen him rather than the minister of war to present the reluctant hero. 'It is not the general, it is the peacemaker, and above all the citizen that you must single out to praise here,' he had written to Talleyrand. 'My colleagues are terrified, not without reason, of military glory.' This was true.
'No government has ever been so universally despised,' an informant in France had written to his masters in Vienna only a couple of weeks before, assuring them that the first general with the courage to raise the standard of revolt would have half of the nation behind him. Many in Paris, at both ends of the political spectrum, were expecting General Bonaparte to make such a move, and in the words of one observer, 'everyone seemed to be watching each other'. According to another, there were many present who would happily have strangled him.
The forty-three-year-old ex-aristocrat and former bishop Talleyrand knew all this. He was used to shrouding his feelings with an impassive countenance, but his upturned nose and thin lips, curling up on the left-hand side in a way suggesting wry amusement, were well fitted to the speech he now delivered.
'Citizen Directors,' he began, 'I have the honour to present to the executive Directory citizen Bonaparte, who comes bearing the ratification of the treaty of peace concluded with the emperor.' While reminding those present that the peace was only the crowning glory of 'innumerable marvels' on the battlefield, he reassured the shrinking general that he would not dwell on his military achievements, leaving that to posterity, secure in the knowledge that the hero himself viewed them not as his own, but as those of France and the Revolution. 'Thus, all Frenchmen have been victorious through Bonaparte; thus his glory is the property of all; thus there is no republican who cannot claim his part of it.' The general's extraordinary talents, which Talleyrand briefly ran through, were, he admitted, innate to him, but they were also in large measure the fruit of his 'insatiable love of the fatherland and of humanity'. But it was his modesty, the fact that he seemed to 'apologise for his own glory', his extraordinary taste for simplicity, worthy of the heroes of classical antiquity, his love of the abstract sciences, his literary passion for 'that sublime _Ossian_ ' and 'his profound contempt for show, luxury, ostentation, those paltry ambitions of common souls' that were so striking, indeed alarming: 'Oh! far from fearing what some would call his ambition, I feel that we will one day have to beg him to give up the comforts of his studious retreat.' The general's countless civic virtues were almost a burden to him: 'All France will be free: it may be that he will never be, that is his destiny.'
When the minister had concluded, the victim of destiny presented the ratified copy of the peace treaty to the Directors, and then addressed the assembly 'with a kind of feigned nonchalance, as though he were trying to intimate that he little liked the regime under which he was called to serve', in the words of one observer. According to another, he spoke 'like a man who knows his worth'.
In a few clipped sentences, delivered in an atrocious foreign accent, he attributed his victories to the French nation, which through the Revolution had abolished eighteen centuries of bigotry and tyranny, had established representative government and roused the other two great nations of Europe, the Germans and Italians, enabling them to embrace the 'spirit of liberty'. He concluded, somewhat bluntly, that the whole of Europe would be truly free and at peace 'when the happiness of the French people will be based on the best organic laws'.
The response of the Directory to this equivocal statement was delivered by its president, Paul François Barras, a forty-two-year-old minor nobleman from Provence with a fine figure and what one contemporary described as the swagger of a fencing-master. He began with the usual flowery glorification of 'the sublime revolution of the French nation' before moving on to vaporous praise of the 'peacemaker of the continent', whom he likened to Socrates and hailed as the liberator of the people of Italy. General Bonaparte had rivalled Caesar, but unlike other victorious generals, he was a man of peace: 'at the first word of a proposal of peace, you halted your triumphant progress, you laid down the sword with which the fatherland had armed you, and preferred to take up the olive branch of peace!' Bonaparte was living proof 'that one can give up the pursuit of victory without relinquishing greatness'.
The address meandered off into a diatribe against those 'vile Carthaginians' (the British) who were the last obstacle standing in the way of a general peace which the new Rome (France) was striving to bestow on the Continent. Barras concluded by exhorting the general, 'the liberator to whom outraged humanity calls out with plaintive appeals', to lead an army across the Channel, whose waters would be proud to carry him and his men: 'As soon as the tricolour standard is unfurled on its bloodied shores, a unanimous cry of benediction will greet your presence; and, seeing the dawn of approaching happiness, that generous nation will hail you as liberators who come not to fight and enslave it, but to put an end to its sufferings.'
Barras then stepped forward with extended arms and in the name of the French nation embraced the general in a 'fraternal accolade'. The other Directors did likewise, followed by the ministers and other dignitaries, after which the general was allowed to step down from the altar of the fatherland and take his seat. The choir intoned a hymn to peace written for the occasion by the revolutionary bard Marie-Joseph Chénier, set to music by Étienne Méhul.
The minister for war, General Barthélémy Scherer, a forty-nine-year-old veteran of several campaigns, then presented to the Directory two of Bonaparte's aides bearing a huge white standard on which the triumphs of the Army of Italy were embroidered in gold thread. These included: the capture of 150,000 prisoners, 170 flags and over a thousand pieces of artillery, as well as some fifty ships; the conclusion of a number of armistices and treaties with various Italian states; the liberation of the people of most of northern Italy; and the acquisition for France of masterpieces by Michelangelo, Guercino, Titian, Veronese, Correggio, Caracci, Raphael, Leonardo and other works of art. Scherer praised the soldiers of the Army of Italy and particularly their commander, who had 'married the audacity of Achilles to the wisdom of Nestor'.
The guns thundered as Barras received the standard from the hands of the two officers, and in another interminable address, he returned to his anti-British theme. 'May the palace of St. James crumble! The Fatherland wishes it, humanity demands it, vengeance commands it.' After the two warriors had received the 'fraternal accolade' of the Directors and ministers, the ceremony closed with a rendition of the rousing revolutionary war hymn _Le Chant du Départ_ , following which the Directors exited as they had come, and Bonaparte left, cheered by the multitude gathered outside, greatly relieved that it was all over.
For all his apparent nonchalance, he had been treading warily throughout. The Directory had not welcomed the coming of peace. The war had paid for its armies and bolstered its finances, while the victories had deflected criticism of its domestic shortcomings. More important, war kept the army occupied and ambitious generals away from Paris. This peace had been made by Bonaparte in total disregard of the Directory's instructions, and it was no secret that the Directors had been furious when they were presented with the draft treaty. A few days after receiving it, they had nominated Bonaparte commander of the Army of England, not because they believed in the possibility of a successful invasion, but because they wanted him away from Paris and committed to a venture which would surely undermine his reputation. Their principal preoccupation now was to get him away from Paris, where he was a natural focus for their enemies.
The day's event had been a politically charged performance in which, as Bonaparte's secretary put it, 'everyone acted out as best they could this scene from a sentimental comedy'. But it was a dangerous one; according to one well-informed observer, 'it was one of those occasions when one imprudent word, one gesture out of place can decide the future of a great man'. As Sandoz-Rollin pointed out, Paris could easily have become the general's 'tomb'.
The hero of the day was well aware of this. The ceremony was followed by illuminations 'worthy of the majesty of the people' and a banquet given in his honour by the minister of the interior, in the course of which no fewer than twelve toasts were raised, each followed by a three-gun salute and an appropriate burst of song from the choir of the Conservatoire. Closely guarded by his aides, the general did not touch a morsel of food or drink a thing, for fear of being poisoned.
It was not only the Directors who wished him ill. The royalists who longed for a return of Bourbon rule hated him as a ruthless defender of the Republic. The extreme revolutionaries, the Jacobins who had been ousted from power, feared he might be scheming to restore the monarchy. They denounced the treaty he had signed as 'an abominable betrayal' of the Republic's values and referred to him as a 'little Caesar' about to stage a coup and seize power.
Such thoughts were not far from the general's mind. But he hid them as he assessed the possibilities, playing to perfection the part of a latter-day Cincinnatus. He refused the offer of the Directory to place a guard of honour outside his door, he avoided public events and kept a low profile, wearing civilian dress when he went out. 'His behaviour continues to upset all the extravagant calculations and perfidious adulation of certain people,' reported the _Journal des hommes libres_ approvingly. Sandoz-Rollin assured his masters in Berlin that there was nothing which might lead one to suspect Bonaparte of meaning to take power. 'The health of this general is weak, his chest is in a very poor state,' he wrote, 'his taste for literature and philosophy and his need of rest as well as to silence the envious will lead him to live a quiet life among friends...'
One man was not fooled. For all his cynicism, Talleyrand was impressed, and sensed power. 'What a man this Bonaparte,' he had written to a friend a few weeks before. 'He has not finished his twenty-eighth year: and he is crowned with all the glories. Those of war and those of peace, those of moderation, those of generosity. He has everything.'
## 2
# Insular Dreams
The man who had everything was born into a family of little consequence in one of the poorest places in Europe, the island of Corsica. It was also one of the most idiosyncratic, having never been an independent political unit and yet never been fully a province or colony of another state. It had always been a world of its own.
In the late Middle Ages the Republic of Genoa established bases at the anchorages of Bastia on the north-eastern coast and Ajaccio in the south-west to protect its shipping lanes and deny their use to others. It garrisoned these with soldiers, mostly impoverished nobles from the Italian mainland, and gradually extended its rule inland. But the mountainous interior held little economic interest, and although they penetrated it in order to put down insurgencies and exact what contributions they could, the Genoese found it impossible to control its feral denizens and largely left it alone, not even bothering to map it.
The indigenous population preserved its traditional ways, subsisting on a diet of chestnuts (from which even the local bread was made), cheese, onions, fruit and the occasional piece of goat or pork, washed down with local wine. They dressed in homespun brown cloth and spoke their own Italian patois. They were in constant conflict over issues such as grazing rights with the inhabitants of the port towns. These considered themselves superior and married amongst themselves or found spouses on the Italian mainland, yet with time they could not help being absorbed by the interior and its ways.
It was a pre-feudal society. The majority owned at least a scrap of land, and while a few families aspired to nobility, the differentials of wealth were narrow. Even the poorest families had a sense of pride, of their dignity and of the worth of their 'house'. It was also a fundamentally pagan society, with Christianity spread thinly, if tenaciously, over a stew of ancient myths and atavisms. A profound belief in destiny overrode the Christian vision of salvation.
As there was hardly any coinage in circulation, most of the necessities of life were bartered. The result was a complicated web of favours granted and expected, of rights established or revindicated, agreements, often unspoken, and a plethora of litigation. Any violent move could provoke a _vendetta_ from which it was almost impossible to escape, as nothing could be kept secret for long in such a restricted space. Shortage of land meant that ownership was divided and subdivided, traded and encumbered with complicated clauses governing rights of reversal. It was also the principal motive for marriage. And so it was for General Bonaparte's father, Carlo Maria Buonaparte.
When his son came to power, genealogists, sycophants and fortune-hunters set about tracing his ancestry and came up with various pedigrees, linking him to Roman emperors, Guelf kings and even the Man in the Iron Mask. The only indisputable facts concerning his ancestry are that he was descended from a Gabriele Buonaparte who in the sixteenth century owned the grandest mansion in Ajaccio, consisting of two rooms and a kitchen over a shop and a store room, and a small garden with a mulberry tree.
Where Gabriele came from remains uncertain. The most convincing filiation is to minor gentry of the same name from the little town of Sarzana on the borders of Tuscany and Liguria, some of whom took service with the Genoese and were sent to Corsica. Recent DNA tests have shown that the Corsican Buonaparte belonged to the population group E, which is found mainly in North Africa, Sicily and particularly the Levant. This does not rule out a Ligurian connection, since people from those areas washed up over the ages on the coasts of Italy as well as those of Corsica.
Gabriele's son Geronimo had been notable enough to be sent as Ajaccio's deputy to Genoa in 1572, and acquired, by marriage, a house in Ajaccio as well as a lease on some low-lying ground outside the town known as the Salines. His descendants also married well, within the circle of Ajaccio notables, but the need to provide dowries for daughters split up the family's property, and Sebastiano Buonaparte, born in 1683, was reduced to marrying a girl from the upland village of Bocognano, apparently for the two small plots of land in the hills and the ninety sheep she brought him in her dowry. She bore him five children: one girl, Paola Maria, and four boys: Giuseppe Maria, Napoleone, Sebastiano and Luciano.
The family home had been partitioned by dowries, and the seven of them were crammed into the forty square metres that remained theirs. The building was so dilapidated that a military billeting commission classified it as unfit for any but lower ranks. Thus, although they were still considered among the _anziani_ , the elders or notables of Ajaccio, the family's lifestyle was anything but noble. A smallholding provided vegetables and their vineyards wine for their own needs and some extra to sell or exchange for oil and flour, while their flocks produced occasional meat for their own consumption and a little income.
Luciano was the most intelligent of the brood, and joined the priesthood. He bought out other family members and installed an indoor staircase in the house. His nephew, Giuseppe's son Carlo Maria, born in 1746, also set about rebuilding the family fortunes, and it is his social ambitions that were to have such a profound effect on European history.
History had begun to take an interest in Corsica. The corrupt inefficiency of Genoese rule had sparked off a rebellion on the island in 1729. It was put down by troops, but simmered on in the interior. In 1735 three 'Generals of the Corsican nation' convoked an assembly, the _consulta_ , at Corte in the uplands and proclaimed independence, attracting the sympathies of many across Europe. One of the dominant themes in the literature of the Enlightenment was that of the noble savage, and Corsica seemed to fit the ideal of a society unspoilt by the supposedly corrupted Christian culture of Europe. In 1736 a German baron, Theodor von Neuhoff, landed in Corsica with weapons and aid for the rebels. He proclaimed himself King of the Corsicans and set about developing the island according to current ideals. Genoa called on France for military assistance, the rebels were obliged to flee, and Theodor settled in London, where he died, a declared bankrupt, in 1756. His vision did not die with him.
In 1755 Pasquale Paoli, the son of one of the three 'Generals of the Corsican nation', had returned from exile in Naples and proclaimed a Corsican Republic. Born in 1725, Paoli had been eleven years old when Theodor expounded to him his vision for the island, and it had haunted him throughout his exile. Styling himself General of the Nation, over the next thirteen years he worked at building an ideal modern state endowed with a constitution, institutions and a university. His charisma ensured him the love of the majority of the Corsicans, who served him devotedly, referring to him as their _Babbo_ , their father. He gained the admiration of enlightened European opinion, with Voltaire and Rousseau in the lead. The British traveller James Boswell visited him in 1765 and wrote up his experiences in what turned into a best-seller, further enhancing his reputation.
While Paoli ruled the Corsican Nation from the Lilliputian hill-town of Corte at the heart of the island, coastal towns remained in the hands of the Genoese, who had twice called in French military assistance to maintain their grip. The French at first confined themselves to holding the port cities and surrounding areas, but it was unlikely that France would countenance the existence of a utopian republic on its doorstep for long, and wise Corsicans hedged their bets.
On 2 June 1764, a year after the death of his father, the eighteen-year-old Carlo Buonaparte married Letizia Ramolino, who was just under fifteen years of age. She was by all accounts a beauty, but that was not the motive for the match, which had been arranged by Carlo's uncle Luciano. The Ramolino family, descended from a Lombard nobleman who had come to Corsica a couple of hundred years earlier, were of higher social standing than the Buonaparte. They were also better-connected and richer. Letizia's dowry, which consisted of a house in Ajaccio and some rooms in another, a vineyard and about a dozen hectares of land, enhanced Carlo's position. The marriage did not take place in church since the essence of any Corsican marital union was property, the principal element was the contract, and it was customary to sign this in the house of one of the parties, after which the newlyweds might or might not have their marriage blessed by a priest.
Soon after their wedding, the couple moved to Corte, where Carlo's uncle Napoleone had already joined Pasquale Paoli. Their first child was stillborn, their second, a daughter born in 1767, died in infancy. On 7 January 1768 they had a son, baptised Joseph Nabullion. Carlo enrolled at the university and eventually published a dissertation on natural rights which reveals a degree of education.
Paoli resided in a massive structure made of the same dark-grey rock as all the other houses and the paving of the streets in Corte. He imported furniture and textiles from Italy in order to create within this grim building a few rooms in which a head of government could receive. Good-looking and amiable, the young Joseph quickly won his friendship. Letizia was by Corte standards a sophisticated and well-dressed lady, and her beauty and strong personality meant that along with her sister Geltruda Paravicini she was a welcome member of Paoli's entourage.
Paoli admitted to Boswell that he placed great trust in Providence. That, and the praise being directed at him from various parts of Europe, had lulled him into a state of complacency. He believed that the British, who had taken an interest in supporting the Corsican cause before, and were now in thrall to Boswell's _An Account of Corsica_ , would come to his aid if he were threatened. By the same token France could not countenance the possibility of the strategically important island falling into the hands of a hostile power. Still smarting from overseas losses to Britain during the recently ended Seven Years' War, French wounded pride would welcome the balsam of a colonial gain. Genoa had given up on Corsica, and owed France a great deal of money. By the Treaty of Versailles of May 1768 it ceded the island to France, pending the repayment of the overdue debt. French troops moved out of their coastal bases to impose the authority of King Louis XV.
Paoli issued a call to arms, but his was a lost cause, though the men of the uplands put up a stiff resistance, inflicting heavy casualties on the French. Carlo was at Paoli's side during the decisive engagement at Ponte-Novo on 8 May 1769, but did not take part in the fighting; Paoli hovered some three kilometres away as his men were routed by a superior French force under the comte de Vaux. Paoli fled over the mountains to Porto Vecchio, whence two British frigates took him and a handful of supporters off to exile in England.
Carlo Buonaparte was not among them. Family legend has it that Paoli insisted he stay behind in Corsica, but it is more likely that Carlo made the decision himself. The island had never entirely submitted to any regime, and among its inhabitants family came a long way before loyalty to any cause. While Carlo and his uncle Napoleone had served Paoli, his other uncle Luciano had remained in French-held Ajaccio, where he had sworn fealty to the King of France, as had most of the notables of the coastal cities. Unperturbed by the cause of independence, Letizia was writing to her grandfather Giuseppe Maria Pietrasanta in French-held Bastia asking him to send her bales of Lyon silk and new dresses fit for a noblewoman.
'I was a good patriot and a Paolist in my heart as long as the national government lasted,' Carlo wrote. 'But this government has ceased to exist. We have become French. _Eviva il Re e suo governo_.' Having submitted to Vaux, he went back to Ajaccio. On the way home over the mountains, Carlo almost lost his wife and the child she was carrying in her womb when her mule stumbled in the torrent of the river Liamone.
The child was born on the night of 15 August 1769, and named after his great-uncle Napoleone, who had died two years before. The name did not figure in the liturgical calendar as belonging to a saint, but it was not unknown in Genoa and Corsica, where it was sometimes spelt Nabullione or even Lapullione, and had been given to several members of the family in the past. He would not be christened until July 1771, by which time his father had repositioned himself with considerable skill.
Since the legal profession was the key to obtaining civic office under any government, Carlo set off for Pisa to obtain the necessary qualifications. 'One can have no idea of the facility with which the title of doctor is granted here,' wrote a contemporary French traveller of the university of Pisa. 'Everyone in the locality is one, even the inn-keepers and post-masters.' Carlo presented a hastily-written thesis for which he obtained a doctorate, and within six weeks he was back in Ajaccio, where he found no shortage of work.
With a population of 3,907 according to the French census of 1770, Ajaccio was the second largest city in Corsica, but it was in essence a sleepy, smelly village. When Balzac visited it more than half a century later he was stunned by the 'unbelievable indolence' pervading the place, with the menfolk wandering about all day smoking. It consisted of a minuscule citadel stuck out on the promontory shielding the port, and behind it a walled town not more than 250 metres across in any direction, clustered around three radiating streets intersected by another three narrower ones, with an attractive promenade and square between the two named the Olmo after a large elm that grew on it. Within the walls there was a cathedral whose roof fell in in 1771 and would not be repaired for twenty years, and which was unusable in summer due to the stink emanating from the dead buried under its floor. There was also a Jesuit college and a governor's residence, tucked into an assortment of mean-looking townhouses ranged along narrow streets bordered by small shops whose trade spilled out onto them. The smell of fish drifting over from the harbour mingled with that of the hides put out to dry by the butchers cutting up carcases in the street and the stench from the moat of the citadel. Outside the city walls stood a convent, a hospital, a military barracks and a seminary, and, along the road leading up to the town from the north, an agglomeration of dwellings known as the Borgo, where the poorer inhabitants lived.
The city was dominated by families such as the Ponte, Pozzo di Borgo, Bacciochi and the Peraldi, and an oligarchy of notaries, lawyers and clerics with 'noble' connections such as the Buonaparte. This society was supplemented by the magistrates, judge, officers and other officials of the French administration. The houses within the city walls were mostly divided by multiple ownership like the Buonaparte home, and, since all their inhabitants were related to each other by blood or marriage, the whole area was a familial congeries connected by tangled ties. Ajaccio's lawyers, Carlo among them, thrived on the squabbles generated by the resulting disputes over restricted space and scant resources. Carlo himself would be engaged for many years in a legal battle over some used wine-making equipment and a few leaky barrels. In one case, he pleaded for a client over one kerchief. There was plenty of work, but it was not remunerative enough or commensurate with Carlo's ambitions. On the basis of his doctorate, in 1771 he obtained a minor post at the court of Ajaccio, but he was aiming higher.
He had wasted no time in seeking the favour of the French military governor of the south-west of the island, the comte de Narbonne. On being fobbed off, he offered his services to Narbonne's superior in Bastia. Charles Louis, comte de Marbeuf, needed a party of supporters among the notables of Ajaccio, and the Buonaparte were ideally placed to provide it. Their collaboration developed so well that Carlo felt bold enough to invite Marbeuf to stand godparent at the christening of his son Napoleone on 21 July 1771, and Marbeuf agreed. In the event Marbeuf was prevented from attending, so he sent a Genoese patrician and later royal lieutenant at Ajaccio, Lorenzo Giubega, to act as proxy. Marbeuf did come to Ajaccio less than a month later for the festivities of the feast of the Assumption and the little Napoleone's second birthday on 15 August. He was so struck by the beauty of the child's mother that he insisted she take his arm on the afternoon _passegiata_ up and down the Olmo, and after walking her home he stayed there until one in the morning. Carlo's ambitions soared.
France was interested in Corsica both for its strategic importance and for its economic potential. It was accorded the status of a semi-autonomous province within the kingdom, and the French authorities set about organising it. A survey revealed to them the idiosyncratic nature of Corsican society, with its broad base of land tenure and plethora of hunting, gathering and fishing rights and obligations. These would hinder rationalisation, while the egalitarianism that had so enchanted Boswell and Rousseau impeded not only progress but the establishment of a hierarchy necessary for successful political control. One of the first actions of the new French regime was to correct this by recognising as noble the most prominent families. In large measure thanks to the usefulness of Carlo and the charms of his wife, the Buonaparte were included. 'Ajaccio is struck with astonishment and filled with jealousy by the news,' Carlo wrote to his wife's grandfather.
The connection with Marbeuf was invaluable. In 1772 Carlo was elected to represent Ajaccio in the newly established Assembly of Corsican Estates only because Marbeuf intervened to have his successful rival's election annulled. The governor's direct intercession also helped resolve a lengthy court battle between the Buonaparte and their Ornano cousins over a dowry that included a significant part of the house in which they lived. By way of a series of buy-outs, swaps and court cases Carlo would extend his possession over the years against a backdrop of running battles between the various members of the family involving the use of the staircase and other areas where interests clashed. These occasionally flared into violence, and inevitably ended up in court, where the knowledge that Carlo had the backing of Marbeuf counted.
The rise of Carlo's fortunes and the governor's interest in Letizia aroused jealousy and gave rise to gossip. Marbeuf, a widower, did have an official mistress in Bastia, a Madame Varese, but whatever charms she may have possessed, at fifty she was past her prime, while Letizia was still young. It is difficult to see any reason other than an amorous one for him to spend time with an uneducated woman forty years his junior, and he gave every sign of being besotted by Letizia. There is no evidence that the relationship was sexual, but it was widely believed that it was, and that her son Louis, born in 1778, was his.
Letizia would bear a total of thirteen children, of whom three died young and two in childbirth. The first surviving child was Joseph, born in 1768, the next Napoleone, born in 1769. As his mother was unable to feed him, he was provided with a wet-nurse, Camilla Carbon Ilari, who grew so fond of him that she neglected her own son. Napoleone and his elder brother, christened Joseph but known as Giuseppe, were also spoiled by their father and their grandmother Saveria Paravicini, known in the family as Minanna. But they were kept under strict control by Letizia. Strong, brave and characterful, Letizia was endowed with common sense. Unlike the rest of her family she was pious, and hardly went out other than to church. She was also a strict disciplinarian, administering slaps to all her children, and once giving Napoleone a thrashing which he remembered to the end of his life. She exerted a strong influence on him, and he would later say that he owed everything to her.
There is no evidence that Napoleone ever attended school, although according to his mother he did go to lessons at a girls' school. He was probably taught to read at home by a local priest, the Abbé Recco – presumably in Latin rather than the local patois they all spoke. His great-uncle Luciano, effective head of the family, must have found other teachers, as Napoleone from an early age showed an almost obsessive interest in, and remarkable aptitude for, mathematics.
His seems to have been a happy childhood, much of it spent in the street playing with various cousins, while the summers were passed up in the hills at Bocognano. The family grew, with the birth of a boy, Luciano, in 1775, and a girl, the fourth to be christened Maria-Anna and the first to survive, in 1777. While most of the anecdotes collected by early biographers can be dismissed as 'remembered' under the suggestive influence of the boy's later trajectory, one thing can be retained. His mother admiringly reminisced that of all her children Napoleone had been 'the most intrepid'. In fact, he seems to have been aggressive and quarrelsome, leading to frequent fights with his elder brother.
There was violence all around him, since much of the population continued in its lawless ways, and in order to stamp out the remaining resistance and the inherent banditry, the French applied the harshest measures. Mobile columns scoured the countryside burning down the houses and crops and slaughtering the flocks of suspected rebels, breaking them on the wheel and hanging the corpses on public highways as a warning. The five-year-old boy could not have avoided seeing them.
Whatever his feelings, Carlo had tied his family's fortunes to the French regime and its representative in Corsica. Being thought a cuckold was a small price to pay for the benefits brought by Marbeuf's favour, which he drew on at every upward step. While Luciano saved every penny and literally slept on his money-bags, Carlo spent lavishly, dressing well in order to keep up appearances when he attended the assembly in Bastia or other official functions. Having gained recognition of his status as a Corsican nobleman, he was determined to propel himself into the French nobility, as only that opened the door to careers in the kingdom. It had been decided that his elder son, Joseph, would go into the Church and Napoleone into the army. Marbeuf's nephew was the bishop of Autun, in eastern France, and Joseph was easily secured a place at the city's seminary, with the position of a sub-deacon and a stipend lined up for him.
Placing Napoleone would be more difficult. In 1776 Carlo applied for a place at one of the royal military academies, but the boy would require a royal bursary to pay for his studies. These were awarded to sons of officers and indigent nobles, so Carlo had to prove his noble credentials and provide evidence of his lack of means. The recognition of nobility he had gained in 1771 was based on proofs dating back only 200 years, which was not sufficient. In 1777 Carlo was chosen as one of the deputies to represent the nobility of Corsica at the court of Louis XVI, but he would not be presented to the king unless he could provide proofs of more ancient lineage.
When he had gone to Pisa to obtain his doctorate, Carlo had obtained from the city's archbishop a document attesting that his birth entitled him to the status of a 'noble patrician of Tuscany'. He now returned to Tuscany and located a canon by the name of Filipo Buonaparte, who provided him with documents purportedly relating him to his own family, which could trace noble status back to the fourteenth century. Armed with these, Carlo hoped to be able to gain recognition in France, and with it the right to a bursary for Napoleone.
On 12 December 1778 Carlo left Ajaccio, accompanied by Letizia and their sons Joseph and Napoleone. The party also included two other young men. One was Letizia's half-brother Giuseppe Fesch. When her father had died soon after Letizia's birth her mother had remarried a Swiss naval officer in Genoese service and produced a son. Giuseppe Fesch had been awarded a bursary to study for the priesthood at the seminary of Aix-en-Provence. The other young man was Abbé Varese, a cousin of Letizia who, like Joseph, had been granted the post of sub-deacon at the cathedral of Autun. They travelled by cart and mule via Bocognano to Corte, where a carriage sent by Marbeuf waited to conduct Letizia in greater comfort on the rest of their journey to Bastia. From there, Carlo and the four boys sailed for Marseille while Letizia moved into Marbeuf's residence.
They reached Autun on 30 December, having left Fesch at Aix on the way. On 1 January 1779 Joseph and Napoleone entered the college of Autun, the first to prepare for the priesthood, the second in order to learn French. He would spend three months and twenty days at the college, whose thirty boarders were taught by priests of the Oratorian order. During that time he would learn French well enough to carry on a conversation and to write a simple essay, but he did not, then or ever, learn the language well, and his grammar and use of words remained poor. His handwriting never developed beyond an ugly scrawl.
Carlo travelled on to Paris, where he learned that Napoleone had been deemed eligible for a bursary, subject to the submission of the necessary proofs of nobility. He duly presented these, before joining the other Corsican deputies to be presented to the king at Versailles. On 9 March the three Corsicans were admitted into the royal presence, bowed low and handed their petition to the monarch, who handed it to an attendant minister and graciously watched them leave his presence, stepping backwards and bowing repeatedly. They were then presented to the queen, the dauphin and various dignitaries, after which they were driven around the park in a carriage and rowed up and down the grand canal before being allowed to depart.
On 28 March the minister of war, the prince de Montbarrey, officially informed Carlo that his son had been admitted with a royal bursary to the military academy of Brienne. As he could not leave Versailles, Carlo asked the father of another boy due to be transferred from Autun to Brienne to take Napoleone there. On 21 April, after an emotional farewell to Joseph, the nine-year-old Napoleone set off on his military career.
## 3
# Boy Soldier
Napoleone arrived at the military academy of Brienne on 15 May 1779, three months short of his tenth birthday. The regulation kit each boy brought with him consisted of: three pairs of bed-sheets; a set of dining silver and a silver goblet, engraved with his family arms or initials; a dozen napkins; a blue coat with white metal buttons bearing the arms of the academy; two pairs of black serge breeches; twelve shirts, twelve kerchiefs, twelve white collars, six cotton caps, two dressing gowns, a hair-powder pouch and a hair ribbon. The powder and ribbon would be redundant for the first three years, as up to the age of twelve the boys wore their hair close-cropped.
The academy occupied an inelegant sprawl of buildings in the small town of 400 people, dominated by the château of the Loménie de Brienne family (to whom Marbeuf had recommended the boy). It had some 110 pupils, about fifty of them beneficiaries of royal bursaries like Napoleone. It was an austere institution, run by friars of the Order of Minims, founded in the fifteenth century by St Francis de Paola in Calabria and dedicated to abstention and frugality, so the atmosphere was Spartan. The boys attended mass every morning and discipline was strict, although there was no corporal punishment. At night they were locked in cells furnished with a straw-filled mattress, blanket, ewer and basin. In order to teach them to do without servants, they had to look after themselves and their kit. There were no holidays, and they were only allowed home in exceptional circumstances.
Following the defeats in the Seven Years' War, thought to have been partly due to the dilettantism of the officers, French military thinking focused on ways of producing an officer class inured to hardship and inspired by a sense of duty. Institutions such as Brienne were not meant to provide military training; the curriculum, taught by the friars supplemented by lay teachers, included the study of Suetonius, Tacitus, Quintillian, Cicero, Horace and Virgil, and, most importantly Plutarch, whose lives of the heroes of antiquity were meant to serve as role models for the aspiring soldiers. The works of Corneille, Racine, Boileau, Bossuet, Fénelon and other French classics were to awaken in them the instincts of chivalry, honour, duty and sacrifice, as well as teaching them elocution and rhetoric. The curriculum also included German, history, geography, mathematics, physics, drawing, dancing, fencing and music.
His new environment must have presented a challenge for the young Napoleone at many levels. He was by all accounts a puny child, showing signs of a delicate constitution. He had an olive complexion, which along with his poor French and atrocious accent marked him out as a foreigner. Corsica was seen in France at the time as a land of treacherous brigands. His outlandish first name, pronounced in the French way with the last syllable accented, ended with a sound like ' _nez_ ', leading to jibes based on the nose. Having a bursary singled him out as the son of a poor family, while his noble status was open to question, or at least mockery, from those of a higher social standing. The patronage of Marbeuf, and occasional visits to the château on Sundays, fed rumours about his mother's morals and his own paternity. All this laid him open to teasing and bullying, which must have aggravated the homesickness he would have felt on entering this alien world and the cold, sunless climate of north-eastern France. But in boarding schools where boys are cut off from home those with character or certain gifts easily impose themselves and can achieve a status they do not have in the outside world. And Napoleone did not lack character.
Apart from Charles-Étienne de Gudin, who became a fine general, and Étienne-Marie Champion de Nansouty, later a distinguished cavalry commander, few of Napoleone's contemporaries at Brienne made much of their lives. Later, some could not resist laying a claim to fame by recording memories, true or invented, of their days together. Childhood reminiscences are unreliable at the best of times, and in this case should be treated with the greatest caution. Typical is the story of a snowball fight that probably took place in the winter of 1783, which assumed epic proportions in various memoirs, with Napoleone organising his colleagues into armies, building elaborate fortifications out of snow and staging assaults which supposedly revealed his tactical talents and leadership qualities.
The concurrent image of an alienated youth drawn by such memoirists and developed by romantically-minded biographers should likewise be taken with a pinch of salt. Napoleone was capable of standing up to his schoolmates, displaying a 'ferocity' and even 'fury' born of contempt when provoked, but he did not seek their friendship. 'I do not recollect, that he ever showed the slightest partiality in favour of any of his comrades; gloomy and fierce to excess, almost always by himself,' recalled one of the few fellow pupils whose accounts can be trusted, 'averse likewise to all that is called children's plays and amusements, he never was seen to share in the noisy mirth of his school-fellows...'
He did have friends. One was Louis Antoine Fauvelet de Bourrienne, whose family origins in trade may have made him less arrogant than the others. Jean-Baptiste Le Lieur de Ville sur Arce, four years older than Napoleone, recalled being drawn to him by the 'originality' of his character, his 'somewhat strange' manner and his intelligence, and the two became close. Another friend was Pierre François Laugier de Bellecour, whom Napoleone liked in spite of his frivolity. There were others with whom he was on good terms, and he also had some friends among the friars and the teachers.
What did set Napoleone apart from his peers was his application and his intellectual curiosity. With a library at his disposal for the first time in his life, he read voraciously. The cadets were assigned small allotments of land to cultivate, and Napoleone fenced his off and planted it so as to provide himself with a place of solitude in which he could read. 'Reserved in his temper, and wholly occupied by his own pursuits, Buonaparte courted that solitude which seemed to constitute his delight,' recorded the librarian.
With Napoleone at Brienne and Joseph at Autun, Carlo with a seat in the Corsican Estates and the appointment in 1779 of his uncle Luciano as archdeacon of Ajaccio cathedral, the senior clerical post in the city, the standing of the family seemed assured. But Carlo's social ambitions bred requirements which imposed new struggles on him, and anxieties on his family. By a complicated transaction in 1779 he managed to gain sole title to most of the lease granted to his ancestor Geronimo in 1584 on the Salines, twenty-three hectares of land outside Ajaccio. Originally a salt-marsh, it had been partly drained and turned into a cherry orchard, but had reverted to an unhealthy swamp. Carlo applied for a subsidy from the French government to drain the land on grounds of public health and turn it into a nursery for mulberry trees, which, it was hoped, would be planted all over the island and provide raw silk for the French textile industry. Thanks to Marbeuf's support, the subsidy was granted in June 1782.
The next objective required more tortuous negotiations, in which his patron's assistance would be even more necessary. Almost a century earlier, a great-aunt of Carlo had married an Odone, and in her dowry brought him a property which was to revert to the Buonaparte if the progeny of the union were to die out. But instead of returning the property, the last of the Odone bequeathed it to the Jesuits. When the Jesuits were expelled from France in 1764, the property devolved to the state. Carlo intended to prove that the Odone bequest was illegal, and laid claim to Les Milleli, another former Jesuit property, as compensation.
The matter required a trip to Paris and Versailles, and in September 1782 Carlo set off, taking Letizia with him for a cure at the spa of Bourbonne-les-Bains before going on to Paris. At some stage during this trip she visited Napoleone at Brienne, and recorded being struck by how wasted and sickly he looked.
Carlo marked his social ascent by restoring the Buonaparte home in Ajaccio, putting in marble fireplaces, mirrors, lining his bedroom with crimson silk, draping the windows with muslin curtains and installing a library. Behind the scenes, things looked different, according to inventories of the family possessions, which list every pot and pan in the kitchen, buckets, iron pokers, pewter plates (three large and twenty-nine small), knives, forks and spoons. The path to grandeur was not without its difficult moments. A row over possession of the part of the house occupied by Carlo's cousin Maria Giustina and her Pozzo di Borgo husband, which Carlo escalated by trying to deny them the use of the only staircase, climaxed in Maria Giustina emptying her chamberpot over Carlo's best silk suit, airing on the terrace below, which entailed yet another court case.
The intimacy with Marbeuf would soon be at an end. He had married a young lady of his own class, and lost interest in his Corsican protégés. This came at a bad moment. The mulberry nursery was not going well, and the costs soon outstripped the amount of the subsidy. Another trip to Paris would be required, for family reasons too. Carlo had succeeded in getting his third son, now referred to as Lucien, admitted to Autun, where he joined Joseph. And he had achieved a social triumph in having his eldest daughter Maria-Anna accepted into the Maison Royale de Saint-Cyr, founded a hundred years before by Louis XIV's mistress Madame de Maintenon for the daughters of indigent nobility, which not only provided a free education, but also a dowry when they left. In June 1784 he set off for Paris with her. He needed to get more money out of the government for the Salines project, to press his suit over the Odone inheritance and the Milleli compensation, and to lobby for the nine-year-old Lucien to be granted a bursary at Brienne, where he was now due to join Napoleone. After stopping off at Autun to pick up Lucien, Carlo's appearance at Brienne, dressed in a cerise coat with puce breeches and silk stockings, with silver buckles on his shoes and his hair curled, caused Napoleone embarrassment. 'My father was a good man,' he later reminisced, but added that he was 'a little too fond of the ridiculous gentility of the times'.
Carlo's plans were beginning to come unstuck. Joseph had come to the conclusion that he was not made for the priesthood, and announced that he too would like to pursue a military career, as an artillery officer. Carlo was dismayed, and pointed out that Joseph was neither hardy in health nor courageous. With Marbeuf's backing he would easily obtain a good position and end up a bishop, which would be of advantage to the whole family, while, as Napoleone explained, he could at best make a passable garrison officer, being entirely unsuited for the artillery on account of his lack of application and his 'weakness of character'.
These comments were made in the first extant letter written by Napoleone, to his half-uncle Joseph Fesch in June 1784. He was still only fourteen, but while his spelling and grammar are atrocious, he adopts an authoritative tone, particularly with relation to his elder brother, whom he discusses as a parent might a wayward teenager. Of his younger sibling Lucien he remarks that 'he shows a good disposition and good will' and 'should make a good fellow'. Lucien claimed that on his arrival at Brienne Napoleone received him 'without the slightest show of tenderness' and that 'there was nothing amiable in his manner, either towards me or towards the other comrades of his age who did not like him', but these reminiscences, written down much later by an embittered Lucien, are unreliable.
Napoleone had originally intended to go into the navy. The voyages of exploration of Admiral Louis-Antoine de Bougainville and the creditable part played by the French navy against the British during the War of American Independence had raised its profile and made it fashionable. The navy offered a better chance of action in peacetime, and with it better prospects for promotion. It held greater appeal than garrison service in some gloomy northern town. In the navy consideration rested on talent, and social origins counted for little. Napoleone was good at mathematics and geography, and he was small and agile, all vital assets. But in 1783 higher powers decided that he should go into the army. Carlo's interventions in Paris proved fruitless and he was destined for the artillery – which came as a relief to Letizia, as the navy involved the danger of death by drowning as well as by enemy action. The artillery had also gained in prestige due to recent technical advances, and as it was an arm in which favour could not trump ability and mathematics was a prerequisite, Napoleone would also have an advantage. On 22 September 1784 he was interviewed by the inspector Raymond de Monts and selected for the École Militaire in Paris.
The fifteen-year-old Napoleone and four other cadets set off, under the care of one of the friars, on 17 October, travelling by heavy mail coach to Nogent-sur-Seine, where they changed to a _coche d'eau_ , a barge with a superstructure for passengers and goods, drawn by four Percheron horses along a tow-path. Two days later they disembarked on the left bank of the Seine opposite the Ile de la Cité and walked through what was then known as the ' _pays latin_ ' to their new school. On the way they stopped at a bookshop to buy books, and at the church of Saint-Germain-des-Prés to say a prayer.
The École Militaire, founded in 1751, had been reformed in the 1770s by the war minister Claude Louis de Saint-Germain. The 200 cadets wore military uniform of blue coat with yellow collar and red facings, red waistcoat and breeches. They were housed in a grand stone building which still stands at the end of the Champ de Mars, with a spacious courtyard in which they performed drills and played ball games. They slept in a dormitory with wooden partitions, each compartment containing an iron bedstead with curtains and minimal built-in furniture for their clothes, ewer and basin, and a chamberpot.
The day began with mass at six o'clock, followed by eight hours of instruction, except on Thursdays, Sundays and feast days, when the only obligations were four hours of reading and letter-writing, and sometimes target practice. Although the school was run by laymen, the routine included grace before and after breakfast, dinner and supper, prayers in chapel before bedtime, vespers and catechism as well as mass on Sundays, and confession once a month. The cadets were not allowed out, and were punished by detention on bread and water.
The curriculum included Latin, French and German, mathematics, geography, history, moral studies, law, fortification, drawing, fencing, handling of weapons, letter-writing and dancing (those destined for the navy and the artillery were too busy with technical subjects to attend these). The accent was on developing character and a military ethos: the cadets would be taught soldiering when they joined their regiments.
Napoleone did not take to the establishment, which he found too grand. The food was good and plentiful, and the cadets were waited on by servants, which he found inappropriate. He thought the austerity of Brienne more in keeping with the military life as he imagined it. Although the director, the Chevalier de Valfort, had risen from the ranks, the presence of fee-paying young men not destined for a career in the army lent the place an aristocratic atmosphere Napoleone did not like. At Brienne, the fee-paying cadets had been provincial gentry. Here they were of a higher social and economic standing, and they made the others feel it. Napoleone was teased for his origins, and the allusions to his being Marbeuf's bastard resurfaced. But he should have felt in good company, given that one of his brother cadets, Władysław Jabłonowski, a Pole of mixed race referred to as ' _le petit noir_ ', was supposedly the son of King Louis XV.
In a letter to his father of September 1784, four and a half years after arriving at Brienne, the fifteen-year-old Napoleone had asked him to send a copy of Boswell's book and any other historical works on Corsica he could find. He had left his homeland at the age of nine, at which time he can have known little of its history or circumstances. His reading at Brienne would have exposed him to the current intellectual and emotional trends, which included the cult of the _patrie_ , the motherland which demanded to be served and died for. Paoli's Corsican project chimed with this, and his fate appealed to the growing fashion for glorifying victimhood and lost causes. During his last years at Brienne Napoleone went through a phase of what he called ' _grande sensibilité_ ', and he embraced this one, casting himself as a Corsican patriot and an ardent worshipper of Paoli. The motivation may have been partly the need for a modern hero to emulate. The study of Plutarch had inspired a cult of heroes in late-eighteenth-century France, which was in matters of taste entering the age of neo-classicism. Alexander the Great, Caesar, Brutus, Cicero and others were the lode-stars of Napoleone's generation. A little wishful thinking could cast Paoli in the same mould. Napoleone's new-found emotional association with Corsica may also have had something to do with his sense of social inferiority, with a desire to claim for himself a status distinct from and morally superior to that of his fellow cadets with their noble pretensions, that of the persecuted patriot. It was certainly some kind of attempt to capture the moral high ground. But it sat uneasily with his family's having hitched its fortunes to the French monarchy, let alone his aim of making a career in the service of the King of France. The ambiguities of his situation, both national and social, were inescapable, and made no less real by his father's increasingly desperate efforts to position his family.
Carlo was not well. He had taken Joseph away from Autun and back to Corsica, hoping the boy would take a law degree and assume the responsibilities of head of the family. But Joseph persisted in his desire to become an artillery officer. After undergoing a short cure and assisting at the birth of his youngest son Jérôme, at the end of 1784 Carlo left the island with Joseph, meaning to take him to Brienne and then go on to Paris to petition for a bursary on his behalf, as well as press his own case for the award of the Milleli estate. The sea crossing was so rough they were nearly shipwrecked, and by the time they made land, at Saint-Tropez, Carlo was in a bad way. They travelled to Aix, where they met up with Joseph Fesch and decided to consult doctors at the medical school of Montpellier. There they found a close friend of Letizia from Corsica, now married to a tax official by the name of Permon, who helped Joseph and Fesch look after the thirty-nine-year-old Carlo. But he was sinking fast, and the doctors could do nothing for him. The end came on 24 February 1785: the post-mortem suggests either stomach cancer or a perforated ulcer as the cause of death.
Napoleone had never known his father well. Carlo was away for long spells during his childhood and they only saw each other once in France, when Carlo came to drop off Lucien at Brienne (and possibly when Letizia visited him). That short visit had not made a favourable impression on the boy, and frequent allusions to his paternity made him wonder whether Carlo really was his father. When, as was customary in such circumstances at the École Militaire, his confessor came to console him, Napoleone brushed him off, saying he had enough strength of character to cope with his loss without spiritual consolation. 'There would be no point in expressing to you how much I have been affected by the misfortune which has befallen us,' he wrote to his great-uncle Luciano. 'We have lost in him a father, and God knows what a father, with his tenderness and his attachment.' The letter dwells on the cruelty of Carlo's having had to die away from his home and his family, and ends by dutifully imploring Luciano to take the place of the father he has lost.
His father's death might have come as something of a liberation in one sense: the socially embarrassing and pushy Carlo, with his limited aspirations, fitted ill with Plutarch's heroes who filled the boy's imagination, and his obsequious attachment to France even less with the idealised vision of Paoli's struggle for the liberation of the Corsican nation which had become central to his view of himself. In Napoleone's imagination, Paoli was now not only a modern-day Plutarchian hero, a role model to be emulated, but also a spiritual father figure.
His obsession with Paoli was mocked by his fellow cadets, as a surviving caricature attests. But his pose as a representative of the heroic nation wronged by France was psychologically convenient for confronting the superior airs of his aristocratic comrades: he could parry their arrogance with self-righteous contempt. Such sparring should not be made too much of, and he only seems to have had one real hate in the school, a cadet by the name of Le Picard de Phélippeaux.
Napoleone's friend Laugier de Bellecour had come to the École Militaire from Brienne with him. Le Lieur de Ville sur Arce had left to join his regiment just before Napoleone arrived, but before leaving he had asked his friend Alexandre des Mazis to look out for him, warning him that he was prickly and difficult. Their first meeting bore this out, but the two soon became close. Napoleone found in him 'someone who understood him, liked him, and to whom he could without constraint uncover his thoughts', in the words of des Mazis.
Napoleone hated drill, and his mind would drift, with the result that his was always the last musket to be shouldered or lowered, despite des Mazis nudging him, incurring a sharp 'Monsieur de Buonaparte, wake up!' from the drill-master, at whom on one occasion Napoleone threw his musket in a rage. As a result he was made to perform his drill under the supervision of des Mazis. He loved fencing, but was a dangerous sparring partner. He was aggressive and, if touched, would go for his adversary with such fury that he laid himself open to further touches, which made him all the angrier. He often broke his foil, and sometimes the fencing-master would have to separate the combatants.
The two boys shared an interest in mathematics, and des Mazis admired the way his friend relished the challenge of a mathematical problem. 'He would not give up until he had overcome every difficulty,' he recalled. They were taught by Le Paute d'Agelet, a mathematician and astronomer who had circumnavigated the globe with Bougainville, and who enthralled them with his accounts, reviving Napoleone's naval aspirations. In 1785 he was preparing to set off on a voyage of discovery with the explorer Jean François de La Pérouse, and along with several others Napoleone applied to accompany the expedition. Only one was chosen, and it was not him. The voyage ended in disaster in the South Pacific, and nobody survived.
As well as mathematics, Napoleone showed a great curiosity about geography and history, and read widely in both. Although he loved literature, he seemed to have little interest in improving his French, and the exasperated French teacher eventually told him not to bother attending his classes. He also showed what one teacher described as 'an invincible repugnance' for learning German. But he was generally popular with the teachers, who were impressed by 'the persistence with which he argued his points'.
He struck teachers and cadets alike as serious-minded, and was described by one of them as 'preferring study to every kind of amusement', interested in literature and ideas, 'uncommunicative, fond of solitude, capricious, arrogant, extremely self-centred', 'having high self-esteem' and a good deal of ambition. Much of the time he appeared to be in a world of his own, pacing up and down, lost in thought, sometimes gesticulating or laughing to himself.
According to des Mazis, 'he groaned at the frivolity of the other pupils', and disapproved of their 'depravities', going so far as to say the school authorities should do more to 'preserve them from corruption'. This was not driven by religious feelings: he had taken his first Holy Communion at Brienne and was confirmed at the École Militaire, and while he went through the motions, never rebelling against the obligation to hear mass every day, he showed no religious zeal. It probably had more to do with his own awkwardness, which made him dismiss sex as something silly and embarrassing. He later admitted that puberty had made him 'morose'. This was exacerbated by the behaviour of his friend Laugier de Bellecour, who had found some like-minded young gentlemen at the École Militaire and flaunted his homosexuality. Napoleone admonished him on the subject and declared that they could not remain friends unless Laugier reformed, as he could not countenance such immoral behaviour. When Laugier teased him for a prig he lost his temper and attacked him physically. Napoleone later expressed regret, and often spoke of his former friend 'with sincere affection'. But a prig he remained.
In September 1785 he sat the exam to be admitted into the artillery, and passed forty-second out of fifty-eight candidates. All the others had spent two or in some cases four years longer than him preparing for it, so it was not a bad showing. He was posted second lieutenant to the prestigious regiment of La Fère, stationed at Valence. He quickly put together his new uniform, which consisted of a blue coat with red facings and lining, blue waistcoat, red piping and one epaulette. He was so proud of it that he could not resist showing it off to the Permons and other Corsicans in Paris, as he was now allowed out of the school building.
Des Mazis had been posted to the same regiment, and on 30 October 1785 the two left Paris together. They took a coach as far as Chalon-sur-Saône, where they transferred to the _coche d'eau_ for the rest of the journey to Lyon, and continued by post-boat down the Rhône to Valence. It was the first time the sixteen-year-old Napoleone had been unsupervised, and at one point he exclaimed, 'At last, I am free!' and ran around gesticulating wildly.
## 4
# Freedom
Valence was a medieval town of tortuous muddy streets dominated by a citadel built to guard the valley of the Rhône and surrounded by fortifications designed by the celebrated engineer Vauban. It had a population of some 5,000, a significant portion of which was accounted for by its fourteen convents, abbeys and priories. Napoleone arrived on 3 November 1785 and took lodgings above a café belonging to Claudine-Marie Bou, a merry and cultivated forty-year-old spinster who washed his linen and looked after his needs. He messed with his fellow officers at the Auberge des Trois Pigeons nearby.
Second Lieutenant Napolionne de Buonaparte, as he was listed, was placed in command of a company of bombardiers manning mortars and howitzers. He had never handled a piece of ordnance before, and now acquainted himself with the practical aspects of gunnery during frequent exercises on a training ground outside the town. He also had to familiarise himself with the works of the founders of modern French artillery, Generals Gribeauval and Guibert, take more advanced courses in mathematics, trigonometry and geography, and learn how to draw maps and plans.
The regiment of La Fère was one of the most professional in the French army. Its officers were a close-knit family with none of the snobbishness Napoleone had encountered up till now. His messmates included des Mazis and another friend from Brienne, Belly de Bussy, who had joined the regiment a little earlier, and two new ones who were to have distinguished careers, Jean-Ambroise de Lariboisière and Jean-Joseph Sorbier. Napoleone's company commander was a kindly man who befriended him and invited him to stay at his country house.
The officers of the regiment were welcomed by the local gentry, and Napoleone took dancing lessons to enable him to participate in social gatherings (he remained a graceless dancer). He was befriended by two English ladies who lived nearby, and was a frequent guest at the château of a Madame du Colombier a dozen kilometres outside the town. He flirted with her daughter Caroline, whom he would describe as an ' _amie de coeur_ '. 'Nothing could have been more innocent,' he recalled: they would arrange secret meetings during which 'our greatest delight was to eat cherries together'. He was not yet seventeen, and had spent the past eight years cloistered in all-male institutions, so his first emotional stirrings were confused. There is some evidence that he had tender relations with another young woman, a Miss Lauberie de Saint-Germain, but these probably did not amount to much either. 'He was of a moral purity very rare among young men,' recalled des Mazis, adding that Napoleone could not conceive how anyone could allow themselves to be dominated by feelings for a woman.
Napoleone was able to nourish his mind as well as his heart, as he was a welcome guest at the house of Monseigneur de Tardivon, abbot of the abbey of Saint-Ruf, to whom Bishop Marbeuf had given him a letter of introduction. Tardivon, a friend of the renowned anti-colonialist author Abbé Raynal, was the leading light in the intellectual life of Valence, and the gatherings at his lodgings gave Napoleone an opportunity to broaden his views and for the first time in his life take part in intellectual discussion. He caught the spirit of the times and began to question received wisdom and reappraise the world around him; according to one of his brother officers he became insufferably voluble. There was a bookshop which doubled as a reading room opposite his lodgings, to which he took out a subscription, which gave him access to books he could not afford to buy. He read fast, occasionally misunderstanding texts, and erratically: of Voltaire's works he read some of the least influential, little of Diderot's, and less of Montesquieu's, and only those passages of Raynal which related to Corsica. Given his emotional and sexual immaturity, it is not surprising that he was horrified by Sade, but adored the straightforward sentimentality of Rousseau's _La Nouvelle Héloïse_ and Bernardin de Saint-Pierre's _Paul et Virginie_.
Like most educated young men of ambition at the time, Napoleone began to fancy himself as a man of letters. With France at peace, literature provided a welcome distraction as well as an opportunity to shine, as another artillery officer, Choderlos de Laclos, had shown with his publication four years earlier of _Les Liaisons dangereuses_. For Napoleone it was a way of formulating his views, and more importantly a conduit for his feelings about his island home and his own identity. His first surviving essay, written in April 1786, is a brief sketch of the history of Corsica.
Barely ten days later he produced a short essay on suicide, a stilted piece full of self-pity and self-dramatisation. 'Always alone while surrounded by people', he prefers to come home and indulge his melancholy. He wonders whether he should not end his life, as he can see no useful purpose for himself in this world. 'Since I must die one day, would it not be as well to kill myself?' he asks rhetorically. What does come through the verbiage is unhappiness at having recently suffered 'misfortunes' as a result of which life holds no pleasure for him, and a sense of disgust at the mediocrity and corruption of people, which has led him to despise the society in which he is obliged to live. Whether this was a response to some amorous rejection or social snub, or just an outburst of teenage angst, one can only speculate. It is not the expression of a deeper malaise. Less than a week later, on 9 May, he wrote an impassioned defence of Rousseau against the Swiss pastor Antoine Jacques Roustan's criticism of him. Rousseau's works exerted a profound influence on Napoleone's emotional development, and although he would later change his mind and deride Rousseau's sentimentality, he would never shake it off entirely.
With Carlo gone, Napoleone had become the family's man in France, and it now fell to him to obtain places in various institutions for his siblings and petition on behalf of the family's interests. These were not looking good. The Salines had been only partly drained during Carlo's lifetime, and as only a fraction of the intended mulberry trees had been planted, the government had decided to stop throwing good money after bad. On the other hand, the Buonaparte had won their case for compensation for the Odone legacy in the form of Les Milleli. It was a fine property with a small house and olive groves above Ajaccio. But Napoleone's great-uncle Luciano was ill and incapacitated, and Joseph was proving incapable in practical matters. Aged seventeen, Napoleone was obliged to take over the management of the family's affairs. He applied for leave, and on 15 September 1786 was back in Ajaccio. His mother and Joseph were on the quayside to greet him, but the place was unfamiliar. He was seeing Corsica after an absence of seven years and nine months. He had left as a child, and returned a young man. He met for the first time four younger siblings: Louis aged eight, Maria Paolina six, Maria Nunziata three, and Geronimo only two. He even found it difficult speaking to them, as he had not used his Corsican Italian while he was away.
Luciano had resigned his post as archdeacon, which was taken by Napoleone's half-uncle Joseph Fesch, but he had some money, which lent him weight in family affairs, and it was with Fesch and Joseph that he took charge of them. Napoleone applied for an extension of his leave and busied himself with the harvest, the family properties and other practical matters.
During that time he got to know his family, not only his mother, whom he had seen just once briefly since he was nine, but also his siblings and the extended network of cousins, uncles and aunts. He revisited his wet-nurse and others who had looked after him when he was little, and spent much time with the ailing Luciano, whom he revered. He developed a relationship with his brother Joseph, who recalled with fondness their long walks along the coast, breathing in the scent of myrtle and orange blossom, sometimes returning home only after dark.
Napoleone explored the island and tried to acquaint himself with its people and their lore, of which he had only dim childhood memories. He was taken aback by primitive aspects of Corsican life that had not struck him when he was a child, but convinced himself that his fellow islanders were noble savages whose vices were the consequence of the barbarous French occupation. He had brought with him a trunk full of books, which no doubt sustained him and provided the moral and emotional arguments which would enable him to construct an appropriate vision of Corsica.
He spent almost a year on the island, and did not leave until 12 September 1787. He did not rejoin his regiment, but set off instead for Paris, where he hoped to obtain payment of the 3,000 livres of the subsidy still due for the Salines. It was a considerable sum, roughly equal to three years of his pay as a lieutenant. When he reached the capital he called on ministers and people of influence, probably including Loménie de Brienne, now minister of finances. He also went to great lengths to obtain a place at the seminary in Aix for his brother Lucien. An impecunious outsider in a city in which the aristocracy's wealth and privilege were on display, the provincial subaltern's social inhibitions could only have been aggravated by the need to beg for favour.
When not petitioning ministers, he was reading, taking notes and writing draughts of essays which display a critical attitude to the political system. In one, he argued that while Alexander the Great, Charlemagne, Machiavelli and others were undoubtedly great men, they were driven by the desire to win acclaim, which made Leonidas, who had set out to lay down his life for his country unconditionally at the battle of Thermopylae, superior to them, a typically Romantic value judgement showing the influence of Rousseau and a tendency to reject the practical. It sat uneasily with his own instincts, if his brother Joseph is to be believed. He recalled that during one of their walks on Corsica Napoleone had told him he wished he could perform some great and noble act which would be recognised by posterity, and that he could, after his death, witness a representation of it 'and see what a poet such as the great Corneille would make me feel, think and say'. Such transference of the desire for recognition, normal in any teenager, suggests a disinclination or perhaps inability to engage with the world around him. A combination of awkwardness and disdain certainly marked his attitude to sex.
On the evening of 21 November he went to see a play, and on leaving the theatre strolled through the Palais-Royal, the Paris residence of the Orléans branch of the royal family. It had extensive gardens at the back, flanked by arcades with shops, cafés and small premises in which whores plied their trade. The higher-class ones sat at their windows beckoning to the passers-by, the next degree down would sit in the cafés, and the cheapest would loiter under the colonnade or along the avenues of the garden.
The following morning, Napoleone sat down and described what happened next as though he were writing up a scientific experiment. 'My soul, agitated by the vigorous sentiments natural to it, made me bear the cold with indifference,' he wrote, 'but when my imagination cooled, I began to feel the rigours of the season and made for the arcades.' There a young girl caught his eye. She was obviously a prostitute but did not have the brazen manner of the others, and returned his look with modesty. 'Her timidity encouraged me and I addressed her... I who more than anyone else felt the horror of her kind, and had always felt myself sullied by a mere look from one...' In his account, he makes it clear that he was looking for someone 'who would be useful for the observations I wished to make'. He admits that previous attempts to pick up a prostitute had not been 'crowned with success', which might appear odd, as a young officer would not normally have difficulty carrying out such a transaction in the Palais-Royal. His record of their conversation goes some way to explain why: he began by asking how she came to her present condition, which was neither tactful nor to the point, and after more such banter on a freezing November night, it was she who suggested they go back to his lodgings, only to be asked what for. 'Well, we could warm ourselves and you could satisfy your fancy,' she answered. The clinical account does not mention whether the experience had been pleasurable or not.
On 1 December, having obtained a six-month extension of his leave, Napoleone set off for Corsica once more. His efforts in Paris had come to nothing, which only contributed to his disenchantment with a state of affairs that seemed to exclude him as well as his native land, whose subjugation he was beginning to take personally. His vision of a noble nation oppressed by a wicked and corrupt France fitted well with a feeling that he and his family were being thwarted, or at least disrespected, by the regime in Paris.
He spent the next four and a half months in Corsica, and it was not until 14 June 1788 that he rejoined his regiment, now stationed at Auxonne, after an absence of twenty-one months. This was not unusual, as in peacetime officers were allowed to absent themselves for long periods.
Auxonne was a fortified town on the river Saône with an artillery school under the sixty-six-year-old lieutenant general baron Jean-Pierre du Teil, a clever and innovative commander who worked his men hard by setting them challenges that upset their routines. Du Teil took an immediate liking to Napoleone. He set him the task of designing and constructing earthworks, which involved calculations of firepower, resistance and ballistics, followed by ten days of physical work, with Napoleone marshalling 200 men with picks and shovels. 'This extraordinary mark of favour earned me the ill-feeling of the captains who claimed it was insulting to them that a mere lieutenant be charged with such an important task and that if there were more than 50 men involved one of their rank should be in command,' he wrote to Joseph Fesch on 29 August. He nevertheless pacified them and even gained their friendship; considering him an intellectual, they tasked him with drawing up the _Calotte_ , a regimental code of conduct. He rose to the challenge and produced a document that was both reasoned and idealistic, very much in the spirit of Rousseau, which could have been the constitution for a popular dictatorship.
From his essays and notes it is clear that he was already a republican, having, like Rousseau, come to the conclusion that existing systems of government were absurd and that kings had no right to rule. In the introduction to what was to be a dissertation on royal authority, he argued that this was entirely 'usurped', since sovereignty resided in the people, adding that 'there are very few kings who have not deserved to be dethroned'. He also adopted Rousseau's thesis that religion was destructive, since it was in competition with the state as it held out the promise of happiness in another world, when it was for the state to provide people with the means to achieve it in this.
He continued to read, annotating and commenting as he went, on subjects as varied as ancient and modern history, geography, the fiscal systems of different states, the role of artillery and ballistics, Greek philosophy, Arab culture, biology, natural history, the possibility of digging a canal through the isthmus of Suez, and many more. That summer he read Richardson's _Clarissa_ and Goethe's _Sorrows of Young Werther_ , and himself wrote _Le Comte d'Essex_ , a gothick novella about an imagined conspiracy against Charles I featuring ghosts, blood and daggers, and _Le Masque Prophète_ , a short piece set in the Arab world which is a kind of parable about dictatorship. The plots are melodramatic, the prose bristles with adjectives and metaphors, not to mention spelling mistakes, the characterisation is non-existent.
Auxonne lay in a marshy, misty part of the Burgundian plain, and Napoleone believed it was the insalubrious exhalations from the stagnant moat beyond the ramparts which brought him down with a fever that autumn, but it may in part have been a consequence of his lifestyle. He was economising on food in order to be able to send money home to his mother. He lived in barracks, in a small room with a bed, a table, six straw-seated chairs and one armchair. He messed with the other officers, but although his lodgings were free, he was still only on the pay of second lieutenant, so he had to be careful. But there was also a manic element to his life at this time. 'I have no other resource here but work,' he wrote to his great-uncle Luciano in March 1789. 'I only get dressed once a week, I sleep very little since my illness. It is incredible. I go to bed at ten o'clock and get up at four in the morning. I only take one meal and dine at three; it suits my health very well.' He would keep the shutters closed to help his concentration. He did in fact go out, for, as he proudly explained in the same letter, 'I have gained quite a distinguished reputation in this little town with my speeches on various occasions.'
The French monarchy was virtually bankrupt, and as a last resort to raise money the king called the Estates General. As this body, representing the clergy, the nobility and the non-noble 'third estate', had not been summoned for nearly two centuries, this opened up a Pandora's box of questions about the nature of the government. All over the country people of every station aired their views and propounded solutions to the political crisis. This was accompanied by popular unrest, and on 1 April Napoleone was sent to the town of Seurre with 100 men to suppress riots. The rebellious spirit inspired bad behaviour, and one day he was sent to the monastery of Citeaux to quell a mutiny by the monks. Over dinner a grateful abbot served him 'delicious wine' from the Clos Vougeot in the monastery cellar, which the monks had tried to raid. In a letter to Letizia, he described the sumptuous Easter dinner he was given by a local nobleman. 'But I would rather have been eating ravioli or lasagne in Ajaccio,' he concluded.
He was in high spirits. His health had recovered, the weather was glorious, and he bathed in the Saône (once he got a cramp and nearly drowned). 'My friend, if my heart were susceptible to love, what a favourable moment this would be: fêted everywhere, treated with a respect that you could not imagine,' he wrote to Joseph, boasting that 'The prettiest women are delighted with our company.'
Like most of his generation, he was in a state of excitement about political events. 'This year heralds some beginnings which will be very welcome to all right-thinking people,' he wrote to his proxy godfather Giubega from Auxonne in June, 'and after so many centuries of feudal barbarism and political slavery, it is wonderful to see the word Liberty inflame hearts which seemed corrupted by luxury, weakness and the arts.' But this raised questions closer to home. 'While France is being reborn, what will become of us, unfortunate Corsicans?' he asked. The moment seemed ripe for him to strike a blow for his island nation by publishing a history of Corsica, but he felt he needed the support or at least approval of Paoli, so he wrote to him in his London exile.
'I was born as the fatherland was perishing,' he wrote. 'My eyes opened to the odious sight of 30,000 French who had been vomited onto our shores drowning the throne of liberty in rivers of blood. The screams of the dying, the moans of the oppressed, tears of despair surrounded my cradle from the moment of my birth.' There is some doubt as to the authenticity of this letter, as the original has never been found and there is no trace of a response from Paoli. But it would have been an odd one to forge, given Napoleone's later career, and the melodramatic style is in tune with his contemporary writings, most notably his _Nouvelle Corse_. This is a confused rant against the French, represented as irredeemably cruel and corrupt, with a plot derived from _Robinson Crusoe_ and _Paul et Virginie_ so lurid and violent as to be incoherent, couched in a pornography of gore, rape and mutilation, punctuated by flights of sentimentality.
The history he had been planning for the past few years was finally taking shape in the form of _Lettres sur la Corse_ , an emotional account of events up to the beginning of the eighteenth century which anthropomorphises the Corsican 'nation' in the fashion of the day. When the first two letters were finished he sent them to his former French teacher at Brienne, the Abbé Dupuy, asking him to edit them. As well as rewriting whole passages, Dupuy delivered a withering verdict, suggesting in the politest terms that he cut out all the 'metaphysical' content.
On 15 July, Napoleone was in the process of writing to his great-uncle Luciano when two brother officers came into the room with the news they had just received from Paris about a riot having got out of hand and the mob having stormed the Bastille. Whatever his feelings about the monarchy, he was alarmed at the disorders. Four days later, riots broke out in Auxonne, and in a letter to Joseph he expressed contempt for the 'populace' and the 'assortment of brigands from outside who had come to pillage' the customs house and the tax gatherer's office. Nor was he impressed by the attitude of his own men, who showed reluctance to quell the riot. On the night of 21 July he acted as the general's aide, marshalling troops against the rioters. While he claims to have brought matters under control with a forty-five-minute harangue (which sounds unlikely given his oratorical skills), he makes no bones about his frustration at not being allowed to fire on the mob, a profound distaste for which shines through his account.
He was nevertheless excited by the developments. 'All over France blood has flowed,' he wrote to Joseph on 8 August, 'but almost everywhere it was the impure blood of the enemies of Liberty and the Nation.' His commander had put him in charge of a group of officers with the brief of studying the possibilities of firing bombs from siege pieces, and he wrote up its report diligently, but his thoughts were elsewhere. He had applied for long leave, meaning to go to Corsica and play a part in whatever might take place there. Both his feelings and his ambition drew him there: the ideal of the island nation he had nourished over the past few years beckoned, as did the fact that there he could play a more prominent part than in France.
On 16 August his regiment mutinied. The soldiers confronted their officers demanding they hand over the regimental chest, which they were obliged to do. The soldiers then got drunk and tried to fraternise with the officers, forcing them to drink with them. Napoleone's thoughts are not recorded, but there can be little doubt as to what they were. When, a few days later, the regiment went on parade to swear a new oath, to the Nation, the King and the Law, he was probably thinking of another nation. His request for leave had been granted, and in the first days of September he left Auxonne for Corsica.
## 5
# Corsica
Napoleone reached Ajaccio at the end of September 1789. Apart from Maria-Anna, who was still at Saint-Cyr, the whole family was there. Joseph had a judicial post in the city, but Lucien, who had abandoned a military career because of poor eyesight and then given a clerical one a try, was idling, along with Louis. Their prospects in France had faded and they were reduced to Corsica once more. Napoleone intended to play a part in the island's affairs, but the political scene was not quite as he had imagined.
There had been riots in the coastal cities in the wake of events in France, but there was no impetus for revolution, since none of the grievances which motivated it in France resonated in Corsica, where feudal privilege and class differences were not major issues. Here, the conflict was between the separatists and those who had thrown in their lot with France, and between rival clans. In the early summer of 1789 a Corsican assembly had sent four deputies to the Estates General at Versailles: Matteo Buttafocco representing the nobility, the Abbé Peretti the clergy, and the lawyer Cristoforo Saliceti and Captain Pietro Paulo Colonna Cesari the third estate. The only thing uniting them was resentment of the French administration. Even the French loyalists Buttafocco and Peretti wanted the island administered by its inhabitants, meaning their own sort. The representatives of the third estate, Saliceti and Cesari, belonged to a faction describing themselves as 'patriots', some of whom wanted greater autonomy or even independence, others integration into France.
The Estates General had transformed itself into a National Assembly, and this would decide Corsica's future. On 17 June 1789 Saliceti and Cesari appealed to it demanding that Corsica be governed by a committee of locals and the formation of a native civic guard on the model of those which had sprung up all over France. Meanwhile, a rash of opportunistic disturbances covered the island as latent gripes were voiced and scores settled. On 14 August the assembly which had chosen the deputies to the Estates General set up a revolutionary municipal authority in Bastia. The following day the festivities of the Assumption of the Virgin in Ajaccio resulted in the formation of a 'patriotic committee' there, with Joseph as secretary (since he was the only one of them who could read and write French). Napoleone assumed that the next step would be the formation of a civic guard, and with another young enthusiast, Carlo Andrea Pozzo di Borgo, went about distributing tricolour cockades to be worn as a mark of solidarity with the Revolution in France and encouraging people to form a citizens' militia.
On 17 October the National Assembly, which had by then transferred from Versailles to Paris, decided against allowing Corsica its own assembly and civic guard, on grounds of cost. Napoleone composed a letter of protest, signed by all the revolutionary activists in Ajaccio. He continued to agitate, and on 30 November his appeal demanding for Corsica the same rights enjoyed by the rest of France was read out to the National Assembly in Paris. It was backed by Saliceti and supported by the revolutionary tribune Mirabeau, and in one of those moments of wild enthusiasm characteristic of the early days of the Revolution, Corsica was integrated into the French nation and all those who had fought against the French were amnestied. Paoli was invited to leave London and come to Paris, where he would be welcomed as a hero before travelling on to Corsica. There were celebrations with the _Te Deum_ sung in the island's churches, and Napoleone hung a banner on the façade of the Buonaparte house bearing the inscription ' _Vive la Nation! Vive Paoli! Vive Mirabeau!_ '
The words encapsulated a confusion as to which 'nation' Napoleone now associated with. 'This young officer was brought up at the École Militaire, his sister is at Saint-Cyr, his mother has been showered with benefactions by the government,' the French commander in Ajaccio wrote to the minister of war in Paris, adding that he should be with his regiment instead of stirring up trouble in Corsica. But Napoleone was not recalled, and the question of his allegiance would be complicated further with the arrival on the island of Paoli.
The Babbo was preceded by various of his followers returning from exile whose sufferings in the cause endowed them with a sense of self-righteousness that led them to call into question the loyalty of those who, like the Buonaparte, had accommodated themselves to French rule. This made it incumbent on the Buonaparte brothers to demonstrate their devotion to the Corsican cause. They took down a portrait of Marbeuf which hung in their drawing room and hid it, but it was not clear where they stood.
As Napoleone was writing his violently anti-French history of Corsica at the time, one must assume he still considered himself a Corsican patriot rather than a Frenchman. But given the uncertainties of the situation, he had to hedge his bets and remember that he had a career in the French army. His immediate priority was to secure position and influence. In February 1790 the two brothers agitated for the election of their friend Jean Jérôme Levie as mayor of Ajaccio, and of Joseph to the municipal council (which entailed archdeacon Fesch falsifying his birth certificate to make him of eligible age).
The next step was to get Joseph elected to the general assembly which was to meet at Orezza to set up an administration for the island. Joseph was successful, and Napoleone accompanied him as they set off on horseback on 12 April, but on arrival they found themselves looked on askance by many of Paoli's faithful. Napoleone expressed anti-French feelings and wrote an appeal demanding that all Frenchmen be expelled from the island. He befriended Filippo Buonarroti, a revolutionary and supporter of Paoli from Tuscany, and Filippo Masseria, Paoli's right-hand man who had been sent ahead from London (and was a British agent). He also wrote to his commanding officer asking for an extension of leave, citing health reasons.
None of this did much to enhance his credibility with Paoli's henchmen at Corte, but it did affect his standing in Ajaccio, and when the two brothers returned they faced the enmity of the more conservative inhabitants. In the first days of May, while strolling on the Olmo they were attacked by a gang led by a local priest, but were saved by the appearance of a bandit of their acquaintance. They managed to mobilise their supporters in the Borgo, and on 25 June all French officials were expelled from Ajaccio.
Joseph was one of those selected to meet Paoli on his way from Paris and accompany him back to his native island, where they landed on 14 July 1790. Napoleone and others from Ajaccio met him at Bastia on 4 August, and the two brothers joined some 500 supporters who rode with him on his triumphal progress to Corte.
The General of the Corsican Nation was sixty-five and marked by twenty-one years of exile in London, during which he had grown to appreciate the merits of monarchy. Although it was the Revolution that gave him back his homeland, he was no revolutionary. On 8 September he opened a congress at Orezza which he packed with his family and supporters. Over the next three weeks this reorganised the administration of the island, giving him unlimited executive power, overall command of the National Guard and a considerable income. This was out of tune with what was being done in Paris, and many of the measures taken were against the law, given that Corsica was now a department of France.
Napoleone was not put off by such high-handed methods. Thanks to Paoli's favour, Joseph had obtained a seat in the congress and the presidency of the district of Ajaccio. And although he did not benefit personally, Napoleone supported Paoli, accusing anyone who showed less than full commitment of being 'bad citizens', and suggesting to Carlo Andrea Pozzo di Borgo the physical removal of three officials whose zeal he found wanting. 'The means are violent, possibly illegal, but indispensable,' he insisted. He considered that Paoli was still placing too much trust in democracy and felt he should be more ruthless.
Napoleone's leave was running out, so at the end of October he sailed for France. His ship was twice driven back by gales, and it was not until the end of January 1791 that he would finally make it off the island. In the meantime, he remained politically active. On 6 January, along with Joseph, Lucien and Joseph Fesch he took part in the opening session of the Globbo Patriotico, the Patriotic Club of Ajaccio, affiliated to the extreme revolutionary Jacobin Club of Paris. Napoleone attended regularly, making frequent speeches. He was at his most fervent when it came to denouncing Buttafocco and Peretti, who had been agitating in Paris against Paoli. Napoleone wrote a pamphlet entitled _Lettre à Buttafocco_ in which he denounced the deputy as a traitor and blamed him for all the blood spilt by the French in Corsica. He read the letter out in the club, where it was enthusiastically received, with a vote that a hundred copies be printed.
When Napoleone did eventually sail for France, he took with him his younger brother Louis. The boy was twelve years old and unlikely to obtain an education if he were left in Ajaccio, and as there was no money to send him to a proper school, Napoleone decided to take this in hand himself.
On 12 February he was back with his regiment at Auxonne. He took two small rooms in the town, one for himself and one for Louis. 'He is studying hard, learning to read and write French, and I am teaching him mathematics and geography,' Napoleone wrote to Joseph on 24 April. 'He will be a fine fellow. All the ladies here are in love with him. He has adopted a slightly French manner, correct and elegant; he goes into society, greets people with grace, makes the usual small talk with the gravity and dignity of a man of thirty. I have no doubt that he will be the best fellow of the four of us.' He did not mention that young Louis sometimes required a thrashing to encourage him.
On their journey from the south coast Napoleone had rejoiced in the revolutionary ardour he witnessed everywhere. Passing through Valence he attended a session of the local revolutionary club, and on 8 February in a letter to Joseph Fesch he assured him that the whole country was behind the Revolution, and that the only royalists he had met were women. 'It is not surprising,' he quipped. 'Liberty is a woman more beautiful who eclipses them.' This reflection seems to have prompted him to scribble some thoughts for an essay on the subject of love, which, he maintained, was an entirely superfluous emotion.
He was welcomed at Auxonne by his friend des Mazis and his commanding officer du Teil, but many of his brother officers gave him a chilly reception when he began to voice his opinions. In its first stages, the Revolution had been welcomed by most educated Frenchmen, and certainly by young officers in provincial regiments, who resented the aristocracy's monopoly over higher ranks. The abolition of noble rank itself in June 1790 removed all barriers to advancement, but it was not well received by all, and subsequent developments turned many against the way the Revolution was going. Napoleone's revolutionary enthusiasm grated on them, and his obsession with Corsica would not have won him much sympathy.
He was busy seeing to the printing of his _Lettre à Buttafocco_ , of which he sent copies to the National Assembly in Paris and to Paoli in Corsica. He was hoping to complete and publish his history of Corsica, and wrote to Paoli requesting access to his archive. Paoli was dismissive, describing the pamphlet as a pointless gesture, and not only failed to comply with Napoleone's request for access to his papers, but let off the parting shot that history should not be written by young people, making it clear he considered him immature.
In the process of reorganising the army, the National Assembly replaced the names of artillery regiments with numbers, and that of La Fère now became the First. Napoleone was transferred to the Fourth, formerly the regiment of Grenoble, now based at Valence, in which he was posted first lieutenant. He left Auxonne on 14 June and reached Valence two days later, moving into the same rooms he had occupied before and messing at the same inn. Madame du Colombier and her daughter had left the area, but many of the friends he had made during his previous sojourn were still there. Mademoiselle Lauberie de Saint-Germain, with whom he had flirted before, had in the meantime married Jean-Pierre Bachasson de Montalivet, an intelligent man whom Napoleone befriended.
Having settled in, Napoleone composed _Dialogue sur l'amour_ , a Platonic discourse addressed to des Mazis, who was wont to fall in love and then extol the condition's joys and sufferings to Napoleone. In it he admitted to having been in love himself, but argued that what was at bottom a simple sensation had been garlanded with too many 'metaphysical definitions'. 'I believe it to be harmful to society, to the individual happiness of mankind, and I believe that love does more harm than good,' he argued, 'and that it would be a blessing if some protective divinity were to rid us of it and deliver the world from it.' It seemed absurd to him that men, 'this sex which is master of the world through its strength, its industry, its mind and other faculties, should find its supreme felicity in languishing in the chains of a weak passion and under the sway of a being more feeble than itself in mind and body'. He might have jettisoned the sentimentality of _La Nouvelle Héloïse_ , but Napoleone was still a child of Rousseau in believing that man's first duty is to society and the state.
The nature of the French state was being transformed, testing allegiances and polarising society. A few days after his arrival news reached Valence of the king's attempt to flee the country and arrest at Varennes near the border with the Austrian Netherlands on the night of 21 June 1791. Back in October 1789 Louis XVI had been obliged by a mob of women to leave Versailles and move to Paris. He and his family effectively became prisoners in the royal palace of the Tuileries, and the increasing hostility of the Paris mob precipitated a decision to flee. This was seen as a betrayal, since his intention had been to join the anti-revolutionary forces gathering against France at Koblenz in Germany under his younger brother the comte d'Artois.
Napoleone had joined the Club des Amis de la Constitution, of which he soon became secretary, at whose meetings he made republican speeches. On 14 July, as his regiment paraded to celebrate the second anniversary of the fall of the Bastille, the officers and men swore a new oath of loyalty, to the National Assembly. A _Te Deum_ was sung and at a banquet that evening Lieutenant Buonaparte was among those raising republican toasts. Not wishing to perjure themselves by taking an oath which overrode that pledging loyalty to the king, many of his brother officers resigned their commissions, and some would cross the frontier to join the royalist forces. Napoleone felt no such scruples. In his cherished narrative of a Corsica violated by the French, the monarch was the incarnation of the arch enemy, and since he had begun to develop a more positive attitude to France, the king drew the residue of his negative feelings.
Having to support both himself and Louis, Napoleone was short of money, and it was partly the prize of 1,200 francs (more than his annual pay) that induced him to enter a competition announced by the Académie of Lyon for an essay on the theme of 'Which truths and which sentiments it is most necessary to inculcate in people in order to ensure their happiness'. In the event, neither he nor any of the other fifteen applicants won the prize, as the jury found their efforts wanting. One of its members described Napoleone's essay as a wild dream, and another commented that 'It may be the work of a man of some sensibility, but it is too poorly ordered, too disparate, too rambling and too badly written to hold the attention.' It is indeed pompous, florid, full of cultural references and recherché words (he had made a list of them before starting), but it is nevertheless a fascinating document.
It bristles with contradictions as Napoleone's libertarian instincts jostle with an authoritarian urge to order things for the best. He prefaces it with some verses by Pope to the effect that man is born to enjoy life and be happy, and opens with the sentence: 'At his birth, man acquires the right to that portion of the fruits of the earth which are necessary to his existence.' He rages against those such as profiteers who stand in the way of this, and against authority in general. He stipulates that everyone should have their portion of land and the full protection of the law, and that people should be allowed to say and write what they like. Yet the law should direct people according to the rules of reason and logic, and protect them from 'bad' and 'perverted' ideas, which should not be permitted to circulate in word or in print. Intriguingly, he identifies ambition as the principal scourge of mankind, above all 'the ambition which overthrows states and private fortunes, which feeds on blood and crime; the ambition which inspired Charles V, Philip II, Louis XIV', which he sees as an 'unruly passion, a violent and unthinking delirium', since 'Ambition is never satisfied, even at the pinnacle of greatness.' Although he rejects Rousseau's premise of man's natural goodness in favour of a more cynical view of human nature, he indulges the noble savage myth and holds up Paoli as a paragon of virtue who had revived the spirit of Athens and Sparta.
Having managed to obtain leave once more, Napoleone was back in Ajaccio by the beginning of October 1791. He canvassed for Joseph, who was seeking election to represent Corsica at the Legislative Assembly which was to meet in Paris (the National Assembly had dissolved itself). But Paoli placed his favoured candidates, and Joseph was rewarded with no more than a local post at Corte. Paoli showed ambivalence with regard to the Buonaparte clan, and particularly to Napoleone, who wore a French uniform and was beginning to behave more like a French Jacobin than a Corsican patriot.
Although Paoli had sworn loyalty to the French nation before the National Assembly in Paris on 22 April 1790, he had regarded the French as the enemy for so long that it was difficult for him to trust them. As well as being a monarchist, he was a devout Catholic and a friend of the clergy, who had backed him and sheltered his partisans. The Revolution's disestablishment of the Church and persecution of the clergy was as offensive to him as to most Corsicans.
Only a couple of weeks after Napoleone's arrival, on 16 October, his great-uncle Luciano died. Hardly had he breathed his last than his nephews and nieces groped under his mattress and then ransacked the room in search of the money they assumed he had squirrelled away. It turned out there was little left, as Luciano had been obliged to dig into his savings to pay Carlo's debts. But Joseph managed to persuade the administration (of which he was a member) to reimburse the money Carlo had invested in the Salines over the years. The funds were invested in a number of properties confiscated from the Church, the royal domain and the nobility which were being sold off as _biens nationaux_ , 'national assets'. It seems that in order to scotch rumours of malversation, the Buonaparte brothers put about the story that they had found a fortune under Luciano's mattress.
While Joseph grafted at Corte, Napoleone obtained a command in the National Guard of Ajaccio, which relieved him from having to report back to his regular unit. But a new law stipulated that officers below the rank of lieutenant colonel must leave the National Guard and rejoin their units. Determined to remain in Corsica, he decided to try for that rank. He would have to dispute it with two formidable candidates. One was Matteo Pozzo di Borgo, a member of the most powerful clan in Ajaccio and brother of Carlo Andrea, Paoli's trusted collaborator and currently a deputy to the Legislative Assembly in Paris. The other, Giovanni Peraldi, an infantry captain, was equally well connected, and his brother Marius was the other Corsican deputy in Paris.
Napoleone spent most of February 1792 at Corte, ostensibly as guide and amanuensis to the visiting philosopher Constantin de Volney, but in fact probably trying to obtain Paoli's favour. His behaviour was not calculated to engage it: he was hyperactive, attending political gatherings and holding discussions with people in the street, voicing extreme views and calling for action. He did not cut a convincing figure. Although he was now twenty-two he looked much younger, and people made jokes about his small stature. According to one source, when he challenged Peraldi to a duel, the other did not bother to turn up.
As the elections to the colonelcies of the Ajaccio battalions approached, Napoleone was back at home canvassing. All comers were welcomed into the Buonaparte home to dine. Mattresses were laid out on the floor for supporters from the interior, who would be useful in swaying the national guards, most of whom were also from the country, and it was they who would elect the officers. The opposition also canvassed, but they had not taken into account the determination of the Buonaparte.
The election, set for 1 April, was to be presided over by three commissioners, who arrived in Ajaccio two days before. One, Grimaldi, was lodged with the Buonaparte; another, Quenza, stayed with Letizia's Ramolino family; but the third, Murati, had accepted the hospitality of the Peraldi. On the eve of the election Napoleone sent one of his henchmen from Bocognano, a patriotic bandit who had fought with Paoli against the French, to the Peraldi house with his gang of cut-throats. They burst in while the household were at dinner and kidnapped the commissioner, bundling him off to the Buonaparte house, where his protests were countered by Napoleone with the assurance that he only wished to preserve his independence of judgement from the influence of the Peraldi.
In the morning, the 500 or so national guards gathered to elect their officers. Pozzo di Borgo and Peraldi were shouted down, and in a travesty of procedure Giovanni Battista Quenza was elected commanding officer, with Napoleone as lieutenant colonel and second in command. The celebrations in the Buonaparte home that evening were accompanied by a military band.
The following day Colonel Maillard, commander of the French garrison of Ajaccio, inspected Napoleone's volunteers, but the presence of the two forces in the town made for tension. Just as tense were relations between the generally conservative citizens, who saw in the French regulars a guarantee of stability, and the volunteers, most of them wild men from the hills. On the afternoon of 8 April a quarrel developed between some girls playing skittles on the Olmo, and as onlookers and passers-by took sides insults began to fly which had nothing to do with the original dispute. Shots were fired and Napoleone went out to restore order, but more people spilled out into the streets in a confused outburst of animosities. After one of his officers had been killed, Napoleone was obliged to retire to the safety of the former seminary, where his men were stationed. Quenza and he agreed that the insurgency justified retaliation, and they began shooting at any of the townsfolk who came within range. The fighting gradually turned into a chaotic brawl with guns as private scores were settled. Napoleone tried to exploit the crisis by requesting permission from Maillard to take refuge with his men in the citadel, which aroused the Frenchman's suspicion, and the following day Maillard ordered the volunteers to withdraw from Ajaccio. Napoleone insisted they remain, and again attempted to gain admittance to the citadel – he even tried to subvert the soldiers by denouncing their colonel as an ' _aristo_ '.
Hearing of the disturbances, the authorities in Corte despatched commissioners to find out what was going on. Napoleone set off to meet them in order to tell the facts his way, and wrote up a version justifying himself. After a cursory examination of the circumstances, the commissioners had a number of citizens arrested and ordered Napoleone and his volunteers to leave Ajaccio. He duly led them off on 16 April, and intended to go to Corte himself to explain, but he could not expect a welcome there. Paoli's verdict on the events at Ajaccio was that one could expect nothing less when 'inexperienced little boys are placed in command of the national guards'. He had had enough of the Buonaparte. 'The General returned here yesterday evening, he is badly disposed towards me; I saw him this morning, we had an argument, and all is over,' Joseph wrote to his brother, urging him to go to Paris as soon as he could to justify himself before the government.
## 6
# France or Corsica
Napoleone had much explaining to do when he reached Paris two weeks later, at the end of May 1792. More than one damning report of his activities in Ajaccio had reached the capital, and he had been denounced in the Legislative Assembly by the Corsican deputies Carlo Maria Pozzo di Borgo and Marius Peraldi, no friends of the Buonaparte since the National Guard elections in which their brothers had been trounced. Peraldi had made up his mind that the family had 'never, under whatever regime, had any merit other than spying, treachery, vice, impudence and prostitution'. Pozzo di Borgo was more amenable, and Napoleone managed to placate him.
Napoleone also needed to placate the war ministry, since he had overstayed his leave and could be classed as a deserter. Fortunately for him, war had broken out against Austria barely a month before, and since the emigration of thousands of officers had left a shortage, the ministry was not about to deprive the army of a trained officer on account of a squabble between small-town Corsicans. Colonel Maillard's denunciation was passed to the ministry of justice, and although this had received similar unfavourable reports from other quarters, the matter rested there.
The day after his arrival in Paris, on 29 May, Napoleone unexpectedly met an old friend from Brienne, Fauvelet de Bourrienne. Bourrienne had not pursued a military career but had joined the diplomatic service, which took him to Vienna and Warsaw, and he was now at a loose end. The two young men teamed up, sharing what little money they had and thinking up ways of making some more. Napoleone also found friendship at the home of his mother's childhood friend Panoria Permon, a beautiful woman of doubtful virtue who presided over what appears to have been something of a gaming house in which she received Corsicans and others.
On 16 June he visited his sister Maria-Anna at Saint-Cyr. 'She is tall, well-formed, has learned to sew, read, write, dress her hair, dance and also a few words of history,' he reported to Joseph Fesch, but he was worried that she had lost touch with her roots and become 'an aristocrat', and feared that if she had known he was a supporter of the Revolution she would never have agreed to see him. But his own attitude to the Revolution was about to be tested.
A couple of days later, on 20 June, he met up with Bourrienne for lunch at a restaurant in the rue Saint-Honoré. On coming out they saw a crowd of several thousand men and women armed with pikes, axes, swords, guns and sticks making for the Tuileries. They followed, and took up position on the terrace of the Tuileries gardens, from which they watched as the mob surged up to the palace, broke down the doors, overpowered the national guards on duty and swept inside. Napoleone could not hide his indignation, and when he saw the king submitting to don a red cap of liberty and appear at the window to drink the health of the people, he exploded. ' _Che coglione!_ ' he reportedly exclaimed, disgusted that nobody had prevented the rabble from storming the palace, and declared that if he had been the king things would have turned out differently. He kept returning to the subject, making pessimistic prognoses for the future. 'When one sees all this close up one has to admit that the people are hardly worth the trouble we take to win their favour,' he wrote to Lucien two weeks later, adding that the scenes he had witnessed made their scrape in Ajaccio look like child's play.
A week later, on 10 July, he was reintegrated into the artillery with the rank of captain, and awarded six months' back-pay. Although he was ordered to rejoin his regiment, he was in two minds as to what course to take. He had put the finishing touches to his _Lettres sur la Corse_ , which was now ready for the printer, but as he admitted to Joseph, the political context was unfavourable. He was beginning to think that his future might lie in France, and advised Joseph to get himself elected to the Legislative Assembly in Paris, as Corsica was becoming peripheral. At the same time, he urged him to encourage Lucien to remain close to Paoli. 'It is more likely than ever that this will all end in our gaining independence,' he wrote, suggesting they keep their options open.
Lucien failed to get taken on as a secretary to Paoli. He was seventeen, exalted and rebellious. His spirit was, as he put it himself in a letter to Joseph, gripped by boundless 'enthusiasm'; he had looked inside himself and was 'developing' his character in a 'strongly pronounced way'. His soul had been set on fire by reading the immensely fashionable Edward Young's poem _Night Thoughts on Life, Death and Immortality_ , and he had been inspired to discover his identity through writing. He was composing a poem about Brutus, and his pen flew over the paper 'with astonishing velocity'. 'I correct little; I do not like rules which restrain genius and I do not observe any,' he wrote. He had also embraced the most radical revolutionary ideals. He assured Joseph that he 'felt the courage to kill tyrants' and would rather die with a dagger in his hand than in a bed surrounded by priestly 'farce'.
Warned by his younger brother Louis that Lucien was about to take a step that 'might well compromise the general interest of the family', Napoleone wrote to him more than once, trying to restrain him. Lucien was having none of it. He resented Napoleone's dominant influence, accusing him of having fallen for the courtly attractions of Paris, and expressed his resentment at being told what to do in an impassioned letter to Joseph on 24 June, couched in the obligatory revolutionary idiom. 'He seems to me to be well suited to being a tyrant and I think that he would be one if he were a king, and that his name would be one of horror for posterity and for the sensitive patriot,' he wrote, casting himself as a 'pure' revolutionary and Napoleone as one who had sold out. 'I believe him capable of being a turncoat...'
Napoleone was in fact switching allegiance. He had nourished a vision of himself as the champion of a noble persecuted nation and its heroic leader Paoli, demonising France, on which he heaped responsibility for every ill. But over the past couple of years he had acquainted himself with that downtrodden nation, and found it was less innocent than in his dreams. Its heroic leader turned out to be just as unprincipled and tyrannical as any other ruler – and had failed to accord Napoleone the recognition he felt to be his due. Meanwhile, the demonic France had been reborn as the torchbearer for everything he had come to believe in. Viewed from Paris, Corsica was beginning to look small and mean. On 7 August Napoleone wrote to Joseph that he had made up his mind to remain in France. In its present financial condition, the family would benefit from his rejoining his regiment: at least one member would be drawing a salary. There was a war on, and sooner or later he would get the chance to gain promotion. But only three days later something occurred which changed his mind.
On 10 August he was roused at his lodgings on the rue du Mail near the Place des Victoires by the sound of the tocsin. Hearing that the Tuileries Palace was being stormed, he set off for the place du Carrousel, where Bourrienne's brother had a furniture shop, from where he would be able to see what was going on. 'Before I reached the Carrousel I encountered in the rue des Petits-Champs a group of hideous men bearing a head on the end of a pike,' he reminisced many years later. 'Seeing me passably well dressed and looking like a gentleman, they accosted me and made me shout _Vive la Nation!_ , which I readily did, as one can imagine.'
A mob numbering some 20,000 armed with guns, pikes, axes, knives and even spits had attacked the Tuileries, which were defended by 900 men of the Swiss Guards and a hundred or so courtiers and nobles. The king and his family fled to the protection of the Legislative Assembly, but the defenders of the palace were butchered. When it was over, Napoleone ventured into the palace gardens, where people were finishing off the wounded and mutilating their bodies in obscene ways. 'Never since has any of my battlefields struck me by the number of dead bodies as did the mass of the Swiss, maybe on account of the constricted space or perhaps because it was the first time I had seen anything like it,' he recalled. 'I saw even quite well dressed women commit the most extreme indecencies on the bodies of the Swiss guards.' Napoleone was terrified as well as horrified, and never shed his fear of the mob.
He was not going to remain in Paris to watch the slide into anarchy, and he could not afford to leave his sister in an institution that identified her as a noblewoman. On 31 August he went to Saint-Cyr to collect Maria-Anna, and brought her to Paris. On 2 September mobs began breaking into prisons and slaughtering the inmates in reaction to a declaration by the Duke of Brunswick, commander of the allied army marching into France to restore the monarchy, in which he vowed to deal severely with the population of the French capital if the king or any of his family were harmed. The massacre of aristocrats, priests and others detained for one reason or another went on for five days, and it was only on 9 September that Napoleone and his sister were able to leave Paris. They stopped at Marseille just long enough to collect his pay arrears, and on 10 October, by which time the monarchy had been abolished and France declared a republic, the two siblings embarked at Toulon, reaching Ajaccio five days later. Napoleone promptly set off for Corte, hoping to restore the Buonaparte clan to favour.
Paoli may have been a dictator, but his attempts to set up an efficient executive had failed. The culture of the island had been profoundly affected by French rule: the influx of specie up-ended a system in which the majority of the population had never previously held a coin, while the creation of a salaried administration launched a rush for official posts which opened up new fields for conflict between rival clans and tempting prospects for corruption. Most of those in office were more concerned with score-settling, nepotism and profiteering than running the country. It was they who would acquire the _biens nationaux_ being sold off: these made up 12 per cent of the land surface of the island, but only 500 out of a population of 150,000 were able to benefit. This altered the previously egalitarian pattern of land ownership, while newly-introduced regulations impinged on unwritten age-old grazing and gathering rights, leading to disputes and banditry on a scale no government could control.
Paoli was not well, and was unable to exercise the same authority as in the past. His relationship with France was strained, and he could not but be wary of those who identified with that country or with the Revolution. He viewed the Buonaparte brothers with mistrust. He had dismissed Joseph, whom he regarded as too ambitious for his merits, and had refused to take on the hot-headed Lucien as secretary. When Napoleone appeared in Corte hoping for a senior command, Paoli brushed him off with vague promises and sent him back to Ajaccio to await orders in connection with an impending invasion of Sardinia.
The idea had been mooted in Paris more than a year before. The island was only a few hours' sailing from Corsica. It was rich in grain and cattle, which the French government needed to feed its armies, and it was assumed that its people needed liberating. Its ruling dynasty, the house of Savoy, also reigned over Piedmont and Savoy, and had joined the coalition against France.
The invasion was to be carried out by a combined force of French regulars, volunteers from Marseille and Corsican national guards. At the end of October, a few days after Napoleone's return from Corte, the French naval squadron carrying the regulars and a detachment of volunteers dropped anchor off Ajaccio. Its commander, Rear-Admiral Laurent Truguet, was received by the principal families of the town, who entertained him with dinners and dances. The forty-year-old sailor was a frequent guest at the Buonaparte house, having taken a fancy to the sixteen-year-old Maria-Anna. Accompanying him on his flagship was Charles Huguet de Sémonville, on his way to take up the post of ambassador in Constantinople. He too was courted by the Buonaparte family, and he agreed to take Lucien along as his secretary. According to Lucien, Napoleone contemplated going east too, to take service with the British in India, calculating that his professional credentials would provide the chance for a command that would give him the opportunity of achieving great things. In the meantime, he nearly met his end on the streets of Ajaccio.
When allowed off their ships, the French troops roamed the city picking fights. On 15 December a force of volunteers from Marseille sailed in. It was made up of the dregs of the city's port, and three days later they teamed up with some of the regulars and began lynching people they accused of being ' _aristos_ ', including members of the Corsican National Guard, mutilating their bodies and parading them around town before dumping them in the harbour. Order was restored with some difficulty, but in January 1793 a further contingent of volunteers sailed in and Napoleone was only saved from being lynched by some of his guardsmen.
On 18 February, to the relief of the people of Ajaccio, the expedition sailed. Napoleone was in command of a small artillery section under his colleague Quenza. The expedition had been divided into two forces, the larger of which, composed of French regulars, was to attack Cagliari, the capital of Sardinia, while the smaller, made up mostly of Corsican volunteers, took the island of Maddalena off the island's north coast. This force, commanded by Colonna Cesari, consisted of the corvette _La Fauvette_ and a number of troop transports. Unfavourable winds pushed the flotilla back, and it was only four days later that it sailed, landing on Maddalena on 23 February. The Sardinian garrison took refuge in the small town of Maddalena. Napoleone set up a battery which began bombarding the place into submission, and after two days it was on the point of surrendering. But the crew of _La Fauvette_ decided to sail home, and Cesari was obliged to order immediate withdrawal, with instructions to jettison guns and other heavy equipment. Napoleone and Quenza had to scramble back to the boats, whose crews had been seized by panic. The flotilla was back in Corsica by 28 February.
Napoleone wasted no time in covering his own back. He wrote up a detailed account of the events for Paoli; another, critical of Cesari and by extension Paoli, for the minister of war in Paris; and signed another jointly with the other officers who had taken part, in which he defended Cesari. It was not as easy to defend himself from more direct threats, and he was on the point of being lynched as an ' _aristo_ ' by sailors from _La Fauvette_ when a group of his own men delivered him.
In Paris, Saliceti had been putting it about that Paoli was no longer fit to rule and that his clan was embezzling on a gigantic scale. The Convention, which had replaced the National Assembly, decided to investigate, and designated three commissioners with Saliceti at their head to travel to Corsica. Their official brief was to see to the defence of the island against a potential attack by the Royal Navy, as the international situation had become critical. King Louis XVI had been guillotined on 21 January, which shocked public opinion accross Europe and broadened support for the coalition of Austria, Prussia, Spain and Sardinia already fighting France. On 1 February France declared war on Britain and the Netherlands. Paoli's monarchist and Anglophile sympathies were no secret in Paris. The Convention ordered the four battalions of Corsican national guards to be disbanded and replaced by French regulars, and placed all the forces on the island under the command of a French general.
On 14 March, Lucien, who had accompanied Sémonville back to Toulon when he was recalled, made a speech in the local Société Patriotique denouncing Paoli. He may have been put up to it by some of Paoli's enemies gathered in Toulon, and he would later claim that he did not really know what he was saying. Nevertheless, on 2 April his speech was read out to the Convention in Paris, which only the day before had received news that the commander of the French army facing the Austrians, General Dumouriez, had defected to the enemy. Seeing treason everywhere, it issued a decree outlawing Paoli and ordering his arrest.
Saliceti and the other two commissioners were still riding at anchor in the Golfe Juan awaiting favourable winds when they heard the news, and wrote to Paris asking for the decree to be suspended while they investigated. It was not until the beginning of April that they reached Bastia, where they were joined by Joseph Buonaparte. Given the intricate web of alliances, enmities and motivations spread over the island, and that almost everyone involved later destroyed and doctored documents, falsified evidence and spun colourful tales, it is impossible to be certain what the commissioners intended. Saliceti probably hoped to maintain Paoli but replace those around him with his own clan and associates, in which category he may have included the Buonaparte.
On 18 April news of the Convention's decree outlawing Paoli reached the island. Paoli tried to calm tempers, and sent two delegates to the Convention to justify himself, but Corsican patriots were in uproar, demanding war with France. Napoleone was in Ajaccio, where he wrote a defence of Paoli, which he personally posted on walls around town with a demand for the Convention's decree to be rescinded. He also attempted to persuade his fellow citizens to affirm their loyalty to the French Republic, in the hope of avoiding a break with France. But most of the notables of Ajaccio had turned against the Buonaparte clan, and he was warned of a plan to assassinate him. He thought of joining Saliceti in Bastia, but changed his mind, and on 2 May set off for Corte to see Paoli. By then news of Lucien's Toulon speech had reached the island. Worse, a letter from Lucien to his brother boasting that he had provoked the Convention's decree against Paoli had been intercepted and sent to Corte.
On his way, Napoleone met a kinsman who warned him that if he went to Corte he would never get out alive. He turned back and reached Bocognano on the evening of 5 May. But he was by no means out of danger, as Marius Peraldi, brother of his erstwhile rival for the Ajaccio colonelcy, was hot on his heels meaning to arrest him and take him to Corte. The various accounts of what happened next read like an adventure story, with Napoleone arrested, locked up under guard, freed at night by cunning subterfuge, pursued, caught, held with a gun to his temple in a stand-off, and finally spirited away while rival gangs of bandits settled scores. What is certain is that he was arrested in Bocognano, that he was freed by a cousin, briefly held again, and eventually taken to a kinsman shepherd's hut outside Ajaccio.
Napoleone could not show himself openly, so he slipped into the poor suburb, the Borgo, where he was popular, and that night went to the house of his friend Levie, former mayor of Ajaccio, in which his partisans had gathered. There they cowered, sleeping on the floor, their guns at the ready, for two days, while a boat was prepared to take Napoleone away at night. On the evening of his intended escape the house was surrounded by gendarmes. Levie told his guests to hide, and invited the chief of the gendarmes in. As they talked, both noticed that some of the sleeping-mats had not been hidden. The gendarme, fearing for his life, pretended to see nothing, and the two men continued to drink and talk while Napoleone was smuggled out of the back of the house and down to the beach, where a boat was waiting. By 10 May he was safe in Bastia.
On the night of 23 May, Letizia was woken by a knock on the door; a cousin had come to warn her that Paoli's partisans were on their way to seize everyone in the house. He had brought a handful of armed relatives to escort them to safety. Letizia left her two youngest children, Maria Nunziata and Geronimo, in safe hands and took Louis, Maria-Anna, Maria Paolina and Fesch with her. They crept out of town and made for the hills. A few hours later the Buonaparte home was sacked.
Meanwhile Napoleone had persuaded Saliceti and the other commissioners at Bastia that it would be easy to recover control of Ajaccio with a show of force. Four hundred French regulars were assembled and set sail in two ships, with Napoleone, Joseph and the three commissioners on board. The attempt to take the city failed, but Letizia and her children, Joseph Fesch and various French loyalists were evacuated.
By 3 June Napoleone and his family were in Calvi, one of only three ports still held by the French. The rest of the island was under Paoli's sway. On 27 May a thousand-strong assembly in Corte had issued a proclamation condemning the Buonaparte. 'Born in despotism, nourished and brought up at the expense of a lustful pasha who ruled the island, the three brothers turned themselves with ardent enthusiasm into the zealous collaborators and the perfidious agents of Saliceti,' it ran. 'As punishment, the Assembly abandons them to their private remorse and to public opinion which has already condemned them to eternal execration and infamy.'
Whether the French could hang on at Calvi for much longer was open to doubt, and the Buonaparte could no longer hope to play a part in Corsican affairs. On 11 June Letizia, her half-brother Fesch and her brood sailed for France. It was not a good time to be going there.
## 7
# The Jacobin
On 2 June 1793, eleven days before the Buonaparte family reached the mainland, the Revolution had entered a new phase. The extremist Jacobin faction in the Convention, known as Montagnards or _La Montagne_ because they sat on the highest seats in the amphitheatre, had expelled the more moderate Girondins. France was plunged into what was effectively civil war. In Toulon, where the Buonaparte landed, the Jacobins were laying down the law through terror and intimidation, arresting nobles, dragging wealthy citizens out of their houses and stringing them up from lamp-posts or bludgeoning them to death in the streets.
The Buonaparte family were not immediately threatened: they were unknown and destitute, and Lucien was prominent in the local Jacobin club. But the city was in ferment, crowds could be volatile, and the Buonaparte were, after all, _ci-devant_ nobles. In such a climate nobody was safe. They moved to the village of La Valette outside the city. Having settled Letizia and his siblings there, Joseph made contact with Saliceti, who had also fled Corsica. He had publicly distanced himself from the Buonaparte, declaring that 'Neither of these little intriguers will ever count among my friends,' but he was not a man to burn bridges. He too needed associates, and with his backing Lucien was given an administrative post as quartermaster in nearby Saint-Maximin, and Joseph Fesch, who had shed his ecclesiastical garb, a similar position at Chauvet. Joseph himself accompanied Saliceti to Paris, where he lobbied the Convention to provide funds for the sustenance of exiled Corsican 'patriots' such as the Buonaparte who had suffered in the cause of the Revolution. His efforts were rewarded, and Letizia obtained her dole. Joseph then looked around for career opportunities, and secured the lucrative post of commissary to the army.
Napoleone had gone to Nice, where the greater part of his regiment was stationed as part of the Army of Italy. Given the dearth of officers, he was welcomed back and given 3,000 francs in back-pay. It so happened that the commander of the artillery of the Army of Italy was Jean du Teil, younger brother of Napoleone's old friend and commander at Auxonne. He gave Napoleone the task of inspecting the coastal batteries between Nice and Marseille, as Admiral Hood's fleet was looking for an opportunity to land troops. At the beginning of July he was ordered to Avignon where he was to organise the convoy of ordnance and powder destined for Nice. He had not gone halfway when he found himself entering a war zone.
The events of 2 June in Paris had provoked violent reactions and an anti-Jacobin backlash around the country. Ten provinces defied the Convention, a royalist rising had taken over the Vendée in the west, and in the south Marseille, Toulon and the valley of the Rhône were in open revolt. The _fédérés_ , as the rebels were called, overran the region, including Avignon, stopping Napoleone in his tracks. An army under General Carteaux was marching south to defeat them, and by the end of July the _fédérés_ had been expelled from the former Papal fief. Napoleone was present, but probably played no part in the fighting.
There is little firm evidence about his movements over the following weeks, but he probably spent them carrying out his orders of convoying powder and shot from Avignon to Nice, possibly delayed by a bout of fever at Avignon. If so, it may have given him the time to reflect on his position. France had become a dangerous place for young men like him, and he needed to assert his political stance. He did this by writing _Le Souper de Beaucaire_ , a polemic in the form of a dialogue which may or may not have taken place over dinner shared by a group of people at an inn at Beaucaire, on Napoleone's route from Avignon to Nice.
It is a political diatribe against the _fédérés_ , in which the narrator, an officer, discusses the political situation with a group of citizens of Marseille, Nîmes and Montpellier who had come to the fair at Beaucaire, and argues in support of the Convention in Paris. He admits that the Girondins are good republicans and that the Montagnards might not be perfect, but asserts that the former showed weakness and the latter strength, and their authority should therefore be acknowledged: the successful faction has right on its side. He takes the opportunity to denounce Paoli, who only feigned loyalty to the French Republic 'in order to gain time to deceive the people, to crush the true friends of liberty, to lead his compatriots into his ambitious and criminal projects'.
It was a political manifesto, calculated to establish Napoleone's revolutionary credentials and position himself politically in a way that would shield him from the kind of accusations that had sent many an officer to the guillotine. It also aimed to represent the Buonaparte clan as the victims of the counter-revolutionary Paoli. Patriots such as they had welcomed Paoli believing him to be a good republican, and only gradually became aware of his 'fatal ambition' and his perfidy.
The piece is couched in the flowery hyperbole so beloved of revolutionary France (and every totalitarian regime since), but there are few traces of the idealism that still haunted Napoleone's recent writings, and it represents an emotional as well as an ideological coming of age. Reality had not lived up to his adolescent dreams of a Corsica reborn under Paoli, and his disappointment and sense of rejection had turned into anger, and even bitterness. He renounced Corsica; henceforth he would angrily reprove anyone who called him a Corsican and declare that he was and always had been French, since the island had already been incorporated into the kingdom when he was born. He was not bothered by the apparent inconsistencies or what might be seen as his betrayal of the Corsican and Paolist cause: it was Paoli who had betrayed him, and Corsica had let him down. In addition, he had smelt weakness in Paoli, and he had come to see that as a failing.
The riots he had witnessed over the past three years had dispelled any faith he might have had in the inherent goodness of human nature. The disgust and fear he had felt outside the Tuileries on 10 August the previous year had convinced him that the lower orders must be contained. The small-town struggles for power in Corsica had taught him that subterfuge, cheating, treachery and brute force were the only effective means of achieving a goal in politics. He had participated in several elections in which rules had been disregarded and results falsified, and had taken part in two coups. As an officer on full pay he had tried to subvert troops from under the authority of a brother officer. He still saw himself as a soldier, but the Revolution had politicised the army, and in politics the rules of chivalry did not apply. The winning side was the one to be on. The dreamy romanticism of his youth had been confronted with the seamy side of human affairs, and at the age of twenty-four he had emerged a cynical realist ready to make his way in the increasingly dangerous world in which he was obliged to live.
On his way from Avignon to Nice in mid-September Napoleone passed through Le Beausset, where Saliceti and the _représentant en mission_ of the Convention Thomas Gasparin were staying, and he naturally called on his compatriot. 'Chance served us well,' Saliceti wrote of the encounter: they were in urgent need of a capable and politically reliable artillery officer.
As well as being torn by internal dissent and civil war, France was now under attack from the combined forces of Austria, Prussia, Britain, Spain, the Dutch Republic, Sardinia, Naples and several other small Italian states, on five fronts. By the late summer of 1793 the Prussians had pushed back the French on the Rhine, the Austrians had taken the French fortress of Valenciennes, Spanish forces had crossed the Pyrenees and were moving on Perpignan, the Sardinians were invading from the east, and the British had laid siege to Dunkirk. The minister of war, Lazare Carnot, had ordered a _levée en masse_ to defend the motherland, but things were not looking good.
Marseille had been retaken from the _fédérés_ by the forces of the Convention on 25 August, but Toulon was still holding out, and retaking that was not going to be easy. Horrified by the bloody reprisals visited upon the inhabitants of Marseille, the _fédérés_ and royalists in Toulon had opened the port to Admiral Hood's Anglo-Spanish fleet, which had landed troops and occupied the city in the name of Louis XVII, now languishing in a revolutionary gaol. Toulon, the home of France's Mediterranean fleet, was a natural harbour, with a large inner roadstead sheltered by land and an even larger outer one protected by a long promontory. The city was defended on the landward side by a string of forts and from the sea by batteries that could cover both the inner and outer roads. These defences were now held by nearly 20,000 British, Neapolitan, Spanish and Sardinian regulars, guarding not only the city but the roads in which Hood's fleet was anchored. General Carteaux was not the man to dislodge them. A painter by trade who owed his command to political connections, he had 4,000 men plucked from the Army of the Alps and from among defeated _fédérés_ who sought safety in his ranks.
On 7 September Carteaux began operations, taking the village of Ollioules but in the process losing the commander of his artillery, Lieutenant Colonel Dommartin, a former colleague of Napoleone at the École Militaire, who was gravely wounded. A replacement was required. Saliceti had mixed feelings about Napoleone, but after reading _Le Souper de Beaucaire_ he had no doubts as to his political reliability, and even decided to publish it at government expense. And, as he put it, 'At least he's one of us.' He nominated Captain Buonaparte to the vacant command and sent him off to join Carteaux outside Toulon.
What he found on arrival was not encouraging. The besieging army's headquarters at Ollioules were a nest of political intrigue and infighting between Carteaux and General Jean La Poype, who had joined him with 3,000 men from the Army of Italy. Anyone could see that Toulon was all but impregnable and that only bombardment could yield results, but as Buonaparte quickly realised, Carteaux had no idea how to lay siege to a city. He insisted that he would capture it ' _à l'arme blanche_ ', that is to say with sword and bayonet, and ignored Buonaparte's advice.
If Toulon was impregnable on the landward side, it could not hold out unless it was resupplied by sea, and no ship could approach the harbour if the heights commanding the roads were not secured. Buonaparte was not the first to see that capturing these was the key to taking the city – it was obvious from a glance at the map, as even the governing Committee of Public Safety in Paris had pointed out. But while most of those at headquarters saw the area of La Seyne on the inner roads as the place from which to threaten the allied fleet, Buonaparte believed that it was the two forts of Balaguier and Éguillette on the promontory of Le Caire, commanding access to the outer roads, that were crucial. They were held by allied troops, and it would take artillery to dislodge them. But all Buonaparte found on arrival were two twenty-four-pounders, two sixteen-pounders and two mortars. It was not much to be going on with, but enough to enable him to chase an allied force and a frigate away from the La Seyne area and set up a battery there which he named, to stress his loyalty, _La Montagne_.
Over the next weeks, Buonaparte built up his artillery park. Not bothering to seek authorisation, he scoured the surrounding area, visiting every military post as far afield as Lyon, Grenoble and Antibes and stripping them of everything that might come in useful – cannon, gun carriages, powder and shot, tools and scrap metal, horses and carts, along with any men who had ever handled ordnance. He set up a foundry to produce cannonballs, forges to supply iron fittings for gun carriages and limbers, and ovens to heat the balls to set ships on fire. He also picked men from the ranks to train as gunners.
The first attack on Fort Éguillette on 22 September was a failure. Carteaux did not share Buonaparte's conviction about the fort's importance and deployed too few men, while the British quickly brought up reinforcements. They realised the French had identified the military significance of the promontory, and reinforced the position with a new battery which they named Fort Mulgrave. They added two earthworks on its flanks, covering the approaches to forts Éguillette and Balaguier. Buonaparte complained to Saliceti and Gasparin that his hopes of a quick victory had been scuppered; now he would have to take Fort Mulgrave before he could get at the key positions, and that would take time. He carried on building up his batteries and stores of shot and powder, ignoring orders from Carteaux, who complained but could do nothing as Buonaparte had the ear of the representatives of the government. Saliceti passed Buonaparte's criticisms of Carteaux to his colleagues in Marseille, Paul Barras, Stanislas Fréron and Jean-François Ricord, who wrote to Paris recommending that Carteaux be replaced and Buonaparte promoted. On 18 October he received his nomination as _chef de bataillon_ , equivalent to the rank of major, and five days later Carteaux was removed from his command.
Buonaparte had become adept at disregarding his superiors and bypassing their instructions without giving offence, employing flattery where necessary. He also knew when to force the issue and to intimidate in order to have his way. Saliceti was now permanently at headquarters in Ollioules, and backed him up. Napoleone nevertheless had to tread carefully, as the waves of terror rippling out from Paris led people to denounce others for treason as a means of avoiding being denounced themselves, and with many officers defecting to the enemy the nobleman Buonaparte was not beyond suspicion. He nevertheless did stick his neck out to protect his former superior in the regiment of La Fère, Jean-Jacques Gassendi, who had been arrested, by insisting he needed him to organise an artillery arsenal in Marseille.
Carteaux's command had been given to the hardly more martial General François Doppet, a physician who dabbled in literature, and had only won high rank by finding himself in the right place at the right time. But on 15 November his nerve failed during an attack on Fort Mulgrave: he gave the order to retreat when he saw the English making a sortie, only to have a furious Buonaparte, his face bathed in blood from a light wound, gallop up and call him a _jean foutre_ (the closest English approximation would be 'fucking idiot'). Doppet took it well. He was aware of his limitations, and realised that _chef de bataillon_ Buonaparte knew his business.
Buonaparte's orders and notes during these weeks are succinct and precise, and while their tone is commanding, he takes the trouble to explain why compliance with his demands is essential. In war, as in any other critical situation, people quickly rally to the person who gives the impression of knowing what they are about, and Buonaparte's self-confidence was magnetic. He showed bravery and steadiness under fire, and did not spare himself, which set him apart from many of the political appointments milling around at headquarters. 'This young officer,' wrote General Doppet, 'combined a rare bravery and the most indefatigable activity with his many talents. Every time I went out on my rounds, I always found him at his post; if he needed a moment's rest, he took it on the ground, wrapped in his cloak; he was never away from his batteries.'
Through effort and resourcefulness, Buonaparte had built up an artillery park of nearly a hundred guns and set up a dozen batteries, provided the necessary powder and shot, and trained the soldiers to man them. For his chief of staff he had picked the apparently vain and frivolous Jean-Baptiste Muiron, who had trained as an artillery officer and quickly became an enthusiastic aide. In the twenty-six-year-old Félix Chauvet he identified a brilliant commissary who earned and returned his affection as well as serving him efficiently. During an attack on one of the batteries, Buonaparte had noticed the engaging bravery under fire of a young grenadier in the battalion of the Côte d'Or named Andoche Junot. When he saw that the man also had beautiful handwriting he appropriated him as an aide, only to discover that he had trained for the artillery in the school at Châlons. A couple of weeks later, another young man joined Buonaparte's entourage. He was the handsome nineteen-year-old Auguste Marmont, a cousin of Le Lieur de Ville sur Arce, who had trained for the artillery at Châlons with Junot.
On 16 November a new commander arrived to take over from Doppet. He was General Jacques Dugommier, a fifty-five-year-old professional soldier, a veteran of the Seven Years' War and the American War of Independence who knew how to call the troops to order. He had brought General du Teil and a couple of artillery officers with him, but quickly realised that Buonaparte had the situation in hand, and he did little more than endorse his decisions. 'I can find no words to describe the merits of Buonaparte,' he wrote to the minister of war. 'Much technical knowledge, as much intelligence and too much bravery is only a faint sketch of the qualities of this uncommon officer.'
On 25 November Dugommier held a council of war, attended by Saliceti and, in place of Gasparin, who had died, a newly-arrived _représentant_ , Augustin Robespierre, younger brother of one of the leading lights of the Committee of Public Safety. They considered Dugommier's plan, then that drawn up in Paris by Carnot. Both involved multiple attacks. Buonaparte argued that this would disperse their forces, and put forward his own plan, which consisted of a couple of feint attacks and a massive assault on forts Mulgrave, Éguillette and Balaguier, whose capture he was confident would precipitate a rapid evacuation of Hood's fleet and the fall of the city. The plan was accepted and preparations put in hand.
On 30 November the British commander in Toulon, General O'Hara, made a sortie and succeeded in capturing a battery and spiking its guns before moving on Ollioules. Dugommier and Saliceti managed to rally the fleeing republican forces and lead up reinforcements. They retook the battery, a battalion led by Louis-Gabriel Suchet taking O'Hara prisoner in the process, and Buonaparte unspiked the guns and opened up on the fleeing allies. He had been in the thick of the fighting and earned a mention in Dugommier's despatch to Paris.
The day's fighting had nevertheless demonstrated the lack of mettle and experience of the French troops. The worsening weather combined with food shortages to sap morale. Despairing of their ability to take Toulon, Barras and Fréron considered raising the siege and taking winter quarters. Saliceti pressed Dugommier to attack, but the general hesitated, as a failed assault might cost him his head. As it was, they were being accused in Paris of lack of zeal and of living in luxury.
Dugommier resolved to act on Buonaparte's plan, and the batteries facing Fort Mulgrave began bombarding it on 14 December. The British batteries responded vigorously, and Buonaparte was thrown to the ground by the wind of a passing shot. The attack, by a force of 7,000 men in three columns, began at 1 a.m. on 17 December. A storm had broken and Dugommier hesitated, but Buonaparte pointed out that the conditions might actually prove favourable, and the impatience of Saliceti carried the day. The French infantry went into action in pouring rain, the darkness lit up by flashes of lightning, the sound of the guns drowned out by peals of thunder. Two of the advancing columns strayed from their prescribed route and lost cohesion as many of the soldiers fell back or fled. Other units reached Fort Mulgrave and began escalading its defences. The fighting was fierce – the attack on the fort would cost the French over a thousand casualties – but Muiron eventually forced his way into the fort, closely followed by Dugommier and Buonaparte, who had his horse shot under him at the beginning of the attack, and was wounded in the leg by an English corporal's lance as he stormed the ramparts.
As soon as he had taken possession of the fort, Buonaparte turned its guns on those of forts Éguillette and Balaguier, and ordered Marmont to start bombarding them. The British mounted a counter-attack, but it was repulsed and they were forced to evacuate the two remaining forts. By then it was light, and Buonaparte began firing incendiary shells and red-hot cannonballs at the nearest British ships, blowing up two. He told anyone who would listen that the battle was over and Toulon was theirs, but Dugommier, Robespierre, Saliceti and others were sceptical, believing the town would only fall after a few more days' fighting. They were wrong – the explosions of the two ships were a signal the allies could not ignore, and that morning they decided to evacuate; they began moving men out while the ships struggled in a strong wind to pull out of range of the French guns.
The evacuation proceeded through that day and the next, with the allies towing away nine French warships and blowing up a further twelve, setting fire to ships' stores and the arsenal, and taking on board thousands of French royalists. Anyone who could get hold of a boat was rowing out to the allied ships, and some even tried swimming. They were under constant fire from batteries newly set up by Buonaparte on the promontory and the heights above the city. That night the burning ships lit up the scene, revealing what Buonaparte described as 'a sublime but heart-rending sight'.
The French entered the city on the morning of 19 December, looting, raping and lynching anyone they pleased to label as an enemy of the Revolution. On the quayside people were throwing themselves into the water to reach the departing British ships. Those who did not drown were subjected to the fury of the republican soldiery. Over two decades later, Buonaparte recalled the revulsion he had felt at the sight, and according to some sources he managed to save a number of lives.
Barras, Saliceti, Ricord, Robespierre and Fréron carried out a purge of the population of Toulon. 'The national vengeance has been unfurled,' they proclaimed, listing those categories which had been 'exterminated'. Barras suggested it would be simpler if they removed all those who were proven 'patriots', that is to say revolutionaries, and killed all the rest. The population of the city, which would be renamed Port-de-la-Montagne, fell from 30,000 to 7,000.
On 22 December 1793 Buonaparte was promoted to the rank of brigadier general. He was only twenty-four years old, but this did not make him an exception. Over 6,000 officers of all arms had emigrated since 1791, and another 10,000 would have done so by the summer of 1794. Generals and higher-ranking officers were guillotined by the hundred as suspected traitors. In consequence, the Republic had been obliged to nominate no fewer than 962 new generals between 1791 and 1793. But in the case of Buonaparte, the promotion was merited, and he knew it.
'I told you we would be brilliantly successful, and, you see, I keep my word,' he wrote banteringly from Ollioules to the deputy minister of war in Paris on 24 December, using the familiar ' _tu_ ' form, no doubt to stress his revolutionary attitude. He had already noted that in the current climate the story that was told first was the one that stuck in the mind, and he informed the minister that thanks to his action, the British had been prevented from burning any of the French ships or naval stores, which was a blatant lie.
He had proved not only that he was a capable and resourceful officer, but also that he was a leader of men. He had won the admiration of all the real soldiers present, starting with Dugommier. More than that, he had revealed a charisma that many of his young comrades found hard to resist.
'He was small in stature, but well proportioned, thin and puny in appearance but taut and strong,' noted Claude Victor (another who had distinguished himself at Toulon and had also been made a general), noting that 'his features had an unusual nobility' and his eyes seemed to send out shafts of fire. His gravity and sense of purpose impressed those around him. 'There was mystery in the man,' Victor felt.
Buonaparte was exhausted. Three months of intense activity, poor diet, frequent nights spent sleeping on the ground wrapped only in his cloak, and that during the winter months, must have placed a heavy strain on his constitution. He had a deep flesh wound and had also caught scabies, which was then endemic in the army. That may be why, at a moment when he could have obtained a posting to one of the armies actively engaged against the enemy, he was content to accept that of inspector of the coastal defences along the stretch between Toulon and Marseille. Another reason may have been a desire to lie low. He had seen how easily people could lose their commands, and he had probably made a number of enemies.
It may just have been that he wished to be close to his family, which had moved further away from Toulon, first to Beausset, then Brignoles and finally Marseille, where he joined them on 2 January 1794. His general's pay of 12,000 livres plus expenses would have been welcome, as the cost of living had risen dramatically in the course of 1793. The family had lived through lean times, with Letizia taking in washing, and the daughters, as gossip had it, resorting to prostitution. Maria Paolina, now Paulette, who had grown into a rare beauty, had been caught stealing figs from a neighbour's garden.
## 8
# Adolescent Loves
Buonaparte spent the first weeks of 1794 travelling up and down the coast inspecting the defences and issuing quantities of crisp instructions. These go into minute detail on the exact quantities of powder and shot required, which spare parts should be assembled, and even the manner in which horses should be harnessed for specific tasks.
At the beginning of February he was appointed to command the artillery of the Army of Italy, operating against the forces of the King of Sardinia. They had invaded southern France in 1792 but were driven back, following which Savoy and Nice had been incorporated into the French Republic, but they still held the Alpine passes, from which they threatened to recover the lost provinces. The port of Oneglia, a Sardinian enclave in the territory of the neutral Republic of Genoa and the chief link between the king's island and mainland provinces, was also considered a threat, since it resupplied British warships and harboured corsairs who preyed on French shipping.
Buonaparte's new salary allowed him to install his family in the comfortable if modest Château-Sallé outside Antibes, not far from his headquarters in Nice. Joseph, whose job as commissary had awakened an interest in trade and speculation, was currently in Nice too, exploring business opportunities. Lucien was at Saint-Maximin, where as head of its Jacobin club he had changed the town's name to 'Marathon', in homage as much to the 'martyr of the Revolution' Jean-Paul Marat, who had been assassinated in his bath by the royalist Charlotte Corday, as to the heroic ancient Greek defenders of their homeland. He had also changed his own name, to 'Brutus', and had married Christine Boyer, the sister of the keeper of the inn at which he lodged.
The commander of the Army of Italy was General Pierre Dumerbion, a sixty-year-old professional. He was supervised by the political commissioners Saliceti, Augustin Robespierre and Ricord, who commissioned Buonaparte to prepare a campaign plan. As the Sardinian positions in the mountains were almost unassailable, he suggested ignoring them and striking at their bases: their left wing on the lower ground nearer the sea was vulnerable, and if the French could break through there, they would be able to sweep into the enemy rear. His plan was accepted, and operations began on 7 April, spearheaded by General André Masséna, who captured Oneglia two days later, and by the end of the month the French were in Saorgio, strategic gateway into Piedmont.
Buonaparte's role consisted of ensuring the artillery was in position and adequately supplied. To assist him he had selected two old comrades from the regiment of La Fère, Nicolas-Marie Songis and Gassendi, his new companions Marmont and Muiron, and as aides-de-camp Junot and his own younger brother Louis. By 1 May he was back in Nice, drawing up further plans which would have taken the French into the plain of Mondovi, but the operations were halted by the war minister Lazare Carnot, who was against involving French forces any deeper in Italy. The Midi was still politically unstable, and there might be unrest if the army moved off. Carnot also needed all available troops to roll back the Spanish invasion.
Buonaparte composed a memorandum for the Committee of Public Safety giving a strategic overview of France's military position. He argued that invading Spain would yield no tangible benefits, while invading Piedmont would result in the overthrow of a throne that would always be inimical to the French Republic. More important, it would make it possible to defeat Austria, which would only make peace if Vienna were threatened by a two-pronged attack, through Germany in the north and Italy in the south. Austria, he argued, was the cornerstone of the coalition against France, and if it were knocked out that would fall apart.
Robespierre suggested that Buonaparte accompany him to Paris. The two men had grown close over the past four months, drawn together by the zeal with which they approached their respective tasks and by the shared conviction of the need for strong central authority. Under the dominant influence of Robespierre's elder brother Maximilien, the Committee of Public Safety in Paris was exercising just such authority, through a reign of Terror which sent thousands to the guillotine. But Robespierre's grip on power was weakening, and Augustin's suggestion that Buonaparte come to Paris might have had something to do with that: he allegedly suggested placing him in command of the Paris National Guard.
Buonaparte briefly considered the proposal, and according to Lucien discussed it with his brothers before deciding against it. To Ricord he admitted a reluctance to get involved in revolutionary politics, and his instinct was to stay at his post with the army. Whether the fact that he was also having an affair with Ricord's wife Marguerite had any bearing on his decision is unclear.
At the beginning of July he was sent by Saliceti to Genoa to assess the intentions of the city's government, which was neutral but under pressure from the anti-French coalition, and to inspect its defences for future reference. He left on 11 July, accompanied by Junot, Marmont and Louis, as well as Ricord, but was back at Nice by the end of the month. Yet he was too busy to attend the wedding of his brother Joseph on 1 August.
Joseph's bride, Marie-Julie Clary, was twenty-two years old, not pretty, but pious, honest, generous, dutiful, family-minded, intelligent and rich. She came from a family of Marseille merchants with extensive interests in the ports of the eastern Mediterranean, and she brought him a considerable dowry. With this under his belt, Joseph's bearing changed, and he now assumed a gravitas he felt appropriate as head of the family.
Buonaparte was still at headquarters when, on 4 August, news reached him of the coup in Paris which had toppled Robespierre on 27 July – 9 Thermidor in the revolutionary calendar. He was deeply affected by the misfortune of his friend, who was guillotined along with his brother the following day. And he did not have to wait long to be arrested himself.
As soon as he heard of the fall of Robespierre, Saliceti wrote to the Committee of Public Safety accusing Augustin Robespierre, Ricord and 'their man' Buonaparte of having sabotaged the operations of the Army of Italy and conspired against the Republic with the allies and with Genoa, whose authorities had bribed Buonaparte with 'a million' (the currency was not specified). He ordered the arrest of Buonaparte and the seizure of his papers prior to his being sent to Paris to answer charges of treason.
It is not clear whether Buonaparte was actually put in gaol or merely under house arrest. Junot managed to pass a note to him offering to arrange his escape, but Buonaparte refused. 'I recognise your friendship in your proposal, my dear Junot; and you well know that which I have vowed you and on which you know you may count,' he wrote back. But he was confident his innocence would be recognised and urged Junot to do nothing, as this could only compromise him. Innocence was no guarantor of safety under revolutionary conditions, but Buonaparte was lucky. Saliceti's accusation had been no more than a reflex of self-preservation, and as soon as he felt he was in the clear he sent another letter to Paris stating that examination of the general's papers had yielded no evidence of treason, and, bearing in mind his usefulness for the Army of Italy, he and his colleagues had ordered his provisional release. Nobody apart from Junot seems to have taken the charges against Buonaparte seriously. His landlord Joseph Laurenti, with whose daughter Buonaparte was carrying on a flirtation, had stood bail, and as a result he spent most of the eleven days of his detention in his own lodgings.
Meanwhile, the Austrians had sent an army to reinforce the Sardinian forces, and General Dumerbion felt he had to do something. 'My child,' he wrote to Buonaparte, 'draw me up a campaign plan as only you know how.' On 26 August the child handed him one, and on 5 September he was at Oneglia to implement it. The French forces advanced on the point at which the two enemy armies met, aiming to split them apart. On 21 September Buonaparte witnessed his first pitched battle, an attack on Dego in which General Masséna distinguished himself. But further operations were called off by Carnot in Paris, and Buonaparte was left with nothing to do. This should have been welcome to him.
Shortly after his release from arrest he had gone to Marseille to see Joseph, who was enjoying his new-found wealth and having himself addressed by the title of count by his in-laws. On meeting the family, Buonaparte had been struck by Marie-Julie's much prettier younger sister, Bernardine Eugénie Désirée, and declared himself to be in love. Désirée, or Eugénie as he would call her, was sixteen or seventeen, modest and innocent, with just enough education for a deferential companion and obedient wife. 'A stranger to tender passions', Buonaparte wrote to her on 10 September, he had succumbed to 'the pleasure' of her company. 'The charms of your person, of your character, imperceptibly conquered the heart of your love.' His letters to her are stilted, rushes of passionate prose alternating with suggestions that she buy a piano and take a good teacher, as 'music is the soul of love, the sweetness of life, the consolation of sorrows and the companion of innocence'. They lack conviction, which is not surprising.
A new envoy from the Convention, Louis Turreau, had arrived at headquarters in Loano. As he had only just married, he brought his twenty-three-year-old wife with him, but it turned out to be not much of a honeymoon, as she took a fancy to Buonaparte and wasted no time in having an affair with him. 'I was very young then, happy and proud of my success,' he later recalled, and admitted that his exhilaration had led him to act irresponsibly: he had taken her on an excursion to see the front line, and to impress her he ordered a battery to open fire on an enemy position. The ensuing cannonade had cost the lives of several men. He later reproached himself bitterly for his childish action.
Operations on the Italian front had come to a standstill, and at the beginning of November the Committee of Public Safety switched its priority to Corsica. The British had responded to Paoli's appeal by occupying the island as a colony, with George III as monarch, Sir Gilbert Elliot as viceroy and Pozzo di Borgo as chief administrator. Paoli was bundled off to a second exile in London. As General Dumerbion had paid generous tribute to Buonaparte's talents, he was given the task of preparing the artillery of the expeditionary force intended to recapture the island.
He spent most of the last month of 1794 and the first two of 1795 in Toulon where it was assembling. The city was scarred by the siege and subject to riots by mobs seeking ' _aristos_ ' to lynch. One day a captured Spanish ship with some émigré French noble families aboard was brought into harbour, and a mob gathered in expectation. The city authorities tried to protect the émigrés, only to be accused of being royalist stooges and threatened with lynching. Buonaparte managed to calm the crowd, which contained some gunners who had served under him at the siege, and then smuggle the émigrés out of town in his artillery caissons.
The Corsican expedition sailed from Toulon on 11 March, but soon ran into an Anglo-Neapolitan fleet, and after a brief encounter in which it lost two ships, sailed back into port. Disheartened by the prospect of inaction, Buonaparte asked to be transferred to the Army of the Rhine. His request remained without response, and he spent the next weeks mainly in Marseille, where on 21 April he became engaged to Désirée.
He had been seeing her intermittently over the past months and corresponding with her regularly. Most of his letters are couched in the tone of a schoolmaster, as he tells her which books to read and which not, frets about whether her music teacher is good enough, arranges for a publisher in Paris to send her the latest tunes, reminds her to sing her scales regularly, going into tedious detail about the effects of striking a wrong note. He was a great music-lover, with a passion for the Italian composers of the day, and enjoyed lecturing those French ones he found wanting, sometimes entering into arguments of a technical nature with them.
The engagement had probably been precipitated by the fact that at the end of March he had received a transfer to the Army of the West, operating against insurgents in the Vendée region of western France. The order to take up this posting reached him on 7 May, and to his chagrin he learned that he had been struck off the list of artillery generals, as their quota had been exceeded and he was the youngest, so he was relegated to what he regarded as the inferior status of infantry general.
The following day he set off for Paris, accompanied by his brother Louis, to whose education he was continuing to attend, drilling him mercilessly with mathematical tests even as they travelled up the valley of the Rhône and through Burgundy. He also took with him his devoted Junot and Marmont, who had come to hero-worship him. 'I found him so superior to everything I had encountered in my life, his intimate conversation was so deep and so captivating, his mind was so full of future promise,' wrote Marmont, 'that I could not bear the idea of his impending departure.' When Buonaparte suggested he accompany him he did not hesitate, even though he had no authorisation to do so.
Marmont insisted they break their journey at Châtillon-sur-Seine, where his parents lived. His mother found Buonaparte taciturn to the point of being impossible to communicate with, and took the 'little general' off to visit her friends the Chastenay family who lived nearby. 'On this first visit, in order to pass the time I was asked to play the piano,' recalled the daughter of the house, Victorine. 'The general seemed to appreciate it but his compliments were curt. I was then asked to sing, so I sang one in Italian which I had just learnt the music for. I asked him if I was pronouncing right, to which he just said no.'
The following day the Chastenays dined at the Marmonts', and afterwards Victorine asked Buonaparte about Corsica. He unwound, and in the course of the conversation, which lasted a full four hours, he spoke of his love for the epic poems supposedly written by the thirteenth-century Gaelic poet Ossian and Bernardin de Saint-Pierre's novel _Paul et Virginie_. He spoke earnestly about politics, about happiness and self-fulfilment. On the third day he helped her make a posy of cornflowers and they played games, flirting and dancing. She was dismayed when, the day after that, he continued his journey.
On reaching Paris in the last days of May, Buonaparte called on François Aubry, Carnot's successor at the war ministry, but any hopes of reversing the decision striking him off the list of artillery generals were quickly dispelled. Aubry, a former artillery officer embittered by career disappointments, was not to be swayed. Buonaparte began to look around for someone who might help him.
One of the most prominent among those known as the ' _jeunesse dorée_ ', a faction persecuting the fallen Jacobins, was Stanislas Fréron, who was in love with Buonaparte's fifteen-year-old sister Paulette, whom he had met in Marseille and whom he wished to marry. Buonaparte was not averse to the match if it could help his own cause.
A potentially more useful acquaintance was Paul Barras, who had also been at Toulon. His chequered past included fighting the British in India, voting for the death of Louis XVI in the Convention, a minor role in the downfall of Robespierre, and the defeat of a royalist attempt to overthrow the Republic. A spell as commissary to the army had provided the opportunities for graft which enabled him to acquire considerable wealth, with which he indulged his love of luxury and women. He had turned his Jacobin coat inside out, surrounding himself with a court of roués and courtesans, and would have welcomed another ex-Jacobin with a realist's ability to change his tune, but Barras trusted nobody. There had been Jacobin riots a few days before Buonaparte's arrival, and the political situation remained unstable, with people representing every shade of revolution and counter-revolution manoeuvring in a kaleidoscopic succession of alliances and realignments. Barras would see no point in helping Buonaparte until he needed him. But he did take him under his wing to keep in reserve.
On 13 June Buonaparte received his posting to the Army of the West under General Lazare Hoche, operating against royalist rebels in the Vendée. He had no intention of going and obtained sick leave until 31 August, which gave him time to consider his options.
The fall of Robespierre had put an end to the Terror, and the resulting release from fear produced an eruption of hedonism. Buonaparte was astonished at the extent to which the people of Paris threw themselves into a life of pleasure. 'To dance, to go to the theatre, to parties out in the country and to pay court to women, who are here the most beautiful in the world, is the main occupation and the most important thing,' he wrote to Joseph. 'People look back on the Terror as on a bad dream.'
Antoine Lavalette, a contemporary of Buonaparte, was horrified at what had happened to his native city, where 'the dissolution of society had plumbed new depths'. He noted disapprovingly that 'it was the newly rich who sought to set the tone, combining all the errors of a bad upbringing with all the ridicule of an inborn absence of dignity'. He was shocked at the 'barely believable level of licentiousness' on display, at the 'lovely, well-bred women of high birth' who 'wore flesh-coloured pantaloons and buskins on their feet, barely covered by dresses of transparent gauze, with their breasts uncovered and their arms naked to the shoulder'. As another explained, 'The aim of these ladies and the _ne plus ultra_ of their art was to show as much nudity as possible without being naked'. Some moistened their dresses with oil to make them cling to the body.
There were balls to which only relatives of those who had been guillotined were invited, in some cases held in prisons where the September massacres had taken place, at which the guests wore a red ribbon round their necks in a gesture somewhere between gallows humour and exorcism. Buonaparte may have been shocked, but he showed understanding of people's need to compensate for the sufferings and the anxieties of the past – and he was a good deal less censorious than Lavalette when it came to the _nouveaux riches_.
A disastrous economic situation and a financial crisis provoked by the vertiginous fall in value of the paper currency, the _assignats_ , coupled with the emigration or execution of nobles, entailing the confiscation of their property, meant that there were a large number of properties on the market. People who had grown rich during the Revolution were desperate to park their depreciating cash in solid assets, creating a febrile market in which there was money to be made. On leaving Châtillon for Paris, Buonaparte had made a detour to view a country house at Ragny in Burgundy. 'The château itself consists of a new residence or pavilion in the modern style,' he wrote to Joseph on 22 May, going on to list its merits and pointing out that if the turrets which gave it 'an aristocratic look' were demolished it could be marketed as a splendid residence, with its 'superb' dining room four times the size of their old one in Ajaccio.
The pursuit of pleasure had spawned a taste for luxuries of every kind, and some were scarce in Paris. Three days after reaching the capital Buonaparte took time off from promoting his career to research the price of sugar, soap and coffee. As it was far higher than in Marseille, he instructed Joseph to buy up a stock there and ship it to Paris. Ragny had been sold, he informed his brother a few weeks later, but there were plenty of other investment opportunities.
At the beginning of July he reported that he had put in hand the sale of the coffee Joseph had sent, and urged him to buy up in Genoa, where the Clary family had moved, silk stockings, shawls, and Florentine and English taffeta (which would have to be imported into France through Leipzig, since Britain and France were at war), all of which were at a premium in Paris. He had succeeded in finding a sales outlet in Paris for Joseph Fesch, who had set himself up in the porcelain trade in Basel in Switzerland. He even urged Joseph to investigate the price of pasta in Italy, as the food shortages in Paris might make it worthwhile to import that. He had located a promising property in the valley of Montmorency, and was looking for others. He wanted Joseph to finance these speculations, but he also identified ways of buying on credit and selling on at a profit before having to realise the purchase. If only Joseph had followed his first suggestion, he complained, they would have made a million. Buonaparte could see people making fortunes all around him, and was exasperated by Joseph's lack of interest.
Naturally lazy, Joseph had no wish to hazard his easily acquired fortune in property speculation. He had followed the Clary family to neutral Genoa, where they had managed to take most of their money with them and from where they carried on their Levantine trade. Joseph was living well, and supporting his mother and sisters at Château-Sallé. Yet he badgered Buonaparte to use his influence to obtain for him a post as French consul in some trading city in Italy or the Levant, where he would be able to benefit from the salary and use his position to further his commercial activities. 'We have lived so many years so closely bound together that our hearts have become entwined,' Buonaparte wrote back, promising to try. 'You know better than anyone how profoundly mine is entirely devoted to you.'
He had managed to place Louis in the officers' school at Châlons, which was costing him a considerable share of his half-pay, and was exploring the possibilities of getting the youngest, Geronimo, into school in Paris. He had used his connections to free Lucien – 'Brutus' had got himself arrested for his Jacobin connections. He found Lucien tiresome, impudent and irresponsible, 'a born intriguer', but he was family.
In the culture to which Buonaparte had been brought up, the family operated as a clan, providing a security which he was missing in Paris. Although he was now twenty-five years old, and had been through a great deal over the past few years, he was still in many ways a child, with his displays of aggressive defensiveness and of emotion clothed in cynicism. Yet he was now having to deal with a complex set of challenges and sensations, and was emotionally torn between two different worlds. The one associated with Désirée held strong appeal.
Joseph's was a perfect match. The Buonaparte and the Clary were grounded in the culture of the Mediterranean with its mainstay of the family. Both families were bent on financial and social advancement, but were essentially middle-class in outlook. Their aspirations to noble status were driven by material rather than ideological motives, and had nothing in common with the supposedly chivalric impulses of the _noblesse_. Nor were they bound by its prejudices.
It is unlikely that Buonaparte's feelings for Désirée were profound. Yet he did kindle strong feelings in her. Her surviving letters and drafts exude all the passion and sentimentality one would expect of a lovelorn teenager. When he left for Paris in May she spelled out her desolation, assuring him that every instant they were apart pierced her soul. 'The thought of you is with me always, and will follow me to my grave,' she wrote shortly after his departure, her only consolation the knowledge that he would always be faithful. She hoped he would not find the Parisian beauties too alluring, and reassured herself that 'our hearts are much too closely united for it ever to be possible for them to separate'.
Shortly after his arrival in Paris, Buonaparte wrote saying that although he had met some 'pretty and very charming women' at Châtillon, none could compare with his 'sweet and kind Eugénie'. He wrote two days later, sending her some songs, and again three days after that, with more sheet music, chiding her for not writing more often. On 14 June, on hearing that she had moved to Genoa with her brother and sisters, he wrote a long and barely coherent letter reproaching her for letting him down.
He had made her promise that she would wait for him in Marseille, and her leaving made it impossible for them to see each other. A French citizen who went abroad was liable to be labelled an émigré and proscribed. For a serving officer to do so was tantamount to treason. Her going to Genoa suggested that her family were opposed to their marriage, and he saw it as a betrayal on her part. In an emotional letter of 14 June, Buonaparte assumes that their liaison is over while expressing the conviction that she will always love him. Feigning noble abnegation, he expresses the hope that she will find one worthier than himself. In a welter of self-deprecation he describes himself as a being cursed with 'a fiery imagination, a cool head, a strange heart and an inclination to melancholy', who is 'surrounded by the savagery and immorality of men', believes himself to be 'the opposite of other men' and despises life. Yet he insists that he can only find happiness in her love, and begs her to find a way for them to be reunited. 'There is nothing I will not undertake for my adorable Eugénie,' he affirms. 'But if fate is against us think only of yourself and of your own Happiness: it is more precious than mine.' Perhaps significantly, that was the day he resolved not to join the Army of the West and extended his sick leave.
He wrote again ten days later, complaining of her silence and assuring her that although Paris was brimming with pleasures of every kind he could think only of his Eugénie and consoled himself with looking at her portrait, promising to send her his own. The same day in a letter to Joseph he wrote that 'if the business with Eugénie is not concluded and if you do not send me any funds with which to operate, then I will accept the post of infantry general and go with the Army of the Rhine to seek my death'. He intimated that the engagement was broken off and suggested that as she would not want the portrait he had sent, Joseph should keep it for himself. She continued to cover notebooks with his name and initials, but there is little doubt her family wanted no more to do with him, and he too now had other things on his mind.
'So there we were the three of us in Paris,' recalled Marmont. 'Bonaparte without a job, me without any formal permission, and Junot attached as aide de camp to a general whom they did not want to employ [...] passing our time at the Palais-Royal and at the theatres, having very little money and no future.' Money does not in fact appear to have been a major problem; Buonaparte may have been on half-pay, but that did represent a regular income, and Junot, who came from a comfortably-off family, received subsidies from his father. Their future was indeed uncertain; Buonaparte's military career had stalled and his political connections were not influential enough to restart it.
Barras had opened a new world to Buonaparte by introducing him to those who set the tone in Paris. Chief among them was the great beauty, the daughter of a Spanish banker, Thérèse de Cabarrus, known as ' _Notre Dame de Thermidor_ ' because the revolutionary Jean-Lambert Tallien had fallen in love with her, freed her from prison and then helped bring down Robespierre and end the Terror in order to save his own as well as her neck. Other social lionesses included Juliette Récamier, Aimée de Coigny, Julie Talma and Rose de Beauharnais, as well as the more intellectually prized Germaine de Staël and older, more experienced ladies such as Mesdames de Montansier and Château-Renaud. They were seductive, sophisticated and assertive women who did as they pleased, and Buonaparte's references in letters to Désirée and to Joseph leave no doubt that he was fascinated and excited by them.
He cut a poor figure with his small stature, lean and sallow features, hungry look and worn clothes, and he had no idea of how to present himself, how to enter a room, greet people or respond. His manner was farouche, a mixture of shyness and aggression that baffled people. While it could be appealing to the provincial girls he had encountered up till now, it grew disagreeable when he became defensive. He was particularly awkward with sophisticated women, and gave the impression of not caring what they thought of him. He was out of his depth, not so much socially as in terms of simple human communication: he showed a curious lack of empathy which meant that he did not know what to say to people, and therefore either said nothing or something inappropriate.
His gracelessness, unkempt appearance and poor French, delivered in staccato phrases, did not help. Laure Permon, in whose parents' house he and Junot found a second home, thought him ugly and dirty. Bourrienne's wife found him cold and sombre, and little short of savage. He could sit through a comedy with them and remain impassive while the whole house laughed, and then laugh raucously at odd moments. She remembered him telling a tasteless joke about one of his men having his testicles shot off at Toulon, and laughing uproariously while all around sat horrified. Yet there was something about his manner that some found unaccountably attractive.
The sophistication of the liberated ladies both attracted and repelled him. They made Désirée seem provincial and uninteresting on the one hand, yet pure and sublime on the other. But the ardent love of a virginal teenager would not stand up to the sensual draw of the more sophisticated older woman, particularly in a young man who was still a child craving a mother figure. It seems he made a pass at Thérèse Tallien, who rebuffed him but apparently retained a fondness for him, as he was welcome in her salon, and she even used her contacts to obtain some cloth for him to have a new uniform run up. He appears to have been more successful with other women, perhaps including Letizia's childhood friend Panoria Permon.
He was feeling sorry for himself. On 5 August he wrote to the Committee of Public Safety complaining that his merits and devotion to the Republic had not been recognised. A few days later he admitted to Joseph that he was 'very little attached to life', and suggested he might as well throw himself under a passing carriage. Those are not the only things he said and wrote which suggest that he did on occasion contemplate suicide.
With little else to do, he spent whole days at the Bibliothèque Nationale, established in 1792 with the amalgamation of the old royal library and the noble and ecclesiastical libraries seized during the Revolution. He was not only reading, as he always did when he had time on his hands. He was also writing.
The fruit was a novella entitled _Clisson et Eugénie_ , no doubt in homage to one of his favourite novels, Bernardin de Saint-Pierre's _Paul et Virginie_. Its hero, Clisson, feels the call to arms from earliest childhood, excited by the sight of a helmet, a sabre or a drum. At the age when others read fairy tales he studies the lives of great men; while others chase girls he applies himself to the art of war. He grows up to be an inspired young soldier who 'marked every step with brilliant actions', and quickly attains the highest rank. 'His victories followed one after the other and his name was known to the nation as that of one of its dearest defenders.' But he is the victim of 'wickedness and envy', having to endure the 'calumnies' of his peers. 'They called his loftiness of spirit' pride and reproached him for his 'firmness'. Disenchanted, feeling out of place in social gatherings, he flees society, wandering remote forests and abandoning himself to 'the desires and palpitations of his heart' on moonlit nights, brimming with melancholy and self-pity. He meets Eugénie, who is 'like the song of the nightingale or a passage of Paisiello [his favourite composer], which pleases merely sensitive souls, but whose melody transports and arouses passions only in those which can feel it keenly'. They fall in love, settle down and start a family, but after a few years he hears the call of duty from the endangered motherland and resolves to gird his loins once more. 'His name was the signal for victory', and his triumphs 'surpassed the hopes of the nation and the army'. He sends one of his aides, his best friend, to console Eugénie in his absence, which he does only too well. When Clisson discovers that they have fallen in love he writes her a letter full of generosity and tenderness, and charges into battle and his death.
The work requires little comment. It is a psychoanalyst's feast with its display of emotional immaturity, dreams of glory, and sense of superiority combined with a desperate awareness of inferiority in some areas, with aggression coupled to a curiously mawkish sensibility, and total self-obsession.
On 17 August, having received orders to take up his posting with the Army of the West, Buonaparte called on Aubry's successor at the ministry of war, Doulcet de Pontécoulant. The new head of military affairs was struck by the way the frail, sickly-looking man came to life as he spoke, his eyes sparkling with fire as he uttered the words 'army', 'battle' and 'victory'. He appointed him to the Cabinet Historique et Topographique, a general staff consisting of twenty officers. Buonaparte applied himself with his usual single-mindedness, producing plans and memoranda on every aspect of the military situation, often staying up until 3 a.m. 'When I work on a plan of campaign, I cannot rest until I have finished, until I have worked through all my ideas,' he later explained. 'I am like a woman in labour.' He presented Pontécoulant with a plan for the conquest of northern Italy which when it was sent to the commander of the Army of Italy was rejected as the figment of a madman who should be sent to an asylum.
The work did not distract him from more prosaic matters; he was looking at properties within easy reach of Paris, and had located one with 'a very fine house' whose drawing rooms, dining room, kitchen, pantry, bedrooms, garden, orchard, kitchen garden, fields, pastures and woods he listed for his brother's benefit. 'In any case, I shall buy it, because it seems to me that it cannot fail to be a good deal,' he concluded. His confidence in being able to find the necessary funds may have had something to do with a revival of his marriage plans.
'I have friends, much esteem, balls, parties, but far from my sweet Eugénie I can have only some pleasure, some enjoyment, but no happiness,' he wrote to Désirée at the end of August, urging her to join him, adding, 'time flies, the seasons follow each other and old age advances'. To Joseph he wrote that he wanted to 'conclude the business of Eugénie', as it was interfering with his plans; he felt it was time he married, and there was no lack of willing women in Paris. 'It is for her to sort things out, since she spoiled everything by her journey [to Genoa]. If she really wants it, everything can be easily arranged.'
'You well know, my friend, that I live only for the pleasure I can give my own family, happy only in their Happiness,' he wrote to Joseph. 'If my hopes are assisted by that success which never fails me in my enterprises, I will be able to be of use to all of you, make you happy and fulfil your desires...' He was trying to obtain Joseph a consulate in Italy, and had managed to land Fesch a job provisioning the Army of the Rhine. He was sending Louis 300 francs a month: 'He's a good sort, and, also, just like me, he has warmth, wit, health, talent, attention to detail, all of it.' He was pleased with the way the family was doing, and full of hope for the future. 'I could not be better situated or have a more pleasant and satisfactory position here,' he assured Joseph on 8 September. 'The future should be held in contempt by a man who has courage.' In between various proposals for speculating on property he returned to 'the business of Eugénie', which he insisted must be resolved. 'If these people do not wish to conclude the matter of Eugénie, so much the worse for her, since she is stupid enough to listen to them,' he wrote a couple of weeks later, making out that he would have done her family an honour by marrying her. He had better things to do than wait on them, and he crossed ' _Eugénie_ ' out of the title of his novella.
He got wind of a project to send officers to Constantinople to modernise the Sultan's artillery, and applied to lead it. As he explained to his brother, he would be in command of an important mission, he would probably be able to get him the post of consul, and they would make a deal of money. On 15 September 1795 he was confirmed in command of a military mission to the Porte. He selected Songis, Marmont, Junot and Muiron to accompany him on what promised to be the adventure of a lifetime. Yet a different adventure would change his plans.
## 9
# General Vendémiaire
What really happened on 5 October 1795 remains a mystery. The events of that day, 13 Vendémiaire in the revolutionary calendar, were rich in consequences, not so much for the continuing course of the Revolution as for the future of one man – General Buonaparte. Yet it is his role in the events that is the most elusive.
While he was absorbed by his contradictory feelings for Désirée, his financial speculations, his military career and his dreams of oriental riches, a new political crisis had been brewing. The men who had taken power after the fall of Robespierre had provided neither strong government and stability nor any principles which could unite the nation. They reflected all the vices and uncertainties of a society that had lost its way. Jacobins lurked in the wings, and the more extreme such as 'Gracchus' Babeuf were plotting the ultimate revolution. At the opposite end of the scale, royalists mustered for a restoration of the monarchy.
On 8 June the ten-year-old son of Louis XVI died in the Temple prison in Paris. His uncle, the late king's younger brother, issued a proclamation from Verona, where he had taken refuge, assuming the succession as Louis XVIII. Less than three weeks later the Royal Navy landed 4,000 émigrés in Brittany to support royalist insurgents. General Hoche, commanding the army in which Buonaparte should have been serving, forced them back to the Quiberon peninsula, where they and another 2,000 men landed by the British were defeated on 21 July. The following day peace was signed between France and Spain, whose invasion force had been driven back as far as Bilbao. The Republic appeared to be secure. But royalist feeling remained strong, and discontent with the existing government simmered on.
There was a degree of consensus that the country needed a new constitution. The first, passed in September 1791, had turned France into a constitutional monarchy. It had been superseded, along with the monarchy, by a republican one in June 1793, Year I in the revolutionary calendar. But this had been quickly suspended in the state of national emergency provoked by the threat of invasion. A new one, the Constitution of Year III, was adopted on 22 August 1795. It replaced the Convention with a Council of the Five Hundred and a Council of Elders of half that number, both elected by suffrage based on property ownership. The governing Committee of Public Safety was to be superseded by an Executive Directory of five elected by the chambers through a complex procedure. 'The government will soon be formed,' Buonaparte wrote to Joseph on 12 September. 'A serene future is dawning for France.' He could not have been more wrong.
Those who sat in the Convention had no intention of relinquishing power. Realising that in free elections royalists would capture a majority in both new chambers, they passed a law stipulating that two-thirds of the seats, 500 out of 750, would go to members of the existing Convention. This provoked an insurrection in Normandy and agitation in Paris. Royalists were dominant in several of the sections, the neighbourhood assemblies of the capital, and by the first days of October the city was in a state of ferment.
On the evening of 3 October Buonaparte received a note from Barras, still a member of the Committee of Public Safety, asking him to call at his house in Chaillot at ten the following morning. Barras needed 'men of execution' to deal with what he called 'the royalist terrorists' mustering their forces. It is not known what was agreed at their meeting, but Buonaparte seems to have remained non-committal, and Barras also contacted two former Jacobin generals who had been set aside after the fall of Robespierre: Carteaux and Guillaume Brune.
Insurrection was in the air, and by the time Buonaparte returned from Chaillot one of the sections, Le Pelletier, was mobilising its National Guard. He nevertheless went to the theatre. By the time he came out, at about seven or eight in the evening, the situation had grown critical. The Le Pelletier section was in open revolt, turning its narrow streets into an impregnable fortress. General Jacques Menou and representatives of the Convention had set out with troops to confront the rebels, but seeing the impossibility of dislodging them without heavy casualties and realising that they would soon be trapped, they negotiated a truce and retreated. The Le Pelletier section declared itself to be the rightful authority, and called on other sections to join it.
Menou, a former officer of the royal army, was accused of treason and placed under arrest, and the search was on for someone to replace him. Writing more than twenty years later, Buonaparte asserts that he went to the Convention and found the deputies in a state of panic. The names of various generals were put forward, including his. Hidden among the spectators, he was able to slip out to consider his position. He relates that it took him half an hour to decide whether to take up the challenge: he did not like the existing authorities, but if the royalists were to get the upper hand and bring back the Bourbons, everything that had been achieved since 1789 (and his own future) would be in jeopardy. He maintains that he then offered his services to the Committee of Public Safety, on condition he was given absolute authority, without having to take instructions from its representatives as was usual.
Barras tells a different story. 'There is nothing simpler than replacing Menou,' he claims to have told the Committee. 'I have the man you need; a little Corsican officer who will not be so squeamish.' In Buonaparte's version, Barras assumed nominal command of the Convention's forces, which dispensed with the requirement of government representatives, and he, as second in command, took effective control of operations.
Either way, neither of them slept that night. Sometime after one o'clock on the morning of 5 October, Buonaparte ordered a young _chef d'escadron_ of the 21st Mounted Chasseurs, Joachim Murat, to ride over to the plain of the Sablons and secure forty cannon stored there before the rebels could get hold of them. At first light, as the drumrolls summoning the national guards of the various sections resounded across the city, Buonaparte was positioning the guns at strategic points around the seat of the government at the Tuileries, such as the Pont Neuf in the east, the rue Saint-Honoré to the north, and what is now the Place de la Concorde in the west.
The government troops, numbering just over 5,000 men, supported by 1,500 'patriots' ready to defend the Republic against the royalists, and several hundred deputies armed with muskets, faced probably about four times their number of national guards converging from all sides. There followed a lengthy stand-off. A heavy downpour dampened the ardour of the insurgents, and it was not until around four o'clock in the afternoon that the first shots were fired. The batteries were positioned in such a way that the insurgents could not deploy and bring their superior numbers to bear, and the canister shot they fired precluded any attempt to rush them. It was all over within two hours, and while gunfire was heard at various points in the city during the night, all remaining rebel forces were mopped up the following day. Reports of casualties vary from around 400 to over a thousand.
Buonaparte's version, which became official history and then legend as the 'whiff of grapeshot' which demonstrated his ruthless sense of purpose, has him in charge, directing everything, generously waiting for the insurgents to fire first, using only enough of the canister shot to show that he meant business, and firing blanks thereafter. The truth of this is hard to ascertain. 'The enemy came to attack us at the Tuileries,' he wrote to Joseph. 'We killed a lot of them. They killed 30 of our men and wounded 60. We disarmed the sections and everything is quiet.' Later he claimed that casualties were no higher than 200 dead and wounded on each side.
Long after he had been shunted aside by the 'little Corsican officer', an embittered Barras would describe the events differently. It was he who had planned everything, he who had ordered the guns brought from the Sablons, he who had instructed Brune to fire canister shot over the heads of the oncoming rebels. 'On the 13 Vendémiaire Bonaparte played no role other than that of my aide de camp,' he summed up. In his official report delivered to the Convention on 10 October, he praised Brune and others, and did not mention Buonaparte. When Barras had finished, Fréron, still hoping to marry Paulette, rose to speak and reminded him of Buonaparte's contribution, which Barras reluctantly acknowledged. His report is not the only one to omit Buonaparte. While one account does record that he had a horse killed under him, it states that it was General Verdier who positioned the guns. There must nevertheless have been something remarkable about Buonaparte's conduct on that day.
The events had shown that with well-led troops on its side, a government could put an end to the mob rule that had plagued the Revolution. High prices and food shortages meant that Paris remained vulnerable to riots, and in the following days Barras increased the military presence in the city. He recommended Buonaparte for the post of his second in command, and as he himself was about to take up that of a member of the Executive Directory, he would have to give up the command, which meant that his second would be in charge of the most powerful force in the land. It seems unlikely that he would have placed it in any but the most capable hands. There was no further mention of Constantinople, and Buonaparte was now being referred to as 'General Vendémiaire', which suggests that his role had been decisive.
On 16 October Buonaparte was promoted to divisional general, and ten days later he was confirmed as commander of the Army of the Interior. He had been effective military governor of Paris since 6 October, and had immediately set about pacifying the city, reforming the National Guard and confiscating privately-held arms, discharging officers with royalist leanings and closing down the Jacobin Club, and taking in hand the police of the capital. Not confining himself to his headquarters in the Place Vendôme, he rode about the city, escorted by a retinue of staff officers and a growing number of aides, including his brother Louis, for whom he had obtained the rank of lieutenant, Junot, Marmont and Murat, whose dash in the early hours of 5 October had impressed him. 'He never went anywhere without his moustachioed officers with their long sabres,' recalled Barras. 'He would mount his tall palfrey, wearing a huge hat with its tricolour plumes and its turned-up rims, his boots turned down, and a dangling sabre larger than its wearer.' Junot and Murat had been promoted by Buonaparte, and wore with panache the distinctions of a rank they did not officially hold, while Murat embellished his uniform with various outlandish accoutrements.
Buonaparte himself had grown into his role. Gone was the awkward gait. 'He already had extraordinary aplomb, a grand manner quite new to me,' remembered Marmont. He would go to the theatre, making a dramatic entrance with his entourage of swaggering young bloods, their spurs and sabres clinking as they went. He was developing a taste for the theatrical, and was learning a new part. During a food riot in one of the poorer _quartiers_ as he rode through it one day with his glittering cavalcade, he confronted a huge woman who accused his like of growing fat on their salaries by asking her which of them was the fatter, which provoked mirth and defused the situation.
While he had not gained weight, he was certainly growing fat in the sense the woman meant. Barras, himself one of the great embezzlers of history, had seen to it that Buonaparte was well provided for. How, we do not know. Although he was drawing a salary of 4,000 francs a month, the value of the _assignats_ in which it was paid had fallen dramatically: by 23 October it had dropped to 3 per cent of its nominal value, and specie was extremely scarce. With a pound of sugar costing 100 francs and a bushel of potatoes 200, his salary would not have gone far. He did get a daily allowance for food and other essentials, and fodder for his horses. But that does not explain how he was able to provide his mother with financial assistance adding up to more than his annual salary, send Joseph 400,000 francs, and badger Bourrienne to find him a property to buy.
As well as money, he was not short of influence. He now wrote to Letizia that Paulette must not marry Fréron, who no longer counted politically. He was in the process of arranging a consulate in Italy for Joseph, and in the meantime obtained for him letters of marque licensing two corsairs to operate out of Genoa and prey on British shipping. He found Lucien a job as commissary to the Army of the North, and Fesch one as a secretary, pending a better job overseeing the Paris hospitals. Nor did he forget more distant relatives. 'The family wants for nothing,' he declared to Joseph with satisfaction in a letter of 18 December. 'I have sent them all money, _assignats_ , clothing, etc....'
Barras relates that he was arranging to set Buonaparte up by marrying him off to Mademoiselle de Montansier, an older lady who owned several theatres in Paris, a sure source of income at the time. Thoughts of Désirée would not stand in the way: in a letter to his sister-in-law Marie-Julie Clary, Buonaparte mentions every member of the family but her. In a letter of 9 December he bids Joseph to give her his regards, but for the first time refers to her as Désirée, not Eugénie. He does ask for news of her in one written ten days later, but without the impatience that accompanied previous requests. Buonaparte did not, however, marry Mademoiselle de Montansier.
Shortly after he had ordered all privately-owned arms to be confiscated, a fourteen-year-old boy called at his headquarters, begging that he might be allowed to keep the sword which had belonged to his father, a general guillotined under the Terror. Moved by the boy's request, Buonaparte agreed. The following day, the story goes, the grateful mother called. Or he may have called on her, bringing the document permitting the family to keep the sword. Or, as Buonaparte would have us believe, he sent along one of his aides, who reported back that she was a beautiful widow. Or the whole story may be a fable woven round some incident to do with the sword. It is unlikely that Buonaparte had never met the widow in question, since she was a close friend of the ladies whose salons he had been frequenting for months, and, being the mistress of Barras, was often at his side. One thing is certain – that General Buonaparte fell madly, almost obsessively in love with her.
Marie-Josèphe-Rose de Beauharnais was born into the parvenu and scandal-ridden family of Tascher, who owned La Pagerie, a plantation in the French island colony of Martinique. She was brought to France and married off at an early age to an undistinguished nobleman, Alexandre de Beauharnais, who paraded under the assumed title of vicomte. He was jealous and abusive as well as unfaithful, and repudiated her after having sired two children. During the Revolution he had briefly presided over the National Assembly and then been put in command of the Army of the Rhine. An inept soldier, he had allowed the fortress of Mainz to fall to the enemy in 1793 out of fecklessness, but was accused of treason and executed the following year. His wife, known in childhood as Yéyette and later as Josephine, was incarcerated in the same prison, Les Carmes, where, while he was conducting an affair with the widow of an executed general, she was doing the same with General Lazare Hoche, also a prisoner.
Prisons were hotbeds of sexual activity during the Terror, and Les Carmes, whose walls were still smeared with the blood of the 115 priests massacred there in September 1792, was no exception. The usual instinct in the presence of impending death was in this case reinforced by the hope of getting pregnant, which would spare a woman the guillotine. As a result, the multiple-occupancy chambers throbbed to the sound of couplings, often with the warders themselves, in scenes of fear and degradation which left their mark on those like Josephine who were fortunate enough to survive.
On her release from prison following the fall of Robespierre, Josephine made the most of the friendships forged there with, amongst others, Thérèse Tallien. She resumed her affair with General Hoche and was prominent in the exuberant new society, the salons and the extravagant macabre entertainments of the capital. Sometime in the early summer of 1795 she became the mistress of Barras, but by the beginning of the autumn he was ready to move on and began looking around for a husband who might provide for her. She had no money and was living from day to day on the generosity of lovers, currently that of Barras, who had rented a small house for her off the rue Chantereine.
Josephine was thirty-two and, as Barras put it, 'growing precociously decrepit'. She had never been a beauty, and with her freshness wilting she had to resort to what he called 'the most refined, the most perfected artistry ever practised by the courtesans of ancient Greece or Paris in the exercise of their profession'. She knew how to overcome every disadvantage, concealing her rotten teeth by keeping her mouth shut when she smiled, which many found irresistible. She possessed an almost legendary charm, grace, and a languor of movement which people associated with her creole origins, lending her a certain spice in their imagination. She was both dignified, with elegant manners and bearing, and girlishly light-hearted, displaying a devil-may-care attitude to practicalities. And there is little doubt that she was an accomplished lover. But she had no position to fall back on when these assets failed, and marriage was the only practical way of securing her future.
According to Barras she had set her cap at Hoche, but he was married, and had allegedly commented that 'one could take a whore as a mistress for a time, but not as a legitimate wife'. It seems that Barras then suggested she marry Buonaparte. She was not taken with the idea, allegedly saying that of all the men she might bring herself to love, this 'puss in boots' was the last, and objecting that he came from 'a family of beggars', even though he was by then showering her with presents. Barras encouraged the match, partly in order to establish her on a respectable footing, perhaps also to tighten his grip on the useful young general, who was growing alarmingly independent.
Buonaparte had begun to do as he pleased, appointing and cashiering officers, reorganising units, and extending his brief beyond military matters. He called on the Directors almost daily, not so much advising them as telling them what to do, and castigating them for their incompetence. When they reproved him for acting in an arbitrary manner, he reputedly countered by saying it was impossible to get anything done if one were to stick to the law, and he usually managed to get them to see things his way. Getting Buonaparte settled might make life easier for the Directors. Barras advised him that 'a married man finds his place in society', and that marriage gave a man 'more substance and greater resilience against his enemies'. Most people thought he was merely trying to park an unwanted mistress, and the Marquis de Sade would publish that version, thinly veiled, in his _Zoloé et ses deux acolytes_.
Buonaparte was not as fussy as Hoche. He allegedly told Barras that he did not like the idea of seducing a virgin, and preferred to find ' _l'amour tout fait que l'amour a faire_ ', in other words the ground well prepared. Whether those really were his words or not, there is a ring of truth about what they expressed; such cynical bluster is characteristic of the sexually insecure.
The first extant letter from Buonaparte to Josephine is undated, but it was written at seven in the morning, probably in the second half of December 1795, and almost certainly after their first night of love. 'I have woken full of you,' he wrote. 'The picture of you and the memory of yesterday's intoxicating evening have left no rest to my senses. Sweet and incomparable Josephine, what a strange effect you have had on my heart!' He goes on to say that he cannot stop thinking about her and what she is doing, and cannot wait to see her again, in three hours' time. 'Meanwhile, _mio dolce amor_ , a million kisses from me; but do not give me any, as your kisses set my blood on fire.'
The incomparable courtesan had clearly given him his first pleasurable amorous experience. 'It was, it seems, his first love, and he experienced it with all the intensity of his nature,' noted Marmont. He also noted something else. 'What is incredible, and yet absolutely true, is that Bonaparte's vanity was flattered,' he wrote, explaining that for all his republican talk, the young general was beguiled by the social grace of the old nobility, and that in the company of the former pseudo-vicomtesse de Beauharnais he felt as though he had been accepted into its charmed circle; he was not Carlo Buonaparte's son for nothing. Josephine fed Buonaparte's social aspirations with talk of her estates in Martinique, cleverly disguising her penury and hinting at great wealth. She had taste and flair, and had managed to create a sense of elegance in the little house on the rue Chantereine with the few sticks of furniture and meagre ornaments she possessed, and despite the chipped assorted china and unmatched flatware her dinners exuded refined aristocratic ease. The house itself, designed for the philosopher Condorcet by Claude Nicolas Ledoux, was an intimate retreat, reached by a narrow walled lane, a refuge from the political turmoil of the capital. Buonaparte felt well there not just on account of his love for Josephine. He quickly captivated her two children, the fourteen-year-old Eugène and the twelve-year-old Hortense. They had begun by resenting his intrusion, but gave in when he started telling them ghost stories and playing with them. Still something of a child himself, he had found a home in Paris.
Josephine was unsure about this third child. 'They want me to marry, my dear friend!' she wrote to a confidante. 'All my friends urge me to, my aunt almost orders it and my children beg me to! "Do you love him?" you will ask. – Well... no. "So you find him unappealing?" – No, but I find myself in a state of tepidity which I find unpleasant...' She goes on to say that she feels she should feel greater ardour: 'I admire the general's courage, the extent of his knowledge in all things, of which he speaks equally well, the agility of his mind, which allows him to seize the thoughts of others almost before they have expressed them; but I am fearful, I confess, of the control he seems to wish to exert over everything around him. His piercing look has something about it quite mysterious which impresses even the directors: you can judge for yourself how it intimidates a woman!'
What seems to have bothered her most was his ardour. His various sexual encounters to date had evidently left him cold, and what he experienced with Josephine had opened up a gamut of new sensations and unlocked feelings he had either never known, or had repressed with all the vehemence with which he had lambasted his friend des Mazis at Valence. 'Above all,' continues Josephine, 'that which should please me, the strength of a passion of which he speaks with a force which does not permit any doubt as to its sincerity is precisely that which holds back the consent which I am often ready to give. Having passed my first youth, can I hope to preserve this violent love which, in the general's case, resembles an access of madness?' She also found it faintly ridiculous to be the object of adoration of a younger man. She was astonished at his 'absurd self-confidence', while admitting that at moments she believed him capable of anything. Her friends encouraged her, and Barras reassured her that he would soon be sending the young general off to war to cool his ardour.
By then the coalition against France was in poor shape: Tuscany, Prussia, Holland and Spain had dropped out and made peace. Only Austria, Britain and Sardinia were actively pursuing the war. On 31 December an armistice was signed with Austria, but it was expected that hostilities would resume in the spring, and Buonaparte had pronounced ideas on how they should be conducted. Although he was now in command of Paris and the interior, he could not help meddling in overall strategy, to the annoyance of most of the Directors.
Buonaparte's plan for a two-pronged attack on Vienna, to be delivered through Germany by the Army of the Rhine under General Jean-Victor Moreau and through the Tyrol by the Army of Italy, had been sent to the relevant commanders in September 1795. It had been ridiculed by General Kellermann, who had succeeded Dumerbion at the Army of Italy, but was implemented by General Scherer, who had replaced him in command. He carried out the first stage successfully, but then, instead of moving on as prescribed, came to a standstill, pleading insufficient strength and the low morale of his troops. In January 1796 Buonaparte produced an amended version of the plan, but this too met with a critical reception, and one of the commissioners attached to the Army of Italy protested at orders being sent by 'project-mongers' 'gnawed by ambition and greedy for posts above their abilities', 'madmen' in Paris who knew nothing of the realities of the situation on the ground yet thought they could 'seize the moon with their teeth'. Scherer tendered his resignation.
The Directory sent Saliceti to Nice to investigate. He reported that the Army of Italy was not only lacking in all the necessities, it was suffering from low morale, due largely to Scherer's poor leadership. At the suggestion of Barras, the head of the Directory, Carnot, appointed Buonaparte to succeed him. Carnot regarded the Italian theatre of operations as secondary, and supposed that this 'little captain', as he referred to him, would be up to the limited task. The appointment nevertheless raised eyebrows, as Buonaparte had never commanded a unit, let alone an army in the field, and had never been in a real battle. There were plenty of experienced generals to choose from who, as some observed, were not treacherous Corsicans.
Buonaparte set to his new task with his characteristic sense of purpose. He bought all the maps and books on Italy he could find and shut himself up for a week in his office reading, lying on his stomach on maps spread on the floor and tracing possible routes and lines of advance. On the afternoon of 8 March he met Josephine at the offices of her notary Raguideau to draw up their marriage contract and sign a _séparation de biens_ , a prenuptial agreement, after which they parted and spent the night apart (Barras claims she spent it with him). Buonaparte almost certainly worked through the night, and did not emerge from his offices until that night of 9 March, when he remembered, two hours late, an important appointment.
At ten o'clock he drove across a Paris thickly carpeted in snow, accompanied by his aide Jean Le Marois, to the offices of the _deuxième municipalité_ of Paris, housed in the former residence of an émigré marquis, situated in the rue d'Antin. Josephine had been waiting for him there for two hours, along with Barras, Jean-Lambert Tallien, now a member of the legislative chamber, and her lawyer Étienne Calmelet, who were to witness their marriage. The man who was to marry them, the _officier de l'état civil_ Carles Leclercq, had grown tired of waiting and gone home to bed, leaving a minor functionary to act in his stead.
The resulting marriage was invalid. The functionary in question had no authority to marry anyone; Buonaparte's witness Le Marois was under the required age of twenty-one; and the documents provided by both parties were spurious: pleading the impossibility of providing a birth certificate due to the British blockade of Martinique, Josephine produced a document drawn up by her notary attesting that she had been born on the island in 1767, four years after her real date of birth, while Buonaparte, using the same argument, produced a similar one giving his date of birth as 5 February 1768 (the day Corsica became French).
After the ceremony, without so much as a celebratory drink, the participants went home singly, except for the newlyweds. But their wedding night was not a success, as Josephine's pet pug, Fortuné, would not let Buonaparte get into her bed, and bit him in the calf when he tried. The next day he accompanied her to Madame Campan's school at Saint-Germain-en-Laye to visit Hortense. That night he may have had access to his spouse, but by the following evening he was on his way south, travelling by night in the company of Junot and the commissary Félix Chauvet. Wisely, he had opted to have his own men running the supply services, and he trusted Chauvet, who was an old friend of the family from Marseille and had served him at Toulon. After much begging he had also persuaded Jean-Pierre Collot, an efficient victualler, to come with him.
They went by way of Marseille, where Buonaparte had a serious matter to attend to. He had not asked his mother for permission to marry, a mark of disrespect and a sin against Corsican family lore, nor had he informed any of his siblings of the forthcoming event – with good reason. He knew that Josephine did not conform to their idea of a desirable wife or a useful addition to the family. She came from an alien milieu, and not only did she not bring any money with her, her interests and those of her children were bound to conflict with those of the Buonaparte. He had himself berated Lucien for his marriage to the lowly Christine Boyer, and more recently had ruled out allowing Paulette to marry the waning Fréron. Lucien, who knew Josephine and disliked her, would no doubt have enjoyed alerting Letizia to his brother's _mésalliance_. On reaching Marseille, Buonaparte apprised Letizia of his marriage and delivered a fittingly deferential letter from Josephine. She took some persuasion, and consulted Joseph before grudgingly responding with a letter whose text Buonaparte had prepared in advance.
He did not call on Désirée, now back in Marseille, but she heard his news and wrote him a suitably heartbroken and melodramatic letter: 'You have made me miserable for the rest of my life, and yet I still have the heart to forgive you. My life is a horrible torture for me since I can no longer devote it to you... You, Married! I cannot accustom myself to the idea, it is killing me, I cannot survive it.' She ended by assuring him that she would never marry another.
Her letter might have moved the 'Clisson' of a few months earlier, but now Buonaparte had thoughts only for Josephine. 'Every instant takes me further away from you, my adorable love, and with every instant I find less and less strength with which to bear being away from you,' he wrote as he sped south two days after leaving her in Paris. 'You are the constant object of all my thoughts,' he assured her, wishing he could be back reading 'our wonderful Ossian' together. It is the first extant document he signed 'Bonaparte'.
## 10
# Italy
When he reached the headquarters of the Army of Italy at Nice on 26 March 1796, the twenty-six-year-old Bonaparte faced one of the greatest challenges of his life. He had never held independent command of so much as a platoon in the field, yet he was now commander-in-chief of an army, staffed with men older and more experienced than him, with sound reputations. Such was André Masséna, eleven years his senior, a big, tall man with expansive gestures and an ironic, malicious smile, the son of a petty grocer from Nice who had been orphaned early and run away to sea, then joined the royal army in which he rose as high as a plebeian could, before, after a spell as a smuggler, fighting his way to general's rank in the army of the Republic. He was a force of nature, uneducated, ostentatiously brave, determined and effective in battle, displaying tactical flair – and a piratical lust for treasure. Another was Charles-Pierre Augereau, twelve years older than Bonaparte, the son of a servant and a Parisian fruit-seller who had a long career behind him as a mercenary in the Neapolitan and Prussian armies before rising in that of the Republic by his conspicuous bravery. He too was a tall, martial figure, with a big nose, the blustering demeanour of a bully and the subversive attitude of a proletarian revolutionary. Foul-mouthed and violent, this child of the streets was popular with his men. The only thing the third corps commander shared with the others was a massive physique. Jean-Mathieu Sérurier was an educated fifty-three-year-old minor nobleman and veteran of the royal army who had seen action in the Seven Years' War, a conscientious, steady, brave and efficient general.
Unlike regular armies, in which a man's rank is taken as a mark of his worth, in the armies of the Republic officers and men learned to trust and esteem only those with a reputation bestowed by those who served under them and spread by word of mouth. Masséna had come across Bonaparte at the siege of Toulon, but was unaware of his contribution to the fall of the town, and to him and the other officers in the Army of Italy, its new commander was an unknown quantity. But they did know he had taken part in the events of Vendémiaire and that he was a political appointment, a 'Parisian general' and an 'intriguer' with no substance, in the words of another who had come across him at Toulon, _chef de bataillon_ Louis-Gabriel Suchet. They had been expecting the worst, but when they actually saw the man they despaired. In their eyes his diminutive stature, pathetic appearance, awkward manner and rasping voice ruled him out as an effective leader of men.
Bonaparte immediately assumed a tone which brooked no argument. 'I have taken command of the Army of Italy,' he wrote to Masséna less than forty-eight hours after his arrival. 'Nominating me, the executive Directory hopes that I may be of use in leading it towards the brilliant destiny which awaits it. Europe contemplates it with awe, and France expects from it all the triumphs of a campaign.' At the same time he flattered the commanders, officers and men, raising their hopes of action, glory and rewards, while Junot and Marmont spread their own admiration and love of the new commander. With a dose of wishful thinking, four days after his arrival he assured Josephine that 'my soldiers display a confidence in me impossible to describe'.
The troops were in poor shape. To have any idea of the conditions, one has to forget all the paintings of finely-uniformed officers leading ranks of men with immaculate white facings and bright-red epaulettes on their well-cut blue coats, with blue, white and red plumes in their hats. Few of the men had boots, and many had no trousers. Some had no uniform jackets. They made themselves footwear out of woven straw and in the absence of hats wore knotted handkerchiefs on their heads. Most of them looked more like scarecrows than soldiers.
They had scant equipment, and were expected to find themselves shelter for the night as best they could when on operations, as there were no tents. Disease and infections dramatically reduced the number of effectives. The companies contracted to supply them pocketed most of the money they received from the government. Even in cantonment around Nice the troops were poorly fed, with meat once every four days, beans once in three, and bowls of rice flavoured with lard the rest of the time. In the autumn they had been able to supplement their diet by gathering chestnuts, but the winter had robbed them of this resource. They could not buy food as they were paid irregularly, and then only in worthless _assignats_. Some of the senior officers who received cash contributions from the local administration to pay the men did not pass it on. The men had been stuck in the same place for months with nothing to do, and morale was low. Desertion was rife and acts of insubordination frequent. Disaffection had reignited anti-government and even royalist feeling among the older men, and shouts of ' _Vive le Roi_ ' were not infrequent. One demi-brigade mutinied shortly before Bonaparte's arrival, one soon after.
Bonaparte realised extreme measures were needed, and with Saliceti as the Directory's commissioner, he was in a position to take them. He had a couple of officers court-martialled to set an example. He sent Chauvet to Genoa to raise a loan and purchase supplies, and wrote to the local authorities demanding food and forage, threatening to send the men out to loot and rape if these were not provided. With a mixture of threat and flattery he managed to get the contractors to disgorge victuals and the local administration to make up for some of the arrears in pay. He gave instructions that the men must have fresh or salt meat every day.
He had selected as his chief of staff a man of experience, his senior in rank and age, whom he had met only recently. The forty-two-year-old Alexandre Berthier had trained as a military engineer and cartographer before receiving his baptism of fire as a captain in the American War of Independence. With his steady temperament, extraordinary memory, unmatched attention to detail, precise mode of expression and legible handwriting, Berthier was the perfect man for the job. He could grasp in a second some hastily-rapped-out order and give it coherent form, while his team ensured it was passed on to the appropriate quarter with a professionalism hitherto unknown in the army of the Republic. Bonaparte supervised and inspected, noting deficiencies and passing them on to Berthier, demanding immediate action. He was so confident that within two days of his arrival he reported to Carnot that 'I have been very well received by the army, which shows a confidence in me for which I am deeply grateful.' Quite how much confidence the army felt is questionable.
François Vigo-Roussillon, a sergeant in the 32nd Demi-Brigade under Masséna, was astonished when his neighbour whispered that the diminutive figure who had just ridden up to their ranks was the new commander-in-chief. 'His appearance, his dress, his bearing did not appeal to us,' he recalled; '... small, slight, very pale, with great black eyes and hollow cheeks, with long hair falling from his brow to his shoulders in two dog's ears, as they were then known. He wore a blue uniform coat and over that a nut-brown overcoat. He was mounted on a large bony sorrel horse with a docked tail.' He was followed by a single servant 'on a rather sad looking mule' borrowed from the supply train. The new general introduced himself to the assembled troops with a speech in which he held out the prospect of glory and the possibility of rich plunder if they managed to defeat the enemy and break into Italy. His address produced little effect, and one officer recalled that afterwards the men made fun of his hairstyle and mimicked his accent.
The troops were an amalgam of former royal soldiers, volunteers and conscripts. Most of the younger men came from the poorer mountainous regions of southern France. They were physically hardened and used to rigorous marches. The make-up of the officer corps was overwhelmingly plebeian (the percentage of nobles had fallen from 80 to 5 between 1789 and 1793), which contributed a sense of fraternity between officers and men, enhanced by the universal penury, as officers and even most of the generals could not afford a horse (the artillery was drawn by mules). The most disciplined units were those which had just been transferred from Spain, where they had fought a victorious campaign.
The infantry divisions each had between three and five demi-brigades, the basic fighting unit at the time. The heavy demi-brigades were supposed to number 3,000 men and the light ones 1,500. Masséna commanded two divisions, Augereau and Sérurier one each. The cavalry, which numbered less than 5,000 men and was of poor quality and short of horses, was led by General Henri Stengel, a fifty-two-year-old German who had been in French service from the age of sixteen. The overall strength of the French Army of Italy was, on paper, 60,000 men, but most historians agree that the real figure was no more than about 47,000. Some put it as low as 35,000.
Facing them in the Alpine passes were 18,000 men of the Sardinian army, well-trained, hardy Savoyard mountain men under the command of the Austrian field marshal baron de Colli. Beside them stood 35,000 Austrians under the seventy-one-year-old Field Marshal de Beaulieu, a Belgian by birth. His troops were disciplined, well-trained, steady and motivated, but they were used to set-piece battles and methodical manoeuvres, which would disadvantage them in the tight valleys and boulder-strewn terrain on which they were to fight.
Bonaparte's orders were to stage a diversion that would tie down the maximum number of Austrian forces in Italy while the two stronger French armies poised on the Rhine defeated the main Austrian army in Germany and marched on Vienna. But he did not think like a soldier content merely to carry out the task he had been set. He believed that as long as the Habsburgs remained dominant in Italy they would present a threat to France, and that the centuries-old rivalry between the two states for hegemony over the peninsula should be resolved. He had studied the various Franco-Austrian wars over Italy, most recently Marshal Maillebois' campaigns of 1745–46. He had pored over maps of the area during the past two years, becoming familiar with the lie of the land and making mental notes of which passes were practicable by artillery, where rivers could be forded, and which were the possible lines of advance and retreat not only for his own army but for the enemy as well. He meant to wipe out the threat to France by expelling the Austrians from Italy.
One weapon in this struggle would be the nascent Italian national movement, which identified the Austrians as oppressors. Many of the nationalists were living in exile in Nice, and Bonaparte held meetings with them. He did not think much of those he met, and had a poor opinion of Italians in general, but he decided to take 150 of them, led by Filippo Buonarroti, along with him. On 31 March he issued a proclamation to the people of Piedmont announcing that the French nation would shortly liberate them.
The following day his divisions were on the move. On 4 April he set up headquarters at Albenga, where he heard of the death of his friend Chauvet in Genoa. Collot was shocked by the apparent indifference with which Bonaparte received the news, merely instructing him to take over. Here and on similar occasions he made a show of calm, even brash self-control, hiding the emotional turmoil that comes through in his letters, particularly to Josephine. 'Not a day has passed without my writing to you, not a night has passed without me pressing you in my arms, I have not drunk a cup of tea without cursing the desire for glory and the ambition which keep me far from the soul of my life,' he had written from Nice, complaining that her letters were scarce and cold, and that in contrast to his soldiers, only she withheld her trust and remained 'the joy and the torment' of his life.
To her, he poured out his despair at the news of Chauvet's death. 'What is the future? What is the past? What are we?' he questioned, wondering at the purpose of life, and 'what magical fluid shrouds us and conceals all that we should most want to know?' But this was no time to brood, and he must think only of the army. Two days later he wrote to her in more passionate vein, telling of his burning desire for her and sending her a kiss on a point of her body 'lower than the heart, much, much lower'.
On 9 April Bonaparte transferred to Savona as his three corps took up their positions, with Masséna on the right, Augereau in the centre and Sérurier to their left. But it was the Austrians who struck first. Beaulieu had misinterpreted a French reconnaissance along the coast as the vanguard of an attack on Genoa, and, assuming that the whole French army would be following, decided to drive in its flank through Montenotte and Monte Legino. His attack on what he assumed to be the French flank ran head-on into the units at Monte Legino preparing to attack.
Bonaparte had intended to strike at the gap where the Alps ended and the Apennines began, which was the juncture between the Sardinians and their Austrian allies. While Sérurier pinned down the Sardinians frontally and Augereau turned their flank at Millesimo, Masséna was to move into the gap between the two armies. Bonaparte calculated that if he inserted a wedge between the two and prised them apart, strategic imperatives would force the Sardinians to fall back in a northerly direction towards their base at Turin and the Austrians to retreat eastwards towards theirs at Milan. He would then be able to defeat them separately. His studies had convinced him that it was superior numbers that won battles, and that the art of war could be reduced to the one principle of bringing greater forces to bear at a given point.
As they sheltered from the torrential rain that night, planning to renew their attack the next morning, the Austrians at Monte Legino were unaware that, quickly appraising the situation, Bonaparte had ordered Masséna to veer right and make a forced march through the night to Montenotte in their rear. 'Everything suggests that today and tomorrow will go down in history,' Berthier wrote to Masséna with his latest orders.
The following morning, as the Austrian commander was about to push home his attack, the dispersing mist revealed Masséna's divisions deploying on his flank and rear. Coming under simultaneous attack from two sides, he ordered a retreat which quickly turned into a rout. It had been little more than a skirmish, with Austrian losses in dead, wounded and prisoners around 2,700 and the French no more than a hundred, but Bonaparte accorded it the status of a full-scale battle. In his self-aggrandising report to the Directory, he claimed that the main Austrian force commanded by Beaulieu himself was involved, that it had lost up to 4,000 men and 'several' flags (in fact only one was captured), and blew the event up to epic proportions. His order of the day to the troops echoed this, praising them for their glorious exploit. It was the first brush-stroke of what was to be a masterpiece of mendacity.
Beaulieu had in fact spent the day several kilometres away, sitting badly bruised by a roadside while his escort struggled to repair the carriage that had pitched him to the ground. He had realised his mistake too late and had lost valuable time, which Bonaparte was not going to let him regain. He urged Augereau, most of whose men were still marching without boots, and many without muskets, to hasten his attack on Millesimo, and Masséna to strike further into the Austrian rear at Dego. Once Augereau had accomplished his task, he was to swing left and begin to roll up the extremity of the Sardinian line.
Bonaparte needed to keep up the momentum so that neither of his opponents had time to regroup and strike back; if they did, he would be caught between two fires. He therefore reacted violently to any apparent hitch. After Augereau had sent the Sardinians reeling at Millesimo, one force of about 1,000 men under General Provera had ensconced themselves in an old fortress at Cosseria. Knowing them to have no more supplies or water than those they carried, Augereau meant to leave a few hundred men to pin them down and take their inevitable surrender while he went after the retreating main body of Sardinians. But Bonaparte insisted he storm Cosseria. In the ensuing assault the French suffered heavy losses from the Sardinians sniping from the battlements. Provera offered to capitulate, but Bonaparte tried to bully him into unconditional surrender, threatening to take no prisoners, and ordered Augereau to attack once more. This attack proved as futile as the first. Provera duly surrendered the next morning, having lost no more than 150 men, while Bonaparte's impatience had cost the French at least 600 and possibly as many as 1,000 casualties. He did have the good grace to admit his mistake and express regret.
To Augereau's right, Masséna attacked the citadel of Dego, where over the next two days some of the most serious fighting took place, with the citadel changing hands several times. After the final assault, which he directed himself, Bonaparte promoted a young _chef de bataillon_ named Lannes whose dash had caught his attention.
On 16 April Bonaparte learned that Beaulieu was retreating to Acqui on the road to Milan; his plan had worked. He ordered Masséna to move northwards against the Sardinians. Colli's dwindling force was falling back in order to defend Turin. It fought doggedly, inflicting heavy losses on the French, but on 21 April, after a brief defence it had to abandon its base and stores at Mondovi. That evening the King of Sardinia, Victor Amadeus, summoned a special council in Turin. As Beaulieu had signalled that he was not able to come to his aid further resistance seemed pointless; on the morning of 23 April Colli requested an armistice.
Bonaparte replied that he lacked the necessary powers and continued his advance. When pressed by the desperate Sardinians to agree to a ceasefire, he replied that he would be putting himself at risk if he did so without guarantees, and could only sign one if they handed over the fortresses of Coni, Tortona and Alessandria. In order to prevent Beaulieu from attempting to succour his Sardinian allies, he moved quickly on Cherasco and Alba, where he encouraged Piedmontese revolutionaries to establish a 'Republic', as a signal to the king that he could overthrow him if he wished. He applied further pressure by raising his demands to include the cession of Savoy and Nice to France, and the supply of his army with all its needs. These he delivered as an ultimatum on 27 April.
The two men sent to conclude the negotiations and sign the armistice, the old Piedmontese General La Tour and Colli's chief of staff Colonel Costa de Beauregard, found Bonaparte late on the night of 27 April in a barely guarded house in Cherasco. He was haughty and firm, threatening to launch further attacks every time they suggested softening his terms. At one o'clock in the morning he informed them that his troops were under orders to begin the advance on Turin at two. But having bullied them into signing the armistice he offered them a snack of broth, cold meats, hardtack and some pastries made by the local nuns, during which he became talkative. Although Beauregard was impressed by the brilliance and wide-ranging interests Bonaparte displayed, he found him cold, proud, bitter, and lacking in any grace or amenity. He also noted that he was very tired and his eyes were red. As they parted he said to Bonaparte, 'General, how sad that one cannot like you as much as one cannot help admiring and esteeming you!'
Bonaparte had weightier concerns than the affection of his enemies. He had exceeded both his brief and his duty as a soldier. He was single-handedly deciding French foreign policy, presenting the Directory with a _fait accompli_. He was, it is true, acting in concert with commissioner Saliceti who was with him during the negotiations, but he was still at risk of being recalled in disgrace. As he had meant to act independently all along, he had anticipated this eventuality and been shoring up his position.
His treatment of the troops under his command had been designed from the start not only to make them more effective as fighting men, but also to turn them into _his_ men. He had achieved the first aim by giving them victory: nothing acts on the soldier's self-esteem like success. It was clear to them that this success was largely due to Bonaparte's talents, yet he made them feel it was all down to them. He had developed a gift for talking to the men as equals. His extraordinary memory allowed him to remember their names, their units, where they came from, their ages, histories, and above all their military exploits. He would come up to a man and ask about some personal problem or congratulate him on a past feat like an old comrade. He was not shy of reprimanding officers in front of the troops, to show that he was their friend.
He had refrained from being too strict with them at first, allowing these men who had been starved of food, comforts and action for so long to indulge their basic instincts. They preyed on the country they went through, and by the time he had reached Cherasco he had to admit to being frightened by the 'horrors' they were committing. 'The soldier who lacks bread is driven to excesses of violence which make one blush for humanity,' he reported on 24 April. By then they had had a chance to fill their bellies and pull boots and items of clothing they lacked from Austrian and Sardinian dead or prisoners. Once he had halted his advance and managed to capture Sardinian stores, Bonaparte was able to begin reining them in. 'The pillage is growing less widespread,' he reported to the Directory on 26 April. 'The primal thirst of an army lacking everything is being quenched.' He had three men shot and six others condemned to hard labour, then shot a few more for looting a church. 'It costs me much sadness and I have passed some difficult moments,' he admitted.
While he tightened discipline, he took care to flatter the soldiers' self-esteem, making throwaway statements such as 'With 20,000 men like that one could conquer Europe!' He described their feats of arms in superlative terms in his proclamations. In that of 26 April he listed the engagements they had taken part in as if they were great battles, gave inflated figures of enemy dead and wounded, guns and standards captured, and told them they were heroic conquerors and liberators who would one day look back with pride on the glorious epic they had shared in. He encouraged the sense that they were making history with references to Hannibal as they came over the Alpine passes.
A mixture of growing self-confidence and the urge to earn praise fed their eagerness to live up to his expectations of them. 'I can hardly express to what degree of intoxication and pride such resounding, repeated and rapid triumphs transported our army, and what a noble emulation inspired all ranks,' noted Collot. 'They vied with each other to be the first to reach a redoubt, to be the first to storm a battery, the first across a river, to show the most devotion and audacity.'
Bonaparte's despatches to the Directory were no less hyperbolic. He wrote dramatic descriptions of every engagement, exaggerating the obstacles and the efforts with which they had been overcome, playing fast and loose with facts and figures, and singling out individual acts of courage in melodramatic images of republican heroism. At the same time, he stressed his lack of equipment and berated his masters in Paris for failing to send him guns and trained artillery officers and engineers. To Carnot he expressed his 'despair, I could almost say my rage' at not having the tools with which to do the job he had been set.
Desperate to reap the fruits of success, the Directory proclaimed the victories of French arms loudly and published extracts from the despatches. The name of Bonaparte was soon familiar throughout the country, and was becoming subliminally associated with heroism, genius and victory. On 25 April Bonaparte sent Joseph and Junot to Paris with the twenty-one enemy standards captured so far, knowing that their progress through France and their arrival in Paris would make an impression. 'It would be difficult to convey the enthusiasm of the population,' Joseph confirmed. After signing the armistice of Cherasco, Bonaparte sent Murat with the document and more standards. Whatever their feelings about him and his doings, the Directory were happy to bask in the reflected glory, and could only hail him as a national hero.
Murat was burdened with another mission – to persuade Josephine to come to Italy. From the moment he left Paris Bonaparte had not stopped thinking about her and longing for her to join him, and nothing could banish her from his thoughts. He could not understand why she did not write more often, why her letters were often lukewarm, and why she had not made haste to join him. He wrote to her every day, sometimes more than once, even after exhausting marches and hard-fought engagements. He had thoughts for nobody else. After Dego he was brought a beautiful young woman taken prisoner along with an Austrian officer, but he passed up the chance of having her and allowed her to go on her way.
When he sent Joseph to Paris he entrusted him with a letter for Josephine, whom he had yet to meet. She was sure to like him, he wrote. 'Nature has endowed him with a gentle, even and thoroughly good character; he is full of good qualities,' he assured her. He wanted her to come out to Italy with the returning Junot. 'You must come with him, do you understand?' he wrote, urging her to seek inspiration and strength by reading Ossian. 'Take wing, come, come!' He had also written to Barras, asking him to press her to come. From Cherasco the day following the armistice he assured her that no woman was ever 'loved with more devotion, fire and tenderness', and that his love grew with every day that passed. He could not understand how she had come to mean so much to him. He had a carriage, silver and china for her, so all she needed was to bring a chambermaid and a cook.
Josephine had no intention of leaving Paris, with its parties and theatres and the many friends she loved. And she had recently taken up with Hippolyte Charles, a dashing hussar officer, a good lover and a jovial companion who kept her entertained. Bonaparte had begun to suspect something of the sort, but his mind was taken up with more pressing matters.
## 11
# Lodi
Beaulieu was by no means beaten, and given the chance to rally he would be in a position to crush the French. Bonaparte's forces had been whittled down by fighting and forced marches, and although he had received reinforcements, his army's cohesion and morale were still frail. According to his own assessment, the French soldier's outstanding quality was the ability to march quickly in pursuit of a retreating enemy, building up as he went a determination and an impetus which gave him the edge. But this was lost when he came under attack from seasoned regulars.
He ordered Sérurier to feign crossing the Po at Valenza in order to prompt Beaulieu to defend that stretch of the river. He himself led a small body of troops in a forced march covering sixty-four kilometres in thirty-six hours along the right bank of the river to Piacenza. There, deep in the Austrian rear, he crossed the river on 9 May 1796, hoping to cut off Beaulieu's line of retreat. 'The second campaign has begun,' he wrote to Carnot that evening. 'Beaulieu is disconcerted; he calculates poorly and constantly falls into the traps set for him.' But the Austrian commander had realised what was happening and hastily fell back across the next line of defence, the river Adda. Bonaparte pursued him but failed to catch up, reaching the little town of Lodi as the Austrian rearguard was crossing the river. He only just managed to bring up a couple of guns and open fire to prevent them from destroying the bridge.
No sensible general would have considered trying to cross this 200-metre-long wooden bridge, no more than ten metres wide, at the other end of which the Austrians had placed cannon which could rake it with fire. But Bonaparte was not a sensible general, and his men were buoyed by success. Without waiting for the rest of his force to arrive, he drew up the troops at his disposal, made a rousing speech and ordered them to storm the bridge. They surged forward, only to be mown down by canister shot, but others followed, led by Berthier, Masséna and Lannes, who showed total disregard for danger. Having got halfway across, some of the men climbed down the piles onto a sandbank from which they waded across to the opposite bank, where they engaged the Austrian defenders from the flank. After two more attempts the French managed to charge across the bridge and dislodge the Austrians, who fell back leaving 153 dead, 182 wounded and 1,701 prisoners. French losses totalled less than 500, possibly as little as 350.
' _Pero non fu gran cosa_ ,' Bonaparte commented that evening at dinner in the residence of the Bishop of Lodi. But he was determined that to the outside world it should be a _grandissima cosa_. 'The battle of Lodi, my dear Director, gives the whole of Lombardy to the Republic,' he wrote to Carnot that evening, announcing that he was about to pursue and finally defeat Beaulieu. His description of the capture of the bridge was predictably florid, and he claimed for this 'battle' a significance which it would acquire only thanks to his efforts. Saliceti followed up with an account that was outright poetic. These would be broadcast to the public in France, and would soon be supplemented by images. Bonaparte asked the French minister in Genoa, Guillaume Faipoult, to commission an engraving of the glorious feat, the result of which was an image of himself, standard in hand, leading his men across the bridge under a hail of shot. He made sure that from now on every feat of arms was immortalised by an icon.
He needed to enhance his authority by any means available. While at Lodi he had received two letters from Paris, one welcome, one less so. The first was from Murat, informing him that Josephine had only delayed coming out to join him in Italy because she was pregnant and feared travelling. It was not true, but she could think of no other excuse to avoid leaving Paris. Bonaparte was pleased by the news that he was to become a father, and while he was concerned for her health, he felt that her supposed condition would guarantee her fidelity.
Earlier that day he had received less welcome news. The Directory felt he had accomplished his prescribed aim of creating a diversion to assist the two French armies operating in Germany, and now sent him new instructions. They ordered the remainder of the Army of the Alps into Italy, and planned to divide the French forces on the peninsula into a northern one under the sixty-five-year-old professional soldier and acclaimed victor of the invading Prussians at Valmy in 1792, General Kellermann, and a southern under Bonaparte, which was to march on Rome and overthrow 'the last of the popes'.
This did not suit him at all, as he was set on his cherished enterprise of the subversion of Italy. On 1 May he had written to Faipoult in Genoa asking for material on the topography, resources, constitutional arrangements and economic potential of every state on the peninsula. During his march to Piacenza he had crossed territory belonging to the neutral duchy of Parma. He had made a feint as though he were about to attack its capital, which prompted the duke to despatch envoys to ask for his neutrality to be respected – which it was, in return for a huge bribe in silver, corn, oats and other victuals, 1,600 horses, twenty works of art, and an undertaking to maintain hospitals for the French wounded. 'These little princes need to be managed,' Bonaparte commented in his report to the Directory, ignoring the fact that it was not his business to manage anybody beside his soldiers. 'The war in Italy at this moment is half military and half diplomatic,' he explained, instructing his superiors in Paris on the positions they should take in negotiating a treaty with the King of Sardinia.
He sent off three letters protesting against the plan to split the command – an official one to the Directory, one to Carnot, and one to Barras – all three couched in a mixture of petulance and disingenuousness. 'If I have lost the trust I enjoyed at the beginning of the campaign, I entreat you to let me know,' he wrote to Barras. 'In that case I would ask to be allowed to resign. As well as certain talents, nature has endowed me with a strong character, and I cannot be of any use here unless I have your entire confidence. If the intention is to make me play a secondary role, to oblige me to flap about under the orders of commissioners, to be subjected _in my operations_ to a German whose _principles_ I esteem no more than his manner, then I will leave the field to him.' That, as the Directors well knew and Saliceti reminded them, would not have gone down well with the public, which had just received news of the epic feat of Lodi. To drive home his usefulness, Bonaparte sent a number of messages over the next few days, announcing the despatch of two million francs in gold from here, a fortune in jewellery and ingots from there, not to mention a hundred 'fine horses, the finest that could be found' for the Directors' own carriages.
'It is only after Lodi that it struck me that I might become a major actor on our political scene,' he would later tell his secretary. 'It was then that the first spark of a higher ambition was ignited in me.' He was sitting, lost in thought, by the fireside in the corner of a room on the evening of 7 May when it dawned on him that he was better qualified than the government he was serving. In writing up the fluke result of his actions at Lodi as a grand feat of arms he seems to have convinced himself that he possessed, or was possessed by, some kind of superior force. This is not entirely surprising, given that over the past four weeks success had followed success in an almost miraculous progression. Writing home to his father, Marmont could not contain his wonder. The less than admiring Costa de Beauregard reflected that 'Bonaparte makes one think of those heroes who would cleave mountains with a flourish of their sword,' a kind of magician who could do anything. A few days after Lodi, Bonaparte told Marmont that Fortune had singled him out and become his mistress. Such grandiloquent, emotionally charged phrases might sound like so much hot air, but they did express genuine thoughts and aspirations.
The eighteenth century had seen the gradual replacement of the Christian view of life as a preparation for the next world with one which envisaged ways of attaining fulfilment in this. The French Revolution was born largely from the desire to reorder the world in this sense. The rejection of Christianity had suggested a return to the world of ancient Greece and Rome, which seemed more in tune with the republican ideals of the day. This was expressed in and nourished by the neo-classical movement in the arts. The legislative bodies of the French Republic dressed in togas, prominent figures assumed names taken from antiquity such as Brutus and Gracchus, and political discourse was peppered with classical references. The break with the civilisation of Christian Europe was symbolised by the adoption of a new calendar and the metric system with which to measure time and space in the new world the legislative bodies of the French Republic had created. It was Man, not God, who was central to the new value system, and his collective identity, the Nation or ' _patrie_ ', became the object of worship. Henri Beyle, to become famous as the novelist Stendhal, was thirteen when Bonaparte took command of the Army of Italy, and recalled that for his generation 'our only religion was [...] _to be of service to the patrie_ '.
The Revolution generated a cult of self-sacrifice for the cause whose 'martyrs' were represented in paintings by David and others in much the same manner as Christian saints had been. Where the crusaders of old sought Christian salvation, the soldiers of the French Republic believed their exertions would be crowned by a human version of immortality, loosely expressed in the word ' _gloire_ '.
'The eldest of our generals had barely reached the age of thirty,' recalled Bonaparte's contemporary Lavalette, serving in the Army of the Rhine. 'All of them aspired only to glory, and in their eyes it was only real if it involved danger.' Marmont had a signet ring made which 'expressed all the wishes with which my young heart was filled: it featured three interlaced crowns, one of ivy, one of laurel and one of myrtle, with this motto: _I hope to deserve them_ ' (ivy was the symbol of eternity, laurel of fame, and myrtle of manhood and love).
'Of all the passions which affect the human heart, there is none which is more forceful than the love of _la gloire_ ,' wrote Germaine de Staël in her book _De l'influence des passions sur le bonheur des individus et des nations_ , published that very year of 1796. She did not belittle the part played in this by ambition or vanity, but saw the pursuit of _gloire_ as a force in itself. 'It is, without doubt, an intoxicating sensation to fill the universe with one's name, to go so far beyond the bounds of one's being that it becomes possible to delude oneself as to the limits and extent of one's life, and to believe that one possesses some of the metaphysical attributes of infinity.' She pointed out that in this psychological climate, anyone who could achieve _gloire_ and offer to others the chance of a share in it would excite in them the spirit of emulation to such a degree that they would exert themselves to the very limit and beyond, creating a seemingly superhuman surge of energy.
Brought up reading Plutarch's lives of the heroes, Bonaparte and his peers yearned to emulate them. They were also profoundly affected by the Romantic sensibility expressed in the works of Rousseau, Goethe and Macpherson. The conflation of the urge to the heroic with that for emotional transcendence developed in many a subliminal belief that they were living a legend and conquering the impossible, like not just the heroes but also the gods of antiquity.
It was in the guise of a conquering hero that on 15 May Bonaparte made a triumphal entry into Milan, the capital of Lombardy, mounted on a white horse, preceded by a column of Austrian prisoners and followed at a respectful distance by his staff and then his troops. He passed under a Roman triumphal arch and another made of foliage and flowers, greeted with enthusiasm by Italian Jacobins and nationalists who had been awaiting him, in the words of one of them, 'as the Israelites awaited the Messiah', hailing him as their deliverer from Austrian rule and, they hoped, the godfather of an independent Italian state. Those less politically aroused also turned out in force to get a look at this man whose deeds were assuming legendary proportions in the public imagination. As it was a Sunday and the feast of the Pentecost they were dressed up, presenting a curious contrast with the conquerors of the mighty Austrian army.
'Our uniforms, worn out by long spells of mountain warfare, had been replaced by anything the soldiers could lay their hands on,' recalled Sergeant Vigo-Roussillon. 'In place of our long-rotted cartridge-cases we had belts made of goatskin in which we carried our cartridges. Our heads were covered with bonnets made of sheep, cat or rabbit fur. A fox-fur bonnet with the tail hanging down the back was a prized possession.' They wore breeches or trousers of every colour, fancy, even embroidered waistcoats, and a variety of footwear.
Two comrades-in-arms, a major and a lieutenant, shared three shirts, one pair of brown trousers, one uniform coat and one overcoat, which was worn by the one not wearing the trousers that day. One young officer brushed up as best he could when invited to dinner by the marchesa in whose residence he was billeted, but nevertheless padded into the dining room on bare feet.
Bonaparte had gone straight to the archbishop's residence, where he slept for a couple of hours and had a bath before attending a banquet in his honour. He then moved into the Serbelloni Palace, which had been placed at his disposal. He was also offered the beautiful _prima donna_ of La Scala, Giuseppina Grassini, but could think only of Josephine, so Berthier stepped in. Bonaparte was not going to waste time in Milan.
On 20 May he issued a proclamation to his 'brothers in arms': 'Soldiers! You rushed like a torrent from the heights of the Apennines, you defeated, dispersed, scattered all that opposed your progress. Delivered from Austrian tyranny, Piedmont gave in to its natural sentiments of peace and friendship with France. Milan is yours, and the republican standard flies over the whole of Lombardy. The dukes of Parma and Modena owe their continued political existence only thanks to your generosity. The army which threatened you with such arrogance can no longer find a bulwark strong enough to shield it from your courage.' He could see they were already tired of inactivity, and burning to achieve greater glory: 'Well, let us go forward!' he continued. 'We still have forced marches to make, enemies to subdue, laurels to pick, wrongs to avenge.' While they must be ready to defend the Republic, they must also fly to the aid of sister nations: 'You will have the immortal glory of changing the face of the most beautiful part of Europe. The French nation, free, respected throughout the world, will give Europe a glorious peace which will redeem all the sacrifices it has made over the past six years. You will then return to your homes, and your fellow-citizens will say as they point you out: "He was in the Army of Italy!"'
More to the point, he decreed that whereas they had hitherto been paid in paper money, which few, particularly in foreign lands, would accept, henceforth they would receive half of their pay in specie. The move was probably dictated in part by the need to stem the looting, but it also created a new bond of gratitude and loyalty between him and his men. The Directory was appalled by this act of independence, which diverted some of the cash being sucked out of Italy, on which it was coming to depend, into the pockets of the troops. But there was nothing it could do. Bonaparte was the only one of the army commanders helping to finance it; he was winning battles and riding high in public opinion. He was beyond the Directors' control, and whether they liked it or not, their fate was closely tied to his popularity. On 29 May a fête of thanksgiving and victory would be held in Paris at which the captured banners were paraded, a contingent of wounded were honoured with oak leaves, sprigs of laurel and palm fronds, symbolising valour, glory and martyrdom, and a 'Song of Victory', while Junot presented Josephine, now hailed as ' _Notre Dame des Victoires_ ', to garner acclaim for her husband and Carnot praised his 'invincible phalanxes', whose deeds would astonish future generations.
On 17 May Bonaparte wrote to the Directors disingenuously asking for instructions on how to deal with the local patriots. He knew they were thinking of giving Lombardy either to the King of Sardinia, in order to secure his alliance, or to Austria as a bargaining chip in the forthcoming peace negotiations. But he had his own vision. 'Nature drew the limits of France at the Alps, but it also drew those of the Empire at the Tyrol,' he pointed out. He had already promised liberty to the people of Lombardy and sanctioned a national guard, whose colours were to be the tricolour of the French Republic with the blue replaced by green. He began reorganising the former Austrian province along French lines, aided by Italian patriots from various parts of the peninsula who saw this as the cornerstone of an independent Italy. He was by now consciously implementing his own ideas. 'I'm doing what I want,' he told a surprised Italian patriot.
'I believe in the French Republic, and in Bonaparte her son,' ran a _Credo_ composed by some Italian nationalists; but others cursed him. The depredations of the French, both by officials and by soldiers on the rampage, caused hardship to ordinary people, and all those opposed to the French intrusion, be they fearful upholders of the old regime or Catholics horrified at the godlessness of the invaders, gave vent to their grievances. Riots broke out in various places. Bonaparte reacted with energy and in some cases brutality, most notably at Binasco, where the locals had massacred French soldiers. 'Having killed a hundred people, we burned down the village, a terrible but efficacious example,' he wrote to Berthier afterwards. At Pavia, which had risen against the French, he let his troops loose on the town for a couple of hours. He admitted that 'although necessary, this spectacle was none the less horrible, and I was painfully affected by it'. The measures did prove efficacious, and he was soon able to report that the province was quiet. He enrolled young men coming forward to serve in what they believed to be the cause of Italy into a Lombard armed force which could maintain order.
The improved supply situation did not stop the looting; it merely refocused it, as officers and men began to think of enriching themselves rather than just helping themselves to what they needed. The example was set by Masséna, who exacted protection money from towns he passed through, and it was widely followed. Bonaparte turned a blind eye, and even encouraged his subordinates to enrich themselves while ostentatiously declining to accept bribes offered him by the authorities of cities such as Lucca and Modena in order to distinguish himself from other generals by his moral stance.
At the same time, Saliceti was bleeding the country dry in the service of the French Republic, as well as his own. At Lodi he raided the cathedral treasury and the Monte de Pietà, the charity which served as pawnbroker, removing five cases of silver plate and a number of ingots, and requisitioned the city's cash funds. In Milan he helped himself to the contents of the banks, the city chest and the Monte de Pietà, although this time he returned to poor debtors their paltry treasures. He repeated the pattern in every city. 'You are creating a hundred times more currency with your bayonets than we can with all our imaginable financial laws,' one of the Directors acknowledged.
It was not only cash and disposable valuables that were taken. Seeing the French Republic as the second Rome, its rulers believed the greatest works of art and science, libraries and archives, mechanical and scientific instruments, and any collections that could serve progress should be brought together in Paris. A commission consisting of the mathematician Gaspard Monge, the chemist Claude Berthollet, the botanists André Thouin and La Billardière, as well as a number of artists, was on its way with orders to select the objects worthy of being included in the libraries and museums of the capital. (It is worth noting that a protest against this was signed by the painters David, Hubert Robert, Moreau le Jeune, Girodet, the architects Percier and Fontaine, and many others.)
Bonaparte had never accepted the secondary role of staging a diversion in Italy while Moreau carried out the main operations in Germany, and was determined to reverse this by striking first. Assuming that Moreau must have crossed the Rhine, he was eager to press on. Beaulieu had fallen back behind the river Mincio, his right wing resting at Peschiera on the southern shore of Lake Garda and his left on Mantua. Moving briskly, Bonaparte pierced his line at Borghetto and then turned north to roll it up. Disorientated Austrian units raced north in order to avoid being cut off, but some were overtaken by the French advance. At Valeggio, where he had just sat down to a light lunch with Masséna and Murat, Bonaparte was surprised by an isolated enemy unit and only had time to pull on one boot before making a dash for safety over a wall. By dawn the following day he was pursuing the Austrians falling back on Peschiera and Verona, which he reached on 3 June. He was overwhelmed by the beauty of the city. 'I have just seen the amphitheatre,' he reported to the Directory. 'These remains left by the people of Rome are truly worthy of it. I could not help feeling a sense of humiliation when I thought of the tawdriness of our Champ de Mars.'
Beaulieu had made his escape northwards along the eastern side of Lake Garda, pursued by French cavalry, while part of his army took refuge in the fortress of Mantua, where it was bottled up by Sérurier. Bonaparte was now in control of the whole former Austrian province of Lombardy, and he set about securing it. Without consulting with the Directory, he signed an armistice with the kingdom of Naples, which thereby retired from the anti-French coalition, and received a Spanish diplomat sent by the Pope to negotiate peace with the Holy See.
He raced back to Milan expecting to find Josephine waiting for him. Instead he found instructions from the Directory ordering him to march on Rome, which he could not easily disobey. He set off, reaching Bologna on 19 June, where he was met by the Pope's envoy offering a bribe of five million francs to ward off a French invasion. Bonaparte demanded forty million, as well as the treasure of the shrine of Loretto and a hundred works of art. On 23 June the Pope's emissaries agreed, and signed an armistice. Bonaparte then crossed the Apennines and made for Livorno to secure the port against a possible landing by the British.
From there he made a trip to San Miniato to visit Canon Filippo Buonaparte, the last surviving member of the Tuscan branch of what might at one stage have been the same family as his own. He then marched on to Florence, where he went to the opera on the evening of 30 June and the following day lunched with the Grand Duke of Tuscany, brother of the Emperor Francis II with whom he was at war. By 4 July he was back at Roverbella, where he had established his headquarters.
He was worn out physically and mentally, and racked by anxiety alternating with jealousy over Josephine, whom he showered with increasingly despairing letters which reveal his changing moods. The brevity and lack of feeling of her infrequent letters inspired reproach and jealousy, followed by fears that she might be ill and self-reproach for having questioned her feelings. He pestered Joseph for news of her. On 18 May from Milan he wrote a letter full of joyful anticipation of what he thought was her imminent arrival, describing the beauties of Italy and the happy times ahead as they listened to divine music while watching her belly grow (he was still under the impression that she was pregnant). Five days later, worried by the lack of news from her, he wrote of how he had left a ball given for him at which he looked in vain among the many beauties for any who came close to her. 'I could see only you, think only of you, and the thought made everything else unbearable, so, half an hour after arriving I went home to bed full of sadness.' Thinking she would arrive on 13 June, he prepared her lodgings, but then discovered she had not left Paris yet. 'I had opened my soul to joy, and it has filled with suffering,' he wrote. He awaited the couriers with impatience, either to find that there was no letter from her, or if there was that it lacked the passion he craved. He concluded that her feelings for him had only been a 'mild caprice' which he had misunderstood, that while he had given himself to her entirely and lived only for her, she had merely toyed with him, and that she wanted a different kind of man. ' _Farewell_ , Josephine, stay in Paris, do not write to me any more, and at least respect my retreat,' he wrote despairingly. 'A thousand daggers are tearing my heart asunder, do not plunge them any deeper. Farewell, my happiness, my life, everything that existed for me on earth!!!'
Having heard no more from her, three days later he wrote that there was nothing left for him but to die: 'All the serpents of the furies are in my heart, and already I am half dead,' he wrote, still faintly hoping she might be on her way. 'I hate Paris, women and love...' he protested. 'Farewell, my Josephine, to think of you made me happy, but everything has changed entirely,' he went on, saying that he would never stop loving her. He had spent the night rereading all her letters and wallowing in self-pity. The same day he wrote to Barras: 'I am in despair as my wife won't come, she has some lover holding her back in Paris, I curse all women but heartily embrace my good friends.' Writing three days later from Tortona, he apologised to Josephine for expressing himself with such feeling, but explained that he had been 'drowning in sorrow'. He had just received a letter from Murat informing him that she was unwell, and although he assured him that it was only a slight indisposition, Bonaparte flew into a panic that she might die. 'If you die, I will also die, of despair, of devastation,' he wrote, asking her to intercede with Barras to obtain leave for him to return to Paris. He no longer cared for glory or the service of the motherland, and could not think of victory while she was ill. This long letter was followed the next day by another, even longer and more tortured, in which he blamed himself for having accused her of inconstancy. 'My life is a continuous nightmare,' he complained. 'I am suffocated by a deadly presentiment. I no longer live; I have lost more than life, more than Happiness, more than tranquillity; I am almost without hope.' He longed to be able to come to Paris. 'I am nothing without you,' he went on. 'I can hardly imagine how I existed before I knew you.'
Josephine found his letters, and the teenage frenzy they expressed, ridiculous and embarrassing. She amused her friends by reading them out, and after sharing one particularly self-dramatising passage in which he referred to Othello, she exclaimed, 'He _is_ funny, Bonaparte!' But, no doubt fed up with continual enquiries as to her health and afraid that Bonaparte might indeed turn up in Paris, where he was not wanted, Barras persuaded her to go. According to some accounts he bundled her into the carriage himself, along with her dog, her maid, Hippolyte Charles and Junot. She was followed by several men of business to whom she owed money, and to whom she promised to obtain lucrative contracts supplying the army.
Their journey was a regal progress, every city along the way wishing to honour the wife of the national hero. At Lyon she went to a special performance of Gluck's _Iphigénie en Aulide_. At Turin, where she found Marmont waiting to escort her on her onward journey, she was treated like visiting royalty by the king. Her entry into Milan on 13 July was triumphal. She was settled in the magnificent Serbelloni Palace with its pink marble columns, and showered with honours by the city authorities. Bonaparte was in such transports of joy to see her that, as she informed Thérèse Tallien, she thought he would go mad. He could not keep his hands off her, and seemed unaware of the presence of Hippolyte Charles, whose role almost everyone else had guessed.
Two days after her arrival, on 15 July, Bonaparte had to rejoin his troops besieging Mantua, which was sheltering some 12,000 Austrians. Josephine remained in Milan, where she was bored, despite the receptions and entertainments laid on for her, particularly when Lieutenant Charles could no longer delay taking up his duties at the side of General Leclerc in Verona.
Bonaparte, who still suspected nothing, was in ecstasy. 'What nights, my love, were those I spent in your arms!' he wrote. 'In my memory I ceaselessly relive everything we did, your kisses, your tears, your sweet jealousy, and the charms of the incomparable Josephine keep stoking an ardent and burning flame in my heart and in my senses. [...] A few days ago I thought I loved you, but, since seeing you I feel that I love you a thousand times more.'
That night he hoped to storm Mantua with a surprise attack from the lake, but the waters unexpectedly went down and the attempt failed. He was already planning another trick that might deliver him the fortress, but this did not prevent him from thinking of Josephine. The next evening he was walking by the lake by 'silvery moonlight' in the village outside Mantua where Virgil was born, 'not one hour without thinking of my Josephine'. He was by now aware of the gossip about Lieutenant Charles, and had stumbled on evidence when he opened letters to Josephine from Barras and Thérèse Tallien. He playfully cursed her while professing his faith in her fidelity and her love for him. 'Far from you, the nights are long, dull and sad, close to you one wishes it could always be night,' he wrote, inviting her to join him at Brescia.
She arrived on 26 July, meaning to go on to Verona to see Lieutenant Charles under the pretext of sightseeing, but soon after she set off she ran into enemy troops. Bonaparte sent Junot with a squadron of dragoons to escort her back; on the way they came under fire, and she had to leave her carriage and take cover in a ditch. He resolved to send her out of the war zone on a trip to Tuscany. At Parma she met Joseph Fesch, who was busily putting together an art collection by requisitioning anything that caught his eye. In Florence she was received by the grand duke. Bored by Florence, she went back to Brescia and, Bonaparte being absent, summoned Lieutenant Charles to share his quarters with her.
Bonaparte was desperate to take Mantua, whose garrison remained a threat, making vigorous sorties which prevented him from securing the area. Although he had concluded treaties with Naples, the papacy and various smaller states of the peninsula, treaties were regularly broken, and a landing by British or Russian troops in Naples or elsewhere remained a possibility. If one were to take place when his back was turned, these states might be tempted to throw their considerable forces into the fray against him. And by the end of July it was clear that Austria was about to make a concerted effort to relieve Mantua and reconquer Lombardy.
## 12
# Victory and Legend
Beaulieu had been replaced by the no less aged Field Marshal Dagobert von Würmser. He divided his army into three columns which moved out in July 1796. One, consisting of 18,000 men under General Quasdanovitch, marched down the western side of Lake Garda, aiming to take Brescia and cut Bonaparte off from Milan. Another, of 5,000 men under General Meszaros, came down the valley of the Brenta further east in order to distract the French, while Würmser himself with 24,000 marched down the eastern side of Lake Garda aiming for Verona, where it was planned that the three forces were to come together to defeat the French and relieve Mantua.
Bonaparte, who had just under 40,000 men in total, would be overwhelmed unless he defeated the Austrian columns separately. He took a bold decision, ordering Sérurier to abandon the siege of Mantua and pulling all his forces out of Würmser's path. Although this would allow the Austrian to relieve Mantua and add its garrison to his force, it gave Bonaparte the opportunity to concentrate enough men to rout Quasdanovitch, which he did at Lonato on 3 August, before turning about to face Würmser with a slight numerical superiority, at Castiglione on 5 August. In a classic manoeuvre, he encouraged Würmser to turn his right flank, then launched a powerful attack on his exposed centre which cut the Austrian army in two, forcing it into a disorderly retreat back to whence it had come. 'There you have another campaign finished in five days,' Bonaparte rounded off his report to the Directory, in which he grossly exaggerated the enemy's losses.
It had been a brilliant feat of arms, with Bonaparte exploiting his central position to great effect. It had also demonstrated the qualities specific to the French army which gave it such an edge over its enemies. The Austrian army operated like a machine, observing tested routines such as only marching for six hours in twenty-four. The French followed no rules. The poor or non-existent supply system obliged them to operate in self-contained divisions or smaller units that the land they moved through could support, which encouraged greater independence and flexibility, particularly when it came to timing and distance.
Over those five days, Bonaparte had ridden more than one horse to death as he darted about. Marmont had spent twenty-four hours in the saddle, followed by another fifteen after only three hours' rest. Augereau's division had covered eighty kilometres in thirty-six hours, in the August heat. Masséna noted that two-thirds of his men had no coats, waistcoats, shirts or breeches, and marched barefoot. When they complained of the lack of provisions, Bonaparte told them the only ones available were in the enemy camp.
The French army was made up of individuals with minds of their own. Bonaparte's new aide Józef Sułkowski noted their agility and 'astonishing vigour', and was struck by the fact that the French soldier would surrender when cornered on his own, but never in the company of his fellows, and would 'go out to his death rather than face shame'. In some units, shirkers and cowards were hauled before 'juries' of elder comrades who would condemn them to being beaten on their bottoms and despised until they had redeemed themselves with acts of valour.
'The French soldier has an impulsive courage and a feeling of honour which make him capable of the greatest things,' believed Bonaparte. 'He judges the talent and the courage of his officers. He discusses the plan of campaign and all the military manoeuvres. He is capable of anything if he approves of the operations and esteems his leaders,' and would march and fight on an empty stomach if he believed it would bring victory.
Many observers of the campaign of 1796 commented on the almost festive spirit in which these men appeared to banter with death, singing on the march and laughing as they went into battle. 'We were all very young,' recalled Marmont, and 'devoured by love of glory'. Their ambition was 'noble and pure', and they felt 'a confidence without limit in [their] destiny', along with a contagious spirit of adventure. 'It was during this campaign that moral exaltation played the greatest part,' reminisced an old grenadier.'
Exceptional leadership also played a part. At Lonato, Bonaparte led the 32nd Demi-Brigade into withering enemy fire. After the battle he presented it with a new standard, embroidered with the words: 'Battle of Lonato: I was confident, the brave 32nd was there!' 'It is astonishing what power one can exert over men with words,' he later commented about the incident. He also knew when to be harsh. After Castiglione he demoted General Valette in front of his men for having abandoned his positions too soon and allowed his unit to retreat in disorder. He hailed another demi-brigade, the 18th, as it took up positions before battle with the words: 'Valorous 18th, I know you: the enemy won't hold in front of you!' At Castiglione, Augereau had excelled himself leading troops into the mêlée. 'That day was the finest in the life of that general,' Bonaparte later commented. Masséna too had electrified his men with his blustering courage.
The cost of these heroics had been heavy. By the end of the campaign, almost as many men were in hospitals as in the ranks. Some of the older officers were burnt out, and Bonaparte himself was exhausted. Yet there was no time for rest. Würmser had fallen back to where he could be resupplied, and would soon be in a position to attack again. Bonaparte's only hope lay in forestalling him. 'We are on campaign, my adorable love,' he wrote to Josephine on 3 September, having set off up the valley of the Adige. 'I am never far from you. Only at your side is there Happiness and life.' The next day, at Roveredo, he defeated an Austrian force under Davidovitch barring his way and pressed on, forcing Davidovitch to fall back beyond Trento. Würmser instructed him to hold on there while he himself marched down the Brenta valley into Bonaparte's rear, meaning to take him between two fires.
Bonaparte guessed Würmser's intentions. He left around 10,000 men under General Vaubois to keep Davidovitch bottled up, and with the rest of his force set off behind Würmser, who was now marching down the Brenta hoping to penetrate into the rear of the French, without realising that they were on his tail. On 7 September Augereau caught up with and routed Würmser's rearguard at Primolano, capturing his supply train, then forged on, hardly pausing for rest. Bonaparte spent that night under the stars, 'dying of hunger and lassitude', having eaten nothing but a small piece of hard-tack offered him by a soldier. He did not get much sleep, as by two in the morning he was on the move again. Würmser was unable to deploy his forces as they marched down the valley, and the French were able to defeat his divisions singly at Bassano, taking 5,000 prisoners, thirty-five pieces of artillery and most of his baggage. Quasdanovitch veered east with part of the army and made for Trieste, while Würmser with the main body made a dash for Mantua, which he entered on 15 September with no more than 17,000 men. This brought the number of Austrians bottled up in the fortress to over 25,000, including some fine cavalry, whose horses would only serve to feed them. It had been a strategic disaster. Marmont was sent to Paris with the flags taken in those two weeks, to spread the fame of the Army of Italy and its commander.
Not for a moment during those frantic days did Bonaparte forget his 'adorable Josephine', to whom he complained from Verona on 17 September that 'I write to you very often my love, and you very seldom,' announcing that he would be with her soon. 'One of these nights your door will open with a jealous crash and I will be in your bed,' he warned. 'A thousand kisses, all over, all over.' Two days later he was back in Milan, where they would spend the best part of a month.
Quite how happy that month was is open to question. In a letter to Thérèse Tallien on 6 September Josephine admitted to being 'very bored'. 'I have the most loving husband it is possible to encounter,' she wrote. 'I cannot wish for anything. My wishes are his. He spends his days adoring me as though I were a goddess...' She was evidently sexually tired of him; he complained that she made him feel as though they were a middle-aged couple in 'the winter of life'. But he had little time to brood over it.
His recent triumphs had resolved nothing: there was still a large enemy force in Mantua which he reckoned could hold out for months, and while Lombardy was relatively quiet there were stirrings in other parts of the peninsula. The King of Sardinia had disbanded his Piedmontese regiments, with the consequence that bands of former soldiers were threatening the French supply lines. 'Rome is arming and encouraging fanaticism among the people,' Bonaparte wrote to the Directory, 'a coalition is building up against us on all sides, they are only waiting for the moment to act, and their action will be successful if the army of the Emperor is reinforced.' He suggested that given the circumstances he should be allowed to make policy decisions. 'You cannot attribute this to personal ambition,' he assured them. 'I have been honoured too much already and my health is so damaged that I feel I ought to request someone to replace me. I can no longer mount a horse. All I have left is courage, and that is not enough for a posting such as this.'
The Austrians would try harder than ever to relieve Mantua, now that it contained such a large force. And they were in a better position to achieve their goal, since the two French armies operating in Germany had been beaten and had retreated across the Rhine, releasing more Austrian troops from that theatre. Bonaparte wrote to Würmser suggesting an honourable capitulation on humanitarian grounds: Mantua was surrounded by water and marshland, and large numbers on both sides were suffering from fever. Würmser refused and sat tight, knowing help was on its way (it was only by chance that General Dumas, commanding the siege, discovered that Würmser was being delivered messages in capsules hidden in their rectums by men disguised as civilians). By the end of October there was a fresh imperial army in position under a new commander, Field Marshal Baron Josef Alvinczy.
All Bonaparte could muster against it were some 35,000 men, exhausted after eight months of almost continuous campaigning in extreme conditions. He had received reinforcements, but these only just made up for the 17,000 who had been killed, those invalided out, those in hospitals, and the deserters. The troops were also of increasingly dubious quality, as a result of a process of negative selection. 'The soldiers are no longer the same,' wrote Bonaparte's brother Louis. 'There is no more energy, no more fire in them... The bravest are all dead, those that remain can be easily counted.' According to some estimates, only 18 per cent of the original complement were still in the ranks, and the proportion was probably lower among officers. 'The Army of Italy, reduced to a handful of men, is exhausted,' reported Bonaparte. 'The heroes of Lodi, of Milesimo, of Castiglione and Bassano have died for their motherland or lie in hospital.'
His dazzling successes had won him not only adulation but also a host of jealous rivals and enemies. Chief among these were the various civilians – commissioners, administrators and suppliers – in the wake of the army, whom he had been preventing from enriching themselves, and who were sending slanderous reports back to Paris, warning that he was intending to make himself King of Italy. A military setback at this point might prove fatal to him.
His forces were dispersed in bodies of about 5,000, with one around his headquarters at Verona, one at Brescia in the west and one at Bassano in the east, one besieging Mantua, another in reserve at Legnago and a smaller one in a forward position to the north at Trento. They were placed in such a manner that they could easily concentrate, but this time it was going to be more difficult to deal with the enemy piecemeal. The Austrians were on the move by the beginning of November 1796: Davidovitch pushed back Vaubois from Trento while Alvinczy, with the main force of some 29,000, marched down the Brenta and on 6 November forced Masséna's division out of Bassano. Bonaparte rushed to Rivoli to arrest the retreat of Vaubois, which he did in inimitable style. He called out two units which had shown lack of mettle and announced that their standards would be inscribed with the words 'These no longer belong to the Army of Italy!' Many of the men wept, and, as he had anticipated, they would redeem themselves with acts of surpassing bravery a couple of days later.
But Alvinczy was by now threatening the French centre at Verona. Bonaparte attempted to hold him off at Caldiero, but the already dispirited troops were subjected to a violent storm. Drenching rain was succeeded by volleys of hail. 'This storm blew straight into their faces, the heavy rain hiding the enemy who was pounding them with artillery, while the wind blew away even their fuses and their bare feet slithered in the clay soil, lending them no support,' in the words of Sułkowski. They trudged back in mournful silence.
Bonaparte was down to around 17,000 men facing Alvinczy's 23,000, and he was strategically blocked, with Verona at his back. 'We may be on the eve of losing Italy,' he warned the Directory. He decided to take a chance. Leaving a small force in position before Verona, on the night of 14 November he crossed the Adige under cover of darkness and marched east along its right bank, recrossed it at Ronco and, leaving Masséna to cover his own left flank and distract Alvinczy, made a dash for Arcole, where he meant to cross the river Alpone and move into Alvinczy's rear at Villanova. This would have cut the Austrians' line of communications and forced them to retreat into his arms. They were caught in a funnel between the mountains and the river Adige and had no other exit – and the different corps of a retreating army can be taken on and defeated individually, in this case as they tried to cross the Alpone at Villanova.
Everything went smoothly until the French spearhead came in sight of the small town of Arcole on the opposite bank of the Alpone across a thirty-metre-long straight wooden bridge resting on stone piles. It was defended by two battalions of Croat infantry numbering around 2,000 men with several field guns positioned so as to sweep not only the bridge, but the access to it on a dyke raised above the marshy floodplain.
Bonaparte was in a hurry. He ordered General Verdier to storm the bridge, but his men came under withering fire before they got anywhere near it. He despatched a force to cross the river further south and threaten the defenders' flank, but persisted in trying to cross the bridge. News had reached him that Alvinczy had perceived the threat to his rear and abandoned Verona. Masséna could distract him for a time, but if the Austrians crossed the Alpone at Villanova before Bonaparte could do so at Arcole, his plan would have failed and the French position would be critical once more.
Augereau and then Lannes attempted to lead the troops to the bridge, without success. Then Bonaparte dismounted and seized a flag. He challenged the men to show they were still the heroes of Lodi, but they would not follow him, even when he moved forward, accompanied by his aides and a small group of soldiers. Having covered a short distance and still a couple of hundred metres from the bridge, they were met by a volley which killed several around Bonaparte, including his aide Muiron. They rushed for cover, knocking Bonaparte off the dyke and into a drainage ditch where he landed up to his neck in water. He was eventually dragged out of it, but there could no longer be any question of taking the bridge.
That evening, 15 November, he withdrew and recrossed the Adige. Although his initial plan had failed, he had nevertheless positioned himself in such a way that he now paralysed Alvinczy: if the Austrian moved west, Bonaparte could strike in his rear, and if he moved east he had to abandon hope of linking up with Davidovitch to achieve his objective of relieving Mantua. On the night of 16 November Bonaparte learned that Vaubois had been overwhelmed by Davidovitch, which opened the possibility of the two Austrian armies joining forces. The only way of preventing this was to threaten Alvinczy's rear. Bonaparte had a bridge built over the Alpone downstream of Arcole and ordered Augereau to cross it while Masséna moved against Arcole, and despatched another force along the Adige to cross it further east to threaten Alvinczy's communications. The ploy worked, and Alvinczy fell back on Villanova. This allowed Bonaparte to detach troops and send them to head off Davidovitch and force him back up to Trento. Alvinczy, who had moved west again to assist Davidovitch, now gave up and retired up the Brenta valley. He had lost many men and had failed in his purpose to liberate Würmser from Mantua.
The two-week campaign had been a messy, close-run business with no set-piece battle to present to the French public as grand spectacle. It was therefore necessary to fabricate one. In his despatch to the Directory, Bonaparte announced that the battle of Arcole had decided the fate of Italy. He grossly exaggerated Austrian losses while diminishing his own, and presented an account of derring-do to flatter French national pride. The captured flags were borne to Paris by Le Marois, who at the public ceremony in which they were handed over made a speech portraying Bonaparte tracing the path to victory, flag in hand, conveying the notion that he had stormed the bridge. In no time a print appeared in Paris depicting Bonaparte and Augereau leading the troops across it on horseback, each clutching a banner, succeeded by another showing Bonaparte on foot, brandishing the flag and encouraging his troops to follow him.
For centuries kings and commanders had had their deeds immortalised in painting out of a mixture of vanity and political assertiveness. The Revolution had created a thirst for information among the illiterate which was satisfied by crude allegorical depiction, and this led to an explosion of semi-sacral illustration in praise of the nation, its leaders and its martyrs. Generals were depicted in heroic poses, and there were engravings of commanders such as Hoche and Moreau in circulation before any image of Bonaparte.
But he took propaganda to new levels. His mendacious despatches to the Directory, excerpts from which were printed and even plastered on walls for the public to read, were dramatic and exciting. The hyperbolic language of the Revolution in which they were couched created a subliminal sense of the supernatural, of the miraculous, of an adventure being enacted by men who appeared as superhuman as the heroes of the _Iliad_. Poets, playwrights and hacks of every sort saw in this excellent raw material for their own craft, and their works added to the concert of myth-making verbiage. This was accompanied by an iconography to suit, and between the moment he took command of the Army of Italy in 1796 and the end of 1798, no fewer than thirty-seven different prints of Bonaparte appeared on the market, some commissioned, some spontaneous, some based on actual representations of him, others giving him entirely imagined features, but all representing him as a hero.
The propaganda surrounding Arcole saved Bonaparte's position, but it could do little to assuage the pain inflicted by Josephine. 'At last, my adorable Josephine, I am coming back to myself, death no longer stares me in the face,' he had written with understandable relief the day after the fiasco of Arcole. Back in Verona two days later, he wrote her a tender note just before going to bed, reproving her as usual for not writing. 'Don't you know that without you, without your heart, without your love there can be no happiness of life for your husband,' he wrote, going on to say how he longed to touch her shoulder, hold her firm breast and to plunge into her 'little black forest'. 'To live in Josephine is to live in Elysium. To kiss her, on the mouth, the eyes, the shoulder, the breast, all over, all over!' Two days after that, having heard nothing, he wrote in teasing vein: 'I don't love you at all any more, on the contrary I hate you.' He asked her what occupied her days so fully to prevent her from writing. 'Who can it be, this wonderful and new love who absorbs all your time, tyrannises your days and prevents you from caring for your husband? Take care, Josephine, one of these nights your door will be forced and I will be in your bed. You know! The little dagger of Othello!' He then reverts to a more loving tone and looks forward to being in her arms again and planting a kiss on her 'little rascal'.23
He reached Milan panting with love on 27 November, only to find that she had gone to Genoa (with Lieutenant Charles). His disappointment and bitterness are given full expression in a note dashed off to her that evening and a letter the following day. 'Farewell, adorable woman, farewell, my Josephine,' he ended. General Henry-Jacques Clarke, who arrived from Paris the next day, found Bonaparte 'haggard, thin, all skin and bone, his eyes sparkling feverishly'.
Clarke had been sent by the Directory with the ostensible mission of opening negotiations with the Austrians, but in fact to spy and report on the commander of the Army of Italy. He was pleasantly surprised when Bonaparte agreed that negotiations with Austria were in order. Bonaparte knew that having driven back the French in Germany, Austria was about to launch an all-out offensive in Italy and would not be inclined to negotiate. But he had to gain Clarke's support, so he set out to charm him. In little over a week, Clarke was assuring the Directory that 'There is nobody here who does not regard him as a man of genius...' He praised the general's judgement, his authority and his efficiency. 'I believe him to be committed to the Republic, and without any ambition other than that of conserving the glory which he has acquired for himself,' he followed this up.
Clarke's support was an important asset in Bonaparte's long-running battle with the other arm of the Directory's control – its commissioners. Their brief had varied with unfolding events: lured by the cash and spoils he sent back, the Directory charged them with political and financial control of the occupied territories, but with the discovery earlier that year that General Pichegru commanding the Army of the Rhine and Moselle had been plotting with the enemy, their brief had been extended to surveillance of the military. They rode about in civilian dress with tricolour sashes and plumes that gave them the aspect of high-ranking commanders, often overruling officers.
In Saliceti, Bonaparte had at his side a man who for all his venality and opportunism was someone he could work with. The other commissioner, Pierre-Anselme Garrau, an unprepossessing hunchback with a virulently Jacobin background, was a thorn in his side. Soon after the conclusion of the armistice at Cherasco, Bonaparte had received instructions from the Directory that diplomatic negotiations were the preserve of the commissioners, not the army commander. He had by then concluded an armistice with the kingdom of Naples, and was negotiating with envoys of the Pope.
He left these negotiations to the two commissioners, who allowed themselves to be drawn into labyrinthine discussions which withered fruitless after three months. Worse, Garrau had inadvertedly revealed Bonaparte's plan to surprise and capture British ships in Livorno, allowing them to get away. Bonaparte had for some time been informing the Directory of the commissioners' incompetence and reporting the venality and scandalous behaviour of the civil functionaries operating in Italy. In July, after Saliceti was transferred to supervise the French reoccupation of Corsica, Bonaparte set about destroying Garrau. He forbade him to give orders to soldiers while bombarding him with demands for supplies and blaming him for every shortage. Bonaparte appointed his own officers to rule the occupied territories and began eliminating the 'shameless scoundrels', as he termed the officials following in the wake of the army, replacing them with equally venal ones who owed everything to him. Such usurpation of the Directory's authority could end badly for Bonaparte, and the matter had reached a climax in November, at the time of the Arcole campaign. He needed to watch his back.
In October, he ordered the arrest in Livorno of a Corsican by the name of Panattieri, the man Paoli had sent to search the Buonaparte house in Ajaccio in 1793 and bring all the papers he could find to Corte. At Bonaparte's request, all the papers in Panattieri's possession were seized. Meanwhile Joseph, who had gone to Corsica as soon as the British had evacuated it in order to secure the remains of the Buonaparte estate and see what could be added to it as a result of the flight of the pro-British Corsicans, scoured archives in Ajaccio and Corte. It was the first step in what was to be a methodical editing of the Buonaparte brothers' activities on the island.
In the context, the arrival of Clarke proved fortuitous: his glowing reports of Bonaparte's ability and devotion to the Republic persuaded the Directors that it was best to retreat. On 6 December 1796, they abolished the role of commissioners altogether.
Meanwhile, Josephine had returned to Milan and a semblance of harmony was restored. She gave a ball on 10 December at which the couple presided in regal manner. Although he had a low opinion of Italians, considering them to be lazy and effeminate, morally defective and politically immature, Bonaparte went along with the wishes of the Milanese intellectual elites for an independent Italian republic. Pre-empting any hopes the Directory might still entertain of using Lombardy as a bargaining counter, on 27 December he announced the creation of the Cispadane Republic (covering the nearside of the river Po, _Padus_ in Latin). It was given an armed force made up of Poles forcibly enlisted by the Austrians who had either deserted or been taken prisoner, under the command of General Jan Henryk Dąbrowski.
At the beginning of January 1797 the Austrians were on the move once more, Alvinczy marching down the valley of the Adige while two other corps swept down the valley of the Brenta to relieve Mantua. Leaving only a small force to parry these, Bonaparte collected all the troops he could muster and on the night of 13 January made a rapid march up to Rivoli, where Joubert was attempting to stem Alvinczy's advance. He arrived at two o'clock in the morning and quickly took in the situation. Alvinczy had split his force into six columns, and Bonaparte set about them separately, defeating one after the other. By late afternoon Alvinczy was in full retreat. This was turned into a rout by the intervention of Murat on his flank, and the Austrians fled, leaving behind nearly 3,500 dead and wounded and 8,000 prisoners, representing 43 per cent of Alvinczy's total effectives.
This obviated the need for pursuit, which was as well, since late that afternoon Bonaparte received news that one of the Austrian prongs to the south, under General Provera, had broken through and was close to Mantua. He ordered Masséna to gather up his exhausted troops and dashed south. On 16 January, while Colonel Victor contained a sortie from Mantua by Würmser, Bonaparte directed Augereau's division against Provera at La Favorita outside the city, forcing him to surrender. It was an extraordinary result: in the space of less than four days he had depleted the Austrian forces by more than half. In the space of the week the French had taken 23,000 prisoners, sixty guns and twenty-four flags. With all hope of relief dissipated, Würmser would surrender Mantua and its garrison of 30,000 men, half of them too sick to walk, on 2 February, giving Bonaparte another twenty standards to send back to Paris. The victory had been achieved through extraordinary exertion – Masséna's corps had fought at Verona on 13 January, at Rivoli the following day and outside Mantua two days later, covering ninety-odd kilometres in the process.
Bonaparte did not need to wait for the surrender of Mantua to know how complete his triumph was, and on 17 January he wrote to the Directors announcing that in the space of 'three or four days' he had destroyed his fifth imperial army. 'I've beaten the enemy,' he wrote to Josephine that evening. 'I am dead tired. I beg you to leave immediately for Verona. I need you, because I think I am going to be very ill. A thousand kisses. I am in bed.'
She did come, but there could be no question of a long rest. Austria would not admit defeat and was mobilising a new force. It was also negotiating with the Vatican and the kingdom of Naples, which had a sizeable army. The Directory had long before ordered Bonaparte to overthrow the papacy, which it regarded as the source of all obscurantism in the world and the avowed enemy of the French Republic. Bonaparte felt no animus against the Church and treated the clergy in the lands he occupied with respect, if only out of calculation. But he despised Pius VI, whom he regarded as a treacherous opportunist ready to stir against him every time the Austrians looked as though they might be winning. He was also short of cash, both for his army and to send back to France to placate his political masters, and there was no shortage of that to be found in Rome.
With 8,000 men, some of them Italian auxiliaries, he entered Bologna, where on 1 February he declared war on the Pope. He defeated a contingent of papal troops at Imola and took possession of Ancona. He had a cold and was depressed by the farcical nature of 'this nasty little war', as he wrote to Josephine on 10 February. Confronted by badly led mercenaries and displays of religious fanaticism, at Faenza he rounded up all the monks and priests of the place to lecture them about true Christian values.
The Pope sent a delegation to negotiate, but the honey-voiced prelates who had been so successful with Garrau were no match for a bullying Bonaparte. By the Treaty of Tolentino, signed on 19 February, Pius ceded the former papal fiefs in France, Avignon and the Comtat Venaisin, the Legations of Bologna, Ferrara and Romagna, along with Ancona. He also agreed to close his ports to British ships, and undertook to pay 30 million francs and deliver a number of works of art and manuscripts.
Five days later Bonaparte was back in Bologna with Josephine, who accompanied him to Mantua, where he prepared for the next campaign. The Directory had accepted that only he was capable of beating the Austrians decisively, and reversed its policy of treating the Italian theatre as a diversion. It transferred two strong divisions from the northern theatre, under generals Delmas and Bernadotte, reinforcing Bonaparte significantly: he could field 60,000 men while leaving 20,000 guarding his rear. This made him undertake what was under any circumstances a daring enterprise – a march on Vienna.
Three Austrian forces stood in his way, one under Davidovitch at Trento, another blocking the valley of the Brenta, and the main force concentrated along the river Tagliamento. They were under the overall command of Archduke Charles of Austria, a capable general two years younger than Bonaparte who had defeated the French in Germany. His presence was helping to restore the morale of the Austrian troops, and Bonaparte decided not to give him time. On 10 March he went into action, forcing Davidovitch up the valley of the Adige towards Brixen while Masséna advanced up the Brenta and Bonaparte took on the archduke himself on the Tagliamento. He breached his defences and forced him to fall back on Gratz (Gorizia) and Laybach (Lubljana). By then two of the passes were in French hands, and the archduke had to beat a hasty retreat if he were not to be cut off as Bonaparte reached Klagenfurt, on 30 March.
He was now poised to advance on Vienna, but if he did so, the Austrian armies in Germany could sweep into his rear. Behind him lay the whole of Italy guarded by a mere 20,000 men. Anti-French feeling simmered throughout the peninsula, with Naples, Venice, the papacy, Parma and Modena only waiting for a chance to strike. His army had advanced so far that it was running out of supplies, and the rocky region in which it now found itself would not sustain it for long. He therefore had to conclude peace urgently.
The one thing that would convince Austria to give in was a French advance across the Rhine by Moreau and Hoche, who had taken over from Pichegru, and Bonaparte sent request after request to the Directory urging it to order one. But he had learned to rely only on his own resources. On 31 March he offered Archduke Charles an armistice, but pressed on swiftly, reaching Leoben and taking the Semmering pass, less than a hundred kilometres from Vienna. There was panic in the Austrian capital, with people packing their valuables and leaving for places of safety. But with no support from Moreau and Hoche, Bonaparte could not afford to go any further. On 18 April preliminaries of peace were signed at Leoben.
Bonaparte had no right to negotiate a peace, let alone one which redrew the map as drastically as this one. The terms were that Austria ceded Belgium to France, gave up its claim to Lombardy and recognised the Cispadane Republic. In return, Austria was to receive part of the territory of the Republic of Venice.
Venice had remained neutral throughout the conflict, but French and Austrian armies had operated on its territory, using cities such as Verona and Bassano as military bases. Their depredations had provoked reprisals against French soldiers, and on 7 April Bonaparte had sent Junot to Venice with an insulting ultimatum to its government to stop them. When the Venetian authorities sent envoys to Bonaparte he lambasted them and declared that he would act like Attila if they did not submit. On 17 April there was a riot in Verona, almost certainly provoked on his orders, in the course of which some French soldiers were killed. He responded by making fresh demands of the Venetian government, insisting it reform its constitution along French lines. Provocations on either side ratcheted up the conflict, and a French vessel was fired on from one of the Venetian forts. On 1 May Bonaparte declared war on Venice and sent in troops. A puppet government was set up and instructed to settle with Austria the cession of territory, for which Venice was to be compensated with the former papal province of the Legations. Meanwhile, the plunder of the city's treasures began and the horses of St Mark's were removed to Paris.
Such treatment of a neutral sovereign state was nothing new for Austria, which had joined in the partitions of Poland and had long been eyeing Venetian territory, with its access to the sea. But for the French Republic, the liberator of oppressed peoples, to act in such a way was shocking, and when they heard of it the members of the Directory were incensed. Clarke, who reached Leoben two days after the signature, was aghast. But Bonaparte had already sent Masséna to Paris with the document and an accompanying letter in which he listed the advantages for France of the agreement, which he termed 'a monument to the glory of the French Republic'. He went on to state that if the Directory did not accept the terms of the peace, he would be content to resign his post and pursue a civilian career with the same determination and single-mindedness as he had his military one – a clear threat that he would go into politics. There was nothing the Directory could do: news of the signature of peace had been greeted ecstatically throughout France, with celebrations in some towns lasting three days.
## 13
# Master of Italy
By the beginning of May 1797 Bonaparte was back in Milan. In the space of twelve months he had won a succession of battles, taken 160,000 prisoners and 1,100 pieces of artillery, and well over 150 standards, as well as some fifty warships, and forced the emperor to make peace after five years of war. A rest was in order, and finding the summer heat oppressive, he had installed himself at Mombello, a stately villa a short distance from the city. Set on a rise which gave it fine views, of snow-capped Alpine peaks to the north and the Lombard plain to the south, it was a perfect place for him to recover from his travails. But it soon turned into what visitors described as 'a glittering court' to which many gravitated.
Pontécoulant, who had last seen Bonaparte at the War Ministry in 1795 pleading to be given back his rank, could not believe the change that had come over him. His previously hunched figure had assumed a commanding poise, and his features now put Pontécoulant in mind of classical cameos. 'It was difficult not to feel an involuntary emotion on approaching him,' he wrote. 'His height, below the average, rarely equalled that of his interlocutors, yet his movements, his bearing, the decisive tone of his voice, all seemed to proclaim that he was born to command others and to impose on them the ascendancy of his will.' Pontécoulant noted that he was polite and cordial to newcomers, speaking to each of the things which interested them. 'There was no pride in his behaviour, only the aplomb of a man who knows his worth and has found his place,' according to the playwright Antoine-Vincent Arnault, another who had arrived from Paris.
As he exerted authority over the whole of northern Italy, either directly or by proxy, Bonaparte was constantly receiving representatives of the civil authorities and the administration seeking guidance or approval. And as the political system on the peninsula remained fluid, a stream of diplomats trickled through Mombello, from the emperor of Austria, the kings of Sardinia and Naples, the Pope, the republics of Genoa and Lucca, the dukes of Parma and Tuscany, from civic corporations and other bodies, even from Swiss cantons and minor German states. Couriers came and went. So did individuals seeking redress, protection or favour. In order to accommodate the numbers, a large tent was erected beside the villa to extend the drawing room.
An etiquette gradually established itself, distancing Bonaparte from his comrades-in-arms, who were made to feel they could no longer use the familiar ' _tu_ ' when addressing him. In French military custom, a commander kept table for all his officers when on active service, and until now Bonaparte had sat down with his comrades to eat whatever and wherever they could. At Mombello, he dined in public with Josephine as French monarchs had done, to the accompaniment of music and watched by his court, only occasionally inviting one or other of his staff to join them. In the evenings, the company was entertained with music, and La Grassini would drive out from Milan to sing for the conqueror. 'He did not appear in the least embarrassed or put out by these excessive marks of honour, and received them as though he had been used to them all his life,' commented the French diplomat André-François Miot de Melito.
The painter Antoine Gros, who had been travelling in Italy, came to Mombello and started work on a portrait. Bonaparte would not sit still, so Josephine made him sit on her knee, and by playfully holding his head and caressing him she managed to immobilise him long enough for Gros to sketch the face. He would later work these sketches into the memorable painting of Bonaparte on the bridge of Arcole.
Josephine reigned over this court with a relaxed grace that impressed visitors: she seemed born to the station of regal consort. The ladies of Milan who called were charmed by her easy and friendly manner. 'Never has a woman combined more kindness with more natural grace and done more good with more pleasure than her,' in the words of Miot de Melito. She was nevertheless bored, and pined for Paris. Her relationship with Bonaparte seems to have been passing through a good phase, as she informed Barras. 'My husband has promised not to leave me any more,' she wrote, '... you helped to marry us, and you made his happiness and mine. I could not love him more than I do.' To Bonaparte's delight, the cook's dog killed Josephine's pug Fortuné, who could no longer prevent him taking what one observer called 'conjugal liberties' with her in public, but the spontaneous and unaffected nature of his caresses disarmed even the most prudish.
Josephine was less happy at having to put up with her husband's family. Letizia arrived on 1 June, bringing Maria Nunziata, now styling herself Caroline, little Geronimo, and Maria-Anna, who had taken to calling herself Élisa and brought her fiancé, the Corsican Félix Bacciochi. She needed a dowry, which only her brother could provide, and though he disliked Bacciochi, Bonaparte had to give in to the entreaties of his mother, who approved of the marriage, as the man came from a prominent family of Ajaccio. Joseph had also turned up, followed by Joseph Fesch, who brought Paulette and Josephine's son Eugène from Paris.
It was not a happy family gathering. Letizia, who now met Josephine for the first time, saw no reason to change her views on the subject of what she considered her son's disastrous marriage. The rest of the family concurred. For her part, Josephine was unimpressed by her in-laws. She had already met Lucien, whom she detested, and Louis, who did not like her and who since falling ill in February had turned into a hypochondriac prone to fits of depression. She found Joseph amiable enough, as he kept up a diplomatic show of friendliness towards her. It was her sisters-in-law who horrified Josephine. She appears to have believed the gossip that they had all slept with Bonaparte, and Paulette's behaviour did little to gainsay it. She was stunningly beautiful, but her demeanour combined the pranks of a schoolgirl with the morals of a harlot. One moment she would be pulling faces and sticking out her tongue, mimicking and joshing distinguished personages, the next she would be fornicating behind a curtain with whichever young officer came to hand. Bonaparte resolved to put a stop to it by marrying her off to one of his most able officers, Victor-Émmanuel Leclerc, who was in love with her and could be counted on to keep her occupied. They were married on 14 June along with Élisa and Bacciochi. Soon after, Letizia departed for Ajaccio with the Bacciochis, and a little later Joseph left for Rome to take up the job of French ambassador to the Holy See which Bonaparte had obtained for him.
To distract Josephine, Bonaparte arranged excursions to the lakes of Garda, Maggiore and Como, to Monza and Isola Bella. But he was himself not in holiday mood. More than one witness noted that he looked not only exhausted but also sad and often dejected, that on occasion his look was filled with melancholy and reflection, that he was sometimes sombre.
He had experienced a great deal over the past year, and had learned much about himself and others, about war, politics and human affairs in general. Most of it, including the deceptions of Josephine, had lowered his opinion of human nature. He had debased his own standards and made compromises, in his relationship with his wife, his political calculations and his financial dealings. By the beginning of 1797 he was systematically siphoning off a considerable proportion of the resources being sucked out of Italy, and following the last campaign he had taken most, at least a million francs, of the wealth uncovered by his commissary Collot at the mercury mines of Idrija in Slovenia.
In conversation with the agronomist André Thouin at Mombello one day, he said that once peace had been signed he would retire to the country and become a justice of the peace. There is no reason to doubt the sincerity of such sentiments, but they were no more than idle thoughts: in the uncertain state France was in, no government of whatever persuasion could tolerate the existence of a man of his capacities and following as an uncommitted private individual. In August, one of the army victuallers who had known him at Valence wrote to a friend that he could see 'no end for him other than the throne or the scaffold'.
Partly through his ambition and partly by force of circumstance, Bonaparte had become a figure famous throughout Europe. Between the spring of 1796, when he took command of the Army of Italy, and the end of 1797, no fewer than seventy-two pamphlets would have been published about him. People in the most distant parts of the Continent were either inspired or disgusted by him. Some feared him like the devil, others pinned their most ardent hopes on him. He was the source of fascination for young people of all classes and nations. But in France itself, he had become a political figure. Since the army had become an indispensable tool of government any popular general was, whether he liked it or not, a player in the power struggle which was going on over the future governance of France. Having proved his competence during the Vendémiaire rising, he was now both feared and needed by the Directory, and by every political faction in Paris.
For a man not shy of saying what he thought of others, Bonaparte was surprisingly sensitive to criticism. He had recently come under attack from the right-wing press in Paris, which portrayed him as a Caesar only waiting to cross the Rubicon, as a Jacobin and a fiendish 'exterminating angel'. He decided to respond in kind. On 19 July the first issue appeared in Milan of the _Courrier de l'armée d'Italie_ , a paper ostensibly meant to keep the army informed, but whose primary aim was to work on public opinion in France, where it was disseminated. Other commanders had published papers to keep their troops informed, but this one was different. The main feature of the first number was a description of the parade held in Milan on the anniversary of the fall of the Bastille on 14 July. It abounded in touching vignettes, mostly apocryphal. 'As the army marched past, a corporal of the ninth demi-brigade approached the commander-in-chief and said to him: "General, you have saved France. We, your children who share in the glory of belonging to this invincible army will make a rampart of their bodies around you. Save the Republic; may the hundred thousand soldiers who make up this army close ranks in defence of liberty."'
While Bonaparte made it clear that he and his army stood firm in support of the Republic, the _Courrier_ subtly distanced him from the Directory, which, by contrast with the pure republicanism of the Army of Italy and its commander, was made to appear weak and corrupt. A second journal, which came out once a _décade_ (ten days – the revolutionary week) under the editorship of the moderate constitutionalist royalist Michel Regnaud de Saint-Jean-d'Angély, printed articles 'correcting' 'false' impressions of Bonaparte held in Paris and building up the image of him as a miracle-performing hero.
This positioning had a great deal to do with recent events in France, where the April elections had returned a majority of right-wing deputies to the two chambers, setting these in conflict with the Directory. Barras resolved to cow them by force, and summoned General Hoche from the Army of the Sambre-et-Meuse under pretence of giving him the job of minister of war. On 16 July, as his troops crossed the sixty-kilometre exclusion zone supposed to keep the military away from the institutions of government, the chambers denounced the action and the attempted coup was blocked. Barras and his fellow Directors then concentrated on winning over those troops legally stationed within the zone, but they needed a popular general to lead them. Bonaparte wrote to the Directory on 15 July that the Army of Italy was alarmed at news of a slide to the right in Paris and hoped they would take energetic steps in defence of the Republic, assuring them of its support. He had cause for anxiety.
When they invaded Venetian territory in May, his troops had arrested a royalist agent, the comte d'Antraigues, and from him and the papers found on him, Bonaparte discovered that Generals Pichegru and Moreau were involved in a plot to overthrow the Directory and bring back the Bourbons, a plot which specifically involved killing him. This explained why the Austrians were dragging their feet over concluding peace.
The preliminaries signed at Leoben were just that, and a treaty still needed to be negotiated. The Austrian foreign minister Baron Thugut sent the Neapolitan ambassador in Vienna, Marchese Gallo, to negotiate this on his behalf, and when he met Bonaparte in Milan in May they agreed to conclude rapidly. But Thugut was in no hurry. At the last moment Bonaparte had insisted that France be allowed to keep all her conquests on the left bank of the Rhine, which meant that the territory's rulers would have to be compensated. Since their lands had formed part of the Holy Roman Empire, the emperor would need to sanction this and make whatever compensations were necessary. It was also hoped that some of Austria's allies in the anti-French coalition would be persuaded to accede to the settlement, which would be finalised at a congress to be convoked at Rastatt at the beginning of July. The possibility of a restoration of the Bourbon monarchy radically altered the situation; Louis XVIII would be only too happy to recover France reduced to her old frontiers and let northern Italy revert to Austria. When all this dawned on Bonaparte, he was outraged.
Both sides prepared for a resumption of hostilities. Austria took possession of the Venetian territory promised to it, while Bonaparte took over Venice itself and reorganised the area under his control. He had turned the lands taken from Venice into a Transpadane Republic, but then incorporated that with the Cispadane into one, to be known as the Cisalpine Republic. His aim was to deny the whole of northern Italy to Austria and create a political unit that could stand on its own but remain under French control. He hoped to introduce an administration which would allow it to raise and pay for enough troops to defend both itself and French interests. It was not a new idea, as Dumouriez had done much the same in the Austrian Netherlands and Hoche on the Rhine. The policy made sense to the generals operating in the respective areas, if not to the Directory. It was also partly inspired by the _mission civilisatrice_ the Revolution was supposed to be carrying out as it liberated sister nations from feudal 'slavery'. Bonaparte had the establishment of the Cisalpine Republic immortalised in a print showing himself before the tomb of Virgil, with the French people represented by a Herculean figure tearing the chains off a female figure representing Italy.
The reality did not live up to the ideal. Aside from a small number of Italian nationalists and Jacobins, the population had greeted the French incursion with varying degrees of hostility, which was greatly increased by the depredations of the troops and civilian administrators. Bonaparte had been careful not to upset local sensibilities by spreading revolutionary ideas, had refrained from toppling any throne (except that of Modena) or abolishing the privileges of the nobility, and had shown respect for the Church and the Pope (the Directors raged about his use of the terms 'Holy Father' and 'His Holiness' when writing and referring to him). Yet the majority of Italians remained sceptical and uncommitted. There were moments when Bonaparte despaired of the enterprise; and he was beginning to be distracted by other thoughts.
In April, the former French minister in Constantinople, Raymond Verninac, turned up at Leoben on his way back to France. He was concerned at the treatment of French citizens and interests in Egypt by the Mameluke beys who ruled it as a semi-autonomous province on behalf of the Ottoman Porte. For the past two years he had been receiving alarming reports from the French consul in Cairo, Charles Magallon, who since 1790 had been pressing for France to intervene militarily and, if necessary, take Egypt over as a colony.
The Levant had been a French sphere of interest since the Crusades, when a French dynasty was established in Jerusalem, and later France had entertained close diplomatic and commercial ties with the Ottoman Porte. The two powers were united in opposition to Austria and Russia, both of which threatened Ottoman interests in the Balkans. Toulon and Marseille had grown up on trade with the Levant, which attracted colonies of French merchants. An Ottoman province since 1517, Egypt was ruled by a pasha nominated by the Porte assisted by Mameluke soldiers of Albanian and Circassian origin. The pasha had lost control, the beys did as they pleased, and the population suffered from their maladministration, corruption and cruelty. In the course of the eighteenth century many came to believe that Egypt was crying out for stable administration and development.
The loss of Canada and other colonies to the British in the 1760s prompted the French to look east. Featuring prominently in the art and literature of the eighteenth century, in the course of which France developed relations with Persia, the region seemed to offer great promise. The decline of the Ottoman Empire was a source of concern for France: if it were to fall apart, Austria and Russia would be the beneficiaries. A French base in Egypt would permit France to deny them that and Syria at least. It would also enable her to safeguard her interests in India, where she had a number of partisans among the Indian princes, chief among them Tipu Sahib of Mysore, who in October 1797 would make the last of several appeals for military assistance. A French force from Suez landing in Bombay at the heart of Mahratta territory would at the very least divert British forces.
As France lost further colonies to Britain in the West Indies in the 1790s, the case for acting in Egypt grew stronger. Magallon pointed out that the Nile delta provided the conditions to grow all the goods formerly derived from the Caribbean – cotton, rice, sugar, coffee and so on – while others could be obtained from neighbouring Arabia and Persia. When the British seized the Cape of Good Hope, cutting off the sea route to India, the appeal of obtaining a port on the Red Sea grew stronger, as did that of piercing the Isthmus of Suez with a canal. The idea of turning the Mediterranean into a French sea was a logical one, and with Spain onside and Corsica in French hands once more, it appeared practicable.
When he occupied the port of Ancona earlier in the year, Bonaparte noted its strategic value and that of the Ionian islands across the Adriatic. They had been part of the Republic of Venice, and as soon as he was able to, he despatched a force to occupy them. He made overtures to the Ottoman rulers of Albania, assuring them of France's good intentions and respect for their faith, and also to the Maniotes of the Peloponnese. Contemplation of those shores triggered a host of cultural references: Athens, Sparta, Homer and Alexander the Great litter his correspondence at the time.
Another strategic imperative for control of the eastern Mediterranean was Malta, and Bonaparte began gathering information on the state of its defences and the morale of its masters, the Knights of the Order of St John. He pressed the Directory to investigate the possibility of having a Spaniard elected Grand Master, which, Spain being France's ally, would bring the island into France's orbit.
General Louis Desaix, who turned up at Mombello in late July, was intrigued to find Bonaparte poring over maps of Egypt and Syria. A year older than him, looking, according to Lavalette, 'like a savage from the Orinoco dressed in French clothes', Desaix had much in common with Bonaparte, always wearing a plain, poorly-fitting blue coat with no marks of rank, ill at ease in society and paying little attention to women. He caught Bonaparte's enthusiasm, and they discussed the details of an invasion of Egypt sailing out of Venice with a corps of 10,000 French and 8,000 Polish troops.
In his report to the Directory on 16 August Bonaparte warned that Austria was arming and would soon be in a position to field formidable forces for the reconquest of Italy, and argued that France must seek alternatives. 'The islands of Corfu, Zante and Cephalonia are of greater interest to us than the whole of Italy taken together,' he went on. 'I believe that if we were forced to choose, it would be better to restitute Italy to the emperor and to keep the four islands, which are a source of riches and prosperity for our commerce. The empire of the Turks is crumbling by the day; the possession of these isles will put us in the position to support it for as long as that will be possible, or to take our share of it. It will not be long before we feel that, in order to really destroy England, we have to take Egypt.'
Unbeknown to him, the Directory had a few weeks before received a memorandum from its foreign minister, Talleyrand, in which he put the case for seeking replacements in Africa and Egypt for the colonies lost to the British in the western hemisphere, and followed this up with three more documents developing the putative advantages, suggesting Egypt as a suitable place to begin.
The Directors had other things on their mind: they needed a general who could help them intimidate the chambers, and they approached Bonaparte. While he shared their alarm at the counter-revolutionary tide in Paris and urged them to act, he was wary of getting involved. He therefore sent them Augereau, a stalwart republican who was sure to be able to carry the troops with him. The manoeuvre had also rid him of a man he did not like or trust, and who was inconveniently popular among the rank and file.
In the course of the past year, Bonaparte had become aware of the perils threatening him, and he created a unit of bodyguards, the Guides, to act as an escort. But he needed to make sure that the Army of Italy was also entirely his. He bought the loyalty of the other generals with a mixture of encomiums, promotions, mentions in despatches to the Directory and his Bulletins, and cash hand-outs. On the cessation of hostilities with the signature of the preliminaries of Leoben, the army was just over 80,000 strong, but a large proportion was made up of recent reinforcements, men who had seen little or no service under his command. He refrained from promoting more recent arrivals, and filled the higher ranks of every unit with men who had proved themselves under him, even if it meant giving them precedence over senior officers. On 14 July he celebrated the anniversary of the fall of the Bastille with a parade at which he honoured men and units, followed by a banquet for all those who had distinguished themselves in battle. On 28 August he presented a hundred sabres of honour, ten to cavalrymen, ninety to grenadiers, whom he was already singling out as a kind of elite, his Praetorians.
'What I have done so far is nothing,' he said to Miot de Melito and the Italian statesman Francesco Melzi d'Eril as they strolled in the gardens of Mombello one summer day. 'I am only at the beginning of the career I must pursue. Do you think it is to enhance the position of the lawyers of the Directory, the Carnots, the Barras, that I have been winning victories in Italy? And do you think it is in order to establish a republic? What nonsense! A republic of thirty million people! With our manners and our vices! It is an impossibility! It is a dream with which the French are in love, but it will pass like so many others. They want glory, they want their vanity to be satisfied, but liberty? They don't understand it at all. [...] The nation needs a glorious leader and not theories of government, phrases and speeches by ideologues which Frenchmen don't understand. [...] I do not wish to leave Italy until I can go and play in France a role similar to that I am playing here, and the time has not yet come: the pear is not yet ripe.'
For all his cynicism, Bonaparte was still a child of the eighteenth-century Enlightenment, a believer in human progress, to be achieved through the better organisation of society. 'A France with _honest and strong government_ , that is what I want,' he told Pontécoulant. He had long ago come to the conclusion that this could only be achieved by dictatorial means. While dining with his staff at Ancona in February, he had astonished them by affirming that the only decent government since the beginning of the Revolution had been that of Robespierre. Strong central authority, he explained, was necessary in order to carry the Revolution to its logical conclusion; to create new institutions based on solid rational foundations, ensure the rule of law, stabilise the currency by abolishing paper money and introducing a functional system of tax-collection, re-establish the Church as a moral base for society, regenerate its morals and make France great once more. He concluded by saying that Robespierre had only failed because he lacked the experience and strength of 'a military commander'.
The Directory had once again demonstrated the truth of this. Having placed Augereau in command of the troops in the Paris region, on 4 September (18 Fructidor) it felt strong enough to invalidate the April elections, expelling 154 deputies and thereby recovering its majority. Sixty-five were sent to the penal colony of Guyana. Bonaparte had sent his aide-de-camp Antoine de Lavalette to observe and report back on events. Once the coup had been accomplished, he was therefore able to gauge public reactions and act accordingly. As these had been generally unfavourable, he distanced himself from the actions of the Directory. 'Your silence is very curious, general,' wrote Barras, prompting Bonaparte to issue a proclamation expressing his satisfaction at the defeat of 'the enemies of the fatherland'. In private, he condemned the coup and particularly the deportations to Guyana. Barras remained suspicious, and sent his secretary Bottot to Italy to ascertain what was going on.
Bonaparte had acquired a new ally in Talleyrand, who had written him a flattering letter seeking his friendship. He responded with an appropriately cordial one full of praise for the minister's distinguished record, which he, Bonaparte, would certainly reward were he to be in a position to do so. 'You ask for my friendship, and you have it along with my esteem,' he wrote. 'In return, I ask for your counsels, which I will value, I assure you.' He went on to say that the Revolution had destroyed too much and built nothing, so 'everything remained to be done', and the only question was who would be the one to 'close the Revolution'. Subsequent correspondence confirmed that it was not only their views on Egypt that coincided.
With the possibility of a Bourbon restoration dismissed by the Fructidor coup, there was no longer any reason for Austria to delay making peace. Britain too was inclined to end the hostilities, and peace talks had been going on at Lille since July between Lord Malmesbury and Charles-Louis Letourneur. But they were undermined by the Directory, which saw them as part of an Anglo–royalist plot. Bonaparte was highly critical of the missed opportunity, arguing that the British could have been allowed to keep the Cape in exchange for agreeing to a French colonisation of Egypt.
It was not until the end of August that the Austrian chancellor Thugut sent a senior diplomat, the monstrously fat forty-four-year-old Count Ludvig Cobenzl, to direct the negotiations along with Gallo. They took up residence at Udine while Bonaparte installed himself a short distance away at Passariano, a grand country residence set in beautiful parkland belonging to Ludovico Manin, the last Doge of Venice. They skirmished ferociously but dined together, either at Udine or Passariano.
While Thugut was now eager to proceed so as to secure Venice for Austria as quickly as possible, the Directory felt strong and belligerent. Following the unexpected death of General Hoche on 19 September it appointed Augereau commander of the Army of Germany in his place, which suggested the possibility of a fresh offensive against Austria in that theatre. This was unwelcome news to Bonaparte, as it raised the possibility of Augereau stealing a march on him, or at least dimming his glory with a victory. Equally unwelcome were the despatches which arrived from Paris on 25 September informing him that the Directory was sending someone to conduct the negotiations in his stead.
He responded with one of his tantrums. 'I am ill and I need rest,' he wrote to Barras the same day, asking him for a discharge, adding that he wanted to settle outside Paris and enjoy at least a couple of years of peace. He wrote to the Directory in the same vein. 'No power on earth could make me continue to serve after this horrible mark of ingratitude by the Government, which I had been very far from expecting,' he complained. 'My health is considerably impaired, it urgently demands rest and tranquillity. The state of my soul is also such that it needs to reimmerse itself in the mass of my fellow citizens. I have for too long had great power placed in my hands.' The idea of Bonaparte immersing himself in the mass of his fellow citizens was too frightening for the Directory to contemplate.
The negotiations continued, Cobenzl trying to intimidate Bonaparte with courtly mundanity, only to be met with bullying and feigned rages. The Austrian diplomat was unused to such tactics, and through Gallo he persuaded Josephine to exert a calming influence (for which she would be rewarded by the emperor). But Bonaparte was not to be controlled as he steered his own course; he was under strict orders from the Directory not to cede any part of Venice to Austria, and while he had no intention of following these, he used them to pressure Cobenzl over other things, as by then Austria was set on having the territory. At the same time, he did not want to push the Austrian too hard, as he feared a possible resumption of hostilities, for which his army was unprepared, and he reserved his belligerence for the peace talks.
These were eventually concluded, and the treaty was to be signed on 11 October, but at the last moment Bonaparte insisted a guarantee be inserted that France would obtain the left bank of the Rhine. Cobenzl demurred. Bonaparte, who had spent two sleepless nights, was in an agitated state and fortified himself with numerous glasses of punch as he read out his proposed draft of the treaty. When Cobenzl attempted to explain the impossibility of his acceding to the new terms, Bonaparte got up from the table clearly drunk, put on his hat and stormed out of the room, vomiting barrack-room imprecations. By his own account, he smashed Cobenzl's favourite coffee set before walking out, pursued by a vainly emollient Gallo.
Bourrienne records that two days later he awoke to see snow on the mountaintops and informed Bonaparte of it as he roused him. With winter on its way, a French threat to Vienna through the passes was dissolving fast, and Bonaparte realised he had to conclude speedily. The treaty was signed on the night of 17–18 October, and named after a place equidistant from the two in which the negotiations had been conducted, the village of Campoformido, mis-spelt by a French secretary as Campo Formio. Bonaparte had gained most of what he wanted. He was in high spirits, and at dinner he entertained the Austrians by telling them his favourite ghost stories.
'My services have earned me the approbation of the Government and the nation,' He wrote to the Directory. 'I have received many marks of its esteem. It now remains for me only to step back into the crowd, take up the plough of Cincinnatus and set an example of respect for the magistrates and aversion for military rule, which has destroyed so many republics and undermined several States.'
On 5 November he received his nomination as commander of a projected Army of England and also as plenipotentiary at the congress due to convene at Rastatt to settle questions arising from France's acquisition of the left bank of the Rhine. On the morning of 17 November he left Milan with Eugène de Beauharnais. Travelling fast and through the night he was at Mantua the next day, where he paused only to review the troops stationed there, hold a ceremony in honour of the deceased Hoche and attend the theatre, before rushing on, to reach Turin at two on the morning of 19 November. He remained there long enough to have a talk with Miot de Melito, in the course of which he again expressed his conviction that 'those Parisian lawyers who have been put in the Directory understand nothing about government'. 'As for me, my dear Miot, I tell you that I cannot obey; I have tasted command and I would not be able to give it up. I have made up my mind: if I cannot be master, I will leave France...'
At three that afternoon he left Turin, and two days later he was in Geneva. People came out to catch sight of him as he passed through, not just to see the victorious hero whose reputation was spreading over the Continent, but to cheer the man who had brought peace after so many years of war. ' _Vive Bonaparte, vive le pacificateur!_ ' they shouted. According to Bourrienne, Bonaparte was furious when one of their former colleagues from Brienne now living in Switzerland came to see him and addressed him with the familiar ' _tu_ '.
He was even angrier when, after rushing on, through Berne, Basel and Huningue and reaching Augereau's headquarters at Offenburg, he was informed that the commander of the Army of Germany was busy getting dressed and could not see him. He hurried on to Rastatt, which he drove into on 26 November in a magnificent coach drawn like a sovereign's by eight horses, with an escort of thirty hussars, before installing himself in the Margrave of Baden's residence.
He impressed the representatives of the Imperial Diet not just by his grand manner but by his familiarity with the Golden Bull of 1356, the constitution of the Holy Roman Empire and the Treaty of Westphalia. On 29 November he met the prime minister of Baden, and exchanged the ratified copies of the Treaty of Campo Formio. On the same day he received a despatch from the Directory summoning him to Paris.
## 14
# Eastern Promise
Bonaparte arrived in Paris at five o'clock on the dark winter evening of 5 December in an ordinary mail coach, dressed in civilian clothes, a broad-brimmed hat hiding his face, accompanied by generals Berthier and Championnet, also out of uniform. He went home to the house on the rue Chantereine, which was empty since he had left Josephine behind in his rapid journey through Rastatt to Paris. Before going to bed he dashed off a note to Madame Campan asking her to send Hortense to come and join him, and made an appointment to meet Talleyrand the following morning.
He arrived at the ministry of foreign relations at eleven o'clock. Waiting in Talleyrand's anteroom were two eminent people desirous of meeting him: the old admiral and circumnavigator Bougainville and the celebrated writer and bluestocking baroness Germaine de Staël, whom he barely acknowledged in his haste to get down to business with the minister. It was their first meeting, and Talleyrand was enchanted, noting that 'twenty battles won sit so well with youth, a fine look, pallor and a kind of exhaustion'. After an hour's confabulation they set off to meet the five Directors, whom they found assembled in Barras's quarters at the Luxembourg Palace. Bonaparte was greeted warmly by Barras himself and one other Director, the hideously ugly Louis-Marie Lareveillère-Lepaux, a dreamer more interested in horticulture and his pet project of a new religion, Theophilanthropy, than in the minutiae of government. The more practical and dominant Jean-François Reubell was amicable, but the remaining two, Lazare Carnot and Charles-Louis Letourneur, were hostile. They were incensed by the Treaty of Campo Formio and its destruction of the Venetian Republic. While they were powerless to do anything about it, given the popularity of Bonaparte and the universal joy at the coming of peace, they had shown their feelings by giving him command of the Army of England and delegating him to the congress of Rastatt – both designed to keep him away from Paris.
After his meeting Bonaparte stayed to dine with Barras, and then went home. As news of his return spread, people wondered what his next move would be. He was still commander of the Army of Italy, he had been placed in command of that of England, and as president of the French delegation to the congress of Rastatt he had overall command of French troops in Germany. A number of units were making their way across France to the Channel coast, passing within reach of Paris. Bonaparte was therefore in a position to stage a military coup, and many expected him to act. There would be little resistance, as the great hope of the royalists, General Pichegru, had been sent to Guyana and the leader of the extreme left, Gracchus Babeuf, guillotined. But as the Republic was not under threat he had no credible motive.
He was to return to Rastatt in a little over a week, and in the meantime he kept the door of his house firmly shut, instructing his servant to admit nobody and even to refuse to accept calling cards. To his intense irritation, the Directors had decided to hold a ceremony in his honour on 10 December, and he could not wriggle out of it. But afterwards he went to ground once more, and at dinner the following day, to which he had invited a handful of distinguished intellectuals, he talked metaphysics to the philosophically-minded Abbé Sieyès, poetry to the poet Chénier and geometry to the mathematician Laplace.
He only ventured out in civilian dress, his face hidden by a hat, and when he went to the theatre he sat at the back of his box. While the Directory was wary of him, he was afraid lest it feel threatened enough to resort to extreme measures. He could not avoid going to a banquet for eight hundred guests held in his honour by the two chambers on 24 December in the great gallery of the Louvre, hung with the paintings he had sent back from Italy, but he ate nothing. When dining out he partook only of dishes he had seen others taste, and otherwise confined himself to tamper-proof boiled eggs.
On 25 December the Institute of Arts and Sciences elected him a member. He was genuinely thrilled. 'The real conquests, the only ones which come with no regrets, are those one makes over ignorance,' he wrote in his letter of acceptance. 'The most honourable occupation, and that most useful to all nations, is to contribute to the extension of human thought,' he went on, declaring that the real greatness of the French Republic should lie there. The following day he took his seat, between his friends Monge and Berthollet. He would attend over a dozen of the Institute's meetings over the next three months, acquiring a pool of admirers among the intellectual elite of France. He would spend hours with scientists, acting the eager pupil or astounding them by his knowledge, flattering them with his deferential interest, declaring that war, which might be necessary at times, was a lowly trade that could not aspire to the level of an art or a science such as theirs. Although his friendship with Monge, twice his age, Berthollet and some of the others was heartfelt, his courting of the intellectuals was calculated. The same went for the artistic establishment. Astonishingly for someone as impatient as him, he spent no less than three hours sitting for the painter Jacques Louis David. 'Oh, my friends, what a head he has! It is pure, it is magnificent, it has the beauty of antiquity!' David exclaimed afterwards. 'In all, my friends, this is a man to whom in those days altars would have been raised, yes, my friends, yes, my dear friends! Bonaparte is my hero!'
His membership of the Institute also allowed him to sidestep a thorny issue when the Directory insisted he attend the ceremony held annually on 21 January celebrating the execution of Louis XVI. He tried to exempt himself by arguing that he did not hold any public position, protesting that the supposed celebration was inappropriate given that it commemorated a national disaster, that no government, only a faction would ever celebrate the death of a man, and that it brought no credit to the Republic or ease its relations with the other states of Europe, most of which were monarchies. The Directors were adamant, fearing that his absence would be interpreted as a sign of defiance and give heart to royalists. He eventually agreed to attend in the ranks and uniform of the Institute, thereby underlining that his attendance was purely official and did not reflect his views.
He was careful to maintain good relations with the Directors, and Lareveillère-Lepaux was delighted by his modesty, his simplicity of dress, his apparent domesticity and his declared interest in Theophilanthropy. Consistently self-effacing, Bonaparte was all things to all men – the Prussian minister was flattered when he sang the praises of Frederick the Great, dismissing his own victories as the result of 'good luck and some hard work'.
As commander of the Army of England, Bonaparte was supposed to invade it. He saw France as the new Rome and Britain as Carthage, and his vanity would have been caressed by the success of a play entitled _Scipion l'Africain_ in which audiences picked out parallels between him and Scipio. Another, on the fall of Carthage, made even more obvious allusions to the heroics he was about to embark on. But it is doubtful that he ever considered the possibility seriously.
A week after his return to Paris, on 13 December, he issued his first orders relative to the invasion, and over the next days had a number of meetings with the minister of the navy. The French navy had been irredeemably damaged by the Revolution; crews had mutinied and discipline could not be restored for ideological reasons. By 1792 all but two out of nine admirals and three out of eighteen rear-admirals had left, along with three-quarters of the captains. Training replacements was impossible, as most of the ships were confined to port by the British blockade, and after the loss of so many at Toulon, the French navy was not up to carrying out an operation of the sort envisaged.
It is doubtful that Bonaparte felt any desire to invade England. He nurtured an admiration for the British, condemned the Directory's failure to make peace the previous summer, and reproached Barras for the belligerence of his speech at the ceremony of 10 December. He conferred with Wolfe Tone and other Irish revolutionaries, but was unimpressed. If he had intended to carry through the plan he would have applied himself to the task with his usual determination, spending his nights poring over maps and inspecting embarkation ports, identifying landing places and organising the invasion force. He did none of these, and did not present the Directory with a plan for over a month, while in the past he had produced them in a matter of days. It is doubtful that the Directors themselves believed in the possibility of a successful invasion.
The arrival of Josephine on 30 December put an end to Bonaparte's low-profile life. On the same day, the rue Chantereine was renamed rue de la Victoire, and that evening they went to the theatre. Four days later they attended a party given in their honour by Talleyrand, a grand affair for some two hundred guests, widely commented on for its lavish scale and ancien-régime elegance. The rooms were decorated with trees and foliage, with backdrops presenting views of a military camp. The ladies wore scanty 'Greek' dresses, and while Josephine stood out, Bonaparte was self-effacing in civilian dress and did not stay long. He was annoyed when Madame de Staël engaged him in conversation. He would later claim she tried to seduce him, but on this occasion he was plain rude. When she asked him what kind of woman he respected most, no doubt hoping for a flattering response, he replied curtly that he esteemed only those who bore many children, before turning to talk to the Ottoman ambassador Ali Effendi.
His opinion of women would not have been enhanced by the behaviour of Josephine. On his departure for Rastatt he had left her in Milan, from where she was to travel directly to Paris. She prolonged her journey in order to spin out her amours with Lieutenant Charles, who was travelling with her. Once she reached Paris, she dismissed her maid Louise, who had displeased her by having a fling with Junot on their way out to Italy. Louise took her revenge by spilling the beans to Bonaparte about Hippolyte Charles. He angrily reproached his wayward wife, but she managed to placate him.
By mid-January 1798 it had become clear that Bonaparte's presence was not after all required at Rastatt, which left him with no excuse to delay an invasion of England he had no intention of embarking on. He had gradually worked his way into the confidence of the Directors, whom he saw regularly, and contemplated joining them, but being less than forty years old he did not qualify.
He was being urged by many to stage a coup against them, but felt the time was not ripe and remained uncertain as to the depth or durability of his popularity. There were rumours of plots to poison him, and he was aware that he had enemies at both extremities of the political spectrum. It was time he returned to his real trade and took command of an army – in the midst of which he would be safe.
Since England was such an unpromising objective, the only viable alternative was the invasion of Egypt, which Talleyrand was advocating. On 25 January news reached Paris of the death of the French ambassador in Constantinople. While the implications were being discussed by the Directors, Bonaparte set to work with Talleyrand on a fresh report which the minister delivered to them the following day. It repeated the old arguments, adding that the Porte had effectively lost control of Egypt and would not mind France administering the colony provided it remained its nominal sovereign: the corrupt and backward Mameluke administration would simply be replaced by a French one, and the Porte might actually benefit from such an arrangement. French diplomats in the area were of one voice that Mameluke rule was unpopular with the Egyptians themselves, who longed for deliverance. Talleyrand proposed to go to Constantinople himself to arrange matters.
The Directors were divided in their opinions, and ostensibly still favoured an invasion of England. On 23 February, after visiting Etaples, Ambletuese, Boulogne, Calais, Dunkirk, Nieuport, Ostend, Ghent and Antwerp, Bonaparte reported that an invasion was impracticable. The following day he discussed his findings with the Directors and declared that he would not take on the job, offering to resign his commission. Reubell, who hated him, handed him a pen. The gesture was a dig at his vanity, but no more – the Directory did not want a disgruntled war hero hanging about Paris, and they needed to find him an assignment. On 5 March they sanctioned the plan to invade Egypt.
Financing the expedition was not a problem. The weak and largely conservatively-ruled confederation of Swiss cantons provided a base for British secret agents and military access to the borders not only of France but of her Cisalpine 'sister republic', which had long bothered the Directory. Bonaparte had already sliced off the Valtelline and added it to the Cisalpine Republic, thereby gaining control of the Simplon Pass. The Directory encouraged Jacobins bent on revolution in various parts of the country, and French troops marched in to support them in overthrowing the most conservative of all the cantonal governments, that of Berne, whose treasure, as well as its two emblematic bears, were sent to Paris at the beginning of March.
Bonaparte set to work planning the expedition. The new Army of the Orient would be composed mostly of men from the Army of Italy. They would embark at Toulon, Marseille, Ajaccio, Genoa and Civitavecchia. The respective fleets were to assemble off Malta, which was to be captured for France as the first step in denying the Royal Navy bases in the Mediterranean. The next step would be to land in Egypt, overthrow the Mamelukes and organise the country. A naval base was to be created at Suez which would connect with the French colony of Île de France (Mauritius), whose strategic position in the Indian Ocean could be exploited for trade and military purposes. As soon as it was practicable, the Isthmus of Suez was to be pierced with a canal. The plan could only work if the British navy stayed out of the Mediterranean, so it was kept a secret and preparations for the invasion of England proceeded.
Bonaparte was thinking of more than conquest. While they were both in Italy, Monge had drawn his attention to the disparity between how much was known about Greco-Roman civilisation and how little about the Egyptian, and when they discussed the possibility of an invasion he had suggested that a commission of experts should accompany it to study the pyramids and other remains. Bonaparte agreed, and his boundless interests suggested something more. He had a vision of extending the fruits of the Enlightenment to backward lands; the regeneration of what he referred to as the cradle of civilisation by the new metropolis that was France. The venture was to be beneficial to mankind, a voyage of discovery as well as one of illumination. He therefore decided to take with him the most eminent figures in the arts and sciences, as well as engineers and technicians who would develop the country. With the greatest secrecy, he began approaching them without telling them where they would be going. Some, like the painter David, refused. The composer Méhul also backed out, as did the poet Ducis and the renowned baritone François Lays, whom Bonaparte had imagined singing Ossianic odes at the head of the troops on the march. He had the greatest difficulty in persuading Monge, who felt too old and was currently still in Italy; Bonaparte personally visited Madame Monge, pressing her to use her influence on her husband.
He bade Bourrienne put together a travelling library, arranged in the following categories: 1. Sciences & Arts, 2. Geography & Travels, 3. History, 4. Poetry, 5. Novels, 6. Political Sciences (which contained the Old and New Testaments, the Koran and the Vedanta). Pride of place in the poetry section went to Ossian; Rousseau's _La Nouvelle Héloïse_ and Goethe's _The Sorrows of Young Werther_ were among the novels. He also had 2,000 bottles of good Burgundy sent to Toulon. To keep the soldiers happy, he wanted to take along a troupe of actors from the Comédie-Française. He also, it seems, had 'a leather helmet richly embroidered with gold' run up which made him look 'like an actor in an opera'.
As there was a risk of the fleet being intercepted by the British, Josephine would not be sailing with him. He would send a frigate to fetch her once he had landed and pacified Egypt. Their marriage had gone through yet another trauma in mid-March when a delighted Joseph presented his brother with evidence that his wife was shamelessly carrying on her affair with Lieutenant Charles under his very nose, meeting him regularly in the afternoon at the house of a supplier to the military in the Faubourg Saint-Honoré. A natural liar, Josephine denied everything and challenged Bonaparte to divorce her. To Charles, she wrote in torrid terms of her love for him and her hatred for all the Bonapartes. 'Hippolyte, I will kill myself,' she wrote on 17 March. 'Yes, I must end [a life] which will be a burden to me if it cannot be devoted to you. [...] Oh, they can torment me as much as they like, but they will never part me from my Hippolyte: my last breath will be for him. [...] Adieu, my Hippolyte, a thousand kisses as ardent as my heart, and as loving.' As usual, she managed to placate Bonaparte, to whom she seems to have grown sincerely attached. He bought the house in the rue de la Victoire, inserting a clause giving her life tenure in the event of his death. He also agreed to her plan of buying a house outside Paris, at La Malmaison.
On 17 April he ordered Admiral Brueys, who was to command the fleet, to prepare to sail within ten days. There is some evidence that he made one last proposal to the Directors to share power with them, pointing out that if the war with Austria were to resume they would need a strong man. On 22 April, which was supposed to be his last night in Paris, he went to a performance of _Macbeth_. But the next day news arrived of a diplomatic incident provoked by France's ambassador to Austria, General Bernadotte, which momentarily threatened to provoke a fresh war, and it was not until 27 April that the Directory felt it safe to order him to proceed to Toulon.
He went to Saint-Germain with Josephine and Lavalette to visit her niece Émilie, whom Bonaparte had ordered Lavalette to marry, and to take her and Hortense for a picnic in the woods. The following day, 30 April, he attended a session of the Institute and then called on the Directors, who pressed him to leave as soon as possible. Others were still urging him to stay and overthrow the government. 'Bonaparte must either get away or destroy the Directory or be crushed by it,' Colonel Morand of the 85th Demi-Brigade wrote to his parents, revealing that even in Civitavecchia where he was stationed the political situation was no secret.
Bonaparte left Paris incognito at three o'clock in the morning of 4 May, in a mail coach with a passport made out in a false name, accompanied only by Josephine, Eugène de Beauharnais and Bourrienne. They travelled to Lyon, where they embarked on a boat which took them down the Rhône as far as Aix, and from there went by carriage to Toulon, which they reached in the early hours of 9 May. He took a parade of the 18th, and then the 32nd and 75th Demi-Brigades, all old soldiers of his Army of Italy. 'We greeted him with enthusiastic cheering lasting more than a quarter of an hour,' recalled one officer. Bonaparte then walked through the ranks talking to officers and men, and ended with a speech comparing them to the Roman legions which conquered Carthage. He reminded them that only two years before he had found them covered in rags, had led them to glory and provided for their every need. He asked them to trust him now, and assured them that they would return with the money to buy enough land for a farm (six _arpents_ , or about five acres).
The enthusiasm was great, and even the hesitant Monge came to life. 'I am transformed into an Argonaut!' he wrote to Bonaparte, comparing him with Jason but pointing out that instead of going after some worthless fleece, he would be carrying the torch of reason to a land where no light had penetrated for centuries.
Monge was one of the few in on the secret. The rest were kept in darkness, and speculated wildly as to whether their destination was England, Ireland, Portugal, Brazil, Sardinia, Malta, Sicily, Gibraltar, the Crimea or even India. Bonaparte announced to the 75th Demi-Brigade that they were 'one of the wings of the Army of England', which was about to cross the seas and conquer the new Carthage. He assured them that great destinies awaited them, that the eyes of Europe were on them, and that although they would have to overcome great dangers and hardships they would bring lasting benefits to their motherland. 'The genius of liberty, which has made of the Republic the arbiter of Europe from her very birth, wishes that she should be that of the seas and of the most distant lands,' he concluded. Similar exhortations were echoed all over the country. 'Alexander subdued Asia, the Romans conquered the world,' thundered the leading article in _L'Ami des Lois_. 'Do more, make the whole world happy and free, you can, you must...'
On 13 May the ships in the roads were bedecked with flags and fired gun salutes as Bonaparte went aboard the flagship, the 120-gun _l'Orient_ , one of the largest ships afloat and one of the few French vessels of recent construction. He had asked Admiral Brueys to prepare a cabin for him, bearing in mind that he would be spending much time in it feeling seasick. Brueys did not stint, and according to the chief uniform supervisor who went to take a look, 'everything was arranged in the most useful and agreeable manner, with the greatest refinement and good taste'; Bonaparte's ' _salon de compagnie_ ' struck him as 'marvellous' and 'fit to accommodate a sovereign'.
At seven on the morning of 19 May the huge fleet weighed anchor. Five days later it was off Corsica, where it was joined by a flotilla carrying a contingent of troops from Ajaccio, and then sailed down the coast of Sardinia. The soldiers were kept busy with drills and taught to climb rigging and man the naval guns, while military bands played rousing marches and revolutionary hymns. In the evenings, they had less martial music: the band of the Guides was up to playing whole symphonies. Once he had recovered from the first bouts of seasickness, Bonaparte took a keen interest in all things nautical, and in the evenings after dinner either listened to music or held court with his entourage of generals and savants. They took turns to read aloud, the works of Montaigne and Rousseau among others. Junot would fall asleep, and snored so loudly that he was excused. Bonaparte had Arnault read the _Odyssey_ to him aloud, but after a time declared that Homer and the Greeks in general were not heroic enough compared with Ossian. He produced a luxury edition bound in vellum of the fake bard's poems which he kept by his bedside and began declaiming them to the assembled company. Arnault noted that he read very badly, but Bonaparte was entranced by his own rendition, and declared that next to Ossian, Homer was nothing but an old driveller.
Bonaparte did most of the talking, and while he made observations which were original and interesting, he was prolix in sweeping generalisations, holding for instance that the only subject worthy of tragedy in the theatre was politics, and that introducing love into a tragedy was merely to reduce it to comedy. How seriously he meant his perorations to be taken is debatable. On one occasion he began to rant against women in public life. 'Women are at the heart of all intrigues; they should be kept in their family circles and the salons of government should be closed to them,' he pronounced. 'They should be forbidden to appear in public otherwise than in a black dress and veil, in a _mezzaro_ like in Genoa and Venice.' He digressed wildly, skipping from one subject to another. One moment he was discussing Hannibal's military talents, the next he was indulging in flights of fancy. 'If I were master of France,' he declared one evening, 'I would like to make Paris not only the most beautiful city that ever existed but the most beautiful one that could ever exist. I would like to bring together in it all that was most admired in Athens and Rome, in Babylon and Memphis; vast open spaces embellished with monuments and statues, fountains at every crossroads to purify the air and wash the streets, with channels running between the trees of the boulevards surrounding the capital; monuments required for public utility, such as bridges, theatres, museums, whose architecture would be as magnificent as was compatible with their function.' All the skill and resources were there. All that was needed was 'an intelligence to guide them' and 'a government which loved glory'.
On 9 June the contingents from Genoa and Civitavecchia joined the main fleet off the south of Sicily, from where it sailed for Malta, the first object of the expedition. The island was the stronghold of the last of the great crusading orders, the Knights of St John, and its fortress at Valetta one of the most formidable in Europe. But the Order was in terminal decline and unloved by the population, its Grand Master Ferdinand von Hompesch weak and unpopular, its knights demoralised and the French ones mostly favourable to France. This was common knowledge, and several powers, including Britain, Russia, Spain and Naples, had been eyeing the strategic harbour with intent.
Bonaparte sent the Grand Master a message requesting to be allowed to take on water. When he received the reply that only four ships would be allowed into the harbour at a time, he took this as a hostile move and sent troops ashore. The forces of the Order put up a token resistance and fell back. Bonaparte sent the mineralogist Déodat Dolomieu, an erstwhile member of the Order, armed with a mixture of threats and bribes. It did not take long to come to an arrangement, and by 10 May Valetta had surrendered. Hompesch was promised a pension and a principality in Germany, his knights more modest compensation, and the French ones the possibility of moving back home or taking service in the French army. Bonaparte promptly put in hand the transformation of the administration of the island to bring the new colony into line with its metropolis. Titles of nobility were abolished, religious orders dissolved, the judiciary reformed on the French model, and non-criminal prisoners were freed, as were the mostly Muslim galley-slaves. A new French-style schooling system was set up, with the brightest in every year to be sent to Paris for their education (he even designed a uniform for them). The forms Bonaparte introduced were similar to those he had imposed in the Cisalpine Republic, and clearly indicated how he would like to see France itself reorganised. The Catholic Church was left in place, and the Jewish and Muslim faiths were granted equal standing. The treasury and assets of the Order were confiscated, along with those of the Church, which was stripped of everything not essential to its rites – reliquaries were melted down while chalices were left.
On 19 June the fleet sailed on, leaving behind a small garrison under General Vaubois. It now consisted of over 330 vessels, 'an immense city floating majestically on the sea', in the words of one passenger. It was loaded with around 38,000 soldiers and civilian passengers, over a thousand horses and nearly two hundred field guns, as well as seven hundred freed Egyptian galley-slaves. It covered an area of ten square kilometres, presenting a huge target. 'The possibility of an encounter with the British was on everyone's mind,' recalled an infantry officer.
The Admiralty in London had been alerted by its spies to the preparations being made at Toulon and elsewhere, but the reports varied considerably as to their purpose, some speculating about an invasion of England, others about the West Indies, India and Egypt. The Admiralty despatched a fleet under Admiral Horatio Nelson to the Mediterranean to blockade Toulon and destroy the French fleet if it put to sea. Nelson had arrived off Toulon on time, but damage from a sudden storm had obliged him to sail away for repairs and miss the French force's departure. He was now making a dash for Egypt in pursuit of it. He overtook it without spotting it and, on reaching Alexandria and not finding it there, doubled back, assuming it was making for England after all.
The French fleet arrived off Alexandria on 1 July, two days after Nelson had left. Bonaparte had intended to land enough men to secure the port there and sail on to Rosetta or Damietta, from where he could march along the Nile to Cairo, which he must seize quickly if he were to succeed. But when the French consul Magallon came aboard with news that Nelson had called there two days earlier, he realised the English would soon be back, so he decided to go ashore without delay. Disregarding the advice of Brueys he ordered immediate disembarkation in the bay of Marabout to the west of Alexandria, even though night was falling and the sea was rough.
The operation was carried out in small boats under sail which took only fifteen minutes to make it to shore, but a good deal longer to get back to the ships to take on more men. The horses swam ashore, held on leading reins by men in the boats. A number of men were drowned as some of the boats foundered on shoals, crashed into each other or capsized and others lost their equipment. Bonaparte was ashore by one o'clock in the morning of 2 July, and had a short sleep on the beach while his men continued to disembark. By two o'clock he was able to begin the march on Alexandria.
The previous day he had written to the pasha of Cairo, the Porte's governor, assuring him that he came as a friend. He also wrote to the French consul in Constantinople instructing him to explain to the sultan that he was only there to punish the Mamelukes who had been persecuting French merchants, and to defend the country on his behalf against the British. He was expecting Talleyrand to reach Constantinople soon and smooth any feathers that might have been ruffled. He was in for a surprise.
By the time they reached Alexandria its ramparts were bristling with troops and civilians who put up an unexpectedly fierce defence, those who had no weapons showering them with stones. They did not give up even when the walls were scaled, with the consequence that many of the inhabitants were put to the sword by the enraged attackers. They had never come across such 'fanatical' resistance. Combined with the sense of having entered a different world, it affected their view of the enemy, and of the civilian population. In Italy or on the Rhine, there had been no hatred between the soldiers on either side, and even less of the civilian population, which just wanted to be left alone. Here it was different. How different, they would soon find out.
## 15
# Egypt
Bonaparte was determined to reach Cairo as quickly as possible, and chose the most direct route. This turned out to be a mistake. The desert they found themselves marching through, so different from the cultivated landscape of Italy, had an immediate depressive effect on the troops. They were ill-prepared for the temperature, and had not been issued with water bottles. The first cistern they came to was filled with stones, and wherever they did come across water it was so brackish even the horses refused to drink it. 'We marched during the day under a sky and over sand that were equally scorching, without any shelter or water with which to slake our thirst,' wrote Eugène de Beauharnais. The blazing sun and the glare of the sand brought on blindness in some, while others thought they were going mad when they experienced mirages, for which nobody had prepared them. The cold desert nights brought little relief, as their paltry supplies ran out on the first day and the roving Mameluke horsemen prevented them from going in search of food and kept them awake.
Some died of heat stroke, others of exhaustion, many committed suicide. One soldier cut his throat in front of Bonaparte, shouting, 'This is your work!' It was unlike any war they had known. Those who failed to keep up with the marching columns were surrounded by groups of horsemen ready to pick them off, or worse. Bonaparte had delivered an address to his men, warning them that 'the peoples we shall be visiting treat women differently from us, but, in every country, he who rapes is a monster', but neither he nor any of his men had reckoned with another local custom.
He had managed to ransom some men taken by Mamelukes shortly after they disembarked, and these recounted how some of their comrades had been decapitated while they themselves had been beaten and sodomised by their captors. The news was unsettling as it spread through the ranks. Even once they had occupied the town, lone soldiers walking in the streets of Rosetta would be set upon and 'compelled to undergo this shocking outrage', as one wrote to his wife in France. In a letter to his brother Joseph, Louis Bonaparte reported that Rousseau had got it horribly wrong in believing primitive man was born inherently noble and was only spoiled by civilisation.
Buggery was the least of the perils awaiting those who fell into enemy hands. The Bedouin, Mamelukes and insurgent fellaheen regularly tortured and murdered prisoners. To make matters worse, there was a crossover between civilians and combatants, since many of the inhabitants were warriors when the need arose. There were few things more disturbing to regular European soldiers than the possibility that any 'civilian' might suddenly turn into a fighter.
After three days they reached Damanhur, where they found water, and pressed on towards Rahmaniya, where they were cheered by the sight of the Nile. The men leapt into the water and guzzled on watermelons, but morale did not improve much and discipline had all but disintegrated, and the troops took their exasperation out on the villages they passed through. Bonaparte's grandiloquent exhortations assuring them that their efforts would be of immense value for the 'civilisation and commerce of the world', and that 'Destiny is on our side!', sounded hollow. On 12 July he had the army parade before him and promised they would soon be on their way back to France, and then on to attack England. Three days later he was informed that one of his divisions was on the brink of mutiny. 'Courage on the battlefield is not sufficient to make a good soldier,' he admonished the men, 'he must also have the courage to bear fatigues and privations.' Some did rise to his challenge and, as one infantry officer put it, 'wished to live up to the Romans', but they were in the minority, and most blamed Bonaparte for his lack of foresight.
'The lives of many brave men who died of thirst, committed suicide or were assassinated during those terrible marches and the cruel sufferings of the army could have been spared,' noted Sergeant Vigo-Roussillon. 'All that was needed was for every soldier to have been supplied with a small can in which to carry water. The commanding general, who knew which country he was going to lead us into, is responsible for this carelessness.' They had been issued with some stale tack, and not enough of that. At Wardan on 17 July Bonaparte wandered among the troops listening to their complaints and promised them that in a few more days they would find meat and drink in Cairo, but they remained sceptical and morose. Some treated him with outright insolence.
His generals were hardly more respectful, with Berthier, Lannes and even the stalwart Davout complaining bitterly, and General Dumas (the father of the novelist) so critical that Bonaparte accused him of inciting mutiny and threatened to have him shot. Murat was more cheerful. Although he had been shot through the jaw at the taking of Alexandria, the ball, which penetrated below one ear and exited below the other, did not disfigure him. His abundant dark locks would soon hide the scars, and he wrote home triumphantly telling a friend to inform the beauties of Paris that 'Murat, though perhaps not as handsome will be no less brave in love'. He was the exception, and despondency spread through the army, particularly among the officers, who could not accommodate the supposedly heroic nature of their enterprise with the squalor of the reality.
The first encounter with a force of Mamelukes occurred at Chebreis on 13 July. It was no more than a skirmish, with horsemen galloping up to fire their carbines and pistols, seeking an opportunity to slash their way into the French ranks. They did not represent any real threat, but they were no less alarming for that. The onward march was executed in squares, with artillery at each corner, but although it was effective, it required huge effort. 'Every irregularity of the terrain lengthens or presses them in, the artillery hinders them, the wagons clutter them,' noted Sułkowski. 'As soon as the soldiers are tired, they fall behind or press together, bump into each other, and a terrible amount of dust concentrated in a confined space in which no air can circulate blinds and suffocates them.' One such march lasted eighteen hours without a break.
At the end of that, on 21 July, they came up against the main Mameluke army, led by Murad Bey, one of the two rulers of Egypt. Cairo was visible in the distance, and on the other bank of the Nile, the pyramids of Giza. This prompted Bonaparte to exhort his men with a stirring line about forty centuries of history gazing down on them from the top of the pyramids. What impressed the troops more than some nonsense about antiquity which few of them would have understood was the magnificent spectacle that unfurled before their eyes as the Mameluke cavalry galloped up. 'The splendour of their attire and their arms reflected the rays of the sun at us and dazzled our sight,' recalled Captain Moiret. The French were fascinated by their horsemanship and military skill, which, even though it was of another age and bound to fail when confronted by volleys of musketry, was extremely effective when the Mamelukes did manage to cut their way in among the enemy and slice off arms and heads with their scimitars. The outcome was never in doubt. The French held their squares and overpowered the Ottoman foot-soldiers, many of whom were killed or drowned in the Nile trying to escape. The Mamelukes left the ground strewn with corpses, abandoned forty guns and their camp, with its baggage, horses and camels. After the battle this turned into a market as soldiers traded booty.
The next day, 22 July, a delegation from Cairo surrendered the city, and two days later Bonaparte made his triumphal entry. He took up residence in the house of a Mameluke bey, in which he occupied the first floor and accommodated his staff below. It had a garden with trees and pools in which he strolled while giving orders to his staff and administrators. He was delighted by what he had seen of Egypt, and was convinced that given some organisation and sensible development it would flourish. 'The Republic could not wish for a colony within easier reach with such rich soil,' he wrote to the Directory that evening. 'The climate is very healthy, because the nights are fresh.' But at this moment of triumph he endured a heavy personal blow.
When he parted from Josephine at Toulon their relationship was as tender as ever. Bonaparte wrote frequently, saying he would bring her to Egypt as soon as it was safe, and she fully intended to go. In the meantime, she went to the spa at Plombières, from where she wrote to Barras asking for news of her husband. 'I am so sad to be parted from him that I am overcome by a melancholy which I cannot vanquish,' she wrote. 'I am therefore hastening my prescribed cure so that I may quickly be able to go and join Bonaparte, whom I love very much despite his little faults.' She was planning to travel in the company of Marmont's wife, but at the beginning of July a balcony that she and others were standing on collapsed under her and she was so badly hurt that there could be no question of going soon.
'I have much, much domestic sorrow, for the veil has been lifted entirely,' Bonaparte wrote to Joseph the day after his entry into Cairo. Every time he had been told of Josephine's infidelities she had managed to lie her way out of it and make him feel unworthy for having believed what she dismissed as spiteful gossip, but on the evening of his entry into Cairo, Junot, Berthier and his aide Thomas Jullien presented him with incontrovertible evidence. He poured out his grief and indignation to his stepson Eugène. He confessed to Joseph that he wanted to return to France and shut himself away from people, and asked him to find him a house somewhere deep in the country. 'I am fed up with humankind,' he wrote. 'I need solitude and isolation; greatness has damaged me; all feeling has dried up. Glory already lacks lustre at the age of twenty-nine; I am all used up. There is nothing left for me to do but become a complete egoist!'
He had little time for introspection. Murad Bey might have been defeated, but his colleague Ibrahim was hovering in the vicinity with another force. Bonaparte marched out of Cairo on 9 August. He only managed to catch up with Ibrahim's rearguard, which he defeated in a protracted cavalry battle at Salayeh, but having obliged the Mamelukes to retire into the desert, he turned back towards Cairo. On his way, on 14 August, he received news that altered everything.
At 2.45 p.m. on 1 August one of Nelson's ships, HMS _Zealous_ , had spotted Admiral Brueys' squadron at anchor in Aboukir Bay, and by dawn the next day it had ceased to exist. Only two ships of the line and two frigates managed to get away. The rest were sunk or captured, and the _Orient_ blown up, with Brueys on board. Bonaparte took the news calmly. He declared that they had to face up to the new state of affairs and show themselves to be 'as great as the figures of antiquity', and began contemplating the implications of not being able to return to France any time soon.
He lost no time in laying the blame on Brueys, whom he had instructed to take his ships into the harbour of Alexandria or else sail to Corfu. Brueys had decided against the former, fearing his ships might get stuck in the shallow entrance to the harbour, and he had delayed until he was sure Bonaparte did not need to be evacuated. The aide bearing Bonaparte's definite order to leave the bay of Aboukir never reached him, as he was killed on the way, but he would have arrived too late. Brueys' lack of resolution was partly the consequence of a general demoralisation in his squadron and his lack of faith in his crews and the state of his ships. He had disposed them unwisely, allowing the British to sail between him and the land, which meant that he received broadsides from both sides, so responsibility for the disaster must rest with him. Having taken the precaution of distancing himself from it, Bonaparte did write his widow a moving letter praising him as a hero.
Bonaparte was determined that the enterprise should bear fruit despite the naval disaster. His first priority was the health of his troops. He established four hospitals in Cairo, and one each in Alexandria, Rosetta and Damietta. He imposed quarantine on all the ports under French control and introduced measures covering the rapid burial of the dead, street-cleaning and rubbish collection. He ordered his chief physician, Dr René Desgenettes, to study the causes of the dysentery and ophthalmia that had attacked the troops. He gave orders for them to be issued with loose-fitting uniforms more suited to the climate – blue cotton jackets with no facings or tails and a sheepskin cap with a woollen bobble of different colours to distinguish the units from each other.
He ordered the man in charge of uniforms, François Bernoyer, to design a new one for the medical staff, suggesting the colour brown so blood would not show. Bernoyer was also given the task of designing the uniform for a new corps of camel-mounted Guides. The upshot was the normal French military hat with its front turned down to form a sunshade, surmounted by red ostrich feathers, a green 'Greek-style' waistcoat with 'Hungarian' gold embroidery, a 'Turkish' belt, crimson trousers 'à la mamelouk', 'Roman-style' slippers, scarlet 'Polish-style' coat trimmed with gold, and a green cloak. Bonaparte was delighted with the design, and surprised Bernoyer by showing it. 'When one does something for him he does not usually show the slightest approbation, let alone pleasure,' Bernoyer explained. 'In that, he reminds one of the attitude of children, who always seem to want more.'
Bonaparte put in place a new administration, began minting money, brought in a system of taxation based on wealth, introduced street lighting and put in hand a land registry. The benefits of European civilisation bestowed upon the new colony included the introduction of windmills to replace hand querns, new crops and the production of everything, from gunpowder to cloth, that the army would need now that it was cut off from France.
On 22 August he created the Institute in Cairo, and the savants were put to work on the most pressing and practical tasks. 'Some are working out ways of making beer without hops, others with a simple method for the purification of Nile water, others busy themselves with the building of ovens, others still with framing legislation for the country, building wind-powered machines for moving water, etc., etc.,' the zoologist Geoffroy de Saint-Hilaire wrote to his father. Other subjects investigated were the sexual organs of crocodiles, the date palm, magic, dancing, the true colour of the sea, prostitution, the ostrich, sand and the formation of dunes. One group, mainly archaeologists and artists, were sent off with General Desaix, who marched up the Nile on 25 August in pursuit of Murad Bey. His orders were to defeat him and chart the course of the Nile as far south as he could. He was to occupy Thebes, which the archaeologists were to explore, and the port of Koseir on the Red Sea, and to set up a network of forts along the Nile. Wherever the French went, everything, from ancient ruins to geographical and physical phenomena, was to be recorded and studied.
Bonaparte was living out a dream. From his earliest years he had shown a passionate interest in progress as he, and his generation, saw it. He had also shown a remarkable proclivity for organisation. He was now effective ruler of a huge, backward country with a self-imposed mission to civilise it, and could give rein to his most basic instinct of imposing order. 'I was never again as free as in Egypt,' he would later reflect. He did not mean to apply Western forms indiscriminately, but dreamed of a fusion, believing he would be able to organise the country and civilise its inhabitants without offending their sensibilities. He had, primarily from his reading of Voltaire's play, formed a view of the Prophet Muhammad as a kind of wise tyrant, and thought he could understand how his followers responded to authority. He dreamed, as he would later put it, of writing a new Koran.
The organs of administration he established were on traditional forms of _ulemas_ and _diwans_. Officials were under French supervision, often through the agency of local Copts, and were made to wear tricolour cockades and sashes of office, but allowed to administer in traditional ways. He believed he would be able to introduce European forms and practices gradually once he had gained their confidence. They referred to him as 'Sultan Kebir', which flattered him and gave him the impression that they were responsive. He made grand gestures to win their approval, such as publicly liberating the Muslim galley-slaves he had found in Malta and promising to assist the caravan taking pilgrims on the _Haj_. On 18 August he presided over the annual ceremony of the opening of the dykes. Surrounded by sheikhs, he distributed coins to the people as the water was released into the canals that would irrigate the surrounding countryside. On 23 August, the feast of the Prophet, he paid his respects to the Divan of Cairo, and in the evening attended a banquet, at which all the French made great show of respect for the Islamic faith, although afterwards they laughed at the charade. He did not; he was convinced he had captivated the locals.
On 22 September, the anniversary of the founding of the French Republic, Bonaparte staged celebrations meant to underline his loyalty to the French state, boost the morale of his troops and impress the locals. An amphitheatre was created with two columns at its centre representing the Republic, a triumphal arch commemorating the victory at the battle of the pyramids, an obelisk dedicated to the fallen, and so on. A turban featured alongside the red Phrygian bonnet of liberty. All the troops in Cairo were present, drawn up in parade order, and listened as Bonaparte recalled their glorious deeds over the past five years and assured them that a fine destiny awaited them: they would be immortalised in death or on their return home as heroes. He ended with the cry ' _Vive la République!_ ', which normally elicited a hearty cheer, but on this occasion hardly a mutter came out of the serried ranks. They were in no mood to celebrate. 'The army showed only indifference for this feast,' recalled Captain Pelleport. 'It was suffering from _spleen_ that day, which it often did after the loss of the squadron.' The parade was followed by a banquet which the local dignitaries and the soldiers appeared to enjoy more than the official proceedings. Sporting events and horse races were held, and the day ended with fireworks and illuminations.
At the news of the destruction of the fleet there had been much cursing of Bonaparte, who was accused of adventurism and ambition. Some of his generals made defiant statements, but the pointlessness of such talk, and the lack of any prospect of returning to France soon, concentrated minds on making the best of the situation. Cairo would have to make do for Paris. Many found themselves fine houses with gardens, and enjoyed the exotic comfort they provided.
The city contained a number of European residents, mostly traders of one sort or another, and they were quick to spot the opportunities offered by the influx of homesick Frenchmen. They opened shops, coffee houses, Turkish baths and other amenities. Officers and men trotted about the city on donkeys, lounged in the cafés delighting in the hookahs and coffee, and went on excursions, particularly to see the pyramids and other ancient monuments. French ingenuity was stretched to provide comforts of every kind. Balls were held and a theatre built, in which, owing to the lack of women willing to act, young men had to take the female roles.
Yet none of this could cure the underlying homesickness. 'Whatever efforts are made to provide for the well-being of the troops, to keep up the spirit of emulation among the officers, memories of France torment most of them and the officers much more than the men, and the generals and staff officers much more than the officers of the line,' noted Lieutenant-Colonel Théviotte. 'People only address each other to exchange regrets at having left France and to express the desire to return. The deprivation of women is that which is felt most keenly.'
On arrival, most of the senior officers had taken over the wives of prominent Mamelukes along with their houses, but having satisfied their lust they found them wanting and passed them down the ranks. The men were mostly horrified by the local women, mainly because respectable ones were locked away by their families and the only ones they saw were either old, ugly, or prostitutes. A market developed, and a black woman could be bought for 500 francs, 800 if she were a virgin, while Caucasian women cost several thousand. Eugène de Beauharnais bought himself a beautiful black woman, and so presumably did Junot, since he sired a boy whom he called Othello and brought back to France. Despite Bonaparte's ban, possibly as many as three hundred of his men had smuggled their wives or mistresses onto the ships disguised as soldiers, and given the scarcity of European women, these now had the pick of the higher ranks.
Bonaparte had some local girls brought to him, but although he later praised their grace and beauty, he rejected them as too fat if not downright repellent. He dallied briefly with the sixteen-year-old daughter of a sheikh, but was more at home with French women. It was rumoured that he had an affair with the wife of General Verdier, who had accompanied her husband in the uniform of an aide-de-camp.
At the ball which followed the celebration of the birth of the Republic, Bonaparte spotted 'a little woman some twenty years old, charming, plump, vivacious', and took an immediate shine to her. She was Marguerite-Pauline Bellisle, a dressmaker's assistant from Carcassonne, locally known as Bellilotte. She had just married a Lieutenant Fourès when his regiment was assigned to the Egyptian expedition, and decided to follow him. The day after the ball, Bonaparte ordered Junot to invite her and her husband to lunch, and by a subterfuge she was lured into a separate room alone with Bonaparte. She resisted him, and went on doing so stoically despite his showering her with gifts and letters, but finally gave in and they became lovers. Bonaparte was by all accounts besotted by her, and they spent every available moment together, she often riding out with him dressed in uniform. She wore a miniature of him around her neck and he a locket of her hair around his.
Fourès was promoted and sent to Paris with despatches to the Directory, but his ship was taken by the British, and as he had fallen ill they released him on parole and he was back in Alexandria in April 1799. Bonaparte, who was considering marrying Bellilotte but waiting to see whether she would give him a son, asked for Fourès' assent to a divorce, which he was only too eager to give. He was sent away again, just in case. So was the mineralogist Louis Cordier, who had apparently caught Bellilotte's roving eye.
To reinforce his authority, Bonaparte founded a paper, _Le Courrier de l'Égypte_ , which built up his image, and to advertise what he was doing as a triumph of European Enlightenment over backwardness, he started another, _La Décade égyptienne_. He attended sessions of the Institute, discussed religion and local custom with imams, and visited the pyramids and other remains. He went to Suez to look for the ruins of the original canal, which he was excited to discover. He was also fascinated to find the Wells of Moses and other places associated with the scriptures, even crossing the Red Sea at low tide and nearly being trapped when it came in.
'Everything is going perfectly here,' he assured the Directory on 8 September. 'The country has been subdued and is beginning to get used to us.' He went on to list the advantages of France's new colony, and expressed the view that its possession should facilitate reaching a satisfactory peace with Britain. He argued that they should move the whole French navy into the Mediterranean, which would not only improve communications but also force the British to bear the strain and expense of maintaining battle squadrons far from home and friendly bases, which would in the end force them to the negotiating table. He was preparing to build a naval base at Suez to open up communications with French colonies in the Indian Ocean.
On 21 October a revolt broke out in Cairo. It was quickly put down, but it cost a number of lives, including that of one of Bonaparte's favourite aides, Sułkowski. It had been started by young students from one of the mosques, and only spread to other disaffected groups when the rumour got about that Bonaparte had been killed. The reasons behind the discontent included annoyance over taxes, street-cleaning regulations and the land registry which obliged the inhabitants to list their properties. It had not been a grassroots upheaval, and numerous locals had sheltered Frenchmen from the insurgents.
The next day, Bonaparte received the sheikhs and imams and announced that he forgave the city and would not exact any retribution. He delivered a theatrical address, stating that God had instructed him to show mercy and urging them to inform those who had raised a hand against him that they would find refuge neither in this world nor the next. 'Could there be on Earth any man so blind as not to see that it is destiny itself which directs my actions?' he asked rhetorically, before going on to represent himself as a kind of messiah who had been foretold in the Koran, one who knew how to read in their hearts, a superior being against whom all human efforts were vain. He kept on making pronouncements and gestures intended to demonstrate his openness to what he saw as the spirit of the Orient, even though his ultimate intention was to turn Egypt into a French colony.
A child of the Enlightenment, Bonaparte held a set of assumptions and prejudices which he took to be universal. Having moved away from Rousseau's belief in his inherent goodness, he had moved on to the view that man is a rational creature guided by self-interest yet susceptible to being inspired by ideals. He therefore took it as self-evident that when shown the benefits of French administration and technological progress, the inhabitants of Egypt would embrace them. He had liberated them from the cruel incompetence of the Mameluke beys, he had cleaned up and lit the streets of Cairo, he was bringing them civilisation. He had taken the trouble to acquaint himself with their religion and had made a rational assessment of it which was not entirely superficial. He thought the absence of the kind of hierarchy and ritual which characterised the Catholic Church would make Muslims more open to reason. What he failed to grasp was that Islam represented a mentality as much as a faith, and that was fundamentally at odds with Christian and secular Western values, along with their underlying assumption of superiority. He deluded himself that he was gaining acceptance because many styled him with Arab titles and kissed his hand. But however charming they may have shown themselves on occasion, they were at best not interested and regarded him as an alien intruder. Ironically, many of the measures he took would serve as a model for Mehmet Ali when he took over Egypt in 1805, but a Muslim could do what a Frenchman could not.
It took Bonaparte some time to appreciate that people obeyed only out of fear, and that showing mercy or consideration were seen as signs of weakness. He began beheading transgressors as an example, taking hostages or razing villages whose inhabitants had attacked his men. This did not achieve the desired results, as the locals saw it not as just punishment but as unwarranted aggression, and only waited for chances of retaliation. It was only then that he understood reason and logic had no purchase, and began showing he meant business by shooting and beheading suspects almost at random. The locals responded in kind, cutting off the arms, legs, noses, ears or genitalia of prisoners, usually after sodomising them, or beheading, flaying or burying them alive. Outside Cairo and the other towns, the French occupation remained frail.
This was the more alarming as the second assumption on which the viability of the Egyptian venture had been predicated now crumbled. The first had been that Egypt was within reach of France and therefore easier to protect and exploit than more distant colonies, but the destruction of the fleet in Aboukir Bay had made it as vulnerable as the Caribbean ones it had been meant to replace. The second assumption had been that the Ottoman Porte would remain neutral. Yet having packed Bonaparte off on his pet venture, Talleyrand had failed to carry out his part in the plan. Bonaparte had written to him from Cairo, telling him he could inform the Sultan that the Islamic faith and mosques were being protected, pilgrims to Mecca were being assisted, that he had personally attended the feast of the Prophet, and that Turkish shipping and interests were being respected. Yet not only did Talleyrand not go to Constantinople, he had entirely omitted to approach the Porte, which was astonished to discover that a French army had invaded its dominion.
News of Nelson's victory emboldened the Sultan to declare war on France. British supremacy in the Mediterranean prompted the kingdom of Naples to do likewise. Russia, which had long been eyeing the Ionian islands as a potential naval base, buried its hatchet with the Porte and signed an anti-French alliance with it on 23 December and with Britain on 29 January. Two Ottoman forces gathered to expel the French from Egypt. One was to march from Syria under the command of Djezzar Pasha of Acre, the other was to go by sea and land at Aboukir.
Bonaparte had two options: either to wait for the attack in the hope that Djezzar's force would be weakened by a march across the Sinai desert and the other could be prevented from landing, or to attack and defeat one force before the other could be deployed. If he were to defeat Djezzar and take Acre, he would at the same time deny the British squadron blockading Egypt one of its bases, thus opening up the possibility of communication with France. The fall of Acre might also frighten the Porte into making peace.
He therefore left Desaix in Upper Egypt to contain Murad Bey and Marmont at Alexandria to defend the coast, and marched out himself on 10 February 1799. It was just this kind of snap decision that had enabled him to triumph over successive Austrian armies in Italy, and a victorious outcome would open up all sorts of possibilities. He was, as he would later confess, carried away by the dreams they gave rise to.
## 16
# Plague
'All we could see in this new project was another chance of glory as well as incalculable hardships,' recorded Captain Moiret, adding that the moment his men had been told they were to march out to Syria the grumbling ceased; they set off in high spirits on 6 February 1799.
Bonaparte assumed that after a quick march his advance guard would capture the presumably well-stocked fortress of El Arish, and he did not take sufficient supplies with him. As the troops marched over the Sinai, hugging the Mediterranean coast, they ran out of victuals and were reduced to drinking brackish water and eating seaweed, which gave them dysentery. 'We ate dogs, donkeys and camels,' Bonaparte admitted to Desaix. It was not just the troops who were grumbling by the time he joined his vanguard at El Arish on the evening of 17 February. His generals too were fed up, and his theatrical rhetoric only irritated them. General Kléber, an experienced soldier who had served in the Austrian army before the Revolution, was difficult to ignore with his Homeric stature, booming imperious voice and tendency to use it to say what he thought. 'Never a proper plan, everything goes by leaps and bounds, every day rules the action of that day,' he declared of Bonaparte's method. Yet even he had to admit that this 'extraordinary man' possessed something which set him apart and lent him an authority he could not dispute. 'It is to dare, and to keep daring, and he carries that art to the limits of temerity.' That capacity was to be tested severely over the next weeks.
Desperate to move on but fearful of leaving possibly mutinous generals behind to continue the siege, Bonaparte offered the garrison of El Arish generous terms, and it capitulated on 20 February. The men were allowed to leave with their arms and baggage under oath that they would not bear arms against France for twelve months. The chief surgeon of the Army of the Orient, Dr Dominique-Jean Larrey, disinfected the fort against the plague, which had broken out in the area, and established a hospital before they set off for Gaza.
They were now marching through fertile country, but under drenching rain that turned the tracks to seas of mud. Entering Gaza after a brief skirmish, Bonaparte made a pompous speech informing the inhabitants that he was bringing them liberty. He addressed the griefs of his own men with an order of the day full of references to the Philistines and the Crusaders. To some soldiers who complained of lack of food he said that the Roman legionaries had eaten their leather equipment but kept going.
On 3 March they reached the pretty town of Jaffa. The officer sent under a white flag to summon its defenders to surrender was beheaded and his body thrown into the sea. This enraged the troops, who after three days of siege stormed the defences and entered the town. While the soldiers who had been defending it withdrew to a citadel, the French unleashed their rage on the mainly Christian population in an orgy of looting, rape and murder. 'One would require very dark colours in order to paint the hideous scenes which took place,' recorded one officer. Worse was to follow.
Two of Bonaparte's aides, his stepson Eugène and Captain Croisier, had persuaded the soldiers holed up in the citadel to surrender by assuring them their lives would be spared. When he saw them filing out, Bonaparte flew into a rage with his stepson, asking him what he was supposed to do with them, given that he could neither feed them nor spare men to escort them back to Egypt. As they were mostly the same men who had been released on parole at El Arish, after deliberating for some time with his senior officers he concluded that they all deserved to be shot. When Berthier pleaded for their lives, Bonaparte told him to go and join a monastery. Over the next couple of days some 1,500 to 2,000 men (accounts vary) were led out onto the beach and shot, bayoneted or drowned. According to one officer, 'the heart of the French soldier heaved with horror', but it had not done so during the sack of the town, after which the camp had turned into a bazaar where loot, including women, was traded.
Bonaparte's decision to execute the prisoners was seized on by the British and has been made much of by his detractors ever since, but cities which resisted generally suffered the consequences, and British troops behaved no better during the concurrent war in India against the Mahrattas, or later in the Peninsular War; the Spanish and British treatment of those who surrendered at Bailén would be a good deal less humane. The morality of the time was far removed from present-day standards, and it was accepted that a general had to put his own men first.
They may have expressed reservations, but the nerve required to act decisively earned Bonaparte the respect of his officers and men. Visiting the town, he inspected the hospital and impressed his entourage by walking among the plague victims, talking to and touching them. To set an example to reluctant orderlies, he allegedly approached one patient, 'pressed the bubo and forced out the pus'. Whether he actually did this or not, the story circulated among the troops, enhancing his standing.
Image was important, and Bonaparte could not be accused of underestimating its power. 'You should know that all the efforts of humans are powerless against me, as everything that I undertake must come to pass,' he announced in a proclamation to the inhabitants of the area. 'Those who declare they are my friends prosper. Those who declare themselves my enemies perish.' In another, to the inhabitants of Jerusalem, he warned that 'I am as terrible as the fire of heaven to my enemies, clement and merciful to the people and to those who wish to be my friends.' Some of his entourage were growing anxious over what appeared to be an increasingly delusional sense of his role, and expressed fears that he was being carried away by belief in his 'fate' and his 'destiny'. He may by this stage have been bolstering himself psychologically in a situation which was growing increasingly perilous.
The army marched on to Acre, which it reached on 19 March. The city was the seat of the Ottoman governor of Syria, Djezzar Pasha (Ahmad Pasha al-Jazzar), a Bosnian by origin, known colloquially as 'the butcher' (in 1790 he had drowned all the women of his harem and honoured his favourite by personally eviscerating her). Bonaparte sent him an offer of accommodation, stating that there was no reason for them to be enemies. The Pasha's response was to massacre the Christian population of the city.
Bonaparte's siege artillery, which had been sent by sea, had been intercepted by the British, and many agreed with Kléber, who said bluntly that it would be impossible to take a place defended by European methods with Turkish ones. Bonaparte ignored them, and the first assault, on 28 March, nearly succeeded. Two days later the defenders made a sortie, which was successfully repulsed. On 1 April Bonaparte made a second attempt to storm the defences, in which he was nearly killed by an exploding shell, and this was followed by another sortie, which was also repulsed.
Meanwhile Ottoman forces were gathering to relieve Acre, with some 7,000 warriors from Nablus and 40,000 under the Pasha of Damascus moving south. Bonaparte sent Murat with 500 infantry and 200 cavalry out to confront him, while Junot covered his flank at Nazareth with a smaller force. Junot was himself assailed by superior forces and Bonaparte sent Kléber to assist him, but they both found themselves facing more than ten times their own number at the foot of Mount Tabor. They sent urgent messages to Bonaparte and held off the Turks for a full day before being relieved on 16 April by Bonaparte, who had made a night march of forty kilometres.
The following day he visited Nazareth, where he attended mass and stood godfather to a soldier who wished to be baptised. Two days later he was back at Acre planning another assault. This, and the next one, failed just as the first two had done. Without siege artillery the only way to breach the walls was to dig tunnels and trenches in order to place mines underneath them, a painstaking and dangerous business at the best of times. It was made no easier as, being low on powder and shot, the French artillery could not supply adequate covering fire, while the British naval squadron under Commodore Sydney Smith was not only resupplying the defenders, but also bombarding the French trenchworks.
Most of Bonaparte's generals were by now clamouring for him to give up and return to Cairo. He was regularly hissed and booed by the troops, but he insisted on trying yet again to take the fortress. There was undoubtedly an element of personal pique involved: this was his first setback, and he could not accept it, the more so as the man directing Sydney Smith's guns was Le Picard de Phélippaux, a hated classmate from Brienne who had emigrated and fought against the Republic. A weightier motive for Bonaparte's determination to take Acre was that the Druze and the Shiite Muslims who made up the population of the region were keen to rise up against their Ottoman overlords; if Bonaparte could crush Djezzar, he would be able to raise the whole region, march on Damascus and Aleppo and force the Porte to switch sides, thus denying all facilities in the eastern Mediterranean to the British and confirming France's possession of Egypt. But the prospect was dim: news had begun to trickle through that in Europe the coalition against France had gone over to the offensive.
Following the failure of a final assault on 10 May, Bonaparte accepted the inevitable. He sent a report to the Directory announcing that he had destroyed Acre, which, he assured them, was not worth holding on to as it was a ruin full of plague victims. As usual, he diminished his losses. He despatched another declaration to the Divan in Cairo which made even more outrageous claims – that Djezzar was wounded, that he had sunk Turkish ships, and so on. Before striking camp, he praised his troops in an address which suggested that although they had been about to capture Acre they were needed more urgently elsewhere, and promised them more glory ahead.
The march back to Cairo took twenty-five days, and they were among the worst many of the soldiers would remember. They trudged in temperatures in the forties, with no shoes to protect their feet from the scorching sand, and at night the rags to which their uniforms had been reduced could not protect them from the cold of the desert night. They only found food and water sporadically. Many of them were wounded and some sick; those who could not walk were carried on improvised stretchers.
Before striking camp outside Acre, Bonaparte had suggested to Dr Desgenettes that those suffering from the plague and those so badly wounded that they could not be moved should be given fatal doses of laudanum, assuming that if they were left behind they would fall victim to the barbarous practices of the enemy. Desgenettes replied that his duty lay in preserving not ending lives. Bonaparte then approached the pharmacist Boyer and ordered him to prepare the potions. There is no certainty as to what followed, at Acre and at Jaffa and Tentura, where there were also several hundred sick and wounded. The available evidence is wildly discrepant, all of it written down after the events. The British press, conflating Acre and Jaffa, painted a black picture of the evil French general poisoning hundreds of his men. Defenders of Bonaparte's reputation either dismissed the story entirely or brought the number down to a handful of the dying. A careful reading of the evidence suggests that a potion was administered by Boyer on Bonaparte's orders to about twenty-five men, some of whom vomited and survived.
Before leaving Jaffa, Bonaparte ordered all carriages and carts, and horses not pulling field guns, including his own, to be used for the evacuation of the sick and wounded. He gave detailed instructions as to the separation of the sick from the wounded and how they were to be transported. When his groom suggested he keep at least one horse for himself, Bonaparte struck him with his riding crop in fury. He showed his exasperation and dealt out harsh reprimands. He had vented his anger on the 69th Demi-Brigade when it fell back during one of the assaults on Acre, accusing the men of cowardice and having nothing between their legs, and suggested he would put them in skirts instead of breeches when they got home. In the interim he made them march with their muskets butt-end up.
The march from Jaffa to Cairo was the worst part of the retreat, and despite Bonaparte's orders the sick and wounded were dumped by those whose horses had been requisitioned to transport them, and left to die or be decapitated by preying Bedouin. At the same time there were acts of self-sacrifice, and some did slow down to help the walking wounded keep up with the columns.
The Syrian campaign had been an unmitigated disaster. Bonaparte had lost at least 3,000 men, and by some estimates as much as one-third of the force he had set out with had been put out of action. Even those who had never criticised a decision of his expressed the opinion that he should not have embarked on the campaign. At the same time, the episode had demonstrated one thing – that Bonaparte, a man of twenty-nine in charge of an undisciplined army in many cases little better than a rabble, led by unruly generals many of whom resented or even hated him, with no superior authority to support him, was able, in the face of defeat, plague, adverse conditions and lack of supplies, to pull that force together and maintain authority over it. The Syrian campaign had tested his mettle, and shown that he was up to the challenge.
Ever aware of the power of appearances, he prepared his return to Cairo carefully. His uniform officer was put to work, replacements were despatched from every available store, and the remnants of the Syrian expedition were kitted out with the greatest possible panache. Bonaparte entered Cairo at their head through a victory arch with bands playing, marching over streets strewn with palm fronds. Having crossed the city from end to end the columns made their way around it and marched through once again, an operation lasting for five hours designed to confuse anyone who might have been trying to count how many men he had lost.
Back in Cairo, Bonaparte carried on as though nothing had changed, and continued to send optimistic reports to the Directory (many of which never got through, as they were intercepted by the Royal Navy). On 19 June he not only expounded on the advantages of Egypt as a colony for France, but also devoted much ink to criticising the way the French navy was organised. He was building a couple of corvettes at Suez, and was shocked when a French vessel was blown up by a single shot from a British ship as a result of negligence. The French navy would never be of any use, he argued, while the practices brought in during the Revolution survived and until the captain was given absolute authority.
He was confident that he could make up his losses in men by the purchase of a couple of thousand black slaves who could be incorporated into his units. He nevertheless pressed the Directory to send more men, and particularly arms. From his despatches and correspondence it is clear that he found the challenge of running his own fief exhilarating. He had begun to treat the army as his legion, distributing sabres of honour not in the name of the Republic, but his own. He courted the natives, prefacing every statement with the words: 'There is no other god than God, and Mahomet is his Prophet!'
He also attended meetings of the Institute, which had been carrying on its work throughout this time, but at a session on 4 July he ran into trouble when he blamed the lack of success in Syria on the plague and the inability of the physicians to find a cure. He argued that by treating it as a contagious disease, they had undermined morale, and that for the general good it would be better to declare it to be non-contagious. Desgenettes insisted that scientific integrity demanded the truth be told. Bonaparte denounced him and his kind as fastidious theorists, to which the doctor responded by accusing him of despotic leadership and lack of foresight, and laid the blame for all the carnage and death during the Syrian campaign at his door.
On 15 July at the pyramids, where he was encamped, Bonaparte received news that a Turkish fleet had appeared off Aboukir. He quickly gathered a force of some 10,000 men and marched north. The Turks disembarked between 10,000 and 15,000 men and entrenched on the narrow peninsula with the fortress of Aboukir at their back.
On 24 July Bonaparte pitched his tents about seven kilometres from Aboukir. It would not have taken him long to assess what had to be done once he had seen the Turkish positions. Yet that night when everyone else was asleep Michel Rigo, a young painter who had been allowed to bed down in the same tent as Bonaparte and his staff, saw the general get up in the middle of the night and go over to a table on which maps were spread. He observed him pore over them, measuring distances with a compass, pace up and down, return to the table to study the maps again, belabouring the table with a small knife, and then step into the opening of the tent and stare for a long time into the distance.
At dawn two divisions, under Lannes and Destaing, attacked the enemy line, while Murat's cavalry broke through at its extremity and swept into its rear. The Turks had nowhere to retreat to, and most ran into the sea in an effort to reach their ships. Those that did not drown were taken prisoner. Within the space of an hour some 3,000 had been put out of action. Bonaparte then attacked the fortress. The initial assault was repulsed and the defenders rushed out to decapitate the wounded, whereupon the French surged forward and drove the entire Turkish army into the sea. The final toll was 10,000–12,000 Ottoman dead, mostly drowned, to 250 French dead and about a thousand wounded. 'It is one of the finest battles I have seen,' Bonaparte wrote to General Dugua.
He had been at the forefront, directing the troops under a hail of bullets which killed several around him. When one of his aides was struck by a cannonball, 'then, the whole of this army which only yesterday was insulting him during its long and painful march, and seemed for some time to have drifted away from him, uttered a cry of horror', recalled one sergeant. 'Everyone trembled for the life of this man who had become so precious to us, while, only a few moments earlier, he had been universally cursed.' The sergeant's feelings that day were by no means isolated. 'The army had to believe, like him, in fate,' wrote another soldier, 'for it seemed as though he had it written on his forehead that cannonballs and grapeshot must respect his person.' Even the obstreperous Kléber was impressed. After the battle he embraced Bonaparte, with the words, 'General, you are as great as the world!'
The great man spent the next ten days at Alexandria before returning to Cairo. He had much to ponder. The victory of Aboukir ensured that the Ottomans would not be menacing Egypt in a hurry, so he was safe to continue organising his colony. But developments in Europe raised alarming questions. Although he had been cut off from France since the destruction of the fleet, he was kept informed, by small French naval vessels which got through and by neutral shipping, which brought news and even despatches. The British ships of Sydney Smith's squadron blockading the Egyptian coast also regularly communicated with the French on shore, passing them copies of English newspapers.
French gains in Italy had been almost wiped out, and the situation on the Rhine was precarious. It looked as though the coalition might succeed in invading France and toppling the Republic. Bonaparte could hold Egypt and await better days, but if there were to be a Bourbon restoration in France, his future would be bleak. The Republic was in peril, and it must be saved, both because he genuinely believed in it, albeit better governed, and because he had committed to it to such an extent that he would never have a future under any other system.
He had never meant to spend long in Egypt, and had been considering a return to France for some months. There is evidence to suggest that he colluded with Sydney Smith to make this possible, the Englishman seeing in it a chance to get him out of the way, which he supposed would make the French left behind more likely to capitulate. Either way, Bonaparte had already made arrangements for a couple of frigates and two smaller craft to be made ready.
He was back in Cairo on 11 August. Two days later he attended the feast of the Prophet, giving every appearance of intending to continue governing the colony. On being informed that Sydney Smith's squadron had sailed for Cyprus to take on supplies, he and those he had selected to go with him made their final preparations. Officially, he was going to sail down the Nile on a tour of inspection. On the evening of 17 August he called on Bellilotte to say goodbye. He had meant to take her with him, but changed his plans and she was to follow (when she did, she was captured by the British and did not return to France until after Bonaparte had taken power; he never saw her again, but would find her a husband and buy her a château).
He sailed down the Nile to Menouf, where he took a parade of the 32nd Demi-Brigade. 'Don't look so sad,' he said to them. 'Before long we will all be drinking wine in France.' Sergeant Vigo-Roussillon thought he looked preoccupied and anxious, while Lannes, Murat and others in his suite were beaming. The next day he was off, supposedly to inspect various French positions, and on 22 August he turned off his planned route and made for the coast at a point to the west of Alexandria.
Two frigates, the _Muiron_ and the _Carrère_ , rode at anchor a short distance from the shore, along with two xebecs (small three-masted vessels), the _Revanche_ and the _Fortune_. At midnight Bonaparte and his party embarked, jostling each other regardless of rank to pile into the longboats in their anxiety not to be left behind.
The four vessels, under the command of Rear-Admiral Honoré Ganteaume, weighed anchor in the early hours. On Bonaparte's orders they hugged the coast, sometimes sailing only at night. He was terrified of being captured by the British, and preferred the option of putting ashore anywhere and taking his chances. 'Suppose I were taken by the English,' he said to Monge. 'I would be locked up in a hulk and in the eyes of France I would be nothing but a common deserter, a general who had left his post without authorisation.' He had charges laid in the hold, and made Monge promise to blow up the ship if it were boarded by the British.
The winds did not favour them so close inshore, and it took a full month to pass Malta, where they would veer north and make a dash for France. The company included Berthier, Bonaparte's aides Marmont and Lavalette, Lannes, Murat, Bonaparte's secretary Bourrienne, and several of the savants, including Monge, Berthollet and the art expert Vivant Denon. Bonaparte's entourage also included a nineteen-year-old Mameluke named Roustam Raza, taken into slavery in the Caucasus as a boy of seven and presented to Bonaparte as a gift by Sheikh El-Bekri.
Although he railed at the incompetence and corruption of the Directory, Bonaparte did not discuss any political plans he may have been nurturing, and according to Vivant Denon he behaved like a passenger on a cruise, discussing scientific topics, playing cards (cheating shamelessly) and bantering with his friends. He avoided chess, at which he was surprisingly bad. In the evenings he entertained his companions with ghost stories, 'a genre of story-telling in which he was highly skilled', according to Lavalette.
The longueurs of the crossing induced in Bonaparte reflection on the past as well as the future, and one evening in conversation with Monge he broached the subject of his paternity. He referred to the gossip surrounding the relationship between his mother and Marbeuf, saying that he would like to know for certain who his father was. The dates suggested it was indeed Carlo Maria Buonaparte, but he wondered where, in that case, he had got his military inclination and talents from. The uncertainty intrigued more than it nagged him, and he appeared even to derive a slight sense of superiority from it, as it placed him outside the common run.
As they sailed north, past Lampedusa, Pantelleria and the west of Sicily, the danger from hostile ships became greater. Bonaparte ordered Ganteaume to hug the west coast of Sardinia, as he believed that in the worst case he could go ashore there and get away. They were low on water, and had to put in to Ajaccio on 30 September to tank up.
Bonaparte went ashore and revisited his home. Letizia had used the indemnity obtained from the French government as a good Republican patriot whose property had been sacked to enlarge and redecorate the family home to unprecedented grandeur. His sister Élisa's husband Bacciochi was now commander of the citadel and a personage in the town. Joseph and Fesch had been buying land around Ajaccio, and Bonaparte could take his companions to stay at Les Milleli in comfort.
Before leaving Corsica on the evening of 6 October he bought a longboat and hired a dozen strong oarsmen, to enable him to make a run for the coast in the event of an encounter with the Royal Navy. They did spot several British ships as they neared the French coast on the evening of 8 October, and Bonaparte ordered a change of course. They spent the night in a state of anxiety, fearing that they might have been spotted, but in the late morning of 9 October they sailed into the bay of Saint Raphael unhindered.
As soon as news got about that it was the commander of the Army of the Orient who had arrived, the cannon of the local fort fired a salute and people climbed into boats to row out to greet him, ignoring the rules on quarantine which required all ships arriving from foreign lands to lay up for forty days before anyone could land or come aboard. Since the rules had been broken, Bonaparte went ashore and, extricating himself from the enthusiastic attentions of the locals, by six that evening he was on the road to Paris.
## 17
# The Saviour
'Here is our liberator; the heavens have sent him!' people greeted Bonaparte when he came ashore. Others hailed him as their 'saviour', and some wanted to make him king. At Aix, which he reached the following day, crowds gathered outside his hotel and the municipal authorities called on him as though he were a dignitary on official business. Along the road peasants cheered and even carried torches beside his coach at night to safeguard him from the brigands with whom the region was infested – which did not prevent his baggage being stolen by what his Mameluke Roustam termed 'French Arabs'.
At his next stop, Avignon, 'word suddenly got around with extraordinary speed that General Bonaparte had arrived from Egypt and would be entering the city in a few hours', recorded the young artillery lieutenant Jean-François Boulart. 'In a flash the whole city was in motion, the troops stood to and marched out beyond the city walls on the road along which the hero of Italy and Egypt would come. The crowd was immense. At the sight of the great man the enthusiasm reached its peak, the air resounded with acclamations and with shouts of _Vive Bonaparte!_ and that crowd and those shouts accompanied him all the way to the hotel in which he stopped. It was an electrifying spectacle. As soon as he reached it, he received the authorities and the officers; it was the first time I saw this prodigious being. I contemplated him with a sort of voracity, I was in a state of ecstasy. [...] From that moment, we looked on him as being called to save France from the crisis into which the pitiful government of the Directory and the reverses suffered by our armies had precipitated it.' Boulart had no doubt that Fate had brought Bonaparte back.
Similar scenes greeted him at Valence, where his erstwhile landlady came to see him and received the present of a cashmere shawl. When he reached Lyon on 13 October he provoked enthusiasm which turned into a civic festival, with illuminations and fireworks, and a play glorifying his deeds was staged. Enthusiastic crowds obliged him to show himself on the balcony of his hotel time after time. Again, the city dignitaries and prominent citizens called on him to pay their respects as they might to a king on his progress, and the pattern was repeated at every stop.
The news of his advent preceded him in Paris, eliciting the same reactions. 'It is difficult to give an idea of the universal enthusiasm produced by his return,' recalled Amable de Barante, then a student at the École Polytechnique. 'Without knowing what he would want to do, without attempting to foresee what would happen, everyone, of every class, had the conviction that he would not tarry to put an end to the agony in which France was expiring... People embraced in the street, people rushed to meet him, people longed to see him.' The nineteen-year-old poet Pierre-Jean de Béranger was in a reading room when he heard the news, and he and his fellows leapt to their feet as one man with shouts of joy. Workers in the cafés of the Faubourg Saint-Antoine hailed the return of 'our father, our saviour, Bonaparte', while according to a popular verse heard in the streets of the capital, 'The gods, who are friends of this hero, have brought him to our shores.'
Accounts of these events bristle with the words 'fortune', 'providence' and 'destiny', and in many Bonaparte is described and greeted as a 'saviour'. 'Nations cannot escape their destiny,' wrote Mathieu Molé, who, fearing another lurch to the left, was preparing to emigrate when he heard the news of Bonaparte's return. He could not repress a feeling that the French nation was being guided by instinct to submit to the man Providence had intended.
Years of often bloody political upheaval and intermittent war, punctuated by economic crises and accompanied by fiscal chaos, had obscured the benefits of the Revolution and left the nation deeply dissatisfied. The Directory had introduced a modicum of stability and did achieve some positive results, but it was mired in corruption and had a propensity for war. While Bonaparte was in Egypt, it had responded to the new coalition stacking up against France by invading Holland, Switzerland and Naples, setting up new republics which would involve France in further conflict, and by that summer of 1799 its armies were in retreat.
Governments are rarely judged in rational terms, and their popularity is subject to a variety of emotional responses. The Directory, along with the two representative chambers which appointed it, figured in the public imagination as a collection of ineffectual lawyers in togas bandying slogans while pursuing their own interests, venal as well as political. It was despised by the majority across the political spectrum as a pseudo-revolutionary oligarchy, 'a provisional tyranny' too weak to guarantee stability and rule effectively, too corrupt to engage the support of society. Yet nothing could be done to reform it, as the constitution could not be altered before nine years had elapsed.
The situation cried out for a radical solution. 'The state of our country was such that the entire French nation was prepared to give itself to whoever could save them at the same time from the foreign menace and the tyranny of their own government,' according to the royalist Louis d'Andigné. Recent experience had shown that, in the words of one young man, 'nothing could be undertaken or accomplished except by a general and with military force'. That was also the view of the man currently preparing a coup to overthrow the Directory (of which he was a member) and change the constitution, the former priest Émmanuel-Joseph Sieyès. He made no bones about the fact that in order to do so he needed 'a sabre'. But he failed to appreciate that people no longer wanted some politician such as him supported by a general, they wanted the general himself. As another nineteen-year-old put it: 'The time had come for a dictatorship, and everything pointed to the dictator.'
There were other generals on hand, such as Bernadotte, Moreau, Augereau and Jourdan. Bonaparte himself would later say that if it had not been him it would have been another. That is certainly true up to a point, but that 'other' would have served his purpose and been sooner or later hung out to dry. French society was thirsting for something more. The intellectual, moral and emotional conditioning of the past half-century had given rise to new beliefs and mythologies, and to illusory expectations of life and therefore of politics, which had themselves entered a new sphere with the Revolution. The subliminal emotions and expectations traditionally focused on the person of the monarch as the anointed representative of God on earth could, up to a point, be redirected onto abstract concepts such as the Nation and the Republic, which were anthropomorphised in art and ritual for the purpose. But they did not easily settle on a group of officials, however epically they were decked out in their togas and plumed hats. Those emotions and expectations required a cynosure more numinous, a figure sanctioned by some substitute for God, by Fate, Providence, Fortune or whatever other euphemism the theologically challenged intellectuals of the time preferred.
Philosophers had, over the centuries, addressed the question of what differentiated some men from the herd, either by seeking a physical explanation or a celestial inspiration of some sort. In the eighteenth century it became customary to label outstanding individuals as 'men of genius' – Shakespeare, Descartes and Newton were among those thus branded. And while the idea of equality among men eroded respect for traditional aristocracy, a new aristocracy of genius emerged to replace it – the figure of the 'genius' sometimes even replaced the king on decks of cards. The concurrent withdrawal of God and the saints from the public imagination made room for the genius as a kind of lay saint, even a kind of god. For the Swiss philosopher Johann Caspar Lavater, a man who could achieve exceptional things was 'a being of a higher kind', a 'counterpart of the divine', a 'human god'. According to the philosopher Immanuel Kant, genius was something inexplicable bestowed on men by nature. It was not even necessary to be dead to be labelled one. Benjamin Franklin, who had managed to tame the celestial fury of lightning, was widely acclaimed as a saint, and a cult developed around him that included the worship of relics. Rousseau was often referred to as 'divine', and during the French Revolution the former church of Sainte-Geneviève was turned into a Pantheon, a sacred space in which he, Voltaire and others were laid to rest and venerated as saints. The armed struggle in defence of the Revolution had raised military valour to the highest status among virtues. The Paris veterans' hospice the Invalides was renamed the Temple of Mars.
Bonaparte's gift for self-promotion had over the past four years fashioned the image of him as someone out of the ordinary, courageous, wise, modest, but also decisive and above all successful. In excess of 500 distinct images had been produced to cover his exploits during the Italian campaign which represented him not just as a hero but also as the embodiment and symbol of the army, which in the revolutionary imagination was equated with the nation itself. The Egyptian episode had added new dimensions. In the absence of hard facts due to the difficulties of communication, journalists gave free rein to their fantasy, with the result that the public was regaled with visionary depictions of victory and dominion. Prints showed Bonaparte bestowing the benefits of French culture on exotic-looking natives, representing him as a man of peace and an administrator creating a new colony for France, and one even depicting him being greeted in India by Tippu Sahib.
Over this hovered a more subtle suggestion that his triumphs, which were described by himself as well as others as 'prodigious', 'fabulous', even 'miraculous', were the consequence of his being beloved of the gods, or Providence, Fortune or Fate. This explained his seeming invulnerability to bullets and plague alike. The impression conveyed was by no means restricted to revolution-weary France: Shelley, Byron, Beethoven, Coleridge, Blake, Goethe and countless other intellectuals all over Europe saw in Bonaparte a superhuman element which excited their imagination, if only for a time. Young people all over the Continent and even across the Atlantic, including aristocrats firmly wedded to monarchist principles, felt the appeal and in various degrees sought to emulate his example. It is not difficult to see why a despondent society such as France in the autumn of 1799 saw in him a longed-for messiah.
Nor were subliminal factors the only ones at play. The fulsome report of his victory at Aboukir (which conveniently overshadowed the naval disaster in the bay of the same name) had reached Paris after a tortuous journey only a few days before Bonaparte's arrival in France. As it happened, the fortunes of war had turned: General Brune had seen off the British and Russian forces in the Netherlands, and Masséna had defeated the Russians in Switzerland. But it was news of Aboukir that gave people the impression that France was victorious once more, and when five days later it became known in Paris that its victor had come to save the Republic, it produced what the old revolutionary Antoine-Claire Thibaudeau described as 'an electric commotion'. He was at the theatre when it was announced, in mid-performance, and while the actors resumed after the cheering had died down, the audience paid them no heed, arguing over the possible implications: 'every face and every conversation reflected only the hope of salvation and the presentiment of happiness'.
Josephine heard the news of his landing on 13 October, while dining at the Luxembourg Palace with the president of the Directory, Louis-Jérôme Gohier, an admirer of hers hostile to Bonaparte. She had not received her son's letter from Cairo warning her of Bonaparte's fury at having been told the full extent of her infidelities, as it had been intercepted by the Royal Navy (and published, to general amusement, in the London press). She did know that his brothers were out to discredit her, so she was determined to get to him before they did. She set off at once, with her daughter Hortense, of whom Bonaparte was particularly fond, meaning to meet up with him along the way. Unfortunately for her, he had decided against taking the main road.
By the time he reached Lyon, he had all the evidence he needed regarding his popularity. Not wishing to enter Paris with the same _éclat_ as the other cities along his way lest it annoy the Directors, and wishing to give himself time to take stock, he had taken a route through Nevers and Montargis. He reached the capital at six o'clock on the morning of 16 October, and was able to go without being spotted straight to the rue de la Victoire, where he no doubt meant to confront Josephine and tell her of his intention to divorce her.
He found the house empty, except for his mother, who, although she had recently shown some consideration for Josephine, would not have tried to dissuade him. As nobody else knew of his presence in town, Bonaparte had most of the day to brood on the faithlessness of his wife – and indeed on the debts she would have run up, for the house had been redecorated in neo-classical style with Egyptian motifs. The tented bedroom was designed to represent the rigours of campaigning, with what resembled a camp bed and drums as seats. The furniture, in supposedly Roman style, was by the foremost Parisian _ébéniste_ , Georges Jacob, and the rooms were adorned with antiquities Josephine had picked up in or been sent from Italy.
In the afternoon he received a visit from the Directory's executive officer and effective head of police for the department of the Seine, Pierre-François Réal, who had got wind of his arrival. He found the general angry and depressed, railing at the inconstancy of women and comparing his homecoming to that of the returning heroes of the Trojan war. Réal, who was close to Barras and Josephine, did what he could to calm Bonaparte, warning him that a divorce would do his image no good and might make him look ridiculous.
Bonaparte knew the Directory would be less than enthusiastic about his return. He had deserted an army in the field and broken the law on quarantine, a serious offence. He did not know that, faced with the threat of war closer to home, they had in fact sent a despatch on 26 May ordering him to return to France with his army, as this had never reached him. They had subsequently repeated these orders, though how he was to transport an army without a fleet they did not say. From Aix, where he had intercepted this second order, he wrote of his concern for the Republic and declared his readiness to serve it in any way he could.
That evening he went to the Luxembourg to see Gohier, who received him moderately well, from which Bonaparte could deduce that while his desertion of the army had given the Directors a golden opportunity to court-martial and discredit him (which some of them did consider), they felt powerless in the face of public opinion. This gave him confidence when he confronted them as a body the following morning.
His appearance expressed an attitude they had not been prepared for: he wore an olive-green civilian frock-coat and a broad-brimmed hat, and, attached by silk straps, an Oriental scimitar. The Directors received him in open session, and when he arrived he found members of the public and officers present. Among the sentries he recognised veterans of his Italian campaign and shook their hands, bringing tears to their eyes. He addressed the Directors 'like a man who had come rather to demand an explanation of their conduct rather than to justify his own', according to one witness. He assured them that he would never draw his sword except in defence of the Republic, and deflected their questions about the army in Egypt by asking his own about the state of France. Gohier embraced him, as was customary, admitting that the accolade 'was neither given nor received very fraternally'.
Later that day he had an interview with his brother Lucien. Lucien had until now had little time for Bonaparte, whom he did not know well or rate highly. He was intelligent, energetic and unscrupulous in pursuit of his own aims, though liable to take unbending moral stands when it suited him. He was a natural politician and a good orator. Having been elected, like Joseph, to the Assembly of the Five Hundred, he was now angling to be chosen as its president. Whatever they thought of their brother and he of them, they were family, and their Corsican upbringing would not let them forget that.
Joseph's political skills were not on a par with Lucien's. He had enriched himself, acquiring a residence in Paris and an estate at Mortefontaine, and fancied himself as a literary figure, publishing a fatuous novel and surrounding himself with writers. In the interests of enlisting the support of a prominent former Jacobin, he had arranged the marriage of his sister-in-law Désirée to General Bernadotte. Bonaparte's brother-in-law General Leclerc had also set himself up, with a residence in town and a château in the country, and had sent Paulette, now styling herself Pauline, to Madame Campan's school to learn to read and write, not to mention some manners. Of the whole family, only Louis, who had returned from Egypt earlier, had failed to find a place for himself and worried about how Bonaparte was faring there.
Both Joseph and Lucien wanted Bonaparte to divorce Josephine, and for a couple of days it looked as though they would succeed. According to Barras, Bonaparte called on him in despair and announced that he intended to divorce her. Barras claims to have put him off, saying he would make himself ridiculous, that only lower-class people were offended by their spouses' faithlessness, and that she might yet prove useful to him. Collot records giving him similar advice. 'No! I have made up my mind; she will never set foot in my house again,' Bonaparte retorted. 'I don't care what people will say.' Collot observed that his anger betrayed the strength of his feelings for her, and that he would soon give way. 'Me forgive her? Never!... You know me well!... If I were not firmly resolved, _I would tear out my heart and throw it on the fire_.'
Having realised her error, Josephine had turned round and raced back to Paris, arriving at the rue de la Victoire on 18 October. Bonaparte shut himself away and refused to admit her, but she would not go away, weeping and professing her love, begging his forgiveness. She deployed Hortense and Eugène to plead her cause, and after a few hours he opened the door and let her in. However much he had been wounded in his self-esteem by her behaviour, he was still in love with her, and he needed her. She could give him the solace and the domestic warmth he craved, she was a clever, resourceful woman whose advice he had come to value, and she provided the social confidence he was keenly aware of lacking. At a more practical level, Josephine knew a great many people and had access to circles Bonaparte needed to cultivate. Finally, he had to accept that as various people had pointed out, a public domestic row and a divorce would not serve the image of the man who had come to save France.
He moved cautiously, keeping to his pose of the self-effacing warrior at rest. He dressed in civilian clothes, rarely went out, avoided public appearances and assemblies, and refused to receive official delegations, civic or military. He visited wounded veterans at the Invalides and spent time with his friends at the Institute. At one session, he gave a lecture on the Suez Canal.
Yet all the while he was sounding out people across the political spectrum. After his first meeting with the Directory, he called on the minister of justice Jean-Jacques Cambacérès, who confirmed that the political class was exasperated with the state of affairs and that there was widespread desire for change. But there was considerable divergence of expectation as to what kind of change, and what Bonaparte needed to ascertain was which faction was the strongest.
The house in the rue de la Victoire was the scene of constant comings and goings. Among the first to call was Talleyrand, who had been dismissed from the ministry of foreign relations and hungered for power. He was followed by Pierre-Louis Roederer, editor of the _Journal de Paris_ , whose endorsement would be crucial. Bonaparte's firm supporter Regnaud de Saint-Jean d'Angély was on hand to furnish the necessary propaganda. Other callers included Talleyrand's friend Hugues Maret, a minor diplomat who now became Bonaparte's secretary. On 21 October Talleyrand and Roederer brought Admiral Eustache Bruix, with whom they had dined, judging him a potential ally. Others hovered on the sidelines. One such was the police minister Joseph Fouché, a self-effacing man whose cadaverous features sat well with his past as a violent Jacobin, which had earned him the sobriquet of 'butcher of Lyon'. He had long since enlisted the collaboration of the debt-ridden Josephine by providing her with financial and other assistance.
On 22 October Bonaparte dined with Gohier and met General Moreau for the first time. The meeting was written up by Roederer in his paper the following day, giving the public the impression that the two generals were on good terms. This was important, since Moreau was universally popular. He had been approached to save France by the Director Sieyès, who was planning a coup to overthrow the government of which he was a member. When his preferred 'sabre', General Joubert, had been killed at the battle of Novi that summer, Sieyès had cast around for another, and fixed on Moreau. He had invited him to the Luxembourg to discuss this on the evening of 13 October, and the general entered his office shortly after the Director had heard the news of Bonaparte's return. When he was told of it, Moreau reportedly interrupted Sieyès with the words, 'He's your man; he will carry out your coup d'état far better than I.' That did not mean he had given up his own ambitions.
Sieyès had been colluding with Lucien Bonaparte over the past months, but recruiting his brother was not going to be as easy as might appear. Bonaparte did not like Sieyès, considering him a self-important pedant. Sieyès was not popular, and many suspected him of having monarchist leanings; he was hated by the surviving Jacobins. Talleyrand and Roederer believed Bonaparte should ally himself with the other Director who might be prepared to act, Barras. Réal was of the same mind, knowing that Barras would wish to assume a leading role in any event. But Bonaparte remained non-committal.
It had become clear that he was the object of a great deal of wishful thinking. Those who favoured a restoration of the monarchy saw him as the man who could bring it about. The Jacobins were hoping he might be the man to restore the Republic in its more radical guise. Liberal republicans, loosely referred to as 'Ideologues', saw him as the strong man who could bring stability and preserve them from both Jacobins and royalists. If he could keep them all thinking that he was their man, he would not arouse the enmity of any party. He had correctly assessed that what offended public opinion was the sense that politics had been taken over by factions which had only their own interests at heart. If he was to engage wider support he must show himself to have nothing to do with any of them. He therefore remained aloof while Talleyrand, Roederer and others prepared the ground.
Sieyès was offended that Bonaparte had not approached him, while Bonaparte felt Sieyès should make the first step. At one point in this stand-off Bonaparte lost his temper in front of a number of witnesses, shouting that it was to him people should come, because it was he who was 'the glory of the nation'. He nevertheless did call on Sieyès and his fellow Director Roger Ducos on 23 October. Things got off to a sticky start. Bonaparte was offended by the lack of ceremony with which he was received on his arrival at the Luxembourg: the detachment on guard had not saluted him with the appropriate drum-roll, he had been made to wait, and they had not opened both wings of the doors for him. Yet when they got down to business, the three of them agreed that France was not being properly governed, and that something had to be done. The two Directors returned his visit the next day, but that meeting too did not go beyond the exchange of pious wishes.
Fouché, supported by Josephine, was still advocating an alliance with Barras, but although Bonaparte felt comfortable with him and appreciated his intelligence, Barras was hated by the Jacobins and his reputation was tarnished in the eyes of public opinion, which associated him with the worst excesses of the Directory.
Joseph wanted to bring Bernadotte and Bonaparte together – no easy thing, given not only the ideological differences between them but the lack of mutual esteem or sympathy. On hearing of Bonaparte's return from Egypt Bernadotte had publicly called for his court-martial. It did not help that he had married Désirée. Joseph organised a party at Mortefontaine to which he invited Lucien, Talleyrand, Roederer, Regnaud and others in order to create an ambience in which the two generals could make their peace. As Bonaparte and Josephine had to share their carriage with Bernadotte and Désirée, whom he had not seen since Marseille, the four-hour drive would hardly have been merry. Discussions between the two generals over the next two days yielded nothing, with Bernadotte hiding behind his Jacobin principles. Although it was evident he would not be able to enlist the support of the Jacobins, Bonaparte could see that with leaders as indecisive as Bernadotte they were unlikely to prove a serious obstacle.
On the morning of 30 October he went out for a ride with Regnaud, and on the way back his horse stumbled over some rocks in the park, throwing Bonaparte, who lost consciousness. It took several hours to bring him round, but that evening he was back in Paris, dining with Barras, who was still trying to enlist his support. There was something about Barras' behaviour on this occasion that produced a violent reaction in Bonaparte, who made up his mind to have nothing more to do with his former protector. The next morning Barras called, seemingly in apologetic mood, and he returned the following day, 1 November, declaring that he was prepared to back him. But Bonaparte brushed him off, saying that he was not contemplating taking action as he was too tired and ill after his Egyptian exertions and would be good for nothing for at least three months. That evening he met Sieyès at Lucien's lodgings.
Sieyès frankly declared that he meant to take power in order to introduce a new constitution, and needed a general to provide backing and keep the populace at bay. Bonaparte made a show of democratic convictions, stating that he would never support anything that had not been 'freely discussed and approved by a properly conducted universal vote'. Sieyès had no option but to accept Bonaparte's terms, although he was probably beginning to see that he himself would be sidelined. 'I wish to march with General Bonaparte,' he told Joseph, 'because, of all the military men he is the most civilian.'
Bonaparte was now approached by General Jourdan, who had been delegated by a group of Jacobins to propose that if he were to join them in overthrowing the government they would make him head of the executive power, provided it was a strictly republican one. He made a show of gratitude and pretended to give the proposal his consideration.
It was by now common knowledge in Paris that something was afoot, and people speculated openly as to what was about to happen, but there was no sign of alarm on the part of the authorities. The Directors were in the dark, as Fouché kept his police reports bland. At the same time, each of them was either planning something himself, like Sieyès and Roger Ducos, contemplating joining in, like Barras, or had at least been sounded out, like Gohier and his colleague Moulin. But their lack of unity precluded them from taking any action. With so many people looking over their shoulders in what remained a fluid situation in which nobody trusted anyone else, danger lurked everywhere. It was not so much the wish to be on the winning side as the fear of finding themselves on the losing one that made people dangerous.
Bonaparte called on Talleyrand late one night to discuss the action to be taken. At one point they heard a carriage and a troop of horse trotting down the street come to a halt outside the door. There was a sound of voices and some commotion. Fearing they were about to be arrested, Talleyrand blew out the candles and crept to the window. It turned out that a carriage carrying the evening's takings of one of the more popular gaming houses of Paris, which always had an escort of cavalry, had suffered a broken wheel. Talleyrand and Bonaparte laughed, but their fear was not groundless, and tension mounted in the capital. One evening Bonaparte sought relief by listening with Fouché to a recital of the Odes of Ossian set to music.
On 6 November the two chambers hosted a banquet for 750 in honour of Bonaparte and Moreau in the Temple of Victory, formerly the church of Saint-Sulpice. The building was decked out with tapestries and captured standards, and trestle tables had been set up in the shape of a horseshoe, but it was cold, with the autumn damp filling the vast unheated church. When Bonaparte arrived accompanied by his staff, the crowd outside cheered ' _Vive Bonaparte! La paix! La paix!_ ' He duly drank the toasts proposed, from a bottle he had brought himself along with a loaf of bread, the only food he touched. He had also taken the precaution of surrounding himself with a ring of faithful aides. 'I have never seen a more silent assembly with less trust and gaiety among the company,' noted Lavalette. A newspaper report observed that the only conversation was made by musical instruments. Bonaparte left while most of the guests were only halfway through their dinner.
Later that evening he had a long talk with Sieyès about a course of action. They both wished to stick as closely as possible to legality and to avoid the need for military intervention, other than to keep the peace and prevent a possible assault on the assemblies by a mob called out by the Jacobins. The plan was straightforward: a majority if not all of the Directors would resign, creating a vacuum of power which would force the two assemblies to step in, declare that the government had ceased to exist, and sanction the introduction of a new constitution. Sieyès felt the task of drafting it should go to him – he had been writing the ideal constitution in his head for years. But Bonaparte insisted it be drafted by a committee nominated by the two assemblies and then approved by national plebiscite. This committee, which would also fulfil the role of a provisional government, was to consist of three 'consuls': Sieyès, Bonaparte and Roger Ducos.
To ensure that everything went smoothly and to eliminate any possibility of the Tuileries being invaded by a Jacobin mob, it was decided to use the constitutional clause which allowed the two assemblies to transfer from Paris to a place of safety in case of danger. As the presidents of both, Lucien Bonaparte and Louis Lemercier, and the two men in charge of the administration, the inspectors of the assemblies, were in on the plot, there should be no problem in arranging this. The date was provisionally set for 7 November, but Bonaparte would insist on putting it back by two days.
He wanted to make a last attempt to neutralise the Jacobins, and on 7 November he had lunch with General Jourdan at the rue de la Victoire. Jourdan, a principled republican, was probably the only man who could have roused the left to action. After lunch they walked in the garden and Jourdan proposed that Bonaparte join him in a Jacobin coup. Bonaparte told him his faction was too weak, but reassured him about his own republican convictions, and as they parted Jourdan intimated that he would not oppose him. That evening, Bonaparte attended a dinner given by Bernadotte, after which he once more attempted to engage his support, but Bernadotte appears to have thought that he was in a strong position, and that if he kept aloof he would hold the trump card at the decisive moment.
The next day was devoted to final preparations and the composition of announcements and declarations to be posted on walls and published in the press immediately after the event. There was also the question of securing the necessary funds, and last-minute talks with bankers and men of business bore fruit. That evening there was a final confabulation at which the details of the next day's action were finalised.
Captain Horace Sébastiani, a fellow Corsican devoted to Bonaparte, was ordered to deploy his dragoons early the next morning before the Tuileries, seat of the two assemblies. Murat was to rally two other cavalry regiments. Bonaparte had notified those officers who had come to pay their respects and whom he had declined to receive on his return from Egypt that he would now be pleased to see them, but that due to pressing circumstances he could only do so at six on the morning of 9 November. They were invited individually, and until they reached his house in the rue de la Victoire in the early-morning dark they would be under the impression that they were to have a private interview with the hero of Italy and Egypt. He had instructed those already in on the plot to convene there at the same time, so when they arrived they would find themselves in a crowd of over fifty high-ranking officers.
Bonaparte went to bed at two in the morning. At the Tuileries the two inspectors of the chambers, Mathieu-Augustin Cornet and Jean-François Baraillon, sat up all night writing out summonses to members of the Council of Elders to come to an emergency meeting at seven o'clock in the morning. They were watched over by the Guard of the Assemblies, whose non-commissioned officers would deliver the messages at six, but only to those members of the assembly deemed reliable. Those who might cause trouble would be left to sleep.
## 18
# Fog
As the bleary-eyed representatives of the people made their way down still-dark streets on the morning of 9 November (18 Brumaire, the month of mist in the revolutionary calendar), Sébastiani's dragoons and Murat's chasseurs were taking up positions around the Tuileries, and the National Guard stood to on the Champs Élysées. Once the members of the Council of Elders had donned their togas and taken their seats, they were informed by Cornet that there was a sinister plot by infamous brigands to bring down the government. The assemblies were in grave danger, he declared, and they must make immediate arrangements to transfer to a place of safety, suggesting the former royal palace of Saint-Cloud outside Paris. In order to safeguard the move and protect them they must, he went on, call on the hero of Egypt, General Bonaparte, who was devoted to the defence of the Republic.
A few of the deputies raised questions of substance and others of order, but with only the most favourable 150 of the 250 members present, these were easily brushed aside by the president, Lemercier, and a decree whose text had been prepared beforehand was duly passed. It stipulated that on the following day the assemblies would remove to Saint-Cloud, where they would resume their legislative function under the protection of General Bonaparte, who was invested for the purpose with command of all the troops in the Paris region. It was borne by the two inspectors to the rue de la Victoire.
There, Bonaparte had been busy, calling officers into his study one at a time to assure himself of their support or to discuss details of the day's operations. Those who had accepted his invitation as a purely social call were effectively trapped. On seeing the gathering, one reportedly told his coachman to drive away but was prevented by Bonaparte, who almost pulled him out of his carriage. Once there, they found it difficult to leave, and the more notables they saw at Bonaparte's side the more likely they were to go along.
Bonaparte was annoyed at Bernadotte's failure to show. A greater disappointment was that Gohier, whom Josephine had disingenuously invited to take breakfast with her that morning, also failed to turn up. But Moreau came, as did General Lefèbvre, military governor of Paris, whom Bonaparte charmed by presenting him with the sabre he had used at the battle of the pyramids. The old Alsatian was so moved that he vowed 'to throw those lawyer buggers into the river'.
When the copy of the decree of the Elders arrived, Bonaparte emerged from his study and, after reading it out, called on those present to assist him in saving the Republic. Then, mounting a magnificent black Andalusian lent him for the occasion by Admiral Bruix, he set off for the Tuileries, escorted by cavalry and a suite of generals and senior officers in brilliant uniforms, cheered along the way by ignorant yet admiring onlookers. At about ten o'clock he entered the chamber of the Council of Elders, flanked by Berthier and a handful of other generals, and gave a rehearsed speech, praising them for their wisdom in entrusting the safety of the Republic to him, and swearing to uphold it.
Lemercier accepted his oath and confirmed him in command of the guard of the assemblies (Bonaparte surreptitiously added the Directors' guard), which he now went out to inspect. These were not his soldiers, and he could not take their loyalty for granted. An unexpected opportunity presented itself in the person of Bottot, the secretary of Barras, who had been sent out to see what was going on. Bonaparte collared him, drew him towards the ranks of troops and delivered a rousing address, cribbed from a newspaper report he had recently read. 'What have you done with this France which I left in such a brilliant state?' he harangued the unfortunate Bottot. 'I left you peace, and I find war! I left you victories and have found defeat! I left the millions of Italy and I now find only extortionate laws and misery everywhere!' he thundered, accusing, in the person of the hapless Bottot, the entire French political class of having squandered the sacrifices made by the 'hundred thousand' brave men, his 'companions in glory' who had laid down their lives in defence of the Republic. He accused them of factionalism and said it was time to entrust the Republic to the brave soldiers who could be counted on to defend it selflessly. The men were his to command.
Bonaparte mounted his black horse, which he was having some difficulty in mastering, and made the rounds of the units that had mustered in the city, exciting their enthusiasm for they knew not what with dramatic statements empty of substance. He looked heroic, his reputation spoke to every soldier, and his suite of generals and senior officers, which had now swelled to 150, lent him unquestionable authority.
Meanwhile, Sieyès had turned up at the Tuileries, on horseback to give himself added allure (he had taken riding lessons a couple of days before). He was accompanied by Ducos, and they were soon joined by their colleagues Moulin and Gohier. All four Directors endorsed the decree of the Elders for the removal of the assemblies to Saint-Cloud. But when Sieyès suggested that Gohier and Moulin resign their office as he and Ducos had done, they refused and set off for the seat of government in the Luxembourg to compose a letter of protest. This would be of no consequence, since the building was hermetically sealed by troops under Moreau. The Council of the Five Hundred, which had in the meantime convened in its usual seat, the Palais-Bourbon on the left bank of the Seine, was equally powerless. Outraged Jacobin deputies had to accept the decree passed by the Elders as constitutional, and Lucien closed the session, instructing them to reconvene on the morrow at Saint-Cloud.
In order to bring about the key event, the dissolution of the Directory, it was essential that a majority of its members resign, and since both Gohier and Moulin had refused, it was now imperative to get Barras to do so. He had been alerted that something was afoot, but decided to keep out of the way by prolonging his morning toilette, taking twice as long as usual to shave and bathe while he sent Bottot out on reconnaissance. As he waited hopefully for an offer of some kind from Bonaparte, the Luxembourg emptied, first of its guards, then of its servants. Power gradually dissipated around him. At about midday he received a visit from Talleyrand and Admiral Bruix, who produced the draft of a letter of resignation for him. He realised that he was finished. Obediently he wrote out the prepared text, which protested his 'passion for liberty', which alone had made him accept a part in the government. 'The glory which accompanies the return of the illustrious warrior for whom I had the honour of opening the road to glory' had at last allowed him to give up this unwanted task and return with joy to the ranks of ordinary citizens. Talleyrand had brought a purse with two million francs, intended as a reward, but there is some doubt as to whether he did not keep it for himself. Outside, a troop of cavalry was ready to escort the former Director to his country residence.
By all accounts Paris remained peaceful throughout the day and that evening the theatres were as full as ever. The more politically ambitious, or vulnerable, began calling on Bonaparte at the Tuileries to make their act of obeisance just in case. The principals of the coup lingered at the palace that night to discuss plans for the following day, which was to see the decisive act, but they inexplicably failed to agree a concrete plan of action. Sieyès was prolix in abstractions, Ducos said nothing. The only specific suggestion made by Sieyès was that they should have forty of the most obviously hostile representatives arrested. Bonaparte rejected this proposal, declaring that he stood above such methods, confident that his prestige would carry the day. When they parted, the stage had been set but there was no script for what was to be played out on it. As he drove home through the pouring rain, Bonaparte declared himself satisfied with the way things had gone. He nevertheless laid a pair of loaded pistols by his bedside before retiring for the night.
Although he had seemingly neutralised Jourdan, Bonaparte could not be sure the Jacobins would remain passive. He had been using Saliceti, now a member of the Five Hundred, as a go-between to calm their fears about his intentions. Saliceti had warned the Jacobins to stay away that morning, assuring them that it was only thanks to Bonaparte that Sieyès had not had them arrested. But while Bonaparte and his associates confabulated at the Tuileries, Bernadotte had been trying to persuade the Jacobins to use their influence in the assemblies to have himself appointed to command alongside Bonaparte.
Bonaparte was up at four o'clock on 10 November and drove to Saint-Cloud with Bourrienne, escorted by a clutch of aides and a troop of cavalry. He was aware that if he did not carry off the coup he would end up on the scaffold, but he trusted in his luck. He could certainly not trust in many of his associates. As soon as the principal actors had left Paris, Fouché, who was not entirely confident the coup would succeed, set up an efficient chain of communication with Saint-Cloud and prepared to arrest the conspirators if they were to fail.
On arrival at Saint-Cloud, where the two assemblies were to take their seats at midday, Bonaparte found preparations being made to provide them with accommodation in the seventeenth-century palace. The Elders were to convene in the impressive Gallery of Apollo, decorated with frescoes by Mignard, which had been cleaned up and furnished with a few tapestries and rows of unmatched chairs hastily taken from the royal furniture store. The Five Hundred were to meet in the orangery, a long building overlooking the garden with tall windows reaching almost to the floor on one side. As it was too long, a partition was being erected halfway along, and its discoloured, shabby walls were being hung with tapestries, while carpenters laboured to build a rostrum and stepped seating. The building, which had stood empty for ten years, only occasionally hosting a public ball or other festivity, was cold and damp.
Bonaparte took over one of the palace's drawing rooms as his headquarters. Talleyrand had rented a house nearby in which he, Roederer and others waited, ready to climb into a waiting carriage if things went wrong. Sieyès too had taken the precaution of parking his carriage in a discreet place nearby in case he had to make a quick getaway. It was said that some of the conspirators were carrying large sums in ready money for the same reason. Bonaparte himself seems to have had an attack of nerves shortly after his arrival, and flew into a rage with an officer for no reason.
There was good reason to be nervous. As they waited for the chambers to be made ready, the deputies of the two assemblies, most of whom had been excluded from the previous day's session, strolled about discussing the situation, joined by Parisians who had driven out to see what was going on. In the course of these discussions those hostile to any change grew firmer in their resistance, while supporters of the coup began to have second thoughts. Bonaparte had a total of about 6,000 troops at hand, some sitting around their stacked weapons in the courtyard giving evil looks to the deputies, those hated 'lawyers' and 'chatterboxes', others deployed in the grounds and the surrounding streets. He was determined to achieve his end constitutionally, so had no wish to use them, but their presence raised the hackles of many of the deputies, who muttered darkly about the threat of a military coup and bandied epithets such as 'Caesar' and 'Cromwell'.
It was not until well after one o'clock that the Five Hundred were able to take their seats, in a flapping of scarlet Roman togas and plumed Polish caps. Lucien and his supporters were to persuade their assembly to nominate a commission to investigate the dangers threatening the Republic. But things got off to a bad start. Sensing what was afoot, the Jacobins among them began denouncing the incipient dictatorship, declaring that they would defend the constitution to the death. It was the kind of emotive language that swayed the majority in assemblies of the period, and a vote was carried to have every deputy renew their oath to it. That would take all day.
The Elders had already filed into the Gallery of Apollo in their blue togas, preceded by a band playing the _Marseillaise_. They were to take notice of the resignation of the three Directors, declare the government thereby dissolved, and appoint three consuls to prepare a new constitution. But the session had hardly opened when some of the deputies began questioning the legality of the previous day's proceedings. One of the conspirators cleverly observed that the Elders could not debate anything until the Five Hundred had properly constituted themselves – which they had not, as they were still busy renewing their oaths. A letter was then read out from the secretary of the Directory to the effect that the government had ceased to exist. By half past three the entire legislative body of the French Republic had tied itself in a knot, and with every moment that passed the Jacobins' influence grew in the Five Hundred, while Bonaparte's supporters in the Elders, many of them moderates, grew increasingly uneasy.
In the damp room, hardly warmed by a smoking fire, where Bonaparte, his brother Joseph, Sieyès and the other leaders sat, 'people looked at each other but did not speak', according to one of those present. 'It was as if they did not dare to ask and feared to reply.' People began making excuses and slipping away. Bonaparte tried to hide his nerves by giving unnecessary orders and moving troops about. Every so often Lavalette would come and report on what was going on in the chambers.
Outside, more and more people began to drift in from Paris. Jourdan and Augereau had also turned up, alert to the possibility of exploiting the situation for themselves. Augereau advised Bonaparte to abandon his plan. 'The wine has been drawn, it must be drunk,' Bonaparte replied. He sensed that if he were to remain inactive much longer his position would become untenable. Just before four o'clock he announced that he wished to speak to the Elders and, followed by a number of aides, entered their chamber. Their session had by then been suspended, but they gathered to hear what he had to say.
Bonaparte was not a good speaker, often having difficulty in finding the right words. He was flustered and did not have a specific case to put, only a series of slogans which had proved sufficient up until now. 'Allow me to speak to you with the frankness of a soldier,' he began. He had, he told them, been minding his own business in Paris when they had called on him to defend the Republic. He had flown to their aid, and now he was being denounced as a Caesar and a Cromwell, a dictator. He urged them to act quickly, as there was no government and liberty was in peril. He was there to carry out their will. 'Let us save liberty, let us save equality!' he pleaded. At that point he was interrupted by the shout, 'And what about the constitution?' After a stunned silence, Bonaparte pointed out that they themselves and the Directory they had named had violated the constitution on at least three occasions, which was not tactful, and did not lend conviction to his main theme, to which he returned, plaintively assuring them that he was only there to uphold their authority and did not nourish any personal ambitions, and exhorting them to emulate Brutus should he ever betray their trust. His friends tried to restrain him, but many of the members of the assembly had been angered, and now began asking awkward questions. He carried on, growing more and more aggressive in tone and grasping at any words and phrases that came to mind, conjuring up visions of 'volcanoes', of 'silent conspiracies', and at one point defiantly warning them: 'Remember that I march accompanied by the god of victory and the god of war!' He ranted on incoherently until Bourrienne dragged him away by his coat-tails.
Astonishingly, Bonaparte felt he had galvanised his partisans among the Elders, and despatched Bourrienne to Paris to inform Josephine that all was going well. He also sent a message to a worried Talleyrand to the same effect. It is tempting to wonder whether the concussion he had suffered falling from his horse at Mortefontaine just over a week earlier might not have had something to do with his erratic behaviour and lack of judgement that day. It was with astonishing confidence that he now strode forth to confront the Five Hundred. He knew he would be facing a hostile chamber and was expecting trouble, so he took a few trusted grenadiers along as well as his aides.
Hardly had he entered the orangery than shouts of 'Down with the tyrant!', 'Down with the dictator!' and 'Outlaw!' greeted him as the assembly rose to its feet in outrage at this military incursion. He was instantly assaulted by a multitude of deputies pressing in on him, shouting, shaking him by his lapels and pushing so hard that he momentarily lost consciousness. He was rescued by Murat, Lefèbvre and others, who kept the enraged deputies back with their fists, and by the grenadiers he had brought with him. The scuffle grew fierce, and a number of the members of the public in the spectators' gallery fled through the windows. Bonaparte was eventually carried out, pale, struggling for breath, his head lolling to one side, barely conscious, pursued by cries of 'Outlaw! Outlaw!', which in the course of the Revolution had come to signify a condemnation to death. With his brother out of the way, Lucien did his best to calm tempers and to deflect a vote declaring him an outlaw, which would have put in question the allegiance of the troops. The assembly then got bogged down in discussion of what they should do next.
Bonaparte had returned to his centre of operations. He seemed completely undone, making strange statements and at one point addressing Sieyès as 'General'. He soon recovered himself, but for the rest of the day his words and actions remained disjointed and not entirely coherent. Those who were still with him had come to the conclusion that their purpose could no longer be achieved by constitutional means, and that it was time to resort to force. Murat and Leclerc were keen, but Bonaparte felt he needed an excuse, and attempted to obtain some kind of authority from the Elders to brandish against the Five Hundred.
On hearing an erroneous report that he had been voted an outlaw by the Five Hundred, he drew his sword and, leaning out of the window, shouted, 'To arms!' The cry, taken up and repeated, flew through the ranks and the waiting troops mounted up and stood to. Bonaparte came out of the palace followed by his suite and asked for his horse. The fiery beast lent by Bruix had been frightened by the shouting, with the result that when he mounted it began rearing and bucking. After some less than heroic tussles with it, he rode up to the bewildered grenadiers of the legislative guard, who failed to show much interest. It was not until he reached the troops of the line and Sébastiani's dragoons outside the courtyard that he elicited the desired enthusiasm. Riding up and down on his unruly mount he struck a heroic pose, venting his fury at the way he had been treated by the Five Hundred, telling the troops that he had gone to them offering to save the Republic but had been attacked by these traitors, paid agents of Britain, who had brandished daggers and tried to murder him. His agitation had brought out a severe rash on his face, and while considering his next move he had scratched so hard that he had drawn blood, which now seemed to confirm the story of daggers raised against him – the rumour that he had been wounded flew through the ranks, the crowd and eventually all the way to Paris. Murat and Leclerc embellished the story and Sérurier, commanding the troops further out, told them that 'The Elders are behind Bonaparte, but the Five Hundred tried to assassinate him.'
Some members of the Five Hundred had been trying to rally the legislative guard, which was wavering. If Augereau or Jourdan had stepped forward then and taken command of it, they could have defeated the coup. But they merely hung about waiting for an opportunity for themselves. As five o'clock approached and a misty November dusk settled, the fate of the country hung in the balance. Yet most of its political class dithered and watched each other, waiting to see what would happen next rather than acting out of conviction.
In the Five Hundred, Lucien had done what he could to calm things down, but the shouting match continued, so in the end he made a histrionic gesture, taking off his toga and cap, untying his gold-fringed sash and laying them down as a sign that liberty had been silenced and he could no longer preside over the proceedings. At the same time he sent one of the assembly's inspectors with a message for his brother to act immediately. This gave Bonaparte his excuse.
He ordered a captain to take ten grenadiers with him and rescue the president of the Five Hundred. The captain carried out his task, bringing out a dishevelled and haggard Lucien. He was greeted with acclamations. He asked for a horse, which an obliging dragoon provided, and then rode through the ranks beside his brother, telling the troops that the majority of the Five Hundred had been terrorised by a handful of dagger-wielding fanatics in British pay into defying the Council of Elders and declaring its defender and emissary General Bonaparte an outlaw. As president of the Five Hundred, he assured the troops that these deputies had put themselves outside the law by their behaviour, and ordered them to deliver the well-meaning majority from the clutches of these monsters who 'are no longer the representatives of the people, but the representatives of the dagger'. He then took a sword from an officer and, putting the point to his brother's breast, solemnly swore that he would kill him if he were ever to raise a finger against the liberty of the French people.
The legislative guard appeared convinced. They could hear the enthusiasm of the troops of the line behind them, and as the traditional drum-roll that sounded the attack thundered around the palace, Murat formed up a column of grenadiers and led them with bayonets fixed into the building. As the sound of the drum beating the charge crashed into the orangery, some of the Five Hundred climbed onto their benches and began swearing to defend the Republic and the constitution, while others followed the spectators out of the conveniently low windows. Pandemonium broke out as the troops entered the orangery. Murat marched towards the president's podium and declared in a loud voice that the Five Hundred was dissolved and then, turning to the soldiers: 'Chuck this lot out of here!' The grenadiers did not use unnecessary force, only manhandling a few of the more recalcitrant in order to carry them off the premises, and within a few minutes the now darkened building had been cleared.
With their colleagues of the Five Hundred fleeing or skulking in the grounds, the Elders were jerked into life by Lucien, who appeared in their chamber, denounced a member of the Five Hundred who had come to complain, and with tears in his eyes related a version of events worthy of Rousseau. In order to demonstrate that all was well, the assembly then dealt with a couple of matters which had been on the order of the day.
Lucien turned his mind to wrapping up the business legally, which required a vote by the Five Hundred. He had with him those deputies who had been behind the coup, but he needed more. It was by then quite dark, and soldiers were sent out into the park and the surrounding streets, taverns and hostelries in search of any members of the Five Hundred who had not yet made their escape. Even coaches returning to Paris were searched for the reluctant and often terrified representatives of the people. The number thus assembled varies according to different accounts, from thirty to a hundred, but it was certainly far below the required quorum of 200.
They were brought back to the orangery, where among the overturned benches and chairs, by the light of a few candles, Lucien guided them through the formalities of denouncing and excluding the sixty-two of their colleagues who had supposedly tried to 'terrorise' them, followed by a vote of thanks to Bonaparte and the soldiers who had delivered them. They proceeded to constitute a commission which in turn nominated as the executive power three provisional consuls: Sieyès, Ducos and Bonaparte. At around four o'clock in the morning, by the light of guttering candles they solemnly swore fidelity 'to the sovereignty of the people, to the one and indivisible French Republic, to equality, liberty and to representative government'. The Five Hundred also nominated an interim legislative commission, and decreed the recess of the two legislative assemblies until 20 February 1800.
This was then communicated to the Elders, who took an inordinate amount of time nominating a commission to consider the facts and report on them, holding a symbolic debate and then voting on it. The two assemblies then issued a joint declaration to the effect that they had saved liberty and the Republic.
A bulletin composed by Fouché had already been read out in all the Paris theatres, informing the audiences that during the session of the two chambers Bonaparte had nearly perished from an assassination attempt, but had been saved by 'the spirit of the Republic', the _génie de la République_ , and was on his way back to the capital. Printed notices composed earlier by Roederer were going up all over the city, giving a similar version of events and hailing Bonaparte as the saviour of France. In his own description of the events of the day, twenty daggers had been raised above his head to strike him dead. A grenadier whose uniform had been torn in the scuffle would be turned into a hero who had shielded the general with his body.
Back at Saint-Cloud, to which many of those who had decided to distance themselves earlier that day had by now returned, followed by others drawn by the lure of a rising power, Bonaparte read out a proclamation in the grand style. 'On my return to Paris I found division in every branch of government, and consensus only on the fact that the Constitution was half-dead and could not protect liberty. Each of the factions came to me in turn, confided their plans, unveiled their secrets and asked for my support; I refused to be the man of any faction,' he declared, basing the legitimacy of his assumed power on the totality of the nation. He went on to say that conservative and liberal ideas could now take their place alongside other principles.
He had understood that the prime concern of most of the nation was the desire for peace. 'It is peace that we have just conquered,' he announced. 'That is what must be announced in all the theatres, published in all the papers, and repeated in prose, verse and even in songs.' The troops marching back to their barracks sang ' _Ça Ira_ ', the most bloodcurdling of all the revolutionary ditties, but the Jacobin deputies were fleeing the capital or in hiding – Fouché's police were already on their trail. Like the events of the day, it was all rather confused, but one thing was certain – the Revolution was over.
Bonaparte drove back to Paris at five o'clock in the morning with Bourrienne, Lucien, General Gardanne and Sieyès, who were dropped off one by one before the carriage reached the rue de la Victoire. According to Bourrienne they were all tired and pensive. When they were alone, Bonaparte allegedly broke the silence to admit to having said a great many stupid things in the course of the day. 'I prefer talking to soldiers than to lawyers,' he said. 'Those buggers intimidated me.'
When he got home Josephine was still awake, and he sat on the bed for hours reflecting on the day's events. She told him that his mother and Pauline had rushed over in a state of great agitation: they had been at the theatre, where the performance was interrupted and the author of the play came on stage to announce that Bonaparte had survived an assassination attempt and saved France.
## 19
# The Consul
The next day, 11 November 1799, was a _décadi_ , a republican Sunday. The weather was mild and it was raining. At ten o'clock, citizen consul Bonaparte left home in civilian dress, and was driven through empty streets to the Luxembourg in a carriage escorted by six dragoons. He went directly to Sieyès' apartment, where the two of them discussed the situation for over an hour. Shortly before twelve they were joined by Ducos, and all three crossed the courtyard to the council chamber in the main building, where some of the principal supporters of the coup had gathered.
Bonaparte tried to strike a solemn note as he thanked them for their support, but the effect was, according to Roederer, 'painful': he struggled to find the right words, committing a number of malapropisms, and his turn of phrase was abrupt, as though he were giving commands on a battlefield. They were going to need more than fine phrases. They had toppled the Directory and declared themselves the rulers of France, but that was about as far as it went. The notices that had been plastered on the walls of Paris proudly announced the beginning of a new order, but that remained so much wishful thinking. For all the talk of Bonaparte the Saviour, cynics assumed that five Directors had been replaced by three consuls who would govern with much the same levels of honesty and competence. Bonaparte was determined to prove them wrong.
The first thing that needed to be settled was who would preside over the three-man consulate. Sieyès had assumed it would be him, but he was to be disappointed. According to one version of events, Ducos turned to Bonaparte and said, 'It is quite unnecessary to vote on the presidency; it is yours by right.' Another has Bonaparte simply taking the president's chair. On doing so he declared modestly that they should each preside for a day in rotation, but that never happened.
Thus constituted, the consuls, or rather Bonaparte, proceeded to nominate the new government. He replaced the left-leaning minister for war with his trusty Berthier, left Cambacérès at the ministry of justice, and in a gesture to the ideologues nominated as minister of the interior the mathematician and astronomer Pierre-Simon Laplace (his examiner on graduation from the École Militaire in 1785). He left the current incumbents at the ministries of police, the navy and foreign relations (though he would slip Talleyrand into that ten days later), and allowed Sieyès to nominate his candidate, Martin Gaudin, minister of finance. 'He was an honest and thorough administrator who knew how to make himself liked by his subordinates, proceeding gradually but with purpose,' Bonaparte would later write of him, a quality he did not appreciate at the time. 'Come on, take the oath, we're in a hurry,' he chivvied the astonished Gaudin. For reasons that would become apparent later, probably Bonaparte's most significant appointment was that of the thirty-six-year-old Hugues Maret as secretary to the consuls.
'Gentlemen, you have a master,' Sieyès is reported to have said to the others after Bonaparte left the room. '[Bonaparte] wants to do everything, knows how to do everything, and can do everything. In the deplorable position in which we find ourselves, we had better submit rather than excite divisions which would lead to certain defeat.' He had been completely outmanoeuvred. Bonaparte had long ago concluded that effective government required a dictator. He had been borne to power by a disparate assemblage of people who consequently believed they should have a say in shaping the future. He was prepared to include them, declaring that he was willing to work with all honest patriots. But he made it clear that he would not favour any of the factions, since he now belonged to 'the faction of the nation'. The nation, he believed, wanted strong government. The posters proclaiming the establishment of the 'new order' made it clear that this regime would not be like the others. 'The old government was oppressive because it was weak; the one which succeeds it has set itself the duty of being strong in order to fulfil that of being just,' they proclaimed. 'It appeals for support to all friends of the Republic and of liberty, to all Frenchmen.'
As far as hard power went, the consuls could count on most of the military in Paris, but not on units stationed around the country, on the Rhine and in Italy, which would probably follow the lead of their immediate commanders, many of whom were not devotees of Bonaparte and had their own views, political or otherwise. The new regime would have to tread carefully and to be all things to all men in order to disarm opposition, which chimed with Bonaparte's wish to ground his rule on national reconciliation. But he made a false move at the outset.
At their next meeting the consuls took the decision to proscribe what they deemed to be the most dangerous Jacobins, thirty-seven of whom were to be sent to the penal colony of Cayenne and a further twenty-two to be placed under police surveillance on the Île de Ré. The news aroused widespread disapproval and fears that there would be a new wave of score-settling. Cambacérès and Roederer rushed to the Luxembourg and argued vehemently against the measure, which was reversed. It is unclear who suggested it in the first place, as all those involved shifted the blame onto others. Bonaparte did his best to appear as the one who had been for clemency all along, and wrote conciliatory letters to some of those on the list. On 24 December he would proclaim an amnesty for many who had been proscribed following previous coups.
Many royalists saw Bonaparte as a potential French equivalent of General George Monck, who had enabled the restoration of the Stuarts to the English throne in 1660. Bonaparte thought such a restoration neither desirable nor viable. But he did not wish to provoke its supporters; they kept a civil war simmering in the west of France, where royalist and Catholic sentiment was fanned by émigrés based in England. He began by negotiating a ceasefire with the insurgents, on 23 November, and implemented a policy of firmness with regard to the intransigent and leniency to those prepared to lay down their arms. He aimed to weaken the religious resistance to the Republic by permitting churches to reopen and allowing people to worship on Sundays and feast days, and followed this up by releasing imprisoned priests and honouring the remains of the late Pope, who had died at Valence that summer.
A concurrent policy was to drain the pool of support for the monarchist cause. One of his first acts as consul, on 13 November, was to repeal the so-called Law of Hostages, which allowed the authorities to imprison the relatives of émigrés and active royalists. Having abrogated the law, he went to the notorious Temple and other prisons, and personally released the hostages held there. 'An unjust law deprived you of liberty, and my first duty is to return it to you,' he told them.
The previous day, 12 November, he had gone to the Institute to flatter its members, and after releasing the noble prisoners he called on the octogenarian naturalist Louis Daubenton, who was gravely ill. It was no empty gesture. While the threat from Jacobins and royalists was evident, it was the Ideologues, moderate republicans and constitutional monarchists of the centre ground, whose support was crucial; it was they who would draw up the new constitution.
Bonaparte had moved from the rue de la Victoire to the seat of power. He established himself in a set of rooms on the ground floor of the Petit Luxembourg, while Josephine made herself at home on the floor above, in the apartment vacated by Gohier. The two were connected by an internal staircase leading from his study to her apartment and on to private quarters of his own on the floor above that. He rose early and worked, sometimes with Bourrienne, until about ten o'clock, when he would take a light lunch, after which he was joined by aides and ministers to work on specific subjects. He dined at five, after which he would go up to Josephine's apartment, where he met and conferred with other ministers and members of his family in a less formal atmosphere. Establishing himself as the driving force in the Consulate had only been a first step; the next required much informal positioning.
Following the coup, each of the two chambers had delegated a commission of twenty-five members to work on a new constitution, which would be proposed by the Five Hundred and vetted by the Elders once they had reconvened. Its nature would determine whether there had been any purpose to the coup; only if it created a strong executive could political stability be achieved and the work of rebuilding France begin.
Since Sieyès considered himself an authority in this sphere, many looked to him. He set to work with alacrity, and soon came up with a project based on universal male suffrage in which the democratic element was, as Bonaparte put it, 'entirely metaphysical': six million voters would elect 600,000, who would in turn choose 60,000, who would select 6,000 'notables', whose votes would determine the composition of two legislative chambers. These would be supervised by a ' _collège de conservateurs_ ' and presided over by a 'Grand Elector' who would reside in the palace of Versailles and fulfil largely ceremonial functions, assisted by two consuls.
According to Fouché, after Sieyès had read out his draft on 1 December, Bonaparte burst out laughing, dismissing it as metaphysical twaddle. He pointed out that the Grand Elector would be no more than the idle king of caricature. 'Do you know anyone vile enough to enjoy playing such a farcical role?' he asked, whereupon Sieyès, who had presumably devised it as a political padded cell for Bonaparte himself, accused him of wanting to rule as a sovereign. In a state of dudgeon, he threatened to withdraw from the whole business. Although he had a considerable following, Sieyès had no way of mustering it. On the morning after the coup, the leading Ideologue Benjamin Constant had told him that he had made a mistake in assenting to the adjournment of the two assemblies for three months, as it deprived him of a forum in which to oppose Bonaparte.
At their meeting the following day, Sieyès delivered a lecture on the principles of democracy in support of his project, and Bonaparte made a show of submission; he decided not to oppose it, and to concentrate instead on the status and powers of the executive. He suggested that five delegates from each of the commissions meet in the presence of the consuls to give it final form, and they duly convened in his rooms on the evening of 4 December. He kept them there until the early hours of the following morning, going through each article, stripping it of unnecessary verbiage and dictating the lean précis to Pierre-Claude Daunou, who had been designated as secretary. The exercise was repeated relentlessly over the next days. Bonaparte found 'those long nights of lengthy discussions during which one had to hear out so much nonsense' utterly exhausting. These men were all significantly older than him. They represented a wealth of knowledge and experience, and watching them grapple with the task taught him that brilliant minds could be remarkably cloudy when it came to converting concepts into comprehensible prose and practical form.
Although he did manage to slip in a visit to the opera on 9 December, he devoted most of his time to the task, holding meetings on consecutive evenings until he judged it had been accomplished, on 10 December, seven days after the first session. There were still elements to be added, but he feared the process might drag on if it were not wrapped up, so on the evening of 13 December he persuaded all fifty members of the two commissions to sign the project as it stood.
It was a brilliant fraud. It guaranteed universal male suffrage, with every citizen aged over twenty-one having the right to vote. But there were to be no elections as such: they would meet in their commune and choose a tenth of their number. These would convene at the level of the department and repeat the process, designating a tenth of their number, who would then select a tenth of theirs as notables at the national level. These notables would provide a pool from which communal and departmental authorities and members of the four new assemblies were picked – by nomination in the first instance and rotating cooption thereafter.
Only the executive had the right to propose new laws, which were to be formulated by the Council of State ( _Conseil d'État_ ), a body of thirty to forty experts. The proposed legislation would be submitted for evaluation to the Tribunate ( _Tribunat_ ), a body of one hundred nominated for five years, a fifth of whom would be replaced annually. It would then be passed to the Legislative Body ( _Corps législatif_ ), consisting of 300 members also renewed by a fifth each year, which would listen to the spokesmen for the executive and the Tribunate, and then pass or reject the law. The members of the Tribunate and the Legislative Body were to be nominated by the Senate, composed of eighty men aged over forty who were the ultimate guardians of the law, sitting in closed sessions and making up their number by coopting new members.
This roughly conformed to Sieyès' project, but his idea of a Grand Elector was replaced by an executive consisting of three consuls nominated by the Senate for terms of ten years. The first consul's prerogatives included the power to initiate laws, nominate members of the Council of State, ministers, state functionaries and judges (except for justices of the peace, who were locally elected), to declare war and sign peace. The other two consuls had a purely consultative function. They did not, like the Directory, constitute a Consulate: they were Consuls of the Republic. And since the Senate had not yet constituted itself, the first three were to be chosen by the two commissions that had just endorsed the new constitution, on 13 December.
A ten-litre measuring jar was placed on the table in lieu of an urn, and the fifty members of the two commissions duly wrote out their choices on slips of paper, folded and dropped them in. Before they could be counted, Bonaparte, who had been nonchalantly leaning on the mantelpiece warming his legs before the fire, strode over and snatched the urn. Turning to Sieyès, he addressed him solemnly as though on behalf of the whole assembly, saying that they should acknowledge his outstanding merits and contribution by allowing him to nominate the three consuls. Sieyès knew he had been sidelined, and was rapidly losing the will to stand up to the energetic young man. He duly nominated Bonaparte as first consul, and acquiesced in his choice of Cambacérès as second, and as third the sixty-year-old former ancien-régime functionary Charles-François Lebrun. As Bonaparte emptied the contents of the urn onto the fire, it was recorded that he and the others had been nominated 'by unanimous acclamation'. The coup d'état of Brumaire was complete.
The 'Constitution of Year VIII' was proclaimed two days later, on 15 December 1799. In Paris, the garrison was under arms as municipal officers read out the text in the streets and public places. The new constitution came into being ten days after that, and was endorsed by a national plebiscite the results of which would be announced on 7 February 1800: by over three million votes to 1,562. It has been generally assumed that the figures were rigged, but only recent research has revealed to what extent. Lucien, who had by then replaced Laplace at the Ministry of the Interior, made his functionaries in the departments 'round up' the figures, giving another 900,000 'yes' votes, and simply added on a further 550,000 in the name of the army, which had not been consulted, adding nearly one and a half million votes in total. In reality, only 20 per cent of the electorate voiced their approval, but that was not much less than in other plebiscites held at various points during the Revolution.
The publication of the constitution was accompanied by a proclamation composed by Sieyès which affirmed that it was based on 'the real principles of representative government, on the sacred rights of property, equality and liberty', and ended with the words: 'Citizens, the Revolution is affirmed in the principles which initiated it. It is accomplished!'
Nothing could have been further from the truth. The ninety-five articles of the constitution did not include anything about liberty, equality or fraternity, and made no mention of the Rights of Man. The constitution gave absolute authority to one man, and provided no channels of opposition that he could not block with a stroke of the pen. It was highly prescriptive, Article 88 stipulating, for instance, that the National Institute must work for the perfection of the arts and sciences. Sieyès, who was nominated president of the Senate, summed up its underlying principle with his comment, 'Authority comes from above; trust from below.' It established absolutist rule decked out in the spirit of the age.
It would be wrong to see in the constitution purely the product of Bonaparte's lust for power. Sieyès and other idealists who had launched the Revolution had seen with their own eyes where unbridled democracy could lead, and all but a very few of those who had witnessed the events of the 1790s longed to close the Pandora's box they had opened. The new constitution promised to do just that. 'Here we have democracy purged of all its inconvenience,' noted the physiologist, philosopher and revolutionary Pierre Cabanis, a member of the Five Hundred, adding that 'the ignorant classes no longer exert any influence'.
On 22 December Bonaparte convened in his private apartment at the Luxembourg the twenty-nine men he had chosen to make up the Council of State. Two days later, after he, Sieyès and Ducos had resigned their office as provisional consuls, he held a meeting at eight in the evening with his two new colleagues, his ministers and the Council, at which he formally took office as first consul. Aged thirty years and four months, he dictated a proclamation to the French nation pledging 'To make the Republic dear to its citizens, respectable to foreigners, formidable to enemies.' The task ahead was immense, but he could count on the assistance of some of the greatest brains and most talented administrators, jurists, economists and statesmen of the day.
The second consul, Cambacérès, was a highly intelligent forty-six-year-old lawyer from Montpellier. He had played an active part in the Revolution, working on successive projects for a new civil code of laws worthy of the times. He had been in the Convention that condemned Louis XVI, but voted for a suspended sentence. His political activities had not interfered with his flourishing legal practice, which made him a wealthy man. An urbane homosexual, he was a fastidious dresser, with cascades of lace at his throat and cuffs, who wore his hair studiously curled. He was also a gourmet, boasting the finest table in Paris, at which guests were served by liveried servants. His judgement was sound, his manner subtle, and, thanks to his position as a senior Freemason, his contacts widespread. He valued Bonaparte for what he had done and could do for France, and would serve him well; he was not blind to his faults, and would prevent him making many a mistake.
The third consul, Lebrun, was thirty years older than Bonaparte, a minor noble from Normandy who had been secretary to René de Maupeou, the chancellor of France under the ancien régime who had fought to reinforce the authority of the crown. A man of literary tastes, he had translated the works of Homer and Tasso, and written poetry of his own. He had sat in the Convention as a moderate royalist, miraculously escaping the guillotine under the Terror, and was a deputy under the Directory. Bonaparte had been wary of Lebrun on account of his monarchist connections, and before making up his mind insisted on being shown his literary works. Though retiring by nature, Lebrun was a clever man with a firm grasp of economics, convinced of the necessity of strong executive power and opposed to unruly parliamentary structures. In this he reflected his senior colleague's views: Bonaparte was determined to work through people and bodies he could direct and control, not 'chattering chambers' which wasted time and impeded the efficient functioning of the state.
His prime instrument for the reconstruction of the French polity was the Council of State, initially composed of twenty-nine people chosen by himself, grouped in five sections (Legislation, Interior Affairs, Finances, War and Naval), all of them with high levels of expertise in their fields, and well versed in the issues of the day. They represented a spectrum of social origins, ideology and political affiliation. It was the powerhouse in which the wishes of the first consul took shape.
Bonaparte worked them hard, as he did himself, almost frantically determined as he was to get as much done as quickly as possible. 'At that time, the work of a councillor of state was as painful as it was extensive,' recalled one of them. 'Everything needed to be reorganised, and we would meet every day, either as a whole council or in our sections; almost every evening we would have a session with the First Consul, in which we would discuss and deliberate from ten o'clock until four or five in the morning.' According to Bourrienne, the first consul would give vent to his elation after work well done by singing – horribly flat.
In order to cut out needless discussion, the eight ministers who made up Bonaparte's executive did not operate as a cabinet – he sent for them when he needed them, as a general might his officers. He communicated with them through the secretary of state, Maret, who acted as a kind of civil chief-of-staff. 'I am a man you can say anything to,' he instructed Maret when he took up the job, and Maret claims he did in those days often argue with Bonaparte. A lawyer under the ancien régime and a diplomat during the Revolution, Maret was regarded by some as an obsequious nonentity, but he had the requisite skills for this task, marshalling the eight ministers to do his master's will. They had to regularly submit written reports of their activities and be prepared to be summoned into Bonaparte's presence to answer questions about them. Like his generals, they soon learned to have the facts at their fingertips, as he might suddenly ask how many barges with grain were moored on the Seine, or how much had been expended on a given project, and would not accept an approximate answer.
That did not mean they were subservient cyphers. Laplace, who had been overwhelmed by the task facing him at the Ministry of the Interior, had been replaced by Lucien. Cambacérès had been succeeded at the Ministry of Justice by André-Joseph Abrial, a distinguished lawyer and an efficient administrator. The minister of finance, Gaudin, had worked in the treasury under Louis XVI and under the Revolution, had stood up to Robespierre and not only managed to save his own neck but those of his employees from the guillotine.
The minister of police, Fouché, was nothing if not independent, and he did communicate directly with Bonaparte. His position gave him information that made him invaluable to the first consul. He had created an independent source of funding, by imposing taxes on brothels and gaming houses, 'making vice, which is endemic to all large cities, contribute to the security of the state', as he put it, and used the money to pay a web of informers of every rank and station. He made himself useful to many, and wielded considerable influence. 'Fouché has a detestable reputation,' Bonaparte admitted to Cambacérès. 'He talks ill of everyone and well only of himself. I know that he has not broken off relations with his terrorist friends. But he knows who they are and that will make him very useful to us. I will keep an eye on him. If I discover any infidelity in him I will not spare him.' Fouché records that their meetings occasionally led to ugly scenes, but he valued Bonaparte for his ability to make things happen and impose order on chaos.
Imposing order on the country was a challenge. Ten days after the coup, the consuls sent envoys to the twenty-two military districts into which the country was divided to sound out public opinion and 'explain' what had happened. The new government had received professions of loyalty and congratulations from many local authorities, but these were largely valueless, and twenty out of the ninety-nine departments had not reacted at all. The envoys found public opinion around the country indifferent or suspicious. In some areas the National Guard had refused to swear loyalty to the new authorities, there were protests from Jacobins, and the administration of the department of Jura proclaimed Bonaparte a 'usurping tyrant'. In the west and the south, where royalist sentiment was strong, news of the coup was greeted with hostility by those who assumed it to have brought republicans to power and with joy by those who fancied it heralded a Bourbon restoration.
Bonaparte could take nothing for granted, not even the army, which was underpaid and on the brink of mutiny. 'The spirit of the army is not at all favourable to the events of 18 and 19 brumaire,' Masséna reported from the Army of Italy. He had recently had to conduct a military operation against a band of 1,200 deserters who had gone on the rampage. Marmont, who had been sent to ascertain the mood in the Army of the North, was badly received. Bonaparte had already instructed Berthier to carry out a gradual purge of politically unreliable officers and malcontents.
A virtuoso of manipulation, he had been quick to take control of the levers of public opinion. 'If I give free rein to the press, I won't survive in power for three months,' he asserted. Fouché needed little prompting. 'Newspapers have always been the tocsin of revolutions,' he wrote. 'They foretell them, prepare them and end up making them inevitable.' Bonaparte nevertheless recognised the usefulness of an element of press freedom. On 17 January sixty out of the total of seventy-three papers were closed down, leaving a few to reflect the views of factions such as the royalists. Through the Interior Ministry he supported _Le Mercure_ , a counter-revolutionary journal edited by the returned émigré and ardent royalist Louis de Fontanes, who as well as being the lover of Élisa Bacciochi was convinced Bonaparte was the only man who could reform not only France but the world. Another journal, _Le Moniteur_ , was taken over and turned into the mouthpiece of the government, propounding Bonaparte's views and explaining his actions in unsigned articles.
Fouché extended censorship to the theatre, and henceforth every word uttered on stage was strictly controlled. Bonaparte had pronounced views and tastes when it came to the theatre, and was alert to its political potential. He despised comedy, with the exception of Molière's _Tartuffe_ , and believed only grand tragedy worth watching, since it revealed truths about human nature and affairs. He held Corneille and to a lesser extent Racine to be the masters, and in his lifetime he saw the former's _Cinna_ at least a dozen times, _Oedipe_ at least nine, and _Le Cid_ at least eight, and Racine's _Phèdre_ and _Iphigénie en Aulide_ at least ten times each. Wishing to avoid the representation of historical events that might suggest parallels with the present, he instructed Fouché not to allow any plays set after the fifteenth century. By flattering and favouring writers who knew how to please, Bonaparte would gradually nurture a literature of approval which bordered on adulation.
He also looked to his own reputation by putting in hand a thorough search through the archives for all documents relating to his past, particularly his relationship to Paoli and his attempts to take over the citadel of Ajaccio from French government forces in 1792. Some papers were destroyed, others replaced by forgeries rewriting history, and some of his own writings were doctored in the process.
The only other minister who had as direct access to Bonaparte and worked as closely with him as Fouché was Talleyrand. Although his loyalty was always in question, he had proved useful in the past, and as Bonaparte remarked to Cambacérès, who had warned him of Talleyrand's treacherousness and rapacious venality, 'his personal interests are our best guarantee'. Talleyrand was not only a talented negotiator and an instinctive diplomat, he was also, for all his revolutionary past, an aristocrat of the ancien régime, and thereby well placed to conduct unofficial negotiations through his kin all over Europe. This was vital in securing peace within France as well as abroad, and the first was a high priority, essential not only for reasons of security but also for Bonaparte's credibility as the man who would bring all Frenchmen together and cauterise the wounds of the Revolution.
Talleyrand had got wind of the arrival in Paris of two agents of Louis XVIII, the baron Hyde de Neuville and the comte d'Andigné, who had been sent to organise a royalist coup, or alternately to persuade Bonaparte to bring about a restoration of the monarchy. Bonaparte seized the opportunity this offered, and bade Talleyrand arrange a meeting.
On 26 December Talleyrand duly picked up Hyde de Neuville in his carriage and drove him to the Luxembourg, where he was ushered into a room and told to wait. When 'a small insignificant-looking man dressed in a scruffy greenish tail-coat entered, his head lowered', Hyde took him to be a servant, but the man walked over to the fireplace and, leaning against the mantelpiece, looked up and, as Hyde notes, 'he appeared suddenly taller and the flaming light in his eyes, now piercing, announced Bonaparte'. The first consul accepted that the royalists had a right to resist what they saw as oppression, and expressed his admiration for their loyalty to the cause of the Bourbons, but told Hyde it was now time to accept the new reality. He dismissed him after a short interview (there was a session of the Institute he wished to attend), asking him to return the following day with his colleague. Andigné too was astounded at finding himself face to face with a 'small man of mean appearance' in an 'olive coloured' tail-coat when he called with Hyde. Bonaparte urged them to give up their struggle, proposing various concessions. 'I will re-establish religious practice, not for your sake, but for mine,' he promised among other things. 'We nobles have no great need of religion, but the people need it, so I shall re-establish it.' He angrily rebuffed their suggestion that he pave the way for a Bourbon restoration, for which he would be richly rewarded. He accused the Bourbon princes of cowardice, saying that if they had had the courage to land and lead their partisans in the Vendée he might well have embraced their cause himself. He urged Hyde and Andigné to rally to him, offering to make them generals, prefects or whatever they liked.
'In his disagreeable foreign accent, Bonaparte expresses himself with brevity and energy,' noted Andigné. 'A very lively mind causes him to run his sentences one into the other, so much so that his conversation is quite difficult to follow and leaves much to be guessed at. As animated in his conversation as he is nimble in his ideas, he continually leaps from one subject to another. He touches on a matter, leaves it, returns to it, appears to hardly listen to one while not missing a word of what one says... An immoderate pride which causes him to place himself above all that surrounds him leads him continually back to himself, and to what he has done. He then becomes prolix and listens to himself speak with visible pleasure, and does not spare one a single detail that could flatter his amour-propre...'
The following day Bonaparte proclaimed an amnesty to those who laid down their arms, and freedom of religious practice. He opened negotiations with the royalist commanders through the militant monarchist Abbé Étienne-Alexandre Bernier, while declaring that troops would be deployed against those who continued to fight. The stick-and-carrot policy bore fruit, and on 18 January the royalist commander on the left bank of the Loire submitted, followed a few days later by his colleague on the right bank. They recognised that they were fighting for a lost cause, and lost faith in their ally. 'England was inclined to furnish us with some of the means to resist, but refused us those which would have allowed us to triumph,' reflected Andigné. On 25 January, in response to a sally by diehard royalists further north, the army moved in and carried out savage reprisals. Within a couple of weeks all the remaining royalist forces capitulated, and in Normandy one of the most unrepentant leaders, Louis de Frotté, was shot. Isolated bands continued to resist, crossing the line into more or less outright brigandage, even if they did claim to be robbing 'in the name of the King'. Three weeks later Bonaparte made another move to pull the rug from under the royalists' feet by setting up a commission to vet émigrés wishing to return to France: in under two years, some 40 per cent of them (around 45,000) would do so and accept the new regime. On 6 March he held an audience for the principal royalist commanders in the course of which he managed to impress them with his professions of national reconciliation, and indeed his charm. One who resisted this was the Breton Georges Cadoudal, and there were others in the country and among the émigrés who would carry their struggle underground. But Bonaparte had managed to achieve what successive governments had failed to for more than half a decade: to put an end to the civil war.
'Even the most impartial will not hesitate to admit that it seemed as though a kind of predestination had called him to command men,' wrote the forty-two-year-old barrister François-Nicolas Mollien. The veteran General Mathieu Dumas reflected that Bonaparte 'did not destroy liberty, because it no longer existed; he smothered the monster of anarchy; he saved France'. A much younger man, Mathieu Molé, declared that only one man could have achieved this, explaining that Bonaparte's origin, his exploits, his virtues, his vices and 'the kind of magic that enveloped his life' 'made him the only instrument Providence could have employed for such a purpose'. The young aristocrat Philippe de Ségur did not deny his achievement, but felt that 'it was also the work of France'.
## 20
# Consolidation
On 19 February 1800 the consuls transferred from the Luxembourg to the Tuileries. The move was dictated by the need to make room for the Senate at the Luxembourg, and by the fact that the former royal palace was more centrally situated and easier to defend against mob violence. According to Cambacérès, Bonaparte was also concerned that if a use were not found for it the building would fall into ruin. On inspecting the palace before the move he was disgusted to see revolutionary graffiti scrawled on the panelling.
On the day, in fine spring weather, the three consuls left the Luxembourg in some pomp in a coach drawn by six white horses, with Roustam resplendent in his Mameluke gear riding alongside. They were preceded by the ministers, who had to make do with ordinary Paris cabs, their numbers papered and painted over for the occasion, and by a detachment of Bonaparte's Guides. Behind the carriage came the cavalry of the new Consular Guard and an escort of other troops. The cortège was cheered by a small crowd of onlookers as it arrived before the palace. The consuls alighted, and while Cambacérès and Lebrun entered the palace, Bonaparte mounted a horse and inspected three demi-brigades which were drawn up on parade in front of the building. He then installed the Council of State in one of the galleries and formally received the city's civil and military authorities.
With the ceremonial over, Bonaparte and Josephine settled into their new abode. She was uneasy, as the place brought to mind the fate of its last occupant, Marie-Antoinette. Her apartment, which she had redecorated in yellow silk and filled with mahogany furniture, was on the ground floor. The windows opened on to the Tuileries gardens, from which the palace was separated only by a narrow terrace and a few steps. As the gardens were open to the public she made little use of them, but Bonaparte often did when he felt the need for some exercise.
He took over a set of rooms above, linked to hers by a hidden staircase. He installed his study in a room with a single window overlooking the gardens which had been a queen's bedroom, decorated in the reign of Louis XIV with a fresco of Minerva being crowned by Glory on the ceiling and landscapes on the walls. With time he would tailor the quarters to suit his working needs, but to begin with he accommodated himself as best he could, using a desk that had belonged to the last king and converting a small oratory into a bathroom.
His household consisted of ten men, including a librarian, a groom, a cook and a valet, and a dozen or so lesser staff, all marshalled by Bourrienne. He was also constantly attended by Roustam, who slept in the next room. At the end of March, Bonaparte took over from Josephine the twenty-one-year-old Belgian Constant Wairy, who became his principal valet.
He usually rose at seven and had the newspapers and sometimes a novel read to him while he washed, had himself shaved (something he was slow to learn to do for himself) and dressed. He would then work with Bourrienne in his study, only leaving it to receive ministers or officials in an outer office. He usually ate lunch alone, seldom spending more than fifteen minutes over it and often less. He preferred simple dishes, although he had brought home from Egypt a taste for dates, and enjoyed a 'pilaff'. He only ever drank a single glass of wine, always Chambertin, usually watered down. He would follow this with strong coffee. He was sometimes joined by Josephine, and often employed the time talking to people such as artists or writers he wished to see, who stood around as he lunched.
The other two consuls had been meant to take up their quarters in the palace too, but while Lebrun obliged, Cambacérès preferred to stay in his own house. The prospect of being able to keep his own table probably played a part, as no doubt did the freedom to take his pleasure without censure from the prudish Bonaparte, but so did his wise prescience that he might with time have to face the indignity of being asked to vacate the palace, as Lebrun would one day.
On the morning after he moved in, Bonaparte held the first meeting of the three consuls in the former royal palace. By coincidence, that same day its would-be occupant, Louis XVIII wrote to him from his Warsaw exile proposing he assist him in recovering the throne. Bonaparte did not reply. Cambacérès believed that at this stage he had no clear idea of the future, beyond the reconstruction of France. 'All the signs were that he wanted to be the master,' he wrote. 'Nothing suggested that the title of First Consul seemed insufficient to him.' In conversation with Roederer, Bonaparte said he would retire if he felt the French people were 'displeased' with him. 'As for me, I require little,' he told him. 'I have an income of 80 or 100,000 livres, a town house, one in the country: I do not need more.' But, he added, so far they seemed satisfied with him. He was there to stay, and made a point of showing it.
The next day the consuls held a reception for the diplomatic corps, headed by the ambassadors of the King of Spain and the Pope, then the various administrative bodies of the Republic. A former royal chamberlain was dug out of retirement, told to conduct the proceedings exactly as they had been under the last king and handed a staff for the purpose. Bonaparte received the guests as head of state, after which they were offered coffee and hot chocolate before being conducted by Talleyrand to Josephine's apartment to be presented to her and a gaggle of women who were already behaving as though they were in waiting. She had slipped into the role of royal consort as effortlessly as he had adopted the attitude of a head of state.
Gone was the threadbare 'greenish' tail-coat. He had designed a uniform for the consuls which was a clear break with the togas and plumes of the Directory. It consisted of a blue tail-coat buttoned up to the chin, with a standing collar and cuffs enhanced by gold embroidery, white breeches and stockings, and a more sumptuous version in scarlet velvet for ceremonial occasions such as this. Gone too were the lanky strands of hair limply framing his sallow face, replaced by a closer crop _à la Titus_. He also began to take greater care over his toilette, insisting on frequent changes of linen and manicuring his hands, of which he was inordinately proud. He bathed frequently and doused himself in eau de cologne.
A couple of days after this first reception, Bonaparte asked the minister of finance to locate the crown jewels; not long afterwards, visitors to the Tuileries noted that the first consul's sword blazed with diamonds, its hilt topped by the famous _Régent_ , the largest in the world. Stung by some amused comments, he felt it necessary to publish in _Le Moniteur_ an article explaining that it was not merely a piece of jewellery but a symbol of the greatness of France.
Bonaparte's new role meant he had to learn to behave. Until now, he had operated in a military environment with sallies into small-town politics and wartime diplomacy. He had never had to accommodate the niceties of convention, or adapt to civil procedure, and had not had the opportunity to develop normal social skills. He was tactless and had, according to one of his ministers, all the grace of a badly-brought-up subaltern, using his fingers at table and getting up from it regardless of whether his companions had finished eating. His pronounced views, attitude and character did not predispose him to begin a social apprenticeship at his age, and he suffered from one fundamental disadvantage in his relations with others, which Germaine de Staël perceptively identified as a total lack of the faculty of empathy.
He was kind by nature, quick to assist and reward. He found comfortable jobs and granted generous pensions to former colleagues, teachers and servants, even to a guard who had shown sympathy during his incarceration after the fall of Robespierre. He was generous to the son of Marbeuf, promoted his former commander at Toulon Dugommier and looked after his family when he died, did the same for La Poype and du Teil, and even found the useless Carteaux a post with a generous pension. Whenever he encountered hardship or poverty, he disbursed lavishly. He could be sensitive, and there are countless verifiable acts of solicitude and kindness that testify to his genuinely wishing to make people happy.
He possessed considerable charm, and only needed to smile for people to melt. He could be a delightful companion when he adopted an attitude of bonhomie. He was a good raconteur, and people loved listening to him speak on some subject that interested him, or tell his ghost stories, for which he would sometimes blow out the candles. He could grow passionate when discussing literature or, more rarely, his feelings. When he did, he was, according to Germaine de Staël, quite seductive, though the actress Ida Saint-Elme found 'more brusquery than tenderness' in his attempts to charm. Claire de Rémusat also found his gaiety 'tasteless and immoderate', and his manners often more suited to the barrack room than the drawing room. He was generally ill at ease with women, not knowing what to say and making gauche remarks about their dress or their looks, and allowing his lack of consideration for their sex to show. Only in the presence of Josephine was he less prickly.
He was most at his ease with children, soldiers, servants and those close to him, in whom he took a personal interest, asking them about their health, their families and their troubles. He would treat them with a joshing familiarity, teasing them, calling them scoundrels or nincompoops; whenever he saw his physician, Dr Jean-Nicolas Corvisart, he would ask him how many people he had killed that day. His way of showing affection was giving people a little slap on the cheek, or pinching their nose or ear. He was curiously unconscious of causing pain, even when a hard pinch of the nose brought tears to the victim's eyes, and since they regarded it as a mark of great favour, which it was, nobody objected. At the end of a stormy meeting in the course of which he roundly told off a minister about his handling of his brief, Bonaparte invited him to dine. The minister bowed, respectful but defiant, at which point he was seized by both ears, which he took as 'the most intoxicating sign of favour for him who is honoured enough to receive it'. It was a gesture of familiarity that defused many an awkward situation. Yet real familiarity was something Bonaparte seemed to fear, and only a select few, such as Duroc and Lannes, ever got away with addressing him with the familiar _tu_.
He did lose his temper, but he was quick to calm down and forgive. He did on occasion lose control and break things or stamp on his hat. He once hit the interior minister Chaptal with a roll of papers, and was known to use his riding crop, on one occasion striking a groom across the face for negligence which had led to a horse throwing him, for which he would make generous amends. Most of his rages were feigned, either to frighten people, to make an example of an officer in front of his men or a general in front of his peers, or just to test someone's reactions. His principal interest on meeting a man was to assess whether he would be of use. He expected quick and precise answers, appreciated a snap retort if it was in order, but according to his chamberlain General Thiard, 'his amour-propre was flattered if he noticed the signs of fear and confusion caused by his presence'. This is confirmed by Claire de Rémusat, who noted that in great as in small things, he applied the rule that 'people only showed zeal if they were scared'. Chaptal's assertion that 'Nobody was at ease in his company except himself' may sound harsh, but it is borne out by the testimony of others.
'The fact is that for him human life was a game of chess,' reflected Mathieu Molé, 'and people, religion, morality, affections, interests were so many pawns or pieces which needed to be moved about and used as the occasion demanded.' According to Molé, 'he was quick to grasp an individual's character, to seek out each person's weak spot, and to address it with remarkable skill and perceptiveness'. This suggests, as does Bonaparte's behaviour in general, that he was no more at ease in the company of others than they in his.
His new position aggravated the awkwardness, and his attempts to strike the right note as the head of government often went very wrong. As a token of thanks to Roederer, he decided to give him a jewelled snuffbox. On hearing of this through Talleyrand, Roederer felt offended, explaining that he would have gladly accepted a signed copy of a book on Bonaparte's Egyptian campaign, but this smacked of the classic royal gesture of giving tips to faithful servants. 'I have done nothing for Bonaparte,' he wrote. 'All I wanted was to help him do what he has done for us, I mean for all patriotic Frenchmen. It is for us to give him presents, and I have an oak-leaf ready.'
Equally gauche were his attempts to position his family in a manner he deemed appropriate. He saw it, and his close military entourage, as an extension of himself, and felt an urge to direct and control its members, both for practical reasons and in order to project a suitable image of himself. He liked to arrange the marriages not just of his family but of his military entourage too, and often selected names for their children – usually from antiquity or from the poems of Ossian; Leclerc's son was _Dermide_ , Bernadotte's _Oscar_ , Murat's _Achille_.
He ensured that Letizia was comfortably housed, and gave her enough money to live and entertain like a grande dame, but her experience of penury had made her parsimonious and, not trusting to the permanence of her son's good fortune, she squirrelled away for a rainy day every penny he gave her, some of it in foreign banks.
Joseph continued to play a role in politics, and although he was generally supportive, he affected a degree of independence. He created his own court at Mortefontaine with literary figures and members of the old aristocracy. His wife Julie was charming and docile, universally loved for her kindness and amiability, and endlessly tolerant of Joseph's infidelities.
Élisa, the least good-looking of the siblings but possibly the brightest, had moved to Paris and installed herself as hostess to the widowed Lucien, while her husband Bacciochi remained at his provincial military post. She held a salon with a literary flavour in which her lover, the poet Fontanes, held sway. Although she was admired by the writer René de Chateaubriand, whom she helped bring back to France and into favour with her brother, her salon was dull.
Despite having played a crucial role in bringing his brother to power, Lucien's attitude to him remained ambivalent. He made it clear that he regarded Joseph as the head of the family, and disapproved of what he saw as Bonaparte's usurpation of that role. He was proving an able and suitably unscrupulous minister of the interior, but being a widower he felt at liberty to pursue women, and abused his position to have his way.
Caroline had married Murat, in a civil ceremony at the Luxembourg in January, followed by a pseudo-religious one in a temple at Mortefontaine. Bonaparte had opposed the match. While he appreciated his military dash and his devotion, he considered the Gascon innkeeper's son, with his picaresque past, too coarse and low-born. 'I do not like these silly little love marriages,' he commented, speculating that one day she might be in a position to marry a monarch. But Caroline was headstrong and he could not afford to make an enemy of Murat. Pauline was also wayward, and Bonaparte felt obliged to lecture her on her marital duties to her husband. Louis, whom he loved most of all his brothers, he had the highest hopes for.
Josephine was both his greatest asset and his greatest liability. She had all the necessary grace and polish to hold court, as well as the charm to win people over and soothe anger or hurt. She was, if anything, too kind and approachable, and she lent a sympathetic ear to a stream of petitioners begging her to press their case for favour or redress. Bonaparte expressed his annoyance but found it difficult to resist her pleas, which only encouraged others to join the queue. More of an irritant to him were the jewellers, dressmakers, hatters, glove-makers, cobblers and other tradesmen who swarmed on her, indulging her insatiable appetite for luxury of every kind. This was an uncontrollable urge, possibly a disorder brought on by her experiences during the Terror, and the tradesmen knew it. However much he raged, often having them ejected physically and in one case having a dressmaker thrown in prison for twenty-four hours, they crept back when he was away or occupied with work.
One of her fancies that he shared was the house at La Malmaison, which she had bought while he was in Egypt. They drove down there at every opportunity, as she loved the privacy and he the fresh air. In November 1799, shortly after the coup, she brought the architect Pierre Fontaine to see it; he agreed the site was delightful and the gardens pleasant, but thought the house a mess. He started work on it in January 1800. He had to work around their visits so as not to interfere with their leisure, and put up with criticism of his work and frequent changes of plan from Bonaparte. When he was first presented to him on 31 December, Fontaine heard of his plans for Paris, and was commissioned to embellish the Invalides, where Bonaparte intended to have the horses of St Mark's installed along with a statue of Mars brought from Rome. He was bombarded with new ideas and projects faster than he could work on them, and found Bonaparte's impatience as well as his attention to detail and continual questioning of costs exhausting as well as irritating.
Fontaine was not the only one to feel the strain of the first consul's manic urge to get as much done as quickly as possible. Berthier was pressed to purge the army of inefficient or politically suspect officers, improve conditions for the troops, see to it that they were paid and fed, organise the supply of uniforms and equipment, improve discipline and stem the endemic desertion. Every minister was similarly harassed. Nor did Bonaparte spare himself. 'There were no fixed hours for his meals or his sleep,' recalled Chaptal. 'I saw him dine at five o'clock and at eleven. I saw him go to bed at eight o'clock in the evening and at four or five in the morning.' He generally slept about seven hours out of twenty-four, but often in three short bursts. His only means of relaxation was either violent exercise such as riding, when he would gallop furiously, or a hot bath, in which he might spend up to an hour.
Between going to the theatre and the opera, attending sessions of the Institute and inspecting troops, Bonaparte found the time to supervise such matters as the standardisation of the metre throughout French territory, appoint David as 'painter of the government' and give instructions concerning the next year's _Salon_. He absorbed information rapidly, stripping it down to essential facts, and made snap decisions after a moment's reflection – usually the right ones. His secretaries could hardly keep up with him as he dictated, racing ahead as though he were talking to someone in the room, never pausing and intolerant of being asked to repeat anything. He treated his secretary 'like a machine, to which one does not speak', as one of them put it. He would become animated as he spoke, pacing up and down his study, either bent forward with his hands in his pockets or swaggering with his hands behind his back, his right shoulder occasionally jerking upwards in a nervous tic, developing his train of thought as he went. Not the least of the difficulties was his propensity for malapropism, substituting 'amnesty' for 'armistice', 'convention' for 'constitution', 'session' for 'section', the Elbe for the Ebro, Smolensk for Salamanca, and so on. But since his writing was almost indecipherable, they nevertheless preferred to take dictation rather than copy his notes. They never stopped him to clarify a point, as his features would set in 'an attitude of imposing severity' when he was at work, and it was only when he stopped that he would smile 'with great warmth', as one of his secretaries recalled. 'He rarely laughed, and when he did, it was in a great burst, usually to show irony rather than great joy.'
His contacts with others, whatever their station and whatever their relationship, were bedevilled by a mass of insecurities, social, intellectual, physical and sexual. 'There was no kind of merit or distinction of which he was not jealous,' according to Mathieu Molé. 'He aspired to strength, grace, beauty, to the gift of being able to please women, and what is most curious is that his pride was so successful in containing his vanity, his real superiority in covering up his pettiness, that with so many opportunities to appear ridiculous he never did.' His insecurities were, however, reflected in the way life was lived in the Tuileries.
Bonaparte felt it should be conducted according to a strict etiquette in order to add dignity to his person and office, and, as he later put it, to stop people slapping him on the back – though there is no record of anyone ever having dared to do so even when he was a mere cadet. His close friend and aide since the Italian campaign, General Duroc, was put in charge of arrangements in the palace, and liveried footmen soon joined officers in uniform. Old courtiers were sought out, along with documents describing procedures at the court of Louis XVI, and quizzed about details of life at Versailles under the ancien régime. Madame Campan, former lady of the bedchamber to Marie-Antoinette, was consulted. Josephine acquired a series of noble ladies as companions. At the same time, the first consul clung to his familiar habits, walking into Josephine's dressing room to tell her what to wear. They shared the same bedroom and lived, as he put it, 'in a very bourgeois way'.
He was aware how much the coterie of men of business and women of slight virtue that had gathered around Barras and other Directors had tarnished the image of the government, and he wanted that of the consular administration to remain untainted. This accorded with his personal dislike of what he saw as profiteers and his prudish morality, and led to his banning Thérèse Tallien and other friends of Josephine's whom he regarded as morally sullied; he took a high tone when it came to any amorous activity, other than his own, and made plain his disapproval of revealing female dress.
The result was a stuffy parody of a court, which only Bonaparte seemed satisfied with as he strutted about making awkward conversation with the ladies or holding forth on some subject. Those of his entourage who had spent the past years on campaign found it difficult to comply with the imposed rules of behaviour, and had to be called to order; Junot had an unfortunate habit of attracting a lady's attention by slapping her on the thigh. Bonaparte himself disregarded etiquette when it suited him, and would on occasion escape the constraints of the Tuileries. He would put on an old overcoat, pull a scruffy hat over his face and walk the streets of an evening with Bourrienne to observe, and sometimes to engage people in conversation to find out what they thought of his regime.
In their retreats in the Faubourg Saint-Germain, the old aristocracy made fun of the parvenu court, which did lend itself to mockery; as the need to underline revolutionary credentials receded, old forms of dress revived, but lack of savoir-faire produced a mixture of fashions described by one as 'a real masquerade'. Republicans were no less scathing, and when in Josephine's drawing room people began addressing each other as 'Madame' rather than _Citoyenne_ , they voiced their horror and predicted the worst.
A routine was established, with two receptions a month for the diplomatic corps, one every second day of the _décade_ for senators and generals, on the fourth for the members of the Legislative Body and on the sixth for those of the Tribunate and the top judiciary. Once a _décade_ there was a parade at which Bonaparte would review troops, dressed in his blue consular uniform, wearing boots rather than stockings and pumps. These parades became a popular spectacle for Parisians and tourists alike. For the first consul they were an opportunity to demonstrate the power and discipline of the new state, and his own. They also provided an opportunity for units which had not served under him to see Paris and their new master.
Though vanity undoubtedly played a part, these rituals were inspired principally by the need to create the institutions and framework which Bonaparte believed to be essential props of the nascent French polity. They were all of a piece with everything else he was doing, which he famously described as laying down blocks of granite on which the state would rest.
He was not insensible to the fact that the authoritative government and strong hand required to put France back together were in conflict with the ideals of the Revolution, most of which were his own. That it had degenerated into a series of murderous convulsions he ascribed to a lack of discipline and the pursuit of consensus through discussion, which ultimately led to the rule of the mob. The tensions between liberty and effective government had been one of the principal preoccupations of eighteenth-century thinkers; in the first sentence of _Du Contrat Social_ , a seminal Enlightenment text, Rousseau sought a formula that could tailor good legislation to the imperfections of man. 'In this quest I shall everywhere try to reconcile what the law permits with what is required by the common good, in such a manner that justice and utility should not conflict,' he wrote, recognising that laws too rigid to adapt to developing events can prove pernicious in certain situations, even leading to the downfall of states.
The Revolution, Bonaparte believed, had shown the way and then got lost. 'We have finished the novel of the Revolution,' he told the Council of State. 'We now have to write its history, to pick out only those of its principles which are real and possible to apply, and not those which are speculative and hypothetical. To follow a different course today would be to philosophise, not to govern.'
Rousseau defined the man who usurps royal authority as a tyrant and the one who usurps the sovereignty of the people as a despot. 'The tyrant will break the law in order to take power and govern according to the law; the despot places himself above the law itself,' he explained. 'Thus a tyrant may not be a despot, but the despot is always a tyrant.' France needed a tyrant, and Bonaparte fitted Rousseau's definition, but he did not at this stage aspire to the role of despot. 'My policy is to govern people as the majority wishes to be governed,' he would explain to Roederer a couple of months later. 'That is, I believe, the best way to acknowledge the sovereignty of the people.'
He had gone to great lengths to allow a voice and a forum to everyone who was not opposed to the state as it was constituted. The credibility of the four constitutional bodies was grounded in his non-partisan appointments, which gave many who were ill-disposed to him a platform on which to air their views. As the various bodies met in different places – the Legislative at the Palais-Bourbon, the Tribunes at the Palais-Royal, the Senate at the Luxembourg and the Council of State at the Tuileries – they were not in a position to form a nexus of resistance. And there were few prepared to stand in his way, if only out of fear. The prominent liberal Benjamin Constant had invited a number of friends to dinner at his house on 6 January 1800, but the previous day he had criticised one of Bonaparte's projects in the Tribunate, and in consequence only two turned up – and they only because he had bumped into them that afternoon, which left them no excuse. Such self-control provided no guarantee, and Bonaparte realised the necessity of building state structures of requisite strength and stabilising the political, economic and social situation to the point at which the benefits of the status quo would outweigh any desire for change. A key element in this was local administration.
A law of 17 February 1800 fixed the administrative structure of the country (which survives almost unchanged to this day). It was based on a project devised by Sieyès at the beginning of the Revolution in 1789, and its guiding principle was centralisation, with every department run by a single prefect. 'Discussion is the function of many, execution is that of one man,' was how he had introduced it. As with many of Sieyès' projects, it was theoretically sound but wanting in practice, and the new structure put in place by Bonaparte, Daunou, Roederer and Chaptal was more effective. The administration of the country was divided up into ninety-eight departments, each with a prefect exercising full authority, assisted by a sub-prefect and a General Council ( _Conseil général_ ). A department consisted of a number of districts ( _arrondissements_ ), which grouped together the communes, run by a mayor and a municipal council. The new law abolished the election of prefects, sub-prefects and mayors, who were henceforth to be nominated by the first consul. In the interests of stability, most incumbents were maintained, but as they now held their office by the grace of the first consul, he acquired a control throughout the provinces which the monarch under the ancien régime could only have dreamed of.
Lying in the department of the Seine, Paris was granted special status, with twelve mayors overseeing the arrondissements, but the city's real mayor was the prefect of the Seine – an autonomous mayor of Paris would have been a potential focus for political opposition. Fear of the city's populace made Bonaparte act fast; barely a week after the coup d'état, some 70 per cent of the municipal authorities had been sacked, with those of lower-class origins replaced by men of property, mostly shopkeepers, who were admonished to act in such a way as to 'extinguish all hatreds'.
A month later, on 18 March, a new system of justice came into being, with 400 local courts, a high court ( _cour de première instance_ ) for every department, and twenty-nine courts of appeal, all overseen by the highest court in the land, the Tribunal de Cassation. Before any case came to court, it was brought before one of 3,000 justices of the peace. The prestige of the law was enhanced by regulations which created a new class of magistrates who were given the robes and titles which had obtained before the Revolution. This class, along with the wealthier and more active citizens in every locality, constituted what were termed as 'notables', a social grouping described by Thibaudeau as 'a kind of aristocracy destined exclusively for public office'. They would become the backbone of the new French state.
As important as any political or administrative measures were those Bonaparte undertook to stabilise the economic and financial situation. The French state had been struggling to avoid bankruptcy for most of the eighteenth century, and the crisis of the late 1780s had led to the outbreak of the Revolution. The ensuing chaos and wars had wrought yet more havoc with the economy. Consecutive revolutionary governments had issued vast quantities of _assignats_ , paper money backed by the supposed value of the confiscated _biens nationaux_. More and more notes were printed, precipitating a headlong fall in their value, leading to a monetary crisis which by 1793 had become endemic. The introduction of the silver franc in 1795 only served to underline the worthlessness of the paper currency (the printing costs of which exceeded its value), and in February 1796 the Directory attempted to halt the slide by holding a ceremonial smashing of the plates, hoping to convince people that no more would be printed. But in March it issued a new form of paper currency – which lost 80 per cent of its value in the space of a month and had to be withdrawn within less than a year. It then resorted to a sleight of hand that made two-thirds of all paper currency valueless.
The Directory just about managed to survive on the proceeds of successful wars which brought millions in specie as 'contributions' and straight looting from Italy, the Netherlands, Switzerland and western Germany. But the majority of the people suffered. While the rural population could feed itself it could not sell its produce at a reasonable price, and the knock-on effect on manufacturing led to stagnation. The only sector which thrived was that of supplying the armies, and fortunes were made by unscrupulous entrepreneurs (members of the Bonaparte clan among them) who were paid in specie by the government, bought victuals and goods at knockdown prices and often did not even pass them on to the troops but sold them to locals in occupied territories. The situation began to improve in the last year of the Directory, but this went largely unnoticed. In time, Bonaparte would take the credit, but when he took power the situation was dire. The coffers of the treasury contained no more than 167,000 francs. Expected receipts were 470 million, to cover a budget of 600 million and service a debt of 500 million.
Financial milieus, badly battered by the Directory's attempts to deal with the liquidity crisis, were ready to pin their hopes on any government that looked as though it might provide fiscal stability. Cambacérès' prestige stood high in these circles, and they were prepared to follow his lead. Shortly after the coup, on 24 November, Bonaparte received five leading financiers whom he assured that his government would respect private property, defend the social order and provide stability. He then withdrew, leaving the finance minister Gaudin to ask them for a loan, which they readily subscribed.
Gaudin instituted a lottery, sold off government property and imposed a levy on the Sister Republics. He persuaded Bonaparte to introduce a range of indirect taxes, including duties on tobacco, alcohol and salt – the very taxes which had done so much to provoke the Revolution and been repealed in 1789. In order to provide a new mechanism for raising credit for the government, on 13 February he established the Banque de France. Gaudin's work on enforcing the payment of arrears and bringing in efficient methods of collecting taxes gradually began to pay off.
Bonaparte had already gone a long way to destroy, disable or disarm the political malcontents on both the right and the left. Their capability had been eroded by the general mood of contentment. He had managed to win over many without necessarily fulfilling their hopes or expectations. Hyde de Neuville admitted that the advent of the new regime had induced 'a sense of relief and acceptance', and that 'the desire for order and stability was so universal that people were delighted to find themselves taken in hand by one capable of re-establishing them'.
'The favourable opinion of the talents and principles of the First Consul grows daily, and that opinion, along with his authority, is really held by the people,' reported the Prussian minister on 2 January. 'It is difficult to imagine in what a state of relief and happiness France soon found itself,' recorded the young Amable de Barante. 'After ten years of anarchy, of civil wars, of bloody discord, after the fall of an ignoble tyranny, we saw public order re-establish itself as though by miracle.' He did note that some far-sighted people were alarmed that these benefits all stemmed from the absolute power of one man, but the price seemed worth paying.
## 21
# Marengo
If he was to achieve his aim of rebuilding the French state, Bonaparte needed to put an end to the war. The enemies of France were preparing to resume hostilities in the spring of 1800, and the condition of the French forces did not inspire confidence. As Britain was the paymaster of the coalition, he believed that the road to peace lay through London. One of his first acts on taking office as first consul on 25 December 1799 was to write to George III professing his desire for peace and offering to open negotiations. He also sent Louis-Guillaume Otto to London to arrange the exchange of prisoners along with a brief to try to initiate peace talks.
Writing a personal letter to the king was a breach of protocol, and the response, from the foreign secretary Lord Grenville, was haughty. Addressed to his counterpart Talleyrand rather than Bonaparte, it accused France of ten years of aggression, and declared that since Britain did not recognise the present authorities in France as legitimate, it would only negotiate with the restored Bourbons. Bonaparte's response, delivered by Talleyrand, rejected the charge of aggression and challenged Grenville's attitude to the French government, given that every other state in Europe had recognised the Republic and Britain had itself conducted negotiations with it only two years before. Every nation had the right to choose its rulers, he went on, pointing out that the house of Hanover itself reigned in Britain thanks to a revolution. The point was picked up in the House of Commons by a member of the opposition who asked Prime Minister William Pitt what he would say if a victorious France were to declare she would only negotiate with the Stuarts. Pitt countered that there was no point in entering into negotiations with Bonaparte, an adventurer who would not last long, as he was 'a stranger, a foreigner, and an usurper'. Grenville replied to the second French note only to say that he would not accept any further correspondence.
Pitt could see no reason to enter into negotiations. Victory appeared to be in sight: Nelson's destruction of the French fleet in the bay of Aboukir had established British dominance in the Mediterranean, the French force on Malta was besieged, and it was thought that the French occupation of Egypt was about to collapse.
Bonaparte's departure had caused consternation in the army he left behind, followed by an explosion of anger, but this soon died down as most of the men accepted that he knew what he was doing and would soon return with reinforcements or send ships to bring them home; they had grown to trust him, and Kléber had raged against 'that little bugger' for deserting his army mainly because he missed him and his firm command. He could hold out with the 20,000 or so men he had left, all of them seasoned troops. They were regularly resupplied with essentials by blockade-running despatch boats known as _avisos_ , and by Genoese, Algerian and Tunisian trading vessels, and from the moment Bonaparte came to power a fast sloop and two frigates began making regular runs out of Toulon. But Kléber lacked the will to carry on the enterprise. He entered into negotiations with Sydney Smith, and at the end of January 1800 signed the Convention of El Arish, by which the French would evacuate Egypt with their arms.
Believing they could obtain an unconditional surrender, the British government disowned the convention and resumed hostilities. Kléber defeated an Ottoman army at Heliopolis and recovered control over the whole of Egypt. But British troops from India had landed on the Red Sea coast, and another force was preparing to come ashore at Alexandria. The letters of French officers writing home intercepted by the Royal Navy painted a picture of low morale. The ease with which the British were able to land small contingents of troops in areas of France where royalist feeling was strong suggested that France itself was vulnerable. Pitt took Bonaparte's peace overtures as a sign of weakness, believing that 'the whole game is in our hands now, and it wants little more than _patience_ to play it _well_ , _to the end_ '.
Bonaparte had also written to the emperor proposing peace negotiations, and although it was more diplomatic, the response from Vienna was just as clear as that from London. The emperor had every intention of pursuing the war. His armies had driven the French out of Italy and overthrown the Cisalpine Republic. In the north, they had pushed the French back across the Rhine. Like his British ally he misjudged the significance of what had taken place in France, seeing it as a sign of internal chaos, and was confident of victory. Austrian armies were preparing to launch a two-pronged attack in the spring, over the Rhine from Germany, and into the south of France through Italy, supported by the Royal Navy, which was to land British troops on France's south coast.
Bonaparte later admitted that 'This response could not have been more favourable to us'; if Britain had accepted his offer to negotiate, she would have used her position of power and France's weakness to force France out of Holland, almost the whole of Italy and Malta. In order to entrench his political power, Bonaparte needed to make good some of France's recent losses and regain the initiative. 'The war was essential [to France] at that moment in order to maintain the energy and unity of the State, which was still weak,' he would explain, adding that as it also strengthened his own hand, he had received the news of the British refusal 'with secret satisfaction'.
On 8 March he issued a proclamation stating that he had done everything he could to negotiate a peace, but since the allies were set on war, France must fight. 'The kings of Europe may well regret not having wished to make peace,' he said to Cambacérès as he faced up to the challenge. He meant to bring Austria to the negotiating table by a vigorous strike through Germany to defeat the 120,000 men massing there under Field Marshal Kray and then march on Vienna. He was building up a Reserve Army around Dijon which could be used either to move south against the Austrians in Italy or to reinforce the forces operating in Germany. His main problem was the condition of the troops at his disposal, which were in many cases little better than a mutinous rabble. He held parades, inspected barracks, talked to soldiers and took an interest in their wants. He took every opportunity to enhance their self-esteem, signing off a letter to a grenadier who had distinguished himself with the words 'I love you like a son.' He wanted the author of the _Marseillaise_ , Rouget de Lisle, to compose a new hymn that might galvanise them.
The question also arose as to who was to command the armies in the field. Rulers had long ago ceased leading their troops into battle, delegating the task to professionals, and as virtual head of state Bonaparte might have been expected to do so too. Yet he considered himself best qualified for the task. Moreover, since he had achieved his position largely through military prowess, if he were to hand over command to another, their success might equal or even eclipse his past triumphs and thereby weaken his right to rule. Yet his setting off to war would raise all manner of possibilities, hopes and fears; with Bernadotte in command of the Army of the West and Moreau on the Rhine, a military coup could not be ruled out. There was also the possibility of his being killed in battle, and Joseph suggested he nominate him as his successor. Political considerations also impinged on his military planning.
The 100,000-strong Army of Germany was under the command of Moreau, whom Bonaparte could not very well replace, even though he was neither willing nor capable of carrying out the operation Bonaparte had in mind. He tried to stimulate him through flattery. 'I envy your good fortune, for you have a brave army with which you will do fine things,' he wrote to him on 16 March. 'I would gladly exchange my consular purple for the epaulette of a chef de brigade under your orders.' Moreau was unmoved.
Since Moreau could not be relied on to deliver the main blow, Bonaparte would have to strike at the Austrians in Italy. 'What he doesn't dare do on the Rhine, I shall have to do over the Alps,' he concluded. 'He may soon regret the glory he is leaving to me.' He nevertheless kept his intentions secret. He had put Berthier in command of the Reserve Army, replacing him at the War Ministry by Carnot, who was dependable and competent, and popular with the Jacobins. Ten days later the Consular Guard marched out of Paris in a southerly direction, but Bonaparte remained in Paris.
On 6 April the Austrians went into action against Masséna's Army of Italy. Less than 40,000 strong, it was strung out in a defensive screen and the Austrian commander, Field Marshal Melas, had no difficulty in forcing a wedge through the middle, slicing it in two and driving one half under General Suchet back towards the Var while Masséna fell back on Genoa. Bonaparte ordered them both to hang on at all costs while he accelerated the formation of the Reserve Army, with which he would have to come to their aid. Despite his repeated pleas Moreau had still not made a move, and it was not until 25 April, after what amounted to an ultimatum, that he crossed the Rhine.
On his last day in Paris, 5 April, Bonaparte received news of a victory by one of Moreau's divisions under General Lecourbe at Stockach. After sending a letter replete with flattery and congratulation to Moreau, he went to the opera, and at two o'clock in the morning climbed into a carriage with Bourrienne and left the capital. Officially, he was only going to inspect the Reserve Army, now about 36,000 strong.
The following evening, at Avallon, he encountered a courier from Masséna who informed him that he could not hold out in Genoa for long. 'Are you not the brave, the victorious Masséna?' Bonaparte wrote back, urging him to stand firm. He sped on, inspecting the various units of the Reserve Army still on the march along the road. The next day, at Auxonne, he visited the artillery barracks and several erstwhile acquaintances came to see him. At Dôle he inspected the cannon foundry and saw the former chaplain of Brienne, Father Charles. But there was little time for banter, and at three o'clock in the morning of the following day, 9 May, he was in Geneva, where he joined Berthier. He had been enthusiastically cheered by the troops along the way and, tired as he was, appeared in high spirits.
'The whole army is on the move and in the best condition possible,' he wrote to Cambacérès, from whom he had received a report on the situation in Paris. He was pleased to hear that the capital was quiet, but repeated his order to 'strike hard the first one, whoever he might be, who steps out of line'. 'The Italian campaign was a real trial for my colleague [Lebrun] and me,' Cambacérès later recalled. 'Even in the tumult of war, Bonaparte never took his eye off us.' Joseph reported their every move to his brother.
Bonaparte lingered three days in Geneva. He was called on by its burghers, whom he edified with professions of pacifism and predictions of a general peace founded on justice and liberty. He also received a visit from the renowned Jacques Necker, minister of finance of Louis XVI before the Revolution and father of Germaine de Staël, who appeared to be fishing for an invitation to become his finance minister. Bonaparte had avoided seeing him on his previous passage through Geneva, and remained unimpressed after a two-hour conversation with him.
On 12 May he ordered Lannes to begin crossing the Great St Bernard Pass, which would bring him into the Austrian rear in Italy. He then left Geneva for Lausanne. On arriving there he wrote to Josephine telling her that she would be able to join him in ten or twelve days. His spirits were lifted by the news that Desaix had managed to get back from Egypt safely, 'good news for the whole Republic but more especially for me, who has vowed to you all the esteem due to men of your talent, along with a friendship which my heart, already very aged and knowing men all too well, bears for no other'. He urged him to make haste to join him.
Taking the army over the pass was a difficult undertaking. Everything had to be carried, by man, horse or mule. The ordnance had to be dismantled, the wheels and limbers transported on muleback and the barrels dragged along in the hollowed-out trunks of trees, with as many as a hundred men pulling each one up the steep inclines.
Bonaparte made the ascent on the back of a mule led by a guide. Although he peppered his talk with references to Caesar, Alexander and Hannibal, he did not cut much of a figure, his hat protected by an oilskin cover, his uniform hidden under a cloak. Impatient as always, at one point he tried to hurry his mount, which slipped and nearly pitched him down a precipice into the stream below. He was saved from this indignity by the guide (meaning to reward him, Bonaparte asked to know his dearest wish, which turned out to be a good mule of his own, so when he returned to Paris, he sent him the best mule money could buy). No more gloriously, on the descents he was obliged to imitate his men, who slid down the icy slopes on their bottoms.
At the summit he visited the hospice and monastery of St Bernard, and dined with the prior. On being shown the library he pulled out a copy of Livy and looked up the passage on Hannibal. His onward march was impeded by the fort of Bard, defended by a small force of Croat grenadiers with twenty-six cannon. They refused to surrender, and an attempt by the vanguard to storm the fort came to nothing. An attack commanded by Bonaparte also failed, so he decided to bypass the fort across country and press on, leaving the artillery to follow once it had surrendered. The next day he was at Aosta, from where on 24 May he reported to Cambacérès and Lebrun that events were moving fast. 'I hope to be back in Paris within two weeks,' he wrote. The following day, having ridden ahead of his escort with only Duroc at his side, he was surrounded and almost captured by an Austrian cavalry patrol, but he pressed on regardless, reaching Ivrea on 26 May. There he paused to take stock.
Leaving a force of 25,000 men under General Ott blocking Masséna in Genoa, the Austrian commander Melas with some 30,000 men had driven the French forces under General Suchet back as far as Nice. He disposed of another 50,000 or so strung out along his lines of communication or manning fortresses in his rear. If Genoa were to fall, the Royal Navy would be able to supply him through that. As well as making it possible to land allied troops, this would free up those 50,000 guarding his communications with Austria, bringing his effectives up to around 100,000 men. With such a force he would be able to sweep into the south of France unhindered.
Bonaparte only had 54,000 men. He could have made for Genoa, defeated Ott and delivered Masséna, but he decided instead to take Milan, where he would find Austrian guns to replace those he had left behind at Bard. He would also be able to join up with 14,000 men under General Moncey detached from the Army of the Rhine and another 3,000 who had crossed the Alps over the Mont Cenis pass. He calculated that on hearing of the fall of Milan Melas would race back to dislodge him and would be caught between two fires, with Masséna free to act once the siege had been raised. 'I hope to be in the arms of my Josephine in ten days' time,' he wrote to her from Ivrea on 29 May, convinced that his strategy would yield a quick result.
He reached Milan on the evening of 2 June, annoyed to find no cheering crowds. Before going to bed he dictated a Bulletin in which he reported that he had entered the city greeted 'by a people animated by the utmost enthusiasm'. Two days later, when he went to La Scala he really was cheered, and he spent the night with the prima donna Giuseppina Grassini, who was surprised he wanted her now, having rejected her when she was young and fresh. Then, he had had thoughts only for Josephine.
At eleven on the night of 7 June a captured Austrian courier was brought to him, from whom he learned shocking news. Pressed by Ott on the landward side and bombarded from the sea by Admiral Keith's squadron, fearing an insurrection by the starving inhabitants, Masséna had capitulated, leaving Genoa in Austrian hands. This not only removed his force from the scene, it raised the possibility that Melas might ensconce himself behind the walls of the city, where, supplied by the Royal Navy, he would be able to hold out indefinitely, facing Bonaparte with an impasse similar to that of Acre. For political as well as military reasons, he must obtain a quick victory. He woke up his staff and began dictating orders. By the early hours his troops were on the move.
He followed on 9 June, in the rain, with a bad cold. 'I cannot stand the rain, and my body was drenched in it for hours,' he wrote to Josephine; while she had forfeited the exclusivity of his sexual interest, she still had his affection, and he wrote to her regularly, almost always including an impish message for 'Mademoiselle Hortense'. This apparent nonchalance could not disguise his anxiety. That same day the vanguard under Lannes had come across Ott's army returning from Genoa on its way to join Melas at Alessandria and defeated it at Montebello. But Bonaparte was no clearer as to where Melas was and what he intended to do next. At Stradella he was joined by Desaix, and the two sat up all night talking.
In the morning Bonaparte sent Desaix south with two divisions to get between Melas and Genoa, and another division westwards to check him if he were intending to move on Turin instead. After another day without intelligence on the Austrian's whereabouts, he moved forward with the rest of his forces, reaching the small village of Marengo under pouring rain on 13 June. He went up a tower to survey the surrounding countryside, but came down none the wiser. From what he could tell, there was only a small Austrian force facing him at Alessandria on the opposite bank of the river Bormida. He dried his clothes and dined with a local nobleman, then made another attempt to assess the situation by counting the number of Austrian campfires. He slept badly, and was up at five in the morning.
At seven, a large number of Austrians began crossing the river over three bridges, backed up by heavy artillery fire, at which point he realised he was facing Melas, who had concentrated 30,000 men and a hundred field guns at Alessandria. Bonaparte was down to 22,000, with only twenty guns. 'Come back, in God's name, if you still can,' he wrote to Desaix. Desaix received the order at one o'clock and immediately set off, his men occasionally breaking into a run as they covered the thirteen kilometres that separated them from the field of battle.
Meanwhile, Bonaparte mounted up and led all his available reserves up to support Lannes and Victor, who were trying to hold on against the Austrian onslaught at Marengo. At two o'clock the division he had sent to cover the road to Turin returned, followed by the Consular Guard. But the best these reinforcements could do was to prevent the more or less orderly retreat from Marengo turning into a rout under pressure from the overwhelming Austrian artillery and cavalry. 'The battle appeared to be lost,' recalled Victor, and by three o'clock in the afternoon Bonaparte was preparing to disengage. Melas judged that he had won, and having had two falls from his horse that day, painful at his age of seventy-one, retired to Alessandria and lay down to rest, leaving it to his generals to finish off and pursue the French.
Just as Melas had taken to his bed, around five o'clock, Desaix turned up and, after a brief exchange with Bonaparte, led his two divisions into the fray. Simultaneously, General Kellermann, son of the victor of Valmy, gathered up his cavalry and charged the Austrian flank. As the astonished Austrians faltered, the entire French line surged forward, causing them to fall back and then flee in disorder.
It was not much of a victory. Although Austrian losses were almost twice as high as French ones, Melas could easily replace them, while the French could not make up theirs. A particularly painful loss was that of Desaix, who was killed leading his men into the attack. 'I feel the most profound grief at the death of the man I loved and esteemed the most,' Bonaparte wrote to Cambacérès. He took on his late friend's two aides, Generals Rapp and Savary, adding them to his own staff.
Fortunately for Bonaparte, Melas was demoralised by the turn events had taken, and requested an armistice. Bonaparte was good at browbeating his enemies in such circumstances and, aware that he must use his less than decisive victory to maximum effect, forced him to agree to evacuate Piedmont, Liguria and Lombardy and retire behind the river Mincio. In order to keep up the pressure, and perhaps to sway his master the emperor while he was still under the shock of his defeat, Bonaparte wrote to him saying that it had been British perfidy that had prevented them coming to terms at his first request. 'The war has taken place,' he continued. 'Thousands of Austrians and Frenchmen are no longer... Thousands of desolate families mourn their fathers, their husbands, their sons!... It is on the field of battle of Marengo, surrounded by suffering and 15,000 corpses [no more than about 2,000 were killed], that I conjure Your Majesty to listen to the cry of humanity and not allow a whole generation of two brave and great nations to go on murdering each other in the interests of others.' He argued that the interests of all the causes the emperor held dear were best served by peace, while the revolutionary ideals he was trying to contain were best spread by war. He followed this up with a letter to Melas on 20 June, bewailing the fact that their brave troops had to die in the interests of 'English merchants', complimenting him on his military talents and presenting him as a mark of his esteem with a fine sabre he had captured in Egypt. Unbeknown to him, that very day Austria signed a fresh subsidy treaty with Britain which bound her not to make a separate peace with France for another six months.
Bonaparte could not afford to waste time in Italy. The next day he was back in Milan, where he attended a _Te Deum_ at the Duomo on 18 June and enjoyed La Grassini. He also made arrangements for the reoccupied territories, leaving behind under Masséna's command a strong detachment of the Consular Guard in case he was forced to return. A week later he was hurrying back to Paris, greeted along the way like a hero. He hardly noticed as he raced on; a wheel came off his coach as it was hurtling down a hill, and he had to be pulled out of the wreckage of the vehicle through a window. At two o'clock on the morning of 2 July he drove up to the Tuileries.
The French public had been treated to exciting blow-by-blow accounts of the campaign. The Bulletin describing the battle of Marengo is largely fantasy, and reads like a bad novel. It describes Bonaparte galvanising the troops by his presence in the thick of battle, records the heroic modesty of the dying Desaix's last words and Bonaparte manfully holding back his tears on hearing them. The Bulletin of 18 June described in sentimental terms how the two black boys given to Desaix by 'the King of Darfur' had mourned him 'in the custom of their country, and in the most touching manner'. It related various glorious deeds and noble utterances of the dead hero in such a way that they fitted into and enhanced the overall narrative of Bonaparte's campaigns both earlier in Italy and in Egypt.
In order to illustrate it, his propaganda machine produced a series of prints, and he commissioned a painting from David which was to become, like that of him on the bridge of Arcole, an icon. He was to be portrayed crossing the Alps, evoking memories of Hannibal and Caesar. David proposed depicting him sword in hand, but Bonaparte told him it was not with a sword that battles were won, and he should paint him looking serene on a fiery horse. The Brutus of Vendémiaire, the Hannibal of the first Italian campaign and the Alexander of the Egyptian had been superseded by Caesar. From now on painters would depict Bonaparte not as the flamboyant general, rather as a great captain absorbed in thought – pondering the sad necessity of making war, the horrors of which were inflicted on him by 'English merchants' and European monarchs in their pay. As Bonaparte would not sit for the portrait, David used his own son as a model.
The thoughts that assailed the first consul on his return to Paris were not happy, and Josephine complained to a friend of daily 'scenes' poisoning her life. She ascribed his moodiness to the presence of La Grassini, whom he had invited to Paris and whom she correctly suspected him of visiting at night. But he had more serious reasons for displeasure: it had not taken him long to get an idea of what had been going on during his absence, and he did not like it.
A few days after the battle of Marengo, rumours had begun to circulate in Paris of a French defeat and the death in battle of 'a great general'. Confidence plummeted, as did government stocks. It was not until 20 June that news of the victory reached the capital, confirmed two days later by the official report, announced by gun salutes. Confidence surged once more, and government stocks staged a dramatic recovery. Although there is some evidence to suggest that Bonaparte, Berthier, Talleyrand, Fouché and others made a killing and may have been behind the original rumours, the episode was nevertheless unsettling, as it underlined the fragility of the consular government. That was not the only thing that bothered Bonaparte.
Sieyès and other disgruntled ideologues met regularly at Auteuil just outside Paris, and with Bonaparte off to war the question of replacing him featured in their discussions. Other malcontents met at a restaurant in the rue du Bac and at the salon of Germaine de Staël, where the subject also came up. Among the candidates suggested as possible replacements were the hero of the American and French Revolutions Lafayette, the minister of war Carnot, generals Moreau, Brune and Bernadotte, and two émigré royal princes, Enghien and Orléans.
That in itself was understandable, but what upset Bonaparte was what he saw as the lack of faith in him amongst those he depended on. Fouché and Talleyrand had both known of the confabulations, and both waited anxiously, ready to swing either way. Although they detested each other, they were drawn together by the common interest of preventing a Bourbon restoration, which would entail their political, if not physical, death. Bonaparte's colleagues Lebrun and Cambacérès were also aware of what was going on, and while the latter assured him that in the event of his death he would have persuaded the Senate to nominate Joseph as his successor, they too had waited nervously to see which way to jump. There was nothing surprising or reprehensible in this. It was only natural for people to look to the future, and there was no evidence of any kind of plot against him, but Bonaparte's sense of insecurity made him touchy. He told Roederer that what he had feared most at Marengo was getting himself killed and being replaced by one of his brothers.
The overblown accounts of the victory of Marengo had produced the wanted effect throughout the country, and he kept up the celebratory mood by staging a series of public ceremonies. On 14 July he held one to commemorate not the fall of the Bastille but the Fête de la Fédération held a year after that, on 14 July 1790. This had brought units of national guards from every corner of France to Paris to participate in an act of nationwide solidarity which involved swearing an oath of loyalty to the king and the nation before an 'altar of the fatherland'. Bonaparte celebrated this tenth anniversary with a parade on the place de la Concorde (whence the statue of Liberty which had replaced that of Louis XV was discreetly removed). Captured flags were paraded and Bonaparte praised the bravery of generals and troops, likening them to the heroes of antiquity. Although there was no oath of loyalty to him, the message was clear as to whom France should place her trust in. He admitted to Roederer that it was a profound sense of insecurity, which his apparent popularity could not assuage, that made him seek to build up his image in the public imagination.
On 20 July he received news that Kléber had been assassinated in Cairo by a native on 14 June, the day of the battle of Marengo and the day Desaix had died. Bonaparte made much of both generals, and announced that he would erect a monument to them. On 22 September he used the celebration of the anniversary of the foundation of the Republic in 1792 to stage a ceremony in which the remains of one of France's greatest generals, Marshal Turenne, were laid to rest under the dome of the Invalides. They had been rescued from the desecration of the Basilica of Saint-Denis and stored in an attic at the Jardin des Plantes, and subsequently in a convent converted to a museum, to which Bonaparte had traced them.
The two ceremonies promoted the image of Bonaparte as a man prepared to acknowledge the merits of others, even to defer to them, but in doing so he arrogated a share of their fame and glory, which were thereby incorporated into his own legend. The ceremony at the Invalides was also notable for the speech made by Lucien, according to whom the new century would be the century of France, which was recovering a greatness she had not known since the days of Charlemagne. The reference to the first French emperor was no coincidence.
## 22
# Caesar
'The state of France is greatly changed over the past year, a perfect tranquillity and general confidence have replaced civil war and despondency,' a former nobleman wrote to his son who was in Egypt with the Army of the Orient in September 1800. 'I do not know whether you realise how great is the enthusiasm of the French for the First Consul. We are as tranquil as under the ancien régime.' That was something Bonaparte would have been glad to hear; he himself was far from tranquil.
On 7 September he answered the letter he had received from Louis XVIII six months earlier, thanking him for the flattering things he had written about him, but ruling out a restoration, as that could not be achieved without civil strife and bloodshed on a vast scale. He advised him to sacrifice his interests to those of France, and activated Talleyrand's contacts with royalists and the Russian and Prussian governments, to investigate the possibility of obtaining from Louis the abdication of his rights and those of his dynasty to the throne of France (Warsaw, where Louis had moved after being expelled from Mittau (Jelgava) by Tsar Paul I, was under Prussian rule). The options held out to him ranged from a generous pension and a grand residence in Russia to some minor kingdom in Italy. But Louis replied in a letter to Bonaparte which he had published in the British press thanking him for recognising that he did have rights to the throne, and rejecting the offer of a pension. The snub produced no effect in France.
The royalist insurgents in the west had been defeated earlier that year. The British agent William Wickham, who had been coordinating espionage and plots against the French government from Switzerland, had been recalled to London. The royalist agency in Augsburg had been wound up due to lack of funds, and the British had ceased to finance the royalist émigré army under the prince de Condé, which gradually disintegrated.
Yet the question of who was to rule France was not one that could be easily settled, any more than other issues raised by the Revolution, and Bonaparte realised it. During a visit to Joseph's country house at Mortefontaine in August, he went over to the park of Ermenonville to see the tomb of Rousseau, now empty, in its picturesque setting on an island in the lake. 'It would have been better for the peace of France if that man had never existed,' he said to the owner, Stanislas de Girardin. 'Why do you say that, citizen consul?' asked the other. 'He paved the way for the French Revolution,' replied Bonaparte. Girardin pointed out that Bonaparte had only gained by that, to which the consul replied, 'History will tell whether it would not have been better for the peace of the world if neither Rousseau nor I had been born!'
The younger brother of Louis XVIII, the comte d'Artois, now based in London, continued to foster plots through agents in France, supported by the British government. The first was in the spring of 1800, when Hyde de Neuville and Georges Cadoudal had planned to kidnap and assassinate Bonaparte while General Pichegru, who had escaped from Guyana, prepared to subvert elements of the army and march on the capital. Fouché had got wind of the plot, but proceeded slowly, hoping to find out more and, by giving the conspirators time, to catch as many as possible in the act. Lucien, who as minister of the interior had his own intelligence networks, became aware of what was going on and saw an opportunity of denouncing Fouché, whom he loathed, as a co-conspirator. Fouché was not to be caught unawares and arrested the ringleaders, revealing the plot to Bonaparte on 4 May, just before his departure for Italy. There would be more than thirty plots to kill him over the next decade, most of them by royalists.
Bonaparte regarded the Jacobins as a greater threat than the royalists, as they had more supporters in the army. He contrived to keep these as far from the capital as possible: Augereau was in the Netherlands, Brune in Italy, Joubert had been sent to Milan as ambassador to the Cisalpine Republic. Potentially more dangerous than any of them was Moreau, who allowed himself to be courted by all parties – Jacobins, royalists and ideologues – and, by making the right noises, playing the honest soldier concerned only for the good of his country and remaining all things to all men. The officers in his entourage enhanced the image of him as a guileless patriot and a brilliant commander, and at his headquarters Bonaparte was seen as a self-seeking usurper.
Fouché foiled a number of attempts on the life of Bonaparte, most notably one to kill him at the Opéra. The plotters included Joseph Aréna, a Corsican Jacobin whose brother Barthélémy had allegedly tried to stab Bonaparte during the scuffle in the Orangery at Brumaire, and Joseph Ceracchi, a sculptor and pupil of Canova. They were seized red-handed at the Opéra on 10 November, but were not brought to trial. Bonaparte believed in hushing up most attempts on his life, as news of them would only dent the image of his immense popularity and put in question the stability of his regime. In some cases the culprits were locked up for a few weeks or months and then let out. In this case, they were executed.
He paid little attention to his own safety. 'He realised the impossibility of foreseeing an attempt on his person,' according to one senior policeman. 'To fear everything struck him as a weakness unworthy of his nature, to be guarded everywhere a folly.' He gave the impression of being remarkably detached. 'Well, see to it, it's your job,' he would say when informed of a threat to his life. 'It is up to the police to take measures, I haven't the time.'
He really did not have the time. From the moment he returned from Italy he adopted a punishing work schedule, holding a meeting with his fellow consuls nearly every day and sessions of the Council of State several times a week through the whole of July, in the course of which he only managed one visit to Malmaison and one to Mortefontaine. In August there were only three days on which he did not have a meeting with the consuls, in September only one. He managed three days at Malmaison and one at Mortefontaine in the course of August. That month saw the achievement of one of his principal obejctives and the initiation of a number of others.
For one who disliked 'men of business' as much as he did, Bonaparte was remarkably interested in money; having reflected on the causes of the Revolution, he appreciated its importance for the security of the state. His views on economics were unsophisticated. Like everyone else in France, he had seen the dire consequences of paper currency inflation. His personal experience contributed to a fear of penury, and he liked to have cash in hand. He did not understand or like the idea of well-balanced debt and government credit, which he saw as no more than betting on a favourable outcome. He liked specie and wanted to amass as much of it as possible.
One of the first things he did on coming to power was to charge Gaudin with reorganising the collection of tax. The next was to address the problem of the Republic's huge debt, which hindered attempts to balance the budget. Gaudin called in a friend, Nicolas Mollien, the son of a wealthy weaver of Rouen, who had started out as a barrister and who, in the course of a clandestine sojourn in England under the Directory, indulged a long-standing interest in economics. Brought down to Malmaison by Gaudin, in the course of a two-hour session in the presence of Cambacérès and Lebrun, he explained to a bewildered Bonaparte the workings of the stock market and the principle of a sinking fund, suggesting the creation of one as an agency for managing government debt. Mollien was not convinced that the first consul fully understood the concept, but Bonaparte was never slow to grasp a good idea, and Mollien was duly appointed director of the _Caisse d'amortissement_ , the sinking fund.
In a bold move, Bonaparte decreed on 11 August that interest on government bonds would henceforth be paid in specie rather than paper money. The effect was immediate; government bonds doubled in value. The 'men of business' were now firmly behind him, and the return of public confidence in the state finances stimulated economic activity and paved the way for the introduction of the silver franc in March 1803 (it would remain stable until 1914).
Another measure initiated that August was the codification of the multifarious laws in existence. France had been waiting for over a century for this, and in 1790 the revolutionary National Assembly addressed the matter. A committee under Cambacérès came up with a project for a Civil Code consisting of 719 articles. This was discussed, amended, resubmitted and rejected by the Convention in 1794. Cambacérès produced a third draft, of 1,104 articles, in June 1796, but only a few were promulgated and the commission was dissolved.
Shortly after his return to Paris, on 12 August 1800, Bonaparte appointed a commission consisting of Jean-Étienne Portalis, François-Denis Tronchet, Jacques de Maleville and Félix-Julien Bigot de Préameneu to draw up a Civil Code of Laws. Its leading light was Portalis, a brilliant lawyer and a friend of Cambacérès. He was fifty-four, Bigot only a year younger, Maleville nearly sixty and Tronchet seventy-four. They were products of the ancien régime (Maleville was a _ci-devant_ marquis) and had all been active during the Revolution. They brought a wealth of experience and a heavy dose of pragmatism to the task, and produced a draft which was passed for comment to the judges of the highest courts before being presented to the Council of State in January 1801, less than six months after their nomination.
Over the next year the Council of State would devote more than a hundred sessions to it, at least fifty-seven of them presided over by Bonaparte, who stamped his own views and personality on the final version. This was a marriage of Roman and common law, incorporating much of the legislative legacy of the kingdom of France but deeply marked by the spirit of the Revolution. It was in some ways more than a code of laws. As Portalis stressed in his introduction, it was a kind of rulebook for a new society, secular and modern. Bonaparte's contribution was considerable, and is particularly evident in the Code's stress on property as the basis of social organisation, and even more so in the domestic sphere.
His background is detectable in the Code's assumption of the family as the basis of society and of the manner in which it should function. His personal experience is detectable in the clauses governing marital relations and the rights of women. According to the Code, the husband had a duty to provide for and protect the wife, but she must obey him in everything, and could not perform any legal action without his authorisation. The husband could divorce an adulterous wife, but the opposite was only possible if he moved his mistress into the family home. A woman convicted of adultery was obliged to spend between three months and two years in a house of correction. The minutes of the meetings reveal Bonaparte's input, which is marked by his disenchantment with women caused by Josephine's infidelities and profligacy. 'Women need to be contained,' he declared, explaining that they were naturally more flighty than men when it came to sex, and liable to spend their husband's money like water. 'The husband must have the absolute power and right to say to his wife: Madame, you will not go out, you will not go to the theatre, you will not see such and such a person.' At the same time, he was sensitive on matters such as divorce, making it easier for couples living in unhappy marriages. He also sought to elevate adoption into a secular sacrament, granting it solemnity.
The _Code Civil des Français_ , as it was called, would not become law until 21 March 1804, and would be known as the _Code Napoléon_. Bonaparte was immensely proud of it. 'Proud as he was of his military glory, he was no less so of his legislative talents,' according to Cambacérès. 'Nothing moved him more than the praise frequently bestowed on the merits of a code of which he liked to see himself as the creator.' He was neither its creator nor even its editor, but he was the catalyst, and without him it would not have come into existence.
That was true of almost everything that was achieved during his consulship. In the Council of State he had gathered together the most brilliant minds and the greatest experts in the country, and he drove them like slaves. As one of them put it, 'one had to be made of iron' to work with him. In the course of 1800 alone, the Council of State dealt with 911 separate measures (in 1804 it would be 3,365). Over a period of not much more than five years it would create the entire framework of the state and, in its _auditeurs_ , the young men who sat behind the councillors taking minutes and notes, a new administrative class to run it. It was not unusual for Bonaparte to keep them at it for eight or ten hours with only a fifteen-minute break for lunch. 'Come, come, citizens, wake up,' he would exclaim if he saw them flagging after midnight, 'it is only two o'clock, and we must earn the money which the people of France give us.'
He would prepare himself before every session by reading up on the relevant subject. Taking his place at the head of a long table at which the councillors were seated he would open the discussion, which he expected to be conducted without deference to him. 'Gentlemen, it is not to be of my opinion but to hear yours that I have summoned you,' he would say if he noticed a trace of complaisance. 'The Council was made up of people of very diverse opinions, and everyone freely supported his,' recalled Thibaudeau. 'The majority view did not prevail. Far from bending to that, the First Consul would encourage the minority.' He would listen to them attentively, toying with his snuffbox, opening and shutting the lid, occasionally taking a pinch, most of which fell on the white facings of his uniform, and, without looking passing the snuffbox to an aide waiting behind his chair, who would hand him another. To help himself think, he would produce a pen-knife from his pocket and belabour the arm of his chair with it (this was regularly replaced by a cabinetmaker). He asked questions, demanded more precision, and sometimes applied the rules of mathematics to the process of arriving at a conclusion. He encouraged them to contradict and correct him, saying, 'We are amongst ourselves here, we are _en famille_.' Once a conclusion had been reached, however, he would close the discussion and quickly pass on to the next matter.
His input was considerable. 'What he did not know he seemed to anticipate and divine,' according to one. 'He had a prodigious facility to learn, judge, discuss, and to retain without confusing an infinite number of things.' His extraordinary memory, combined with an ability to pinpoint the key idea, stimulated colleagues who were more learned, wiser and more expert but needed to be pinned down, and in the words of Mathieu Molé, 'the most learned and most experienced legal minds would come out confounded by the sagacity of the First Consul and the illuminating insights he introduced into the discussion'. Roederer confirms that at the end of every session they would part feeling wiser. 'Under his governance, a rather extraordinary thing happened to those who worked with him,' he wrote. 'Mediocrities found they had talent, and men of talent felt their mediocrity, so much did he inspire the one and unsettle the other. People hitherto thought to be incapable became useful, men who had been considered brilliant were confounded...' Even Lucien, who gave his brother little credit, admitted to being impressed by his brilliance when he first saw him in action at a session of the Council.
His capacity for work was extraordinary. He would on occasion preside over a Council from ten o'clock at night until five in the morning, then retire to have a bath, after which he would get back to work. 'An hour in a bath is worth four hours' sleep,' he used to say. His work schedule outside the meetings of the consular council and the Council of State was equally punishing. He would sometimes wake up at one or four o'clock in the morning, summon his unfortunate secretary and, dressed in a white dressing gown with a scarf wrapped about his head, start dictating. He hardly ever wrote himself, mainly because his writing could not keep up with his thought process, but also because neither he nor anyone else could read it. He might take a break for some ice cream or sorbet, and sometimes for something more substantial, then resume where he had left off.
As a man of action with a military background and a mathematical mind, Bonaparte had a clear idea of how to proceed with the task he had set himself. Following the Brumaire coup he had provided himself with the means of getting on with it, and after Marengo he acquired even greater power. Many welcomed this. Germaine de Staël was enthusiastic about the 'glorious dictatorship' of 'this great man' who according to her had the ability to 'uplift the world'. Lafayette too expressed his approval of the 'restorative dictatorship' he was exercising, seeing in it the only hope of repairing the state and safeguarding liberty. But there were many who disagreed.
A decade of debate had encouraged speculation and discussion, as well as a sense of self-importance among the intellectual elites which had dominated politics from the start of the Revolution, at the expense of pragmatism. In the interests of including representatives of the whole spectrum of French politics, Bonaparte had given seats to them in one or other of the assemblies. As soon as they took their seats his opponents began to denounce him as a tyrant, emboldening the more moderate who were alarmed at the developments. His doings were also discussed and criticised in salons and at the Institute, towards which he had cooled markedly, no longer addressing its members endearingly as 'colleagues'. Much of it was harmless verbiage, but like many witnesses of the Revolution Bonaparte was wary of demagogy. Having got used to giving orders and brooking no discussion, he saw any dissent as a challenge to his authority. His sense of insecurity made him umbrageous, and he took obstruction or even delay personally.
There was also resistance in the army, which was highly politicised and clung to the ideals of the Revolution more tenaciously than the rest of society. Generals did not look favourably on one of their kind being placed above them, and there were some who felt equally entitled to such distinction. Bonaparte's best hope here, as in the political field, where he reached over the heads of the political class and appealed to the nation, was to bypass the generals and capture the hearts of the soldiers. That task was not going to be made any easier by his intention of bringing about a national reconciliation involving what he called a social 'fusion' of those who had served the ancien régime with those wedded to the Republic, which involved the reintegration into the mainstream of royalist dissidents and émigrés. This would both eliminate a threat to the state and at the same time capture a wealth of talent for it. It also involved something which was bound to offend most soldiers as well as the entire political class.
The Bulletin of 18 June from Milan had carried an unctuous account of the first consul's attendance at the _Te Deum_ in the Duomo, where the clergy of the city had treated him with the utmost respect. It was not a gratuitous piece of self-promotion. Bonaparte's views on religion were influenced by the writings of the Enlightenment, and like many of his contemporaries he rejected much of Christian teaching – he found the divinity of Christ not credible, the resurrection physically impossible, and miracles ridiculous. He could not accept that, as he put it, Cato and Caesar were damned because they were born before Christ. He was also anti-clerical. But he displayed lingering attachment to the faith, making the sign of the cross at critical moments and admitting to a love of the sound of church bells. He pondered the meaning of life, seeking explanations which were not always rational, and with time even came to believe that he had a soul. 'I do not believe in religions, but in the existence of God,' he said to Thibaudeau in June 1801, adding, 'Who created all this?' 'Everything proclaims the existence of a God, that is beyond doubt,' he asserted to another.
More important, he valued the role of religion itself. 'As for me, I do not see in religion the mystery of the Incarnation, only the mystery of the Social Order,' he told his councillors. 'How can one have order in a state without religion?' he challenged Roederer. 'Society cannot exist without inequality of wealth and inequality of wealth cannot exist without religion. When a man is dying of hunger next to another who is gorging, he cannot possibly accept this difference if he has not had it on good authority that: "God wishes it so: there must be poor and rich people in the world, but afterwards, and for eternity, things will be divided up differently."' A proper religion, he assured the Council of State, was 'a vaccine for the imagination', inoculating people against 'all sorts of dangerous and absurd beliefs'. He held atheism to be 'destructive of all social organisation, as it robs Man of every source of consolation and hope'.
He also appreciated that religious observance lay at the heart of the spiritual and temporal lives of the rural masses which made up the overwhelming majority of the population, and that by attacking it the Revolution had alienated them from the state. Attempts at introducing new, supposedly rational, substitutes such as the cult of the Supreme Being and Theophilanthropy he dismissed as inept since they lacked a numinous dimension. He was convinced that France could only be 'restored' (and his domination firmly established) if the state could engage the acceptance, if not the affection, of the rural masses and the old nobility, and this meant re-establishing the Church. Circumstances favoured him in one way.
The death of Pope Pius VI in August 1799 was followed by a long interregnum, and it was not until 14 March 1800 that the conclave, sitting in Venice, elected a new pope in the fifty-seven-year-old Cardinal Barnaba Chiaramonti, who took the name Pius VII. Not only was he an open-minded and intelligent man not averse to republican forms of government, he was locked in conflict with Austria and Naples, which both had designs on the Papal States.
A week after the _Te Deum_ in Milan, at Vercelli on his way back to Paris, Bonaparte encountered Cardinal Martiniana, to whom he expressed the wish to open negotiations with the Pope to regularise the status of the Church and religious practice in France. It was not going to be easy to achieve; most of the political class was dogmatically irreligious, while most of the military were 'cassock-haters' who had only ever entered churches in order to loot.
Many in Bonaparte's entourage were appalled when he mentioned the idea. Neither Cambacérès nor Lebrun relished it. Fouché and Talleyrand were horrified – the first had been a teacher in Oratorian schools, the second a bishop, and any reminder of their ecclesiastical past was unwelcome. Fouché argued that it would be unpopular among the people. Talleyrand, who was still technically in holy orders, did everything he could to discourage Bonaparte, but once he realised the process was unstoppable, he set about trying to get the Pope to release him from his sacerdotal vows – which Pius VII refused to do. On 5 November Monsignor Spina, Archbishop of Corinth, arrived in Paris to open negotiations. Bonaparte greeted him cordially and appointed the Abbé Bernier to prepare the ground, under the supervision of a squirming Talleyrand.
Spina's arrival was overshadowed by another event, which caused a sensation: the publication on 1 November of an anonymous pamphlet entitled _Parallèle entre César, Cromwell, Monck et Bonaparte_. 'There are men who appear at certain epochs to found, destroy or repair empires,' it proclaimed. 'For ten years we have been seeking a firm and able hand which could arrest everything and sustain everything [...] That man has appeared. Who can fail to recognise him in Bonaparte?' The author went on to say that where Cromwell destroyed, Bonaparte repaired, where Cromwell had made civil war, Bonaparte had united Frenchmen. As for Monck, how could anyone believe that Bonaparte would be happy with a dukedom and retirement under some indolent monarch? 'Bonaparte is, like Caesar, one of those characters before whom all obstacles and all opposition give way: his inspiration seems so supernatural that in ancient times when the love of the wondrous filled people's minds they would not have hesitated to believe him to be protected by some spirit or god.' By suggesting the parallel with Caesar, the pamphlet suggested Bonaparte's elevation to the ultimate authority, but also raised fears (the Aréna–Ceracchi conspiracy was fresh in people's minds). 'Happy republic _if he were immortal_. [...] If suddenly Bonaparte were lost to his country, where are his heirs?' The author feared that if he were to be killed they would find themselves back under either the 'tyranny of the assemblies' or a 'degenerate race' of kings. Without proposing anything, he suggested the need to give permanence to Bonaparte's authority and ensure its perpetuation.
The author was Lucien, possibly encouraged by Bonaparte, in the interests of testing public opinion. This reacted with a predictable degree of outrage. The first consul affected to share it, ordering a thousand copies to be publicly burned. For the benefit of insiders who knew or suspected the identity of the author he staged a dressing-down of his younger brother which culminated in Lucien throwing his ministerial portfolio onto the desk and flouncing out of the room. On 5 November he was relieved of his post and replaced by a favourite of the ideologues, Jean-Antoine Chaptal. Letizia attempted to intervene on behalf of her favourite son, and Joseph tried to mediate, but Bonaparte was intractable. Lucien's wife had died, and he was leading a rackety life of promiscuity ill-suited to a leading minister (he would as good as rape any woman unwise enough to call at the ministry), which Fouché was avidly recording and publicising. Talleyrand suggested sending the delinquent to Madrid as ambassador, and he duly left Paris. Josephine and Fouché were exultant – Fouché because he hated Lucien, Josephine for even more weighty reasons.
Whatever the public reaction, Lucien's pamphlet had provoked discussion on how to ensure the survival of the stability achieved over the past year. It had made the connection between that and the person of the first consul, and pointed the discussion in the direction along which he was thinking. What Bonaparte, and the country, needed above all was an end to the war. Whether he believed it or not, he argued that a republic by its very nature represented an affront to the hereditary monarchies of Europe, and therefore a fundamental _casus belli_. The only way of removing this source of conflict was to give the French state's political institutions a 'form', as he put it, 'a little more in harmony' with theirs. The Revolution's primary achievement had been to overthrow the feudal aspects of the ancien régime and establish a constitutional monarchy. The Republic had come into being as a result of untoward events which the majority of the population did not endorse. Turning the state back into a monarchy was unthinkable only to the relatively small number of dedicated republicans. 'The party which longs for a king is immense, enormous, although it is united by nothing other than the deep feeling that there should be one,' reported an informer in Paris to the court of Naples in the spring of 1798, adding that nobody wanted Louis XVIII, only a warrior king and a constitutional monarchy.
The institution of monarchy may have still surrounded itself with anachronistic pomp, but it no longer required the kind of sacral aura it had in the days of divine right. Whereas the Bourbons had been on the throne of France for 300 years, the house of Hanover had reigned in Britain for only eighty-six, the same as the Bourbons in Spain, those of Naples only sixty-six, and the Habsburgs had entrenched themselves on the imperial throne as late as 1745. The elector of Brandenburg had decided to call himself king in Prussia less than a hundred years before, and the tsar of Muscovy emperor of Russia in 1721.
In the circumstances, there was no reason why France should not acquire a new dynasty. The question was who was to found it. There were potential candidates among the cadet branches of the French royal house, but they were too closely associated with the ancien régime. They were also unlikely to possess the qualities requisite to deal with the dangers of the French political scene. The man who had those was currently in charge, so there seemed little point in getting rid of him. But he had no heir. And since he had no ancient lineage, or other assets beyond his talents, military and administrative, there was no _a priori_ reason to differentiate between him and any other capable general.
At the beginning of December, news reached Paris of a brilliant victory over the Austrians at Hohenlinden by Moreau. Bonaparte heaped praise on his general's military skills, and presented him with a magnificent pair of pistols. But he was not impressed, or pleased. He had attempted to neutralise him, even going so far as suggesting he marry his sister Caroline, but Moreau was ruled by his mother-in-law, Madame Hulot, a harridan who hated Bonaparte and particularly Josephine. The feeling was mutual, and Bonaparte's cup overflowed when she made a snide remark about his alleged incestuous affair with Caroline.
Following his victory, Moreau's reputation rode high, and while he was far from eclipsing Bonaparte, he was a reminder that there were alternatives, and his very existence heartened ideologues frightened by Bonaparte and royalists still searching for a 'Monck'. He might well have found himself playing that role if things had turned out differently on the night of 24 December.
That evening, Bonaparte went to the Opéra to listen to Haydn's _Creation_. As his carriage trundled down the rue Saint-Nicaise, it passed a stationary cart loaded with a large barrel. This was filled with gunpowder, and exploded just after his carriage had passed it, devastating the street, killing four bystanders and wounding another sixty, some of whom would die, but inflicting no harm on Bonaparte. He carried on to the Opéra, where he was deliriously greeted by an audience who had heard the explosion and feared the worst.
On his return to the Tuileries after the performance, he found the palace teeming with concerned generals and officials. When Fouché turned up, Bonaparte taunted him for failing to forestall the attempt on his life, which he attributed to Fouché's Jacobin 'friends'. The minister assured him that it had been the work of royalist conspirators, and promised to prove it within a week.
With his colleague Réal, Fouché carried out a forensic examination of the scene and what remained of the horse that had drawn the 'infernal machine' into position. Réal noticed that one of its legs was newly shod. They showed the shoe to every farrier in Paris, until one recognised it and was able to give a description of the men who had brought the horse to him. They took the nag's head to every horse-dealer, which led them to the man who had bought it. The arrests that followed established a direct link to Georges Cadoudal, and to the British government.
It was all of a piece with Hyde's earlier plan to kidnap Bonaparte, and his more recent one, uncovered by the police, of landing a force at Saint-Malo. But Bonaparte feared the Jacobins more than the royalists. 'The [royalist rebels] and the émigrés are a disease of the skin,' he said to Fouché a couple of days after the attempt, 'while [the Jacobins] are a malady of the internal organs.' He ordered Fouché to draw up a list of active Jacobins, whom he intended to have deported to the penal colonies of Cayenne and Guyana. It came to about a hundred names. The assemblies balked at proscribing so many, some of them colleagues. In order to bypass them, Cambacérès and Talleyrand devised a legal ploy whereby the Senate, acting in its capacity as guardian of the constitution, issued a _senatus-consulte_ , an edict dressed up as a constitutional safeguard, enacting the contested measure.
The event had proved a godsend to Bonaparte. A number of royalists were shot, as were some Jacobins. A larger number of those were deported, including what Bonaparte called the sergeants of revolution, those capable of rousing the masses. 'From then on, I began to sleep peacefully,' he confided. More important, the episode had led to the invention of the _senatus-consulte_ , a mechanism for making law on the hoof, which he would soon be using to force through a measure establishing special tribunals without juries to deal with certain categories of criminal activity.
Most important of all, the attempted assassination had shocked public opinion, not only by its violence. It was seen as an attempt not just on Bonaparte's life, but on the future of the state just as it was emerging from ten years of anarchy and violence. It drew to Bonaparte all the sympathy a victim elicits, and at the same time brought home how fragile was the new-found stability, and how closely it was tied up with his person. It thereby bound the future of the country more closely to him and to his survival. After little more than a year in power, he had become the repository of the hopes of many, and he was about to make the dearest of these come true.
## 23
# Peace
Defeated in Italy by Bonaparte and pushed back further by General Brune, and trounced in Germany by Moreau, Austria could not pursue the war any longer. The emperor had sent Cobenzl to Paris in the autumn of 1800 to prepare the ground, and on 9 February 1801, as soon as she was free to do so under the terms of her alliance with Britain, Austria made peace with France by the Treaty of Lunéville. News of its signature reached Paris on 12 February. The carnival was in full swing, and people reacted with joy.
The terms were less favourable to Austria than those of Campo Formio, as she lost some of the land she had then acquired in Italy. In addition, Austria recognised France's incorporation of Piedmont and the existence of the Batavian, Helvetic and Cisalpine republics, the last expanded by the incorporation of Modena and the Legations. The former Habsburg fief of Tuscany was renamed the kingdom of Etruria, and was to be ruled by the Bourbon Duke of Parma (which had been incorporated into the Cisalpine Republic). By the terms of a treaty negotiated with Charles IV of Spain, the new King of Etruria married one of his daughters, and his kingdom became a French satellite. Austria was also obliged to admit France as a party in the process of rearrangement of the Holy Roman Empire, made necessary by the dispossession of the former rulers of states on the left bank of the Rhine, which had been incorporated into France.
The settlement was hard on Austria, but it was an even more severe blow to Britain, which lost her principal ally and proxy on the Continent. Worse still, by a separate treaty the kingdom of Naples ceded the island of Elba to France and closed its ports to British shipping, while further treaties with Algiers, Tunis and Tripoli enhanced France's position in the Mediterranean. Malta and Egypt were still in French hands, and an agreement signed in February 1801 guaranteed France the support of the Spanish fleet.
The situation begged for a general settlement, to include all the powers involved since the outbreak of war in 1792, but that would not be easy to achieve, given the nature of the conflict; its roots reached into the second half of the eighteenth century, when traditional dynastic considerations were superseded by the need to keep up with rivals and seek security through a 'balance of power'. If one state made a gain, others felt they must make an equivalent one, precipitating a Darwinian process in which stronger states grew at the expense of weaker ones. Recent wars and the partition of Poland had demonstrated that no frontier could be considered immovable and no throne permanent. The process was accompanied by the disintegration of old networks of alliance and restraining rivalries – Franco-Austrian control over the smaller states of Germany, the French-Swedish-Polish-Turkish barrier against both Russia and Austria, the Franco-Spanish family compact to check British ambitions in the colonies, the Anglo-Dutch equivalent, and so on. The situation was complicated by the spirit of the times: anachronistic structures such as the Holy Roman Empire and feudal monarchies came under fire from the intellectual forces unleashed by the Enlightenment and from nascent nationalism.
Two powers were growing faster than the rest. To the east, Russia had moved her frontiers 600 kilometres into Europe in the space of fifty years while advancing eastwards and reaching the Pacific Ocean. To the west, Britain was extending her overseas dominions. The only power to rival them was France, which alone could help Austria check Russia's westward expansion and, with her Spanish ally, stand up to Britain's drive for control of the seas.
The Revolution had curtailed French ambitions and its leaders had sent out pacific messages to all nations, but as their doctrines challenged the social order, they drew monarchs and ministers all over Europe together in its defence. In August 1791 the Holy Roman Emperor Leopold II and King Frederick William II of Prussia issued a declaration after a meeting at Pillnitz in Saxony in support of the beleaguered Louis XVI. In France, this was received as a challenge, and led to the outbreak of war in 1792 and an invasion by Austria and Prussia aimed at restoring the ancien régime. The invaders were defeated and the French proceeded to 'liberate' the Austrian Netherlands (Belgium). The French Convention issued an Edict of Fraternity pledging to support all nations struggling for freedom from feudal oppression. Britain, along with Sardinia, the United Provinces, the Holy Roman Empire and Spain, joined the coalition against revolutionary France. The army of émigrés at Koblenz and popular risings in the Vendée and the south of France were financed, armed and supported with troops. While Britain did not have a standing army of any significance on hand, she paid others to fight on her behalf. But while both sides made much of the ideological crusades they were fighting, this thinly veiled what remained essentially opportunistic policies.
At the beginning of 1793 Georges Danton had put forward the idea that France had 'natural' frontiers designated by the Channel, the Atlantic, the Pyrenees, the Mediterranean, the Alps and the Rhine, which meant the annexation of large areas that had not lain within the borders of 1789. While 'liberating' oppressed sister nations, the French Republic shamelessly relieved them of their riches. Austria saw the possibility of reinforcing its grip on Italy and of helping itself, along with Russia and Prussia, to what remained of Poland. Russia acquired a longed-for naval base in the Mediterranean by occupying the Ionian islands. Britain seized France's colonies and those of her Dutch allies. Prussia was not averse to taking the British royal family's fief of Hanover.
Although it was through war that he had achieved power, Bonaparte knew that only peace could ensure his survival. His first success came on 3 October 1800, with the signature at Mortefontaine of a treaty with the United States brokered by Joseph. It took place in the presence of Lafayette, who had fought alongside George Washington, and was celebrated with a banquet followed by theatricals and fireworks. (A prolonged downpour marred the proceedings by turning the gardens into a sea of mud and delaying the building of the stage, providing time for the workers to join the artificers in helping themselves to the wine meant for the banquet, which did not begin until midnight, to the accompaniment of an erratic firework display.)
The next step had been peace with Austria, then Naples, followed by the signature of new treaties with Spain and Portugal, negotiated by Lucien. That left Britain and Russia. Since Britain refused to enter into negotiations, Bonaparte sought to apply pressure by isolating her, which could best be done through alliance with Russia, which resented Britain's command of the oceans and felt threatened by her colonial reach in Asia.
The tsar, Paul I, had grown disenchanted with his partners in the coalition and withdrawn his troops. Increasingly resentful of the Royal Navy's high-handed searching and confiscation of neutral vessels, he combined with Sweden, Denmark and Prussia in setting up the League of Neutrals, which denied British ships access to the Baltic. Using the opportunity provided by the presence in France of Russian troops taken prisoner in Switzerland in 1799, Bonaparte opened negotiations and suggested a similar league in the Mediterranean. 'It is in the interests of all the powers of the Mediterranean, as well as those of the Black Sea, that Egypt remain in French hands,' he wrote to Paul on 26 February 1801. 'The Suez Canal, which would connect the Indian seas with the Mediterranean, has already been drawn; the work is simple and requires little time, and it would yield incalculable benefits to Russian commerce.' He urged the tsar to pressure the Porte to allow the French occupation of Egypt to continue.
Bonaparte also pointed out that their two countries had no quarrel and many common interests, and that only British perfidy had turned them against each other. He even raised the possibility of joint action to despoil the Ottoman Empire, and, knowing that Paul had assumed the role of protector of the Order of St John, he threw in a present for the tsar – the sword of Grand Master Jean de la Valette, taken after his capture of Malta on the way to Egypt. It was a gesture bound to appeal to the impetuous tsar, with his chivalric fantasies. Paul despised the French on account of the Revolution, but he was fascinated by Bonaparte, and he sent two envoys to Paris.
At the beginning of March Paul ordered the British ambassador, Lord Whitworth, to leave St Petersburg. Before his departure Whitworth encouraged and gave funds to a group of noblemen who were conspiring against the tsar, and on the night of 23 March 1801 Paul was assassinated in his bedroom. Bonaparte had no doubt as to who was behind the act. On 2 April the Royal Navy bombarded Copenhagen and the Armed Neutrality rapidly unwound, the new tsar, Alexander I, making peace with Britain in June.
Britain was nevertheless isolated, internationally unpopular, and threatened with unrest at home. The Armed Neutrality had interrupted grain shipments, leading to a rise in the price of wheat and a number of 'bread or blood' riots. The crisis over the Act of Union with Ireland precipitated Pitt's resignation on 16 February 1801. He was succeeded by Henry Addington, whose foreign secretary Lord Hawkesbury began talks in London with the French envoy Louis Otto.
Coming to terms was made no easier by the role played in the wars by propaganda. British public opinion was moulded by the rhetoric of Edmund Burke, a raucous press and a flood of scurrilous cartoons, all of which demonised the French Revolution as a disgraceful, bloodthirsty breakdown of civilisation. Its key figures were represented as degenerate, vicious and ridiculous, and 'Boney' came in for the most vile, if often amusing, treatment. The French response was to represent the toiling masses of Britain as the slaves of the monster Pitt and the oligarchy of lords ruling the country. They were accused of wanting to dominate the world and behaving like, in Talleyrand's words, 'vampires of the sea' who needed to be 'exterminated' in the interest of 'civilisation and the liberty of nations'. The rhetoric on both sides incited hatred, and Nelson instructed his men that 'no delicacy can be observed' when making raids on the French coast. British treatment of French prisoners of war shocked Bonaparte. 'Is it possible that the nation of Newton and Locke has so far forgotten its standards?' he wrote to Talleyrand.
The negotiations were complicated by the two countries still being engaged in military operations against each other, with minor stand-offs in various colonial outposts, continual clashes at sea, and a major confrontation in Egypt; Bonaparte was doing everything he could to supply and support his forces there. A British force had landed on the Red Sea coast, and on 1 March another 15,000 British troops landed at Alexandria. But Kléber had been succeeded by General Menou, who unlike his predecessor did believe that Egypt could be held. He had married an Egyptian woman and converted to Islam, taking the name Abdullah, which earned him some popularity with the locals, as did a number of sensitive improvements in the administration of the country. He managed to hold off the British force which had landed at Alexandria in an inconclusive battle, but was hemmed in there while General Belliard was besieged in Cairo. On 31 August 1801 Menou capitulated, ending France's Egyptian venture.
This helped bring matters to a head, since the British cabinet had not wished to sign a peace with the French in Egypt, and there was now some urgency in London to conclude. Britain's ally Portugal had been forced by the Treaty of Badajoz on 6 June to give up the province of Olivenza to Spain, to cede part of her colony in Guyana to France, and to close her ports to British shipping. France had reached agreement with Russia, and a treaty would be signed in Paris on 8 October, further isolating Britain. Preliminaries of peace were signed in London on 1 October, and Lord Cornwallis was delegated to France to negotiate the treaty.
He was greeted at the Tuileries on 10 November with a splendid reception followed by a banquet for 200 people. The sixty-two-year-old Englishman, who had been in public service all his life, fighting in America and governing in India and Ireland, made a favourable impression on the first consul. He then went to Amiens, where he would flesh out the details with Joseph Bonaparte. Cornwallis thought Joseph 'a very sensible, modest and gentlemanlike man', and the negotiations assumed a cordial tone. In recognition of his military past, Bonaparte placed a regiment at Cornwallis's disposal so he could distract himself by making it parade and manoeuvre.
Bonaparte sent his brother detailed instructions, providing him with arguments to use against the British, but Joseph was confident that with 'patience and firmness' he would be able to stand up to and wear down his opponent. He argued that the British 'have in previous treaties always triumphed over what they like to call French petulance' with their chief weapon, which he identified as 'imperturbability and inertia', and by keeping calm himself he would disarm his opposite number. The negotiations were complicated by Bonaparte, who had a habit of upping his demands on a matter just as it had been settled. He also introduced new ones, such as access to the Newfoundland fisheries and expansion of the French enclaves in India. Cornwallis stood firm on many of these points, but his superiors were impatient to conclude, as the country was exhausted and desperate for peace after nearly a decade of war during which the lower classes of the population had suffered serious hardship.
Bonaparte would not allow considerations of foreign policy to distract him from his principal task of rebuilding the French state, and hardly a day passed during the first eight months of 1801 without a session of the Council of State or of the three consuls, dealing with everything from the legal system to the repair of roads, and including the reorganisation of the government itself, with the creation of a new Ministry of the Treasury. When the price of bread had risen because of shortages, causing discontent and even riots in the spring, he reacted not just with characteristic speed and decisiveness, purchasing large quantities of flour in order to produce subsidised bread, he also put in place a mechanism whereby such events could be anticipated and crises avoided in the future.
He had returned from Egypt with a pulmonary inflammation, and was still afflicted with scabies contracted at Toulon. A succession of doctors had failed to alleviate his condition, which was aggravated by his punishing work schedule, not to mention the exertions of the Marengo campaign. His lifestyle, with its irregular eating and sleeping hours and frequent overnight travel by jolting carriage, cannot have helped. By the end of June 1801 he was so ill some thought him moribund. It was then that he engaged the services of Jean-Nicolas Corvisart, an eminent physician with an empirical and holistic approach to medicine. Soon after, Josephine was delighted to note that his spots were clearing up. By means of poultices and other natural expedients, Corvisart cured Bonaparte of his ills, so much so that over the next months his appearance would be transformed, his complexion losing its sallow sickliness and his face its hollow look.
Partly on account of his health, Bonaparte had spent most of the summer of 1801 at Malmaison. Thanks to Josephine, the house had acquired neo-classical interiors filled with furniture by Jacob and vases of Sèvres porcelain. She had transformed the gardens, filling them with roses and rare plants, and landscaping the park in the English manner. She also collected animals in a menagerie, which would with time contain a kangaroo and an orangutan, while llamas and gazelles roamed the park. It was characteristic of Bonaparte that while he kept quibbling with the architect Fontaine over the expense of every bit of work he carried out there, he had installed as librarian his erstwhile French master the ageing Abbé Dupuis, and as gatekeeper with a generous pension the man who had been the concierge at Brienne.
Although he worked just as hard there as in Paris, holding meetings of the consuls and the Council of State, interviewing ministers and generals, and sometimes staying up at night dictating to Bourrienne, after dinner, which was usually at six o'clock, Bonaparte would take his leisure in a way that he never could in the Tuileries. There were several guest rooms, and there was usually a house party. They would put on amateur theatricals, stroll in the garden or play children's games, with Bonaparte taking off his coat and rushing around to catch or get away from others like a schoolboy – and often cheating. He was amused to discover that the gazelles liked snuff, and would regularly treat them to some. Glancing out of the window during his toilette one morning, he noticed some swans on the ornamental canal and told Roustam to bring his guns. He then started shooting at them, laughing like a child. When a horrified Josephine rushed in and snatched the guns away from him, he said, 'I was just having some fun.'
At Malmaison he was approachable, relaxed and affable. 'I was expecting to find him brusque and uneven of temper,' recalled Joseph's secretary Claude-François Méneval, 'instead of which I found him patient, indulgent, easy in his manner, not remotely demanding, of a gaiety which was often boisterous and provocative, sometimes of a charming bonhomie, though this familiarity on his part did not encourage reciprocity.' It did not discourage the painter Isabey, who, seeing Bonaparte leaning over to inspect a flower one day, leapfrogged him.
Bonaparte was now regularly having affairs – with Giuseppina Grassini earlier that year, then with Mollien's wife, then Adèle Duchâtel, the wife of one of his functionaries, not to mention the odd conquest among others of his entourage. Josephine was jealous, and made her servants and ladies patrol the corridors in the Tuileries. With her husband's elevation and the talk of who might succeed him, she felt threatened by her thirty-seven years and her inability to produce an heir. She had consulted Corvisart, and that summer went to take the waters at Plombières in the hope of enhancing her fertility, accompanied by Letizia. Bonaparte himself did not attach much importance to the lack of an heir, and showed no signs of dissatisfaction with his marriage. 'You should love Bonaparte very much,' Josephine wrote to her mother on 18 October. 'He is making your daughter very happy; he is kind, amiable, he is in every way a charming man, and he loves your Yéyette.'
He had for years treated his younger brother Louis as more of a son than a sibling, and noticing this, Josephine had determined that he should marry her daughter Hortense. She was eighteen, pretty and endowed with her mother's charm (and bad teeth), and Bonaparte had immediately taken to her. She would keep him company when Josephine was away taking the waters, and a deep friendship developed between them. He had adopted her along with her brother Eugène, and if she were to marry Louis their son would be as good as his grandson.
This incipient assumption of Bonaparte's heritage by the Beauharnais clan was not the least of the sources of discord between him and his siblings, who insisted on maintaining a degree of independence while riding on his success. Joseph, who had amassed immense wealth over the past few years and set himself up as a grandee, hosting house parties and hunts at Mortefontaine, maintained close links with many of those who voiced their opposition to Bonaparte and blocked his plans in the Tribunate. He was also, for family reasons, close to Bernadotte, whom Bonaparte despised and would long ago have destroyed had he not been married to Désirée Clary. Joseph considered himself the intellectual equal of his brother and, influenced by liberals such as Benjamin Constant and Germaine de Staël, often argued with him.
Lucien had returned from his posting as ambassador in Madrid vastly enriched, having won the favours of the queen of Spain and exacted bribes at every step in the negotiation of treaties with Spain and Portugal – along with twenty paintings from the Retiro collections (to add to his already impressive 300, including works by Rembrandt, Raphael, Michelangelo, Poussin, Caracci, Rubens, Titian and Leonardo), a sack of diamonds and a large quantity of cash (a portion of which he invested in London) – and he brought back a Spanish marqueza whom he installed in his Paris mansion and the château at Le Plessis he now acquired. Unlike Joseph's, his house parties there were anything but sophisticated, with childish games being played and guests subjected to apple-pie beds and itching powder. That did not stop him taking a high tone with Bonaparte, denouncing him as a tyrant and encouraging others in opposition to him.
The tyrant still governed through institutions, and these were made up of people with ideas of their own. His inability to see things from the perspective of others meant that he could not discuss or persuade, only dismiss their views as 'metaphysical nonsense' and see criticism as opposition. In his view, expressed in a discussion of the plays of Corneille, the public good, which he described as 'the reason of State', was a higher aim which not only justified but demanded behaviour which in any other circumstance might be criminal. Corneille had understood this, and were he alive, Bonaparte declared, he would make him his first minister. Convinced of the rightness of the mission he had embarked on, and intolerant of those who could not see it, he was not inclined to waste time trying to persuade them.
This came as a shock to early supporters such as Germaine de Staël, who had expected her salon to become the ideological powerhouse of the new regime. She had encouraged Benjamin Constant to provide constructive opposition on the English model in the Tribunate, but his criticism of the legislation presented to it enraged Bonaparte, who pointed out that since none of those sitting in the various assemblies had been elected they had no legitimacy, while he, whose assumption of power had been endorsed by the plebiscite on the constitution, was the elect of the nation. When Joseph tried to patch things up between him and the inconvenient bluestocking, Bonaparte merely told him to ask her what her price was for submitting. 'I do not know how to show benevolence to my enemies,' he snapped at Talleyrand when he suggested a more emollient approach. 'Weakness has never led anywhere. One can only govern with strength.'
To Lafayette, he said that the people were 'fed up' with liberty. He had a point – the ideologues chattering away in their assemblies and salons were out of touch with the majority of the population. This was glaringly obvious when it came to Bonaparte's intention of reinstating the Catholic Church. The ideologues saw it as a betrayal of the Revolution, which had banished religious 'prejudice' and all the flummery that went with it. They tried to persuade him to abandon the idea, but he was adamant; when Volney tried to change his mind, their exchange flared into an argument in the course of which Bonaparte allegedly kicked the eminent _philosophe_.
Talleyrand's negotiations with Spina were not going well. The principal stumbling blocks were the Pope's insistence that Catholicism be declared the religion of state, the return of or compensation for confiscated Church property, and the resignation of all existing bishops. To these he added a demand for the return of the province of the Legations. Bonaparte's response was to bully Spina, flying into one of his feigned rages, threatening to occupy the entirety of the Papal States, to found a national Church in France, and even to become a Protestant if he did not sign an agreement within five days.
The Pope replaced Spina with the more intelligent and skilful Cardinal Ercole Consalvi. Bonaparte welcomed him with great pomp at an audience for which he encouraged him to wear 'the most cardinalesque costume possible', but began bullying him too, setting an unreal ultimatum of five days. After much horse-trading, agreement was reached, and the Concordat (as it was named, after a twelfth-century precedent) was to be signed on 13 July 1801. At the last minute the Abbé Bernier warned Consalvi that Bonaparte had made some alterations, and the text he would be presented with was not the one agreed. When Consalvi declined to put his signature to it, a furious Bonaparte dictated yet another version, which Consalvi also rejected. Bonaparte threatened to act like Henry VIII of England, but he had met his match in Consalvi, who was not to be bullied. The Concordat was eventually signed at midnight on 15 July.
Catholicism was recognised as the religion of the majority of the French. A new network of dioceses was created. The first consul would choose the bishops, who would then be invested by the Pope. Church property would not be returned, but the French state would pay for the upkeep of churches and salaries to priests, who would swear an oath of loyalty, effectively becoming its functionaries.
The Council of State voiced reservations about the agreement, and there was vociferous opposition in the Tribunate, the Legislative Body and the Senate, which demonstratively coopted the former Abbé Grégoire, a revolutionary firebrand who denounced it. Reactions in the army were even more violent. Ever the opportunist, Bonaparte exploited the uproar to pressure Rome into accepting a number of changes, couched in 'organic articles' which altered the nature of the agreement in his favour.
As the opening of the second session of the assemblies approached in the autumn of 1801, it became clear that malcontents of every hue were preparing to unite in opposition to Bonaparte's increasingly autocratic rule. They were outraged that in a treaty with Russia the word 'subject' had featured with respect to French citizens, and were determined to reject the Concordat. More distressing for Bonaparte was the Tribunate's critical reception of the projected Civil Code, which was close to his heart. To hear it picked apart piece by piece and criticised for being too old-fashioned and a betrayal of the Revolution was more than he could stand. He raged at the 'dogs' who had led the attack, likening them to lice infesting his clothes, and contemplated sending troops into the assembly. 'Let nobody think I will let myself be treated like Louis XVI,' he warned. 'I am a soldier, a son of the Revolution, and I will not tolerate being insulted like a king.'
Cambacérès persuaded him to avoid confrontation and allow the Legislative Body to reject the Code; he had thought of a way round the problem, which Bonaparte adopted. On 2 January 1802 he declared that he was withdrawing all projects, which effectively closed the session of the assemblies, since they had nothing to do. On the same day he went to the Senate and berated its members, particularly Sieyès, whom he accused of trying to turn him into the ineffectual 'Great Elector' of his dreams. Bonaparte was a hard man to stand up to in a situation such as this, and they obediently coopted a number of his supporters, giving him a majority.
The following day he attended the marriage of Louis to Hortense. They had both resisted the match vigorously, but had been forced into it by Bonaparte and Josephine, who had set their minds on it, each for reasons of their own: he because he saw Louis as his possible successor, or the one who would sire his successor, she because it should guarantee her position against the onslaughts of the Bonaparte clan. Neither realised how psychologically damaged Louis was, and that this would lead to problems in time. Bonaparte had little time for reflection, and at midnight on 8 January he left for Lyon, where he had serious business to attend to.
After its resurrection following Marengo, the Cisalpine Republic, enlarged by the Treaty of Lunéville with the addition of the Legations and Parma, had been administered on the French model by a provisional government under Francesco Melzi d'Eril. He nurtured hopes of eventually extending it to embrace all of northern Italy and turning it into a strong buffer state between France and Austria, possibly ruled by either Bonaparte's brother Joseph or a Spanish Bourbon. But in the first instance he had to go to Lyon, along with 491 deputies, in order to have the constitution he had drawn up endorsed by Bonaparte and, he hoped, the republic's name changed from Cisalpine to Italian.
The deputies, many of whom had brought their wives and families, had a terrible time getting to Lyon. They crossed the Alps in blizzards, were holed up for long periods in poky inns and cottages – princes, bishops and generals cheek-by-jowl with merchants and servants, all forced to eat the same meagre rations. One died along the way. They had finally reached Lyon on 11 December 1801, but their discomfort did not cease. Prince Serbelloni had brought his own cook, but most of them had to make do with local fare, which they found revolting, and nothing could lift the gloom of the winter mists as they waited for Bonaparte to arrive.
He was preceded, on 28 December, by Talleyrand. The deputies assumed they would at last be able to take their seats in the former Jesuit college church which had been turned into an amphitheatre of green leather chairs. They were disappointed. The last thing Bonaparte wanted was an assembly. He had instructed Talleyrand to divide the deputies up into five groups which were to discuss the proposed constitution separately. Talleyrand and Murat, who as commander of French forces in Italy was also present, circulated among the deputies, softening them up with a mixture of emollience and menace that made one of them think of the reign of Tiberius.
Bonaparte arrived on the evening of 11 January 1802. He was met outside the city by an honour guard of young Lyonnais gentlemen accoutred in splendid pale-blue uniforms and plumed headgear of their own invention. As he approached the city he was greeted by artillery salvoes and the cheers of troops lining the streets. Despite the intense cold (the river Saône was freezing over) and the falling snow, a dense crowd waited to catch a glimpse of him sitting beside Josephine in his carriage.
The Italian deputies waited patiently to be convoked. There were two banquets and two balls, graced by Josephine and rushed through by Bonaparte, and on 20 January they finally took their seats in plenary session. But their hopes of a hearing by the first consul were dashed. Talleyrand appeared, to announce that Bonaparte wished them to select thirty of their number whom they considered worthy of a place in the future government.
When the thirty had been chosen by ballot, they were instructed to meet in two days' time, on 22 January, to elect a president of the Cisalpine Republic. Bonaparte had originally wanted Joseph to fill the post, but Joseph thought it beneath his dignity and realised that he would only be a placeman, so he refused. Bonaparte would not countenance any possibility of the new state drifting beyond his control, so he would have to fill the post himself.
When the votes of the thirty deputies were counted, three were blank, one was for Bonaparte, one for another Italian, and twenty-five for Melzi. Having been informed by Talleyrand that the first consul wanted the post for himself, Melzi declined it. A second vote produced another Italian, who also knew what was good for him, and the third an obscure Milanese deputy who was absent, and could therefore not refuse. As they filed off to announce their choice to Bonaparte, who had already been informed, Talleyrand warned them that he was in an evil mood, like a lion with a fever. There are three versions of what happened. According to one, he refused to receive them, another has it that he would not address a word to them, a third that he threw a stool at them.
Talleyrand explained that they must try harder, and after two days of agonising, they agreed. On 25 January they recommended to the assembly that it elect Bonaparte. There was predictable uproar and speeches by patriots demanding an Italian president. A vote was taken by asking the deputies to stand, and although some witnesses recorded that only a third did rise, according to the official record Napoleon Bonaparte was chosen by universal acclamation.
The following day at one o'clock he entered the church in which the deputies were assembled, followed by Talleyrand, Murat and the interior minister Chaptal. A podium had been erected for him, decorated with bronzes and bas-reliefs representing the Tiber and the Nile, surmounted by a canopy depicting a cloudless sky. He eschewed this for the humbler president's chair, and addressed the assembly in his poor Italian. He told them that since the nascent state needed a strong hand and a wise head, and there was none among them with the requisite qualities, he graciously accepted their offer of the presidency. He was not put off by the barely polite applause, and proceeded to present the new constitution. 'Let the constitution of the...' he began, and paused. Various patriots shouted 'Italian Republic!' With a wink to Talleyrand, Bonaparte smiled at the assembly and said, 'Very well, the Italian Republic!' The applause was deafening. The constitution was then read out, and Bonaparte nominated Melzi vice-president.
The following day he reviewed the troops that had returned from Egypt, and then left Lyon. He was back in Paris on 31 January, and resumed his work on emasculating the legislative bodies.
As the Tribunate and the Legislative replaced one-fifth of their members at the end of every session, twenty tribunes and sixty legislators now had to be appointed. Instead of allowing the assemblies to choose who went and who came in, as the constitution specified, Bonaparte contrived to make the Senate intervene and decide for them. As a result, in the spring of 1802 the most cantankerous members of both assemblies would be replaced by men prepared to do Bonaparte's bidding. For good measure, Lucien, who despite his tendency to make trouble could be counted on to toe the line when necessary, was put back in the Tribunate to ensure its docility. In March, Bonaparte crowned his dominance with a triumph that silenced his critics.
## 24
# The Liberator of Europe
Peace with Britain was signed at Amiens on 25 March 1802. The next day Joseph raced to Paris with the document, which he brandished as he entered his brother's box at the Opéra that evening. The performance was interrupted and Bonaparte presented his brother to the cheering audience as the able negotiator. He nevertheless took the credit when commissioning an allegorical painting depicting him leading Gaul and Britannia to cast their weapons into the flames. It was a triumph: when, exactly three months later, a new treaty was signed with the Porte, France was, for the first time in ten years, not at war with anyone. As a sign of the new era, Bonaparte appeared in civilian dress at the diplomatic reception on 27 March to formally announce the peace.
The terms of the treaty were that George III renounced his title of 'King of France', used by his predecessors since the Hundred Years' War, and undertook to return all French colonies and those of her allies except for Ceylon (formerly Dutch) and Trinidad (formerly Spanish). France accepted the return of Egypt to the Porte and the Papal States to the Pope, and recognised the independence of the Ionian islands. Malta was to be returned to the Order of St John and placed under the protection of Naples. France was to evacuate the Neapolitan ports, opening them to British shipping once more. What were considered minor points were left for subsequent agreement, including compensation for the dispossessed rulers of Piedmont and the Netherlands, the question of which side should pay for the upkeep of prisoners of war, and the signature of a trade treaty.
Once the preliminaries had been signed, mail coaches had carried the news 'Peace with France' chalked on their sides; they were greeted with rejoicing all over the country amid shouts of 'Huzzah for Buonaparte!' When General Lauriston arrived in London bearing the ratification, the horses were unharnessed from his carriage and it was pulled through the streets. The British press heaped praise on Bonaparte as the restorer of peace, and one Member of Parliament hailed him as 'the Great Man of the People of France, the Liberator of Europe'. Prints and busts of him sold like hot cakes.
The euphoria could not last; the treaty had been a rushed job which would have required a remarkable degree of compromise and cooperation to implement properly, and both were in short supply. British mistrust of the French was embedded in the national psyche, while Bonaparte's attitude to the British had been radically altered by their hand in the assassination of Paul I and the attempts on his own life, which he saw as evidence of a disgraceful disregard of conventions governing international relations and typical of _perfide Albion_. Peace, however fragile, was nevertheless welcome. He still had much to do to rebuild France.
Ten days after the signature of the treaty, on 5 April 1802, the new session of the assemblies opened. Having lost its most vocal members, the Tribunate was further emasculated by a new measure proposed by Lucien: that instead of meeting in plenary sessions, it should henceforth divide into three sections which would deliberate separately. The measure was adopted, and Lucien took the chair in that designated to deal with the Concordat, which was passed on 8 April.
Easter Sunday, which fell ten days later, was chosen to proclaim the Treaty of Amiens and the Concordat. The twin achievements were to be celebrated by a pontifical high mass in the cathedral of Notre Dame, an occasion rich in allusion, irony and farce. That morning the people of Paris could for the first time in ten years hear the tolling of the great bell of Notre Dame as well as the artillery salutes they had grown used to. The sermon would be delivered by Monsignor de Boisgelin, Archbishop of Tours, who had officiated at the funeral of Louis XV and the coronation of his successor.
The festivities opened with a parade at which Bonaparte presented newly-created units with their standards. Then, dressed in their scarlet uniform, the three consuls drove to the cathedral escorted by a squadron of the newly-formed 'Mamelukes', composed of exotically uniformed veterans of the Egyptian campaign. They were followed by the diplomatic corps, and then the senior functionaries, members of the assemblies, notables, court officials and their ladies. The cathedral was crammed with clergy. An orchestra and choir conducted by Cherubini and Méhul lent solemnity as Bonaparte took his place, with the two consuls flanking him and Fouché and Talleyrand behind. It had been agreed that while he would go through all the motions as a good Catholic should, he would not, as had been the royal custom, kiss the paten. 'Don't force me to make a fool of myself,' he had snapped when the matter had been discussed.
The element of farce entered the proceedings soon after, as Josephine arrived only to find her seat occupied by Madame Moreau (her husband showed his independence and contempt by refusing to attend, spending the morning sauntering around the gardens of the Tuileries puffing on a cigar). Things degenerated further when a number of generals and senior officers made their entry. They were almost to a man fiercely irreligious and furious at having been ordered to come. They swaggered in, chatting among themselves, shoving aside any priest who obstructed their passage. Finding all the seats taken, Masséna ousted a prelate from his chair with a 'Go fuck yourself!' His comrades followed suit and began cracking jokes, and were only silenced by a glare from the first consul.
Several generals angrily accused Bonaparte of betraying all those who had laid down their lives in the cause of the Revolution and its rejection of 'superstition'. He ignored them. Two days later he reconverted his bathroom in the Tuileries, which had been the private chapel of Marie de Médicis, and henceforth he would attend mass every Sunday and command his court to do the same. He dutifully went through the motions, but did not take communion, since, as he explained, he 'was not enough of a believer for it to be of any benefit, and yet too much of one to wish to coldly commit sacrilege'.
Many, particularly the soldiers, hated having to attend, and would stand around chatting in the next room. 'These masses were little more than a travesty,' according to Thibaudeau. 'They could hardly have been more worldly, with the actresses of the opera singing the praises of God.' Some of the ladies nibbled chocolates as they listened. But Bonaparte had judged well, as a concurrent religious revival confirmed. Charitable and proselytising congregations sprang up around the country, and Chateaubriand's _Génie du Christianisme_ , published that year, became an instant best-seller. If the Concordat caused indignation in the liberal salons, it was well received in the country at large.
The measure would take much effort to implement, there would be acrimonious disputes over appointments of bishops, over property and money, and many ruffled feathers would have to be smoothed. But Bonaparte had pulled off a masterstroke. He had not only satisfied the rural population's attachment to the faith, thereby assuaging its resentment of the state and the government, he had also kicked away one of the principal supports of the Bourbon cause, as a return of the monarchy had until now seemed to be the only way of restoring the Church. Louis XVIII was quick to see the threat, and protested vigorously to 'the criminal pope', as his brother Artois called Pius VII. Summing up, Archbishop Boisgelin declared that the consular regime was 'the legitimate government, both national and Catholic, and without it we would have neither the Faith nor the Fatherland'. More important as far as Bonaparte was concerned, he had achieved what Louis XIV had struggled in vain to do, namely to subject the Church entirely to the state. And to himself: his half-uncle and former archdeacon of Ajaccio Joseph Fesch became Cardinal Archbishop of Lyon and primate of the Church in France.
A week after the ceremony, Bonaparte pulled another strut from under the Bourbon cause. He declared an amnesty for all émigrés bar about a thousand of the actively hostile (whom he wanted to see 'exterminated'), provided they returned to France by 23 September, the end of the year in the revolutionary calendar. Those whose property had not been sold would get it back. This measure too angered many, but Bonaparte paid little heed; it brought tens of thousands of educated and capable Frenchmen who loved their country back to serve it. Among them was his old friend Alexandre des Mazis, who came to see him and was warmly received. Napoleon gave him the position of chamberlain, which would provide him with an income. Assuming his friend to be penniless and knowing him to be too proud to accept charity, he sent an officer after him with a letter of credit for a large sum, saying it was something he must have left behind by mistake. Bonaparte did not stop at émigré nobles, and explored the possibility of the return of Paoli. He also issued a proclamation inviting all the artisans and skilled workers who had emigrated to return; he aimed to bring all Frenchmen together in a new nation, the basis for the functional modern state he envisaged.
One of the articles of faith of the Revolution had been the need to wrench education away from the Church and to create a new secular, rational man. Religious establishments had been closed down and education for all decreed, but, left to individual communes, this vision had failed to materialise. All children did benefit from some level of primary education, but little was available at secondary level. On 12 March 1802 Bonaparte set up a directorate within the Ministry of the Interior, with Roederer in charge. 'Public education can and must be a very powerful motor in our political system,' he instructed him. 'It is by this means that the legislator will be able to revive a national spirit. The department of public education is nothing less than the direction of minds by intelligence.'
On 1 May 1802 a new law came into force, establishing 23,000 primary schools for children between the ages of seven and eleven to be administered by the communes. The communes could also open secondary schools, and private institutions were permitted if licensed by the local prefect. But the backbone of the new system were the forty-five _lycées_ which were to teach the classics, rhetoric, logic, morality and the elements of mathematics and physics. Although their pupils wore uniform, underwent some military training and answered to the sound of the drum rather than the bell, they were not strict and there was no corporal punishment – which Bonaparte strongly opposed. They were intended to turn out young men with the same morality and the same sense of service to society and the state – a new class of functionaries and soldiers beholden to it. Bonaparte maintained that this was the only way to instil a unity of purpose similar to that he imagined had existed in ancient Athens and Sparta; as Roederer frankly admitted, the new system was 'a political institution'.
The seeds of another profoundly political institution were sown on 19 May, with the announcement of the creation of a 'legion of honour', a body of men, both military and civilian, who had distinguished themselves in the service of the state. It was to be made up of fifteen 'cohorts' of 250 each, but there were to be no insignia or other outward distinctions – among the first things to be thrown on the bonfire of vanities in the first stage of the Revolution had been the crosses and sashes of the royal orders of chivalry. Even so, the announcement aroused the ire of republicans, who denounced it as an assault on the principle of equality. They could hardly have imagined what was to come.
'People think me ambitious,' Bonaparte exclaimed one evening at the Tuileries. 'Ambitious! – for what? Ambitious, me? Listen to me, gentlemen, what I am about to say I authorise you to repeat. In three years, I shall retire from public affairs. I will have an income of fifty thousand livres, and with my tastes that is more than I need. I will have a country estate, because Madame Bonaparte likes the country.' He added that he would also like to be a justice of the peace. Whether or how much he meant it one cannot say, but he would not relinquish power before he had finished building his political edifice, and in order to do that, he believed he had to reinforce his position.
Since the Brumaire coup, Berthier had been methodically purging the army of Jacobin officers and those hostile to Bonaparte – in the course of two years he had retired seventy-two colonels, 150 majors and thousands of junior officers. But the army had preserved its revolutionary ethos, and Bonaparte was still not popular in those units he had not commanded himself. The Concordat and the amnesty for émigrés had revived residual hostility to him, and those generals who envied his rise to power sensed a new opportunity. Moreau, Brune, Masséna, Augereau, Gouvion Saint-Cyr and Lecourbe were among many who felt varying degrees of outrage at the way things were going. Bonaparte either undercut them, as when he dissolved the Army of Batavia, thereby denying Augereau his command, or he sent them on distant missions: Gouvion to Madrid, Brune to Constantinople, others to the colonies where they could do no harm. That did not put a stop to the grumbling.
From Italy, Murat reported revolutionary sentiment and shouts of ' _Vive Robespierre!_ ' On 14 July troops stationed at Bologna refused to toast Bonaparte. At a dinner given by Moreau in June 1802, a chef de brigade felt he could spew out his hatred of the first consul in company which included Marmont and Berthier. Similar feelings were reflected in a number of conspiracies over the summer and early autumn of that year. One, connected to General Oudinot, never got off the ground. Another, more serious as it meant to assassinate rather than just depose the first consul, which a Captain Donnadieu vowed to do, was unusual in that it involved mostly non-commissioned and junior officers. But most of the plots, like an inept one involving Bernadotte, commander of the Army of the West, had more to do with the hurt pride of Bonaparte's former comrades than any serious purpose. 'As there is not one of them who does not believe himself to be his equal and to possess the same title as him to the first place,' reported Louis XVIII's agent in Paris, Antoine Royer-Collard, 'so there is not one of them who does not see his elevation as a wrong done to himself personally.'
These plots were easily uncovered by Fouché's police, and did not present a serious threat, but they did testify to a lingering sense of uncertainty as to the durability of the consular regime. Bonaparte felt he could not, for family reasons, make an example of Bernadotte by punishing him. Fouché advised against it, on the grounds that it was impolitic for the public to know that there was dissension at the heart of his entourage. Bernadotte was offered a command in Louisiana and an embassy to the United States, both of which he refused. The best Bonaparte could do was to gradually marginalise him. He was also growing wary of Fouché, whom he suspected of shielding his former Jacobin comrade. In September 1802 he abolished the Ministry of Police and gave Fouché a seat in the Senate. His former duties were split up and transferred to the Ministries of Justice and the Interior.
The permanence of the new regime concerned not only Bonaparte. Cambacérès and Lebrun, Talleyrand, Roederer and, for reasons of their own, his brothers Joseph and Lucien had for some time been canvassing for a formal upgrade in Bonaparte's status, and many others had become resigned to what appeared to be inevitable. 'Power was encroaching with large strides behind the words _order_ and _stability_ ,' as Thibaudeau put it. By the end of March 1802 a majority in the Tribunate had accepted the need to extend the first consul's tenure by another ten years.
Among the opponents of this was Josephine, who understood that a man who rises to eminence and amasses an inheritance will sooner or later want an heir – the one thing she could not give him. With every step along a path that was beginning to look as though it would lead to a throne, her position grew more precarious. Bonaparte's family had been urging him to divorce her for years, and their case was growing stronger. She found an ally in Fouché, whose Jacobin instincts were reinforced by his recent loss of power and his hatred of Bonaparte's brothers. In an effort to deflect the Tribunate's expression of gratitude from extending Bonaparte's power, he proposed the erection of a monument. Others suggested a triumphal arch and the renaming of squares. Humble as ever, Bonaparte refused such honours. He showed the same modesty when a delegation of the Tribunate brought him the offer of an extension of his office for another ten years as a token of the gratitude of the French nation; he refused, saying that the love of the people was sufficient reward.
He nevertheless let his displeasure be known; he wanted an extension not for ten years but for life. Pretending to take his feigned modesty at face value, Fouché, Sieyès, Grégoire and others persuaded the Senate to pass a _senatus-consulte_ on 8 May extending his post for another ten years. The following day an irritated Bonaparte graciously thanked the Senate for its trust, but observed that as he had been invested with power by the will of the people, given voice in the plebiscite of February 1800, he would only accept its prolongation by a similar plebiscite. Outmanoeuvred, the Senate could only express its admiration for his reticence and its respect for the will of the people. Bonaparte then left for Malmaison.
The following day, 10 May, at an extraordinary session which Bonaparte demurely refrained from attending, the Council of State under the guidance of Cambacérès agreed that a plebiscite should be held, and since the will of the people could hardly be circumscribed by the imposition of a time limit, that the question to be put must be: 'Should Napoleon Bonaparte be consul for life?' Significantly, this was the first time his first name appeared in an official public document. Lucien (who saw himself as such) added a second question to be put to the nation: 'Should he have the right to designate his successor?'
When the project was communicated to Bonaparte, he struck out the second question. 'The testament of Louis XIV was not respected, so why should mine be?' he said to Cambacérès. 'A dead man has nothing to say.' Only hereditary succession was possible, he asserted. What he did not say but probably anticipated was that while the answer to the first question was bound to be a resounding 'yes', the second would provoke debate in every village.
Josephine spent most of June taking the waters at Plombières in a desperate effort to enhance her fertility. 'I am all sorrow, my dear Hortense: I am parted from you and my heart as well as my whole being suffer from it,' she wrote to her daughter on 19 June. 'I feel that I was not created for so much grandeur, my child...' In her absence, Hortense acted as lady of the house at Malmaison, where Bonaparte spent most of that summer, with occasional visits to Paris to preside over the Council of State. She was heavily pregnant, but Louis was not with her. He had become obsessed with his health and developed a number of neuroses which contributed to estrange him completely from his wife. Combined with Bonaparte's evident affection for Hortense, this provided malicious tongues with material for gossip that Bonaparte was her lover and the father of her child.
Bonaparte did philander, giving Josephine grounds not so much for jealousy as for anxiety, but not with her daughter. He wrote affectionately to Josephine, asking about her health, what she was doing and whom she was seeing (whenever she travelled without him, he would dictate a strict schedule which included travel arrangements, where she could stay, or even pause, and whom she could meet). He also sent news of what he was doing, telling her he had wounded his finger while shooting a boar at Marly, and reporting on a performance of _The Barber of Seville_ , with Hortense playing Rosina, and Lauriston, Bourrienne, Eugène and Savary among the other actors. He missed her and wrote that her forthcoming return 'will make the little man who is bored all on his own very happy', adding, 'It's all very sad here without you.'
On 3 August he was at the Tuileries to receive a delegation of senators who called to present the results of the plebiscite. There had been 3,568,885 'yes' votes and only 8,374 against, with a turnout of close to 60 per cent, which was a triumph considering that the three plebiscites held during the Revolution had never produced a turnout higher than 34 per cent, and in one case below 20. Unlike in 1800, there is no real evidence of manipulation.
There was much disapproval among liberals and ideologues. Lafayette, who had voiced his protest in the Senate, wrote to Bonaparte saying that while his 'restorative dictatorship' had yielded great benefits, a greater good now would be the restoration of liberty, and that he could not believe Bonaparte really wished to see the return of an arbitrary regime. Plenty of others voiced their fears of the encroaching tyranny, and even old comrades such as Junot felt they could no longer say what they thought, aware as they were of the tightening security net around Bonaparte – he was naturally suspicious, and his experiences had taught him to trust nobody, so he had everyone watched, even those closest to him.
He had built up an extensive intelligence network stretching far wider and deeper than the ostensible ones: Fouché's efficient police, Réal's Paris police, Duroc's palace security network, Savary's Gendarmerie d'élite which supervised the army, and the Gendarmerie itself, a nationwide paramilitary police which not only maintained order but also reported on the political mood in every department. Bonaparte could also rely on the confidential reports of the prefects, and he had a web of correspondents, individuals scattered across the country who wrote to him directly, often anonymously (only he knew who they were), telling him what was being said in the provinces about what he did in Paris.
His increasing workload required an expansion of his secretariat. Bourrienne had not been able to resist exploiting his proximity to the first consul in blatant ways, and in the autumn of 1802 he had gone too far; fearing his venality would reflect on his own person, Bonaparte dismissed him. He was replaced by the mild-mannered twenty-four-year-old Claude-François Méneval, formerly a secretary to Joseph, who was presented to Bonaparte one evening and after a short conversation was instructed to come back at seven the following morning. When he did, he was told to sit down and start taking dictation. He was given quarters in the Tuileries and appointed as one of Bonaparte's aides-de-camp, but he never wore any kind of uniform, and many in the first consul's entourage never knew he existed, as he was rarely seen outside his private study. With time, he was joined by Agathon Fain and three others to deal with specific areas, but Méneval remained Bonaparte's right hand and constant companion, woken at all hours of the night to take dictation.
'The government is that of a military despotism, in most respects wisely, but not mildly administered,' was how Cornwallis described the governance of France. He was wrong. Bonaparte did not rule through the army, but through theoretically democratic institutions. Although he did manipulate them shamelessly, he had no intention of abolishing them. He meant rather to turn them into facilitators of his rule and preservers of his political edifice, by filling them with people dedicated to the good of France, as he saw it, and making them more pliable.
The Directory had curtailed the unbridled democracy introduced by the Revolution, restricting the vote to property owners, but while this had introduced an element of stability it had created the conditions for an unprincipled struggle for power and wealth which did little for the public good. The Constitution of Year III, inspired by Sieyès and edited by Bonaparte, had created something more efficient only in that it gave him the power to act decisively. What he now wanted was to create a class of people who would by instinct and interest work for the public good through the existing institutions. As they were nominated, not elected, they were not in a position to build an opposition by claiming to represent the people; they were to be a managerial class.
Bonaparte had been fostering the emergence of this governing caste from the moment he came to power. Although property was the fundamental qualification, his experience of the 'scoundrels' who had followed his army in Italy left him ambivalent about the rich. 'One cannot treat wealth as a title of nobility,' he said in the Council of State. 'A rich man is often a layabout without merit. A rich merchant is often so only by virtue of the art of selling expensively or stealing.' He wanted people whose wealth derived from honest service to the state, military as well as civil, and encouraged Freemasonry, which he saw as an instrument of civic formation. He aimed to fuse this new hierarchy with the old aristocracy by encouraging intermarriage. His growing court, to which he attracted members of the old aristocracy and returning émigrés, provided the framework for mixing them with his predominantly low-born military entourage. He introduced the court ceremonial that had existed before 1789, and for similar reasons insisted on attaching four _dames du palais_ , drawn from the highest aristocracy, to Josephine. He encouraged young noblemen to join the army, frequently promoting them and giving them posts as aides. He would not have been human if he had not relished having young men with names redolent of the Crusades trotting along in his suite, but vanity was not the primary motive. Yet his desire to achieve social and political 'fusion' was ineluctably beginning to affect his own status.
His nomination as consul for life demanded changes to the constitution, and he wasted no time in preparing a new one, which came into force on 5 August. 'A constitution should be fashioned in such a manner that it will not hinder the actions of the government, and will not oblige it to violate it,' he argued. 'Every day one is obliged to violate positive laws; one cannot do otherwise, or it would be impossible to proceed. [...] The government should not be tyrannical [...]; but it is impossible for it not to carry out some arbitrary actions.'
The new constitution replaced Sieyès' pyramid democracy with an even more theoretical version of universal suffrage, since it was dominated by local electoral colleges of notables, which put forward candidates for the assemblies and other offices for the first consul to choose from. Even the justices of the peace were now nominated by him. The Tribunate was cut down by half, the Legislative Body shackled by procedural changes, while the Senate was expanded. The first consul chose five-eighths of its members and presided over it himself, which meant he could legislate by means of _senatus-consultes_. Both the Senate and the Council of State had become little more than administrative tools. He could make and break treaties without consultation or need for ratification by the chambers. He had arrogated the right to nominate his successor and the traditional prerogative of kings, the right of pardon, abolished in 1791.
Bonaparte's thirty-third birthday on 15 August was celebrated with royal pomp. In the morning the members of the assemblies came to the Tuileries with their congratulations, followed by the diplomatic corps. They were entertained with a concert by 300 musicians, after which all drove to Notre Dame for a _Te Deum_. Bonaparte then retired to Malmaison, where the evening ended with amateur theatricals and dancing while Paris was regaled with illuminations and fireworks.
On 21 August he drove alone in a coach drawn by eight horses (another royal attribute) to the Luxembourg to swear in the senators. The route was lined by a double rank of soldiers. He was escorted by a glittering group of aides and generals, and followed by six carriages bearing his fellow consuls and the ministers. As his coach trundled into the courtyard it was greeted at the foot of the stairs by ten senators who conducted him to his seat, which resembled nothing less than a throne. In their reports, the Russian and Prussian ambassadors both remarked that there was but one more step left for him to take – to monarchy.
The next step may not have taken him to Versailles, as Sieyès had once suggested, but Malmaison was a little far from Paris, and too small to be anything but a place for relaxation in intimate company. The road was difficult to police, and there had been more than one plot to abduct or assassinate Bonaparte between there and Paris. Yet he craved fresh air and felt constricted in the Tuileries. The solution was to provide him with an official residence in the palace of Saint-Cloud. The original idea had been to give him the palace and rename it Marengo, following the example of Blenheim in England, but he had rejected it as ridiculous. He moved into the palace on 20 September, and six days later, on Sunday, 26 September the first court mass was held in the chapel, Bonaparte making his entrance with what was supposed to be the debonair gait affected by the later Bourbons, surrounded by courtiers, many of them regicides, who had frequently sworn to strike down any who reached for supreme authority.
Bonaparte understood that ordinary people liked the idea of a head of state, the more exceptional and grander the better, and both he and those close to him had begun to see the new regime as inseparable from his person. That person must therefore be made dear to the people. At the end of October he set off with Josephine on a two-week progress through Normandy, meeting local authorities, functionaries and notables, inspecting the National Guard and military garrisons, visiting factories, hospitals and schools, reviewing building works and planning infrastructure projects.
They travelled in only two carriages, attended by a small entourage, but one ' _service_ ' preceded them by twelve hours and another followed them with the same time-lapse. Each consisted of a full, if reduced, replica of the establishment at the Tuileries which took care of all their needs. By the time they reached a given place, the accommodation provided had been adapted to their requirements, clothes were laid out, food was ready, a bath was waiting, and, most important, an office was ready, with papers, files and a travelling library, so Bonaparte could get down to work immediately. As soon as he arrived, he would call in the local authorities and question them on the needs of the locality and their plans, and often mount up immediately to ride out and see for himself.
He hated having to attend the accompanying receptions, and wanted to get them over with as quickly as possible, but realised their value. He instructed Josephine to wear all the jewellery she could physically display and to behave like a queen – she needed little prompting. Wherever they went they were mobbed by the people, who often travelled long distances to see them, and would stand under his windows half the night waiting for him to show himself. 'The people do not know what to call him,' Josephine wrote to Joseph from Rouen. 'Some call him the pacification of the world, others the father of the people, one man came forward and said: "After God, it's you!" Another told him: "My soul belongs to God but my heart to You!"' He would soon belong to them in more traditional mode: on 12 March 1803, accompanied by Josephine, he went to the Paris mint to watch the first coins being struck with his effigy.
The advent of peace had opened frontiers, and people from all over Europe came to Paris. The French capital had always attracted visitors avid for fashion and culture, and it was now made more enticing still by the frisson of seeing the battleground of the Revolution and the hero or ogre, depending on viewpoint, who had tamed it. The majority were British. They had been starved for a decade of the opportunity of making a Grand Tour, and an estimated 20,000 of them passed through Paris, some going on to Italy or Switzerland, but all stopping long enough to at least catch sight of the man of the moment. They included no fewer than eighty-one Members of Parliament who came to see how his new political system functioned, among them Charles James Fox. Scientists eager to assess the achievements in the field of building, engineering and physics were able to visit an exhibition of French industry at the Louvre. Many noted artists, including Maria Cosway, Flaxman, Fuseli, Hoppner, Turner and West came to see the museum in the Louvre, which provided them with a unique opportunity to study and copy the works of the masters. Few travelled the other way, from France to Britain, notable exceptions being the sculptor in wax Marie Tussaud and the portrait painter Elisabeth Vigée-Lebrun.
Bonaparte ordered Fontaine to ransack the royal furniture stores to fit out the Tuileries in splendour, as he was determined to show the visiting British that France was not bankrupt. He ordered him to clear the area around the palace and to place the horses of St Mark's on the pillars of the gates in front of it. He also had all the remaining liberty trees planted during the Revolution cut down. Foreign visitors were welcome in his apartments following his regular parades, and he encouraged his generals and ministers to give balls and entertainments for them.
The Russian Elizaveta Petrovna Divova thought Paris 'an earthly paradise', and found everything about Bonaparte and his court enchanting. The Polish Wiridianna Fiszerowa thought the court 'striking by its lack of manners and dignity'. Another Polish aristocrat remarked that the servants did not seem to know what they were supposed to be doing. Mary Berry was overwhelmed by the luxury of the first consul's apartments, which she thought surpassed Versailles and Trianon.
Everyone who left accounts found Josephine charming and the atmosphere in her apartments and at her receptions 'very fine and princely', as one Englishman put it. Reactions to her husband were more varied. Divova found him 'amiable, charming, kind, honest, polite'; Maria Edgeworth was less complimentary about his 'pale woebegone countenance', and thought him 'very little'; the eccentric Bertie Greathead was disappointed to find him not as 'melancholy' and 'not so picturesque' as he had imagined, adding that 'his person is not only little, but I think, mean'. The landscape painter Joseph Farington noted that 'He picked his nose very much.' Fiszerowa thought he looked ill at ease, and noticed that 'When he spoke with the ministers of foreign courts, he twisted the buttons of his coat like a schoolboy.' Fanny Burney was transported by his face, in which 'care, thought, melancholy, and meditation are strongly marked, with so much of character, nay, genius, and so penetrating a seriousness, or rather sadness, as powerfully to sink into the observer's mind'.
'The nations admire you. France, made greater by your victories, has placed her hope in you,' wrote Chateaubriand in the dedication to the second edition of _Génie du Christianisme_ , which came out in May 1803. 'One cannot help but recognise in your destiny the hand of the Providence which has marked you out a long time ago for the fulfilment of its prodigious designs.'
## 25
# His Consular Majesty
'It is certain that some of our travelling Nudes of Fashion intended to conquer the Conqueror of the Continent,' reported _The Times_ of 12 January 1803. 'What glory would it have brought to this Country, if it could have boasted of giving a Mistress, or a Wife, to the First Consul.' It would have taken more than that to maintain a peace that many in Britain were beginning to see as little more than a truce. There had been five treaties signed between the two countries since 1697, and only one had lasted more than ten years.
For Britain, the principal benefit of peace was access to European markets – without which dominance of the seas and colonial trade, not to mention its industrial primacy, were worthless. Shortly after the signature of the treaty, Cambacérès warned Bonaparte that it would not last without a commercial one. 'This suggestion appeared to displease him,' he noted. Bonaparte reminded him of the catastrophic effect on the French textile industry of the previous treaty, signed in 1783, which had opened French markets to British imports.
Whether he wished the peace to last or not is impossible to establish, but his inability to see the other's point of view meant that he did not waste time developing good relations with Britain, concentrating instead on using the opportunities offered by the cessation of hostilities to rebuild France's economic and political power. He may not have been a great economist, but he did grasp one thing: whether they were formally at peace or not, France and Britain were in economic conflict. In peacetime, British manufactured goods undercut French ones, hurting France's industries, particularly in the important textile sector. In wartime, British dominance of the seas wrought havoc with France's overseas trade.
As he believed in developing French industry and enriching the country by acquiring hard currency, Bonaparte wanted to export as much as possible while importing as little as possible. This inclined him to protectionism, in which he was backed by many in his entourage, such as his interior minister Chaptal, a chemist by training and a keen supporter of the textile industry. Given the possibility of war breaking out once more, France needed to provide itself with sources of raw materials and markets beyond the reach of the Royal Navy. This seemed possible, since a large part of the Continent was under greater or lesser French control. That in turn suggested the desirability of binding such areas into the French economic sphere and developing them in the service of the metropolis. This entailed the harmonisation of their administrative and judicial systems, and the implementation of infrastructure projects such as roads over the passes into Italy, all of which would in time make their incorporation into France seem no more than an administrative formality: Piedmont, for example, linked directly by the new Simplon road, would become essential to the manufacturing centre of Lyon, and vice-versa.
Although France recovered her overseas empire by the Treaty of Amiens, reasserting control over it presented a challenge; the Revolution had encouraged local elites to assert their independence and seek greater autonomy, mainly to enable them to resist socially progressive and abolitionist tendencies emanating from Paris. In Saint-Domingue (Haiti) the local assembly had passed its own constitution. When the Convention had abolished slavery in 1794 many in the colonies refused to accept its authority and in some cases welcomed occupation by the British, who maintained it.
Restoring France's authority was complicated by the existence of a powerful creole lobby defending the planters' interests in Paris. This opposed Bonaparte's intention of maintaining slavery only where it had not been abolished, and accepting the status quo in colonies such as Guadeloupe and Guyana, where it had. His views on the subject were pragmatic. 'If I had been in Martinique, I would have opted for the English, because above all else one has to think of one's own life,' he told Thibaudeau. Such reasoning was not enough to resolve the conundrum presented by the colony of Saint-Domingue along with the Spanish one of Dominica (Santo Domingo), occupying the eastern half of the island, which was ceded to France by Spain in 1795.
At the outbreak of the Revolution, Saint-Domingue produced three-quarters of all the sugar imported into Europe, as well as large quantities of coffee and indigo. It made up a significant element in the French economy, and nourished the port cities of the Atlantic coast, with half of the trade of La Rochelle dependent on it. It is estimated that, directly or indirectly, one Frenchman in ten lived off the Saint-Domingue trade.
The Revolution had unleashed animosities between the various strata of society, ranging from ' _grands blancs_ ' (white planters), through envious ' _petits blancs_ ' and various degrees of mulattos, quadroons and octoroons, down to the black African slaves, which jostled against each other, often in bizarre alliances dictated by local politics. It inspired slave revolts which were savagely repressed. After much violence, the former slave Pierre-Dominique Toussaint Louverture assumed leadership of the blacks and gained control of the colony. In 1795 the Directory appointed him military governor of Saint-Domingue. He began acting as its master, expelling French officials and confiscating plantations, which he gave to his henchmen, introduced a system of forced labour differing little from slavery, and opened the colony's ports to British and American shipping, thereby breaking the convention of the exclusivity of trade between colonies and their metropolis.
Shortly after coming to power, Bonaparte wrote Toussaint a flattering letter, confirming that France recognised the abolition of slavery, holding out a vision of a new ' _pacte social_ ' and calling on him to show loyalty to France by breaking off contact with its slave-trading enemies the British and Americans. He named Toussaint Captain-General and encouraged him to form a national guard and an army. These overtures were ignored by Toussaint, which strengthened the case of the creole lobby and soured Bonaparte's attitude to him. He nevertheless continued to make conciliatory gestures. 'Whatever your origins and your colour,' he wrote in a proclamation to the inhabitants of the colony on 8 October 1801, 'you are French, you are all free and all equal before God and the Republic.' His recognition of their freedom was confirmed by the assemblies and the Senate a month later. Toussaint defied France by invading the eastern part of the island, which was still administered by Spain pending the arrival of a French force. He entertained ambitions for his country and himself no meaner than those of Bonaparte, and the two were set on a collision course.
The colonies France had recovered in the area included the islands of Guadeloupe, Martinique, Marie-Galante, La Désirade, Les Saintes, Saint-Martin, Saint-Lucia and Tobago, and French Guyana on the South American coast. In 1795 she had also recovered from Spain the vast territory of Louisiana (comprising all of present-day Louisiana, Arkansas, Minnesota, Kansas, Nebraska, Colorado, North and South Dakota, Montana, Wyoming and Oklahoma). This opened up the prospect of creating an important colonial empire which would enrich France by providing natural resources and a market for its manufactured goods, not only within its territory but in the neighbouring United States and New Spain (Mexico).
A week after the signature of the Treaty of Amiens, Bonaparte set out for the minister of the navy Denis Decrès his plan for the colonies. He was to show the flag in India, where France had recovered her five trading posts, reoccupy or reinforce the islands of Réunion, Île de France (Mauritius) and the Seychelles, along with the colony of Senegal in Africa and the islands of Saint-Pierre and Miquelon off the North American coast. A force of 20,000 men was to take back control of Saint-Domingue, another 3,600 to do the same on Guadeloupe, and with time 3,000 in Louisiana.
The Americans and the British did not warm to the prospect of a resurgence of French power in the area, but they relished even less that of the existence of republics ruled by rebellious slaves. There was also the possibility that if thwarted, France might subvert British colonies and the southern states of the United States by fomenting slave rebellions against their British and American masters.
Bonaparte gave command of the expedition to Saint-Domingue to Pauline's husband General Leclerc, who had a good track record not only as a soldier, but also as administrator of Marseille and then Lyon – and he was diplomatic, which would be vital when dealing with Toussaint and later with Spanish and American neighbours: once Saint-Domingue had been secured, he was to sail on to Louisiana. Pauline would go with him, partly to prevent her from behaving scandalously if left to herself, partly to make sure he did not take it into his head to betray her beloved brother. Bonaparte notified Toussaint of Leclerc's impending arrival in a flattering letter holding out promises of honours and riches if he cooperated.
His instructions to Leclerc were to support Toussaint and gradually get into a position in which he could decapitate the black liberation movement. There was nothing in them about slavery. 'The question is not whether one should abolish slavery, but whether one should abolish liberty in that part of Saint-Domingue,' he said to Roederer. 'I am convinced that this island would be in English hands if the negroes were not attached to us by their liberty.' It was therefore best to let things be. 'They will, perhaps, produce less sugar than they would as slaves, but they will produce it for us, and they will serve us, if need be, as soldiers.' As far as he was concerned, the only issue was to regain control of the colonies.
When Leclerc's armada reached Saint-Domingue in February 1802, Toussaint tried to prevent him from landing. Leclerc came ashore, defeated him and forced him to come to terms. He then attempted conciliation, but this was undermined by developments in the neighbouring colonies. Under pressure from the creole lobby and business interests, slavery was being reimposed in Guadeloupe and Martinique, where the slaves had rebelled and thrown off their shackles. As Leclerc struggled to win over the black population of Saint-Domingue, news of this drifted in, arousing suspicion that the same would be done there. He urged Bonaparte to check this, arguing that Saint-Domingue being the most important part of the empire, he should give it priority.
Leclerc's expedition had been under-equipped and under-financed, which limited his potential. But that was as nothing to the threat posed by yellow fever. Within a month of his disembarking, some 3,500 of his men had fallen victim, and they were soon dying at the rate of a thousand a month. Reinforcements could not keep up. By September 1802 only about 10,000 men, some 6,000 of them in hospital, remained of the 29,000 who had sailed from France.
Hostilities had resumed, and Leclerc did his best to navigate the complicated internal politics dividing the black leadership. He succeeded in capturing Toussaint, who was sent back to France and imprisoned as a traitor to the Republic in the Fort de Joux in the Jura, where he would die of tuberculosis on 7 April 1803. Exactly three months earlier, on 7 January, Leclerc himself succumbed to the fever. 'Damned sugar, damned coffee, damned colonies,' Bonaparte burst out when he heard the news. By then the expedition had cost the lives of four other divisional generals, a dozen brigadiers and 30,000 other ranks. He would later admit that he had committed one of the greatest mistakes of his life in not leaving Toussaint in place as a kind of semi-independent viceroy who would inevitably have sided with France and undermined British colonial power in the area.
Meanwhile, relations between London and Paris were growing tense. The choice of Lord Whitworth as Britain's ambassador did not help. His connection with the assassination of Tsar Paul I was not calculated to endear him to Bonaparte. He was a professed Francophobe, ruthless and prepared to cross the bounds of diplomacy in what he saw as his country's interest, and he made no effort to ease tensions or inspire trust. Not that there was much he could do, given that his instructions, which were 'to state most distinctly His Majesty's determination never to forgo his right of interference in the affairs of the Continent on every occasion in which the interest of his own dominions or those of Europe in general appear to require it', were directly opposed to those of the French ambassador in London, General Antoine Andréossy, which were 'to prevent on every occasion any intervention of the British Government in Continental affairs'.
The British cabinet regarded Bonaparte's unwillingness to open negotiations for a commercial treaty as evidence of bad faith. Bonaparte complained that Britain was harbouring thousands of hostile émigrés, some of them hatching plots against his life. He was incensed that apart from giving shelter to people who openly professed their desire to overthrow him by any means, the British government did nothing to prevent the publication of calumnies and slanderous articles vilifying him, as well as a slurry of scurrilous cartoons by the likes of Rowlandson. One London-based émigré paper openly called for his assassination. He could not accept the British excuse of the freedom of the press, as the Home Office regularly clamped down on the radical press and impounded the writings of those campaigning for parliamentary reform. The British press published lurid accounts of his poisoning plague victims and burying alive his own wounded, and titillated readers with scandalous stories on Josephine's past, on Bonaparte's alleged sexual orgies with his sisters and affair with Hortense, and even on his supposed African origins. His insecurity and limited sense of humour meant that he found this deeply hurtful as well as infuriating. He blamed the British cabinet for everything, for, as Cambacérès put it, 'he had the strange conviction that the greater part of the population of England was well disposed to him'.
There had been much pro-French feeling in Britain in the 1790s, fuelled by the movement for parliamentary reform and the excessively repressive policies of Pitt's government, but this had now evaporated, and would soon be succeeded by a new spirit of antipathy and belligerence, largely as a consequence of Bonaparte's behaviour. He had assumed that the return of peace meant France could resume the pursuit of her international interests with no thought of the effect of his actions on public opinion in Britain.
In August 1802 the Imperial Diet met at Ratisbon (Regensburg), as stipulated in the Treaty of Lunéville between France and Austria, to rearrange what was left of the Holy Roman Empire. Bonaparte had as a mark of courtesy (and to neutralise him) invited Tsar Alexander to participate as a fellow arbiter. But it was Bonaparte – through the agency of Talleyrand on the spot, who took hefty bribes from all concerned – who decided everything. The Pope was persuaded to cede the prince-bishoprics of Mainz, Cologne and Trier to France, and that of Hanau to Austria, which would hand it to Ferdinand of Habsburg in compensation for Tuscany, which was now Etruria. Rulers who lost territory to France on the left bank of the Rhine were compensated at the expense of others in Germany: by the Imperial Recess of February 1803, three electorates, twenty bishoprics, forty-four abbeys, forty-five free cities and a number of smaller states, 112 in all, were disestablished and some three million people acquired new rulers. By favouring their claims, Bonaparte gratified Prussia and turned Hesse-Darmstadt, Bavaria, Baden and Württemberg into French client states. The result was a considerable extension of French influence, mainly at the expense of Austria. It had all been done in accordance with the Treaty of Lunéville, but instead of being flattered the tsar felt offended, and the British government could only see French power expanding to an alarming degree. The pattern continued to unfold.
As the Treaty of Amiens had stipulated that all French troops should leave the Batavian Republic (the Netherlands), Bonaparte engineered a political crisis as a result of which the Dutch government requested they remain. To add insult to injury, the former ruler of the Netherlands had not been paid the financial compensation promised. French troops also remained in Etruria. In September 1802 Bonaparte turned Piedmont and Elba, both acquired under the Treaty of Lunéville, into departments of France. But he did not pay the promised indemnities to the King of Sardinia. Taken with the transformation of the Cisalpine into the Italian Republic, with Bonaparte as president, this amounted to a consolidation of French power in Italy acceptable neither to Austria nor to Britain.
It was his actions in Switzerland that tipped the scales for British public opinion. Ironically, this was an area where Britain was not blameless, since it had been using the country as a listening post and point of entry for secret agents, as well as fomenting anti-French feeling there. Switzerland had also been a convenient point of entry into France for Austrian and Russian armies. 'I can see no middle course between a well organised Swiss government friendly to France and no Switzerland at all,' Bonaparte explained to Talleyrand. In the autumn of 1802 the tensions between the pro-French authorities of the Helvetic Republic and anti-French reactionaries developed into armed conflict. The former appealed to France for support, the latter to Britain. British public opinion responded in favour of what it assumed to be the freedom-loving party of independence, and the British ministry felt impelled to act. Before it could do so effectively, French troops had restored order and the crisis was over. On 19 February 1803 an Act of Mediation created a Helvetic Confederation, of which Bonaparte assumed the role of guarantor and effective arbiter.
On 17 October the British secretary of state for war Lord Hobart wrote to the commanders in Malta, the Cape and India ordering them to delay implementing the terms of the Treaty of Amiens. The British cabinet was growing alarmed at French moves beyond Europe. A fleet commanded by General Decaen was on its way to reassert French authority over the Indian Ocean island colonies of Île de France and Réunion and the trading posts of Pondicherry, Karikal, Mahé, Yanaon and Chandernagore in India itself, all of which was in accordance with the Treaty of Amiens. But Decaen's instructions included investigating the possibility of enlisting the support of local rulers in India in the event of war breaking out again.
Bonaparte had sent General Brune as ambassador to the Porte, General Sébastiani to Egypt and Syria, and Jean-Baptiste Cavaignac to Muscat. He opened relations with the pasha of Tripoli, the bey of Tunis and the dey of Algiers, and established French consulates throughout the Middle East. A major gaffe was the publication of Sébastiani's report, in which he suggested that it would be easy to oust the British from Egypt and reoccupy it. Talleyrand and the French ambassador in London Andréossy dismissed the report as mere speculation, and Bonaparte attempted to placate an indignant Whitworth. But by then what trust there had been was gone.
Britain felt its monopoly in India was under threat, and suspected France of imperial designs in the Mediterranean. It could not countenance the banking centre of Amsterdam and the Dutch ports being in French hands. British trade was suffering, with France imposing tariffs on imports not only to France, but to all areas it controlled, such as the Netherlands and much of Italy. When pressed over Malta, which the British were supposed to hand over to the Order of St John, the foreign secretary Lord Hawkesbury declared that he would only do so if France evacuated Piedmont. Whitworth was subjected to a lambasting by Bonaparte, who pointed out that Piedmont had nothing to do with the Treaty of Amiens, and had been ceded to France under a different treaty to which Britain had not been a party.
Whitworth's reports from Paris were consistently unfavourable to Bonaparte, often retailing gossip as fact. He nurtured an invasion scare that gripped Britain in March 1803 by exaggerating the number of French troops in the Netherlands. On 8 March the cabinet decided to enlist 10,000 more sailors and embody the militia, a move probably meant as a show of force and a signal to Bonaparte. All it did was provoke him, and Whitworth was given a second dressing-down at a diplomatic audience on 18 March 1803.
Over the next two months both sides sparred over the issue of Malta, proposing a variety of solutions: Bonaparte suggested Britain hand it over to Russia, Prussia or even Austria, then that Britain keep it for ten years provided the Neapolitan ports of Otranto and Taranto remained under French occupation for the same period, and so on.
On 27 April Whitworth delivered a verbal ultimatum to Talleyrand demanding the immediate evacuation of the Netherlands, acceptance of a continued British occupation of Malta and compensation for the King of Sardinia for Piedmont. He refused to put it in writing, so he may have been bluffing. He raised the temperature by reporting that Masséna had told him Bonaparte was about to invade Hanover, Hamburg, Naples and Sardinia.
This may have been idle gossip, but the thirty-three-year-old Bonaparte was certainly full of bluster and unwilling to back down. When the tsar's envoy told him that Europe could not accept his incorporation of Piedmont into France, he sneered that Europe could come and take it from him. He was in reckless mood. When he went riding or hunting in one of the former royal parks, at Versailles, Marly, Fontainebleau or Rambouillet, he would gallop around madly, bent over his horse's neck with the reins held loosely in his right hand and his left swinging by his side (he was a bad rider, and swayed about on horseback). His disregard for danger alarmed his entourage, who were often left behind, desperately trying to catch up. On other occasions he would leave Saint-Cloud incognito with Hortense and go to a country fair, where he was easily recognised, without any escort or attendants. On 8 May, as he was being driven back to Saint-Cloud with Josephine, Hortense, his sister Caroline and Cambacérès, he suddenly climbed onto the box, and taking the reins, insisted on driving the six-horse team himself, which he had never done before. He drove too fast, struck a bollard at the gate with one of the wheels, and the shock sent him flying so far he knocked himself out on landing; he later claimed he had died for a moment.
The power he had amassed, the conquests he had made and the praise being heaped on him cannot have failed to affect his judgement. He had seen his effigy on the first piece of solid currency the country had known in ten years. There was talk of according him the address of 'His Consular Majesty'. A statue was planned to top a column similar to that of Trajan in Rome. His military instincts inclined him to seize every opportunity and rebelled at the idea of retreat, and were backed up by his innate sense of insecurity.
He was profoundly conscious of his origins. His brother Louis had come up with the idea of exhuming the body of their father, who had been buried in Montpellier, where he had died, and interring it with some pomp in Paris. Bonaparte was horrified by the idea – the memory of his father was an embarrassment. (Louis did quietly exhume the body, sent it through the public _messageries_ hidden in a grandfather clock, and had it laid to rest in a mausoleum on his estate at Saint-Leu.) Bonaparte believed his only claim to status derived from glory – his own and that of his associates. That is why when he heard of the death of Leclerc he declared an official period of mourning lasting ten days, as was traditional in royal courts. It singled out his former brother-in-law and brother-in-arms as a national hero, and equated him with royalty, thereby subtly enhancing his own status.
'A first consul is not like one of those kings by the grace of God who view their states as an inheritance,' Bonaparte said to Thibaudeau. 'He needs brilliant actions, and therefore war.' It was a theme he would return to more than once during his life. He believed that his only title to rule rested on his making France greater than she was when he had come to power. Whatever the failings of the Directory, France had at that point been in possession of a great deal of territory, and he felt he could not preside over loss of any part. By the beginning of 1803, as the first anniversary of the Treaty of Amiens approached, he had enlarged France, which now counted thirty-seven million inhabitants, exceeding Austria with its population of twenty-four million, Britain with sixteen and Prussia with nine. He had placed France where Richelieu and Louis XIV could only have dreamed of it – dominant in western Europe, checking Habsburg influence in Germany and excluding that of Britain from most of the Continent. He equated this with his right to rule.
The probable loss of Saint-Domingue and the possibility of the resumption of hostilities put in question the continued control of other colonies, particularly that of Louisiana, which France would certainly not be able to defend. The United States was keen to acquire it, and since Bonaparte needed to refill his war chest, he agreed to sell it. On 10 April the former governor of Virginia and future president James Monroe disembarked at Le Havre, and before the end of the month Bonaparte had 'with the greatest distaste' sold him the territory for fifteen million dollars, equivalent to fifty million francs.
He was just in time. At the beginning of May 1803 the British prime minister, Addington, issued orders to all commanders in the area to prepare to capture French colonies. He was also planning to take New Orleans and hand it to the United States, as a bribe to join in the coming war on the British side. On 14 May Lord Hawkesbury received an offer to mediate from Tsar Alexander. He had previously advised the British cabinet against giving up Malta, a base that had been in Russia's sights for some time, but had become alarmed at the possibility of the outbreak of war. In the words of his ambassador in Paris, Arkadyi Morkov, the victory of neither side suited Russia, as it would lead to 'either despotism on the seas or despotism on land'. It was too late.
On 15 May 1803 the Admiralty issued orders for the detention of all French ships in British or British-controlled ports and at sea. The following day the frigate HMS _Doris_ attacked and took the French naval lugger _l'Affronteur_ close to the French coast, as the Privy Council reached a decision to make war on France. The declaration of war was published on 18 May, by which time more than a thousand French and Dutch ships had been seized in British-controlled ports.
## 26
# Towards Empire
Bonaparte reacted with fury to the unannounced resumption of hostilities. He decreed that every male British subject in France and its dependencies aged between eighteen and sixty was to be arrested as a prisoner of war, ordered General Mortier to invade the British royal family's fief of Hanover, and announced the formation of an Army of England. Riding a wave of anti-British feeling, he opened a public subscription for the building of boats which were to take it across the Channel to teach 'perfidious Albion' a lesson. 'The anger is extreme,' recorded the architect Fontaine. 'Everyone is eagerly offering the government voluntary subsidies.'
Bonaparte set about the formation of the Army of England, complete with a corps of guides who spoke English, overseeing the building of barges to transport the men and gunboats to protect them. He made frequent trips to its main camp at Boulogne, looking into every detail of the preparations, riding about in all weathers and getting drenched as he inspected and badgered. Soon a large force had assembled on the Channel coast, strung out in camps from Normandy to Antwerp, and hundreds of boats had been built. On the evening of 29 October he assured those gathered at Saint-Cloud that he would plant his flag on the Tower of London or die in the attempt. Two weeks later, from the heights above Ambleteuse he surveyed the English coast through his telescope, and could see people going about their business. 'It is a ditch which will be crossed if one dares to try,' he wrote. Ever the propagandist, he had an article placed in _Le Moniteur_ describing how, when pitching a tent for him, the men had uncovered medals of William the Conqueror and an axe-head left behind by the legions of Julius Caesar.
Across the Channel, George III declared that he would never abandon the cause of the Bourbons, and the Aliens Office went into action once again with the aim of overthrowing Bonaparte. Funds began to flow once more, agents were activated and émigré diehards smuggled into France. Georges Cadoudal landed on 20 August at Biville, with his servant Picot and several accomplices, two of whom had been involved in the explosion of the rue Saint-Nicaise. Ten days later they were in Paris. The next to be sent was General Pichegru, who had escaped from Guyana and had been living in London on a British pension. The plan was to kidnap Bonaparte and send him to the remote Atlantic island of St Helena, replacing him with Louis XVIII.
In an attempt to provide moral justification for what was becoming an increasingly personal vendetta, Bonaparte was henceforth referred to by the British government as a 'usurper'. Despite having maintained official relations and signed treaties with the first consul as 'Bonaparte', it now referred to him only as 'Buonaparte', in an effort to demean him through the suggestion of 'foreign' origins. Encouraged by the government, the press went to town, regurgitating all the slanders and gossip about 'Boney' and his family, and building up an image of him as a demonic figure hungry for British blood; the government used the threat of invasion as an excuse to repress dissent at home and wrongfoot the opposition, denouncing it as unpatriotic or even treasonable.
The resumption of hostilities was useful to Bonaparte as well. The organisation of the Army of England provided an opportunity for disrupting cliques of the discontented in the army by moving around units and commanders, purging the lukewarm and promoting the loyal. But bringing together so many units had disadvantages, and, unbeknown to Bonaparte, a secret society of _Philadelphes_ was formed by hostile officers. The war also strengthened his hand in the assemblies, so he was able to put through a number of projects without trouble. It also helped to distract public opinion from the debacle of his Caribbean enterprise.
In Saint-Domingue the fighting went on in a spiral of unspeakable cruelty, with Leclerc's successor General Rochambeau waging what can best be described as a racial war against the insurgents. On 19 November 1803 he was forced to capitulate and sailed off with his remaining 1,500 troops, but ran into a British naval squadron. He managed to negotiate terms and a return to Europe for his men, but these were not respected, and they were imprisoned until 1811. They were more fortunate than the 800 men left behind in the hospital at Port au Prince under a guarantee of immunity, who were massacred.
Pauline had shown remarkable courage and devotion, nursing her husband in his final illness. She had his body embalmed and wrapped like a mummy's, having cut off her hair to cover his face, and the whole sealed in a lead coffin. His heart she enclosed in a gold urn inscribed with the words: 'Paulette Bonaparte, married to General Leclerc on 20 prairial Year V, has enclosed in this urn her love with the heart of her husband, whose dangers and glory she shared'. As they watched hardy grenadiers straining to carry the heavy coffin on its return to France, cynics quipped that it must contain treasure she had amassed in the West Indies.
Bonaparte was keen to get her married again before she could start misbehaving, but while many lusted, few had the courage to take her on. He offered her to Melzi, who politely declined. Another Italian, Prince Camillo Borghese, did marry her, at Mortefontaine on 5 November. Bonaparte was not present, as he was on a landing barge off Boulogne watching an engagement with British vessels. But he wrote instructing her to refrain from annoying the Romans by praising the pleasures of Paris and to behave as they did, however tiresome she found their customs, and to show respect for the Pope.
He was himself being unfaithful to Josephine with, among others, the actress Mademoiselle Georges, according to whom he was tender and loving, even childlike at times. His philandering always upset Josephine, not least because when engaged on an affair he became irritable, but also because it exposed the inherent insecurity of her position. His siblings acted as little short of pimps, putting nubile women in his path in the hope that one of them might lead to his divorcing her. He protested that he did not want an heir, even going so far as to say that he was not 'a family man', but it was likely that one day he would feel the urge to procreate.
On 11 November he wrote from Boulogne in response to Josephine's reproaches, assuring her that his feelings for her had not changed. 'The good, sweet Josephine cannot be effaced from my heart except by Josephine herself, and only by one who had become sad, jealous and tiresome,' he wrote, explaining that in order to bear all his troubles he needed a happy and understanding home life, and assuring her that 'it is my destiny to love you always'. 'My intention is to console you, my desire to please you, my wish to love you.' This had the desired effect. 'All my sorrows have vanished,' she wrote back, saying she was pressing his letter to her heart. 'It does me so much good! I shall keep it always! It will be my consolation in your absence, my guide when I am with you, because I wish to always remain in your eyes the tender Josephine who thinks only of your happiness.'
He was less successful when it came to the feelings of potential allies. While Britain was engaged on a diplomatic offensive aimed at forming a new coalition against him, he showed few signs of concern. He ignored Talleyrand's suggestion of a rapprochement with Austria to balance British efforts to engage the support of Russia. At the same time, he mishandled Tsar Alexander. He had sidelined him in the process of reorganising the Holy Roman Empire. He then snubbed him when he attempted to mediate in the stand-off with Britain, and in October 1803 the exasperated tsar recalled his ambassador, leaving only Peter von Oubril as chargé d'affaires in Paris. Relations with every country in Europe were about to be placed under even greater strain.
In October 1803 the police arrested a number of royalists, an advance party in a plot to assassinate Bonaparte. Ambushes laid along the Normandy coast to intercept the second wave came to nothing, as British ships bringing them were warned off by signals from land. Those already arrested were condemned to death by a military court, and faced with the firing squad one of them confessed that Cadoudal was in Paris. Another revealed that Pichegru was on his way; the plan was to assassinate Bonaparte and stage a simultaneous rising in Paris, whereupon a Bourbon prince would come and, with Moreau's support, re-establish the monarchy. Pichegru reached France on 16 January 1804, accompanied by an aide to Artois, the marquis de Rivière, and Prince Jules de Polignac. He made his way to Paris, where on 28 January he had the first of several meetings with Moreau.
Réal, who was in charge of the police in Paris, was scouring the city while Lavalette, now head of the postal service, kept his _cabinet noir_ , the interception unit, busy reading suspect letters. Bonaparte's correspondence over the last month of 1803 and the first two of 1804 reveals a murky world of espionage and counter-espionage as his intelligence sources followed the movements of plotters and double agents. The British consul in Munich, Francis Drake, his counterpart in Hamburg, George Rumbold, and the royalist in the pay of Russia and Britain, d'Antraigues, currently in Dresden, handled agents in Paris, some of them in Josephine's entourage. Some of these were double agents, feeding disinformation supplied by Bonaparte. He monitored the situation, ordering the arrest of this one, the tracking of that one and the interrogation of a third, as he and Réal gradually made sense of what was going on.
On 8 February, Cadoudal's servant Picot was picked up, and under interrogation confirmed his master's presence in Paris. Réal was certain that Pichegru was also in the capital and in touch with Moreau. At a meeting of his privy council on the night of 14–15 February, Bonaparte decided to act. The following morning, as he sat by the fireside in Josephine's bedroom with Hortense's baby son Napoléon-Charles on his knees, he suddenly said, 'Do you know what I have just done? I have given the order for the arrest of Moreau.' Josephine burst into tears. He got up, went over to her and, taking her chin in his hand, asked her whether she was afraid. She replied that she was only afraid of what people would say. She was right to be. The news of Moreau's arrest caused outrage in many quarters, particularly the army. Some jumped to the conclusion that the talk of conspiracy was no more than a ploy to incriminate Moreau. Few remembered that it was he who had covered up Pichegru's treachery after he had betrayed the positions and strengths of the army under his command to the Austrians in 1795.
In a letter to Bonaparte, Moreau admitted his involvement in the plot, and explained that he had not committed himself to it since he thought it unlikely to succeed. He had been playing a waiting game, keeping his options open, as ready to assume the role of dictator if the royalists were to succeed in assassinating Bonaparte as to play that of a 'Monck' in the Bourbon cause. But unless Moreau could be definitively implicated in a conspiracy, the first consul would be viewed as a vindictive tyrant bent on eliminating a potential rival. The police combed the city for the evidence that would vindicate him.
This came with the arrest two weeks later of Pichegru, whom the police had finally managed to locate, and on 4 March of Polignac and Rivière. On the evening of 9 March, Cadoudal too was arrested, with the help of a crowd of bystanders after a dramatic chase through the streets of Paris. That brought to forty the number behind bars, and people accepted that there really was a conspiracy. The persistence of these royalists in their determination to overthrow the state caused public opinion to swing back in support of the first consul. Police reports stressed the 'universal joy' expressed by the inhabitants of Paris. But that was not to be the end of the matter.
On 1 March Bonaparte had received a report from a double agent which identified the 'royal prince' who was behind the conspiracy as Louis de Bourbon, duc d'Enghien, the thirty-two-year-old grandson of the prince de Condé, who had commanded the counter-revolutionary forces at Koblenz. After that army had been dissolved he had settled at Ettenheim in Baden, just across the Rhine. When questioned, Cadoudal confirmed that the conspiracy hinged on the arrival on French soil of a royal prince to act as figurehead, though he could not specify which one. Enghien seemed the obvious candidate. His connection to the conspiracy appeared to be confirmed by a report that a number of people had joined him at Ettenheim, including General Dumouriez, who had deserted the Revolution and gone over to the enemy in 1793, and a 'Lieutenant Smith', who was assumed to be the British agent Spencer Smith (the pronunciation of the German informers had turned a General Thumery and the prince's equerry Schmitt into the more dangerous Dumouriez and Smith).
That evening Bonaparte conferred with Cambacérès, Talleyrand, Réal and the chief of the department of the _haute police_ Pierre Desmarest. He was on edge, complaining that he felt like a hunted dog; for the past few months there had been talk only of conspiracy. According to his secretary Méneval, by January 1804 he was gripped by 'anxiety, agitation and painful insomnia'. Desmarest records that when Réal informed him that Pichegru was in Paris and Moreau was involved, Bonaparte surreptitiously made the sign of the cross. He knew that Pichegru and Cadoudal were prepared to risk their lives in order to take his, and he was convinced that the British cabinet was not just supporting them with funds but actively plotting his murder, as he believed they had that of Tsar Paul I. Various Jacobins were restive too, and one police informer had reported at the beginning of December that 'terrible' things were being said ' _against him up there_ '. Even the Russian chargé d'affaires was reporting to his court that 'the conspiracy is far advanced'. Roustam, who normally slept on a camp bed in the next room, placed it across the door of Bonaparte's bedroom (he was told off after, getting up in the night to check something in his study, his master tripped over him).
On the afternoon of 10 March, the day after Cadoudal's arrest, Bonaparte held another extraordinary meeting, attended by Cambacérès, Lebrun, the supreme judge Claude-Ambroise Regnier, Talleyrand, Réal, Murat and Fouché. Although at least two of those present later falsified their own part in it, there is little doubt as to what took place. In the evidence before him, Bonaparte spotted a golden opportunity to catch out all the major players and put an end to royalist plots, by having Enghien and his accomplices arrested and brought to trial. This would expose to the world the perfidy of the Bourbons and their British allies, and possibly that of Moreau. Cambacérès advised caution, but Talleyrand encouraged Bonaparte to act firmly. His personal desire to prevent a Bourbon restoration was in this case reinforced by a need to rehabilitate himself, as Bonaparte had recently been growing suspicious of his contacts with the royalists – Talleyrand always kept several options open. Fouché almost certainly backed up Bonaparte's arguments, for much the same reasons. Later that day, Bonaparte summoned the minister of war and two generals, whom he ordered to cross the Rhine with a small detachment, seize Enghien and bring him to Paris.
Early on the morning of 15 March the duke's residence at Ettenheim was surrounded by French gendarmes and he was arrested. He was whisked across the border to Strasbourg and his papers sent to Bonaparte, who found in them a copy of a letter to the British ministry agreeing to serve under British orders against France, informing it that Enghien had supporters in French units stationed along the Rhine, and describing the French nation as his 'cruellest' enemy. Josephine attempted to plead for the prince, only to be told not to interfere, and later that day Bonaparte summoned Murat, who was military governor of Paris, instructing him to convene a military court.
It was to sit at the fortress of Vincennes outside Paris, where Enghien arrived in a coach escorted by six mounted gendarmes at half past five on the afternoon of 20 March. That morning Bonaparte had signed an order for him to be tried by a military court on charges of having borne arms against France, of being in the pay of the British, and of involvement in a conspiracy to overthrow the French government.
After dictating these orders, Bonaparte drove to Malmaison, where he was joined by Talleyrand. Some time later Joseph arrived from Mortefontaine, to be greeted by a worried Josephine who urged him to persuade Bonaparte to show mercy. According to Joseph, Bonaparte asked his advice, and after hearing Joseph's pleas for the prince's life, agreed to allow him to redeem himself by serving in the French army. This account can be safely ignored. In the afternoon, Bonaparte instructed Savary to go ahead with the trial. He also wrote to Réal ordering him to go to Vincennes to interrogate the prisoner beforehand.
At eleven that evening Enghien was taken from his cell and brought before the military court. He pleaded guilty to all three charges, but asked to be allowed to see the first consul. The request was denied. The verdict was delivered at two o'clock in the morning. A grave had already been dug and a firing squad was waiting; he was led out, shot and buried.
Savary, who had commanded the gendarmes making up the firing squad, went directly to Malmaison to report. According to him, Bonaparte was astonished that the act had been carried out so quickly, and that Réal had not been to Vincennes to question Enghien before the trial. 'There is something I do not understand,' he said to Savary. 'There is something I cannot grasp... This is a crime, and one with no purpose.' Savary's account is probably coloured by the wish to show Bonaparte in a good light. Méneval and Cambacérès both write that he had been intending to reprieve Enghien, and Bonaparte himself in later years claimed that he had never wanted him shot. He may well have been intending a theatrical pardon, which would have left him with a bargaining chip in hand, but there is no real evidence, and all accounts of the event should be treated with the greatest suspicion.
News that a distinguished person had been executed was spread through the city that morning by returning gendarmes and peasants from the locality of Vincennes bringing vegetables to market. When it became known who it was, royalists and aristocrats were horrified, and many would never forgive Bonaparte. But most accepted that the execution had been necessary – only a decade earlier that of an innocent monarch and his consort had been accepted as such. Most people wanted stability, not plots to overthrow the government, particularly as unemployment and the price of bread were both low. There was little sympathy for the Bourbons and their supporters, who, being in the pay of the British enemy in wartime, were seen as traitors. Many of those who were saddened by the execution actually felt sorry for Bonaparte, assuming that he had been regretfully obliged to carry out an act of severity.
Whatever his true intentions, Bonaparte acted as though there had been a serious threat, but no danger, thanks to the solidity of his government. It had been necessary, as he put it, to demonstrate once and for all to the Bourbons, the royalists and the British that he would no longer treat their plots as 'child's play'. To the outside world he took the opportunity to issue something of a challenge. Talleyrand wrote to every court not at war with France demanding the expulsion of all active French émigrés from their territory. One of the first to comply was the elector of Baden, who should have been the first to protest, his territory having been violated. But being so close to France, and having done well out of French support, he had no intention of doing any such thing. On 26 March, at Bonaparte's behest Talleyrand held a reception at the foreign ministry, which every diplomat in Paris attended.
In Warsaw on the same day, Louis XVIII, who had received news of Enghien's arrest but not of his execution, sent an appeal to all the courts of Europe urging them to intercede on the prince's behalf. His letters were returned, mostly unopened. The British government offered a reward to anyone who would free Enghien, and Tsar Alexander took the matter to heart; when he heard of the prince's death, he announced court mourning as for a monarch. As he was treating with Britain over an alliance with the aim of making war on France, he considered making the 'murder' of Enghien a _casus belli_. But the negotiations with Britain were not far advanced, and neither were his military preparations. Instead, he issued a protest against the violation of the territory of Baden and ordered his chargé in Paris to demand 'a satisfactory explanation'. Bonaparte responded with a taunt, referring in the most diplomatic terms to the fact that Alexander had been a party to the murder of his father, and had ascended the throne over his body.
Almost every person involved wrote up the events in colourful ways aimed at justifying their role in what later came to be seen as a heinous act. Both Talleyrand and Fouché asserted that they had opposed the execution, and both claimed to have said 'It is more than a crime, it is a mistake.' But at the time neither regarded it as anything of the sort. They were as anxious as Bonaparte to put an end to royalist plots aimed at restoring a dynasty that would have shown them little kindness. Both had recently aroused his mistrust (and in Fouché's case fallen out of favour), and therefore needed to rehabilitate themselves. Bonaparte had shown a decisiveness and ruthlessness Machiavelli would have applauded, and they would have been of the same mind.
Yet the unholy alliance of these three men sealed by this incident had a seamy side. According to the prefect of police Étienne Pasquier, Talleyrand's collusion with Bonaparte in the elimination of Enghien had revealed to each the degree of ruthlessness the other was capable of, and it frightened them both. 'From then on, they expected nothing but perfidy and betrayal from one another,' he wrote, and while Bonaparte henceforth treated Talleyrand with mounting disgust and hauteur, at the same time fearing him, Talleyrand grew more resentfully servile, while secretly undermining his master. Fouché, on the other hand, used the event to convince Bonaparte of the need for a ministry of police, and got himself reinstated as minister. Instead of gratitude, he henceforth displayed greater arrogance and independence. Having seen his master dip his hand in royal blood, the regicide felt more confident. He extended his brief not only within France but abroad, creating a web of intelligence-gathering and quasi-diplomatic agents all over Europe through whom he entertained relations with most of France's and Bonaparte's enemies.
Machiavellian calculation aside, Bonaparte was emotionally affected by the episode. He noted that people looked at him in a different way, and revealed his unquiet conscience by alternately trying to put the moral case for the execution and making gratingly brutal comments about political necessities. He did not try to shift blame or admit he had blundered, but tried to brazen it out by acting as though nothing had happened. He ignored advice from his entourage to keep out of the public eye for a while, at some cost. One of Josephine's ladies-in-waiting remembered him entering his box at the opera for the first time after the event, with the air of a man leading an attack on a battery of guns. The audience applauded him as usual.
Although he professed feeling no fear, Bonaparte did admit that the many plots against him made him shudder at the thought of what would happen to France were he to be killed. That fear was felt by the majority of the population. He was commonly referred to as 'the man called by Providence and protected by the heavens', and after the discovery of the Pichegru–Cadoudal plot there was talk of 'the happy star which has saved the saviour of the fatherland from the assassins', and of 'the protective spirit which arrested the fatal stroke'. Although some termed him 'the hero, the idol of France, master of the elements, above all perils and all obstacles', there was an underlying fear that the motherland might lose him.
Much the same was true for all those who had played a major role in the Revolution, who feared the consequences for themselves of a return of the Bourbons. Not only would all the achievements of the past decade and a half be overturned, they would at best find themselves obliged to seek safety in obscurity. Émigré nobles who had returned to France, thereby abandoning the Bourbon cause and accepting the legitimacy of the first consul, could also expect little understanding from a returning Louis XVIII, so they too looked for a consolidation of the existing regime. 'They want to kill the consul,' a worried Regnaud de Saint-Jean d'Angély wrote to Thibaudeau. 'We must defend him and make him immortal.' The form this would take seemed obvious to most. 'The question was not whether Bonaparte had those qualities which are most desirable in a monarch,' explained Talleyrand. 'He certainly possessed those which were indispensable...'
'The feasibility of establishing in France a republic like those of antiquity had been dismissed long ago, but people had not given up hope of a government compatible with the dignity of man, with his interests, his nature and his aspirations,' in the words of Thibaudeau. 'People did not believe such a government to be incompatible with having a _single_ head, and the one France had given herself seemed on the contrary to have been conjured up by Providence to resolve this problem so long discussed by writers and philosophers.' In a word, Bonaparte appeared to provide the ideal solution to the conundrum of bridging the ideological gap between monarchy and the sovereignty of the people. As this conviction grew, so did the desire to make his authority permanent, and therefore hereditary. 'Consul for a term, any coup could see him off like the others. Consul for life, it only needed one assassin...' explained Maret. 'He took hereditary government as a shield. It would no longer be enough to kill him; it would be necessary to overthrow the state.' When people spoke of heredity, they meant monarchy. During the negotiations over the Treaty of Amiens, Cornwallis had even suggested that since George III agreed to drop the title of King of France, the first consul should assume it.
Fouché urged his fellow senators to create 'institutions which could destroy the hopes of conspirators by ensuring the survival of the government beyond the life of its head'. On 28 March the Senate duly delivered an address to Bonaparte stressing that every attack on his person was an attack on France, as he had rescued the country from chaos and brought huge benefits for all, and it was therefore his duty to guarantee the future. 'You have created a new era; you must perpetuate it. Glory is nothing if it is not lasting,' it ran. The only opposition came from Sieyès, Volney and Grégoire. When the delegation of senators called to deliver the proposal, Bonaparte affected surprise, but graciously agreed to consider it.
In effect, his brothers Joseph and Lucien, Fouché and Talleyrand, and many others were canvassing hard, encouraging local authorities and military units all over the country to send in appeals begging him to accept supreme authority. He spent most of these months at Saint-Cloud, where he held sessions of his privy council and the Council of State, and received delegations from the assemblies like a monarch attended by his subjects.
On 13 April his privy council directly addressed the question of his becoming emperor. No other title seemed appropriate. Louis XVI had been executed and declared to be 'the last of the Kings', so that title was out of the question. The kingdom of France had been abolished and superseded by the French Republic, which had grown into an empire. People at the time referred to the British and Ottoman empires, even though one was a kingdom and the other a sultanate. Given the size and power of France, her ruler could be compared only with Caesar or Charlemagne. The titles of the only two emperors in Europe both supposedly derived from Rome, the word 'tsar' being a Russian version of 'Caesar', while the title of Holy Roman Emperor spoke for itself. If the head of the French Republic were to take a title, it could only derive from Rome. He was consul, and would become Imperator.
Bonaparte did voice some reservations. 'So many great things have been achieved over the past three years under the title of _consul_ ,' he had said to Roederer in January 1803. 'It should be kept.' Cambacérès agreed. 'As First Consul, your greatness has no limits and the example of your success being a lesson to them, the kings of Europe will, if they are wise, seek to respect you and avoid all cause for war, so as to prevent French troops from spreading the principles of the Revolution in their possessions,' he warned. 'As Emperor, your position changes and places you at odds with yourself.' Although he had embraced the idea of the imperial title, Bonaparte clung to his revolutionary heritage. It would, it was understood, be a liberal parliamentary monarchy. 'The citizens will not become _my subjects_ , and the French nation will not become _my people_ ,' he affirmed.
On 30 April the Tribunate voted in favour of declaring France an empire, with Carnot among the very few dissenters. On 3 May this was communicated to the Senate, which had been working on how to bring it about for the past month. The following day it sent a delegation to Bonaparte which declared that circumstances had made it imperative he accept the dignity of hereditary emperor. It set out a number of conditions, insisting that liberty and equality must never be jeopardised and the sovereignty of the people safeguarded, ending with the hope that the nation should never be placed in the position of having to 'reclaim its power and to avenge its outraged majesty'. The address was accompanied by a long memorandum listing all the conditions in detail, such as the inviolability of laws, the freedom of institutions, of the individual, of the press, and others quite unacceptable to Bonaparte. It was he who was outraged, and he forbade publication of the document.
At Saint-Cloud over the next few days he oversaw the work of a commission working on what was effectively a new constitution. The resulting document opened with the words: 'The Government of the Republic is entrusted to an Emperor, who takes the title Emperor of the French.' The state continued to be referred to as the Republic (and would be until 1809), and the sovereignty of the people was given its titular due. But the succession was to be by male descent in the Bonaparte family, and the master of France was now Napoleon I. It was presented to the Senate for approval and passed into law on the morning of 18 May. Following the vote, the senators climbed into their carriages and drove en masse from the Luxembourg to Saint-Cloud.
Bonaparte, in military uniform, was waiting for them in the Gallery of Apollo, in which he had addressed the Ancients on 19 Brumaire. He was surrounded by the male members of his family, his fellow consuls, ministers and other dignitaries. When Cambacérès ushered in the senators, he addressed Bonaparte as 'Sire' and 'Majesty', words not used in France for over a decade. Many of those present felt uneasy on hearing them, but Bonaparte did not flinch. 'He seemed the least embarrassed of all those present,' recorded one.
Lebrun made a speech, at the end of which he proclaimed Napoleon I Emperor of the French. Napoleon graciously accepted the honour. 'Anything that can contribute to the good of the motherland is closely bound up with my own happiness,' he said. 'I accept this title which you believe to be in the interests of the nation.' As they waited to file in to lunch, Duroc moved among the dignitaries informing them how they should henceforth address each other. They were no longer citizens.
## 27
# Napoleon I
'This new dignity bestowed on the most insolent of all the usurpers who have ever mounted the world stage has accumulated and consummated our shame and our misfortunes,' the Austrian official and British agent Friedrich von Gentz wrote to the British minister in Berlin, Francis James Jackson, on 22 August 1804. 'The ease and indeed the joy with which this impudent procedure has been received and applauded at every court marks the extent of the world's decadence.' Frederick William of Prussia did indeed write a letter of congratulation to Napoleon which was nothing if not cordial. The other states of Europe were more or less grudging, but all except Britain, Russia and Sweden recognised Bonaparte's elevation. Francis II, whose title of Holy Roman Emperor had grown meaningless with the dissolution of that political unit, proclaimed himself emperor of Austria as Francis I, citing as precedents the Russian monarchy and the elevation of 'the new sovereign of France'. He had sought Napoleon's approval first.
Reactions in France were mixed. Scorn was poured on the enterprise by the people of the street in Paris, who were strangers to reverence. During the performance of a play about Peter the Great at the Théâtre-Français on 19 May the words 'emperor' and 'empire' were hissed by the audience. But there were no disturbances, and according to a police report of 25 May the workers of Paris 'were making much of their right to vote [in the plebiscite held to sanction it] for the hereditary empire' and turning up at the Préfecture in large numbers to do so.
Many in the army felt their past glories and the epic days of marching barefoot and beating the Austrians on empty stomachs would be submerged in the new pomp. General Rapp disliked the ceremonial, resented the growing number of nobles in Napoleon's entourage, and regretted his former familiarity with the great man, as did Lannes.
'As for me,' wrote another veteran of Italy and Egypt, 'while regretting the austere yet noble trappings of the Consulship, which suited me better than the pomp of the Empire, along with my old comrades of the Pyrenees, of Arcole, Rivoli and the Pyramids I sincerely welcomed this great political event.' In an official address, General Davout assured Napoleon that the troops under his command saw in his elevation 'not so much an honour for you as a guarantee of future happiness for us'. In a private letter to his friend Murat, General Belliard, then stationed in Brussels, noted that his men were 'on the whole pleased with the new form of Government and the idea of heredity'.
It was unfortunate that the trial of Moreau, Cadoudal and the other conspirators opened only ten days after the proclamation of the empire. Pichegru did not feature, as he had been found strangled in his cell with his neckcloth. The official verdict was suicide, but many did not believe it. Moreau still elicited sympathy, and people were not convinced of his culpability; he defended himself ably and was acquitted. Napoleon put pressure on the judges and a retrial found him guilty. Sentence was passed on 10 June. Cadoudal and nineteen of his fellow conspirators were condemned to death, Moreau and others to two years in prison.
That morning Josephine had brought the parents of the marquis de Rivière and Prince Jules de Polignac to the Tuileries, where they pleaded with the emperor. The mother of Polignac fainted and fell at his feet. Napoleon pardoned the two young men, along with two more nobles for whom his sisters had interceded. In doing so, he sent out a message to royalist nobles that they, unlike the Bourbons, did have a future in the new empire. Not so Moreau, whom he had hoped to see condemned to death so he could pardon him. As it was, Moreau could appeal against the verdict, which would lead to another trial, so Bonaparte quickly commuted the sentence to banishment from France, and sent him to America. The episode had stirred powerful emotions. 'The animosity and outbursts of rage against the government were as violent and as widespread as any that I saw in the days leading up to the Revolution,' noted Roederer. But they did not affect the general acquiescence in the change of regime.
Miot de Melito was surprised at the degree to which people found the idea of hereditary succession reassuring. 'It was not as if any surge of affection for the first consul inclined public opinion to favour this new increase in grandeur for him and his family – he had never been less popular – but the need for peace and stability was so pressing, the future so alarming, the fear of terrorism so great, the return of the Bourbons, who had so much to avenge, so fearsome, that people eagerly grasped anything they could to elude these dangers against which they could see no other means of defence.' Many assumed that Napoleon would, having first dealt with the impediment of Josephine by repudiating her, marry into the network of European royalty, to reinforce his legitimacy and guarantee France membership of the club. Some talked of the sister of the elector of Bavaria, which would have made Bonaparte the brother-in-law of Tsar Alexander.
The marquis de Bouillé, an émigré who had returned during the peace of Amiens, was so struck by how strong and proud France had grown that he felt justified in switching his allegiance from the Bourbons to the man who had achieved this. Being a monarchist at heart, he believed Napoleon had a right to the throne. The ageing Cardinal Maury, a devoted adherent of the Bourbons, congratulated Napoleon on his accession. 'I am French,' he wrote. 'I wish to remain so always. I have constantly and loudly maintained that the government of France must be from every aspect essentially monarchical.'
Most of the hierarchy welcomed anything that could consolidate the rule of the man who had restored France to the Church. The Imperial Catechism treated him as the representative of God on earth, and the clergy would celebrate his victories, read out his Bulletins from the pulpit and condemn desertion from the army as a sin. Bishops referred to him as 'a Hero preordained by Providence', an 'instrument of Divine mercy', 'another Moses', and even in one case described his return from Egypt as being ordained by God.
'It was a unique moment in our history!' wrote the twenty-four-year-old hussar officer Philippe-Paul de Ségur, an aristocrat who had defied his family to join up, and only reluctantly accepted Bonaparte's offer of the prestigious post of aide-de-camp. He had wept when he heard of the death of Enghien, and condemned Napoleon. Yet he was swept along by enthusiasm for the enterprise of restoring France to greatness. 'We were living in a state of exaltation as though in a world of miracles. On that day of 18 May in particular, what enthusiasm, what splendour, what power!'
'Today at last one can say that the Happiness of France is made forever!' ran a letter addressed to Napoleon by a group of soldiers of all ranks on 19 June 1804. 'Today the resounding Glory which envelops this Great Nation has been made imperishable [...] Your glory is immense: the Universe is barely great enough to contain it and posterity would find it difficult to believe the real deeds of your illustrious career if faithful history had not graven them.' Contemporary observers and historians of the times alike agree that these overblown addresses were not mere flattery or the docile mantras of a populace manipulated by Napoleonic propaganda, but the genuine expression of collective exaltation. Many believed he was so favoured by the gods that the sun always came out when he held a parade or some other outdoor ceremony.
In 1807 the philosopher Claude-Henri de Saint-Simon would write that while there had been geniuses of action such as Alexander the Great, Hannibal, Caesar, Charlemagne and Mohammed on the one hand, and geniuses of the mind such as Socrates, Plato, Aristotle, Bacon and Descartes on the other, Napoleon was a miraculous conflation of both. This extraordinary combination of creativity with action and power meant that he made things happen, things that others could only dream of. He was the ultimate creator, a kind of human God. Seven years of propaganda had built up a sense of his superhuman nature and of his being the darling of fortune, providence, fate or the gods. Paintings such as that by Gros of him visiting the plague victims in Jaffa, in which he is seen touching them while his aides cover their faces with kerchiefs, conveyed a subliminal message of his divine untouchability. And, as he pointed out himself, even the name 'Napoleon', unheard-of as it was, added to the mystique.
Ironically, that mystique would be undermined by his attempts to institutionalise what had existed hitherto in the realms of the imagination. As Cambacérès had predicted, Napoleon was now at odds with himself. But the son of the parvenu noble Carlo Maria had been captivated by another mystique – a Romantic vision of a chivalric past. The constitution was amended by the addition of 142 clauses, and the words 'nation' and 'people' disappeared; Napoleon was emperor 'by the Grace of God and the constitutions of the Republic'. He was to be succeeded by his male heirs, natural or adopted, and failing that by Joseph or Louis. A point was made of guaranteeing the possession of property acquired during the revolutionary period. The Senate, which became the dominant body, was swelled by the addition of the Cardinal Archbishop of Paris and grandees of the ancien régime. Its members received grants of land with a significant income, so as to create a new senatorial aristocracy grounded in the regions but connected to Paris, turning it into a kind of _étatiste_ version of the British House of Lords.
The new constitution surrounded the throne with offices copied from the French monarchy and the Holy Roman Empire. On 18 May Napoleon's brother Joseph became grand elector, Louis took the ancient title of _Connétable_ , Cambacérès was named arch-chancellor, Lebrun arch-treasurer, Murat grand admiral. The following day fourteen generals were given the title of marshal of the empire, among them dissidents whom Napoleon wished to flatter such as Masséna, Augereau and Bernadotte. Talleyrand became grand chamberlain, Fesch grand almoner, Duroc grand marshal of the palace, Berthier grand huntsman, and so on. There was confusion as people struggled to remember how to address the bearers of these new charges, whether as _Monseigneur_ , _Votre Grandeur_ or _Altesse Sérénissime_ , and their number did not cease to grow. An imperial _maison_ was created, modelled on the former _Maison du Roi_ , the official structure of the royal court. Napoleon had a _maison civile_ , consisting of ninety-four officials, and a leaner _maison militaire_ , to make up his court on campaign. Josephine had her own _maison_ of twenty-seven officials, as well as twenty-nine _dames du palais_ (Marie-Antoinette had twelve) and her own stables, a total of ninety-three people, including her grooms. Distinctive uniforms and liveries were designed, and a strict etiquette was established, as Napoleon believed that he must create greater distance between himself and other mortals in order to place his authority on a higher plane. The rules were published on 13 July, but people were still confused. Grand Chamberlain Talleyrand, who on being released from holy orders by the Pope was forced by Napoleon to marry his mistress, a lady of shady past, was firmly told that he could not bring his 'whore' to the Tuileries. The eminently sensible and tactful marshal of the palace Duroc was frequently called upon to deal with such delicate matters.
The Legion of Honour, which had grown to a membership of some 6,000, was transformed into an order of chivalry which was to be a pillar of the throne. On 11 July it acquired insignia in the shape of a five-branched cross and was graded in five ranks: _chevalier_ , _officier_ , _commandeur_ , _grand officier_ and _grand'croix_. As well as attributing prestige, inclusion in the Legion brought remuneration and perks such as free education of daughters at a new school in Saint-Denis. On Sunday, 15 July, after a solemn mass at Notre Dame, Napoleon proceeded to the Invalides, where, under the dome where his remains now lie, he handed out the crosses to and took the oath of the first to have been honoured. 'What I felt at that moment made me understand how a hundred thousand men went to their deaths to deserve it,' recorded the returned émigré General Thiard on receiving his.
Symbols and festivals associated with the Revolution, such as the commemoration of the execution of Louis XVI on 21 January, were phased out; the commemoration of the fall of the Bastille on 14 July was replaced by a national holiday on Napoleon's birthday, 15 August, under the name of _la Saint Napoléon_ – though there had never been any saint of that name. The _Marseillaise_ was superseded by the bland _Veillons au salut de l'Empire_. Many wise heads were bowed over the problem of what insignia should distinguish the new state and dynasty; the lacklustre coat of arms awarded to Carlo Maria would not do. Lebrun suggested going back to the Bourbon fleur-de-lys, but was overruled. Among the proposals put forward were a resting lion, the cock of the Gauls, an owl, an elephant, an eagle and an ear of wheat. The cock was a favourite, but Napoleon would not have it. 'The cock is a farmyard animal, it is too weak,' he protested. The eagle was too closely associated with other royal houses, such as the Russian, Prussian and Austrian, but Napoleon was keen. He hesitated between that and the lion, but the association with ancient Rome prevailed, and the eagle became the emblem of the French Empire. It was Cambacérès who came up with the bee, a symbol of industry and community, as that of the dynasty.
Napoleon had insisted that the change of regime be sanctioned, like the others, by a plebiscite to obtain the endorsement of the nation. The question related only to the hereditary nature of the monarchy, not to Napoleon's elevation. The turnout was less than that for the previous one, around 35 per cent. The results were 3,572,329 for and 2,569 against. There was some vote-rigging, with possibly as many as half a million 'yes' votes being added, and it is also probable that many voted out of indifference or fear. But as far as Napoleon was concerned, it proved he held his position from the people. Having obtained their endorsement, he wanted to sanctify the new state of affairs with an act of God, by means of a religious coronation.
He believed that this would crown his policy of fusion, by bringing Church and state together, and grounding his throne in tradition, lending his rule added legitimacy. He meant to outdo the Bourbons. The founder of the first French dynasty, Pepin the Short, elected king by the Franks in 751, had been crowned by the Pope, as had his son Charlemagne and grandson Louis the Pious. Napoleon had sounded out Pius VII before his elevation, and the Pope was prepared to overcome his distaste in the hope of obtaining in return for his presence some concessions on the terms of the organic articles that Napoleon had foisted on the Concordat at the last moment.
Napoleon considered holding the coronation away from Paris, whose populace he regarded with a mixture of fear and contempt, and whose educated classes he disliked for their irreverence and open-mindedness. He considered Aix-la-Chapelle, associated with Charlemagne, and Lyon, which he saw as the model modern industrial city. If it did have to be Paris, he favoured the Invalides over Notre Dame. Discussion of such details continued up to the last moment.
His physical environment had to be adapted. The area between the Tuileries and the old Louvre was being progressively cleared and turned into a monumental open space. Works began in the palace to accommodate his court, including a large chapel in which all its members would be expected to hear mass every Sunday. Saint-Cloud was also adapted, likewise acquiring a chapel large enough to accommodate not just the court but also a choir and orchestra, which Paisiello would conduct. The old royal palace of Fontainebleau, which had been turned into a military prison, was now restored so as to be able to receive the emperor and the court.
If Paris was to be the seat of the new French Empire, the new Rome, it must reflect its glory and be turned into the most beautiful city in the world, as Napoleon had dreamed aboard the _Orient_ on the way to Egypt. He had methodically bought up and demolished crumbling medieval hovels to create wide streets and prospects, with proper paving, guttering and lighting. Since coming to power he had had fifty-six fountains repaired and fifteen new ones built; hospitals had been refurbished, hospices for the terminally ill and shelters for the indigent had been built. New cemeteries had been established outside the city. Two new bridges had been started and the Seine's banks were being cleared. A powerful impulse had been given to the arts, particularly painting and sculpture, with the biannual _Salon_ showing works by David, Gros, Girodet, Fabre, Ingres, Isabey, Prudhon and others. The various museums, principally the Louvre, were a wonder the world had never seen before. Paris had also become the capital of music, with a conservatoire staffed by 115 teachers, three opera houses, and most of the prized composers of the day. There were also seventeen theatres, and despite censorship, literary life continued. The sciences flourished under the directorship of the Institute and the active encouragement of the state. Radiating out of the capital, utilities such as roads and bridges were being built. Since Paris was to be the centre of its universe, the telegraph, a system devised in the 1790s on the basis of a chain of wooden structures with moving arms which relayed messages by semaphore, was extended to carry news fast from the west coast, from the south, from Germany and Italy – and from Boulogne, where a giant one had been built to send signals across to the Army of England once it had landed.
On 18 July, two months after becoming emperor, Napoleon left for Boulogne. Arriving at one o'clock the following afternoon, he immediately mounted up and rode about inspecting troops, harbour and ships, then insisted on sailing out on one of them, and after being fired on by the blockading Royal Navy, returned to port. He was keen to see the transport barges in action, so the following day he gave orders for some to put to sea. Admiral Bruix pointed out that the wind was shifting, making it dangerous. Napoleon insisted and rode off, but Bruix did not carry out the order. On his return, Napoleon was so angry he raised his riding crop as if to strike Bruix, whereupon the admiral put his hand to his sword. Napoleon lowered his arm, but dismissed him and commanded his second to order the operation to commence. The wind did shift, and the vessels were thrown onto the rocks. Napoleon directed the rescue operations through the night, and evidently found the experience exhilarating after months of ceremonial in Paris. 'It was a grand sight: cannon firing warning shots, beacons lighting up the coast, the sea roaring with fury; the whole night spent anxiously anticipating whether we would save these poor wretches or see them perish!' he wrote to Josephine. 'At five o'clock in the morning the light came up, all was saved and I went to bed with the sensation of having lived through a romantic and epic dream.' His Ossianic dream had cost seven ships and twenty-nine lives.
He was in fighting spirit. To Cambacérès he reported that the army and the naval units were in good shape. To Chaptal's successor as minister of the interior Jean-Baptiste Champagny he gave instructions for the Institute to study the American inventor Robert Fulton's plans for steamships and submarines. To Brune in Constantinople he wrote that he had 120,000 men and 3,000 barges and armed galleys 'only waiting for a favourable wind to carry the imperial eagle to the Tower of London'. When Marshal Soult told him that it was impossible to embark the whole army in under three days, he snapped back, 'Impossible, sir! I do not know that word, it is not French, remove it from your vocabulary!'
Napoleon spent the next six weeks with the Army of England. Although a pavilion had been erected for him in the camp, he took up quarters in a small château at Pont-de-Briques just outside Boulogne. The main camp, on the heights above the city, had been established over a year earlier, and the men had made themselves at home, with 'very fine stone living quarters along regular lines to accommodate their officers, the administration, workshops, etc.', according to the commander of the 26th Light Infantry, even building cafés and laying out gardens. This and the other encampments, strung out along the coast from Étaples to Ostend, contained around 150,000 men. There were a further two corps, one under Marmont in Holland and the other at Brest under Augereau, which brought the total number of troops facing Britain close to 200,000.
They were to cross in a variety of craft, mostly flat-bottomed barges powered by sail, some supplemented by oars. Each vessel was to carry its complement of infantry, cavalry and artillery, so that the loss of one would merely diminish the strength of a corps without disabling it. Much thought had gone into their design: cannonballs making up the ballast were covered in sand on which horses could stand attached to posts, arms were stored in the deck above the men's hammocks, gun carriages were suspended over the water fore and aft, while the gun barrels were mounted on deck so as to be able to fire. As it required five tides to get all the vessels out of harbour (which meant three days with ideal weather conditions and no interference by the Royal Navy), they were unlikely to be of much use. Yet over those six weeks Napoleon gave every sign of meaning to go ahead with the enterprise. He thought up an elaborate naval manoeuvre based on sending two fleets out to the Caribbean in order to draw off the Royal Navy, and then bringing all available ships into the Channel to shepherd the barges across. He was confident that once he had reached England he would sweep away any military defences he encountered and be in London within a couple of days. In that he was probably right, but given that the Royal Navy would by then have gathered in the Channel, he would have been completely cut off.
It seems extraordinary that Napoleon should have spent millions of francs on an enterprise he did not mean to carry out, yet everything points to that being the case. He had been actively engaged in the preparations, making frequent visits to Boulogne for over a year, but it was only in July and August 1804 that he busied himself with it most ostentatiously, telling all and sundry that he would be in London in a matter of days. By then he knew that Austria was in negotiations with Britain and Russia, which had massed a large army on its western frontier and was putting pressure on Prussia to join a new coalition against him. He could not possibly in such circumstances take the bulk of his forces off to England, leaving France and Italy exposed. He said as much in a letter to Champagny on 3 August.
Many in Napoleon's entourage, beginning with Cambacérès, believed the exercise was a bluff aimed at draining British resources, which it did to a large extent, and drawing attention away from his real plans. Variants of this opinion can be found among the military and even foreign diplomats in Paris. But it is likely that there were moments when he did consider invading. His exasperation at the repeated attempts on his life and work, such as the recent conspiracy, may have acted as a spur to striking at what he saw as their source in Britain.
Another spur to try a risky throw of the dice might have been the almost supernatural wave of success he was riding. According to Marmont, he was dreaming of achieving ever grander things. 'One has to live up to one's destiny,' Napoleon told one of Josephine's ladies-in-waiting. 'He who has been chosen by destiny cannot refuse.' He was so preoccupied with how he would go down in posterity that he had come to see his life as epic. It was as if the image he had so carefully been fashioning over the past years had begun to direct his behaviour. To Admiral Decrès he complained that he had reached a dead end where glory was concerned, as the modern world was too prosaic for truly transcendental acts. 'Take Alexander [the Great]: having conquered Asia and announced that he was the son of Jupiter, [...] the whole of the East believed him.' Yet if he, Napoleon, were to announce that he was the son of God, every fishwife in Paris would laugh at him, he told the astonished admiral.
He was in fine spirits, riding up and down the coast, inspecting troops, weapons and equipment, chatting with officers and men, putting them through their paces and basking in the reflected glory. On 16 August he held a ceremony in which he handed out decorations of the Legion of Honour. The massed troops looked magnificent, flags fluttered in the sea breeze and bands played martial airs. Against a backdrop of war trophies, surrounded by his men, Napoleon distributed the insignia to the brave. 'No, never, in none of his grandest ceremonies was he so majestic!' in the words of an army physician. 'It was Caesar with his legions.' According to Miot de Melito, Napoleon told his brother Joseph that he believed he had been 'called to change the face of the world'. 'Perhaps some notions of predestination have affected my thoughts,' he admitted, 'but I do not reject them; I even believe in them, and that confidence provides the means of success.'
'My health is excellent,' Caesar wrote to Josephine on 20 August. 'I am longing to see you, to tell you all about my feelings for you and to cover you in kisses. A bachelor's life is a mean one, and nothing like having a good, beautiful and tender wife.' He would soon be joining her at Aix-la-Chapelle, where she was taking the waters. 'As it is possible that I might arrive at night, let the lovers beware,' he wrote jestingly on 25 August, assuring her that he had been too busy for any philandering and dropping suggestive hints.
On 1 September he was in Brussels, from where he set off on a breathless tour of inspection of the left bank of the Rhine. On 2 September, at Aix-la-Chapelle, he received news from Paris that the Russian chargé d'affaires, Oubril, had asked for passports and left, which forecast a state of war, yet Napoleon carried on as if nothing had happened. With Josephine he attended a _Te Deum_ in the cathedral and was shown the relics of Charlemagne. On the evening of 9 September he reportedly suffered something that looked like an epileptic fit. But two days later he was on his way to Cologne, from where he went to Koblenz and on to Mainz, where he received a number of minor German rulers who came to pay their respects. Having finished inspecting French defences along the Rhine, he was back at Saint-Cloud on 12 October.
Although he knew Russia was by now well advanced in preparations for war and Austria was also arming, and Naples only waiting for a chance to strike, Napoleon showed no sign of concern. He spent the next weeks alternating between Paris and Saint-Cloud, hunting there or at Versailles or in the Bois de Boulogne, while maintaining his intent to invade England, chivvying troops and crews to practise embarking and landing. On 27 September he had written to Berthier that 'the invasion of Ireland has been decided', to be led by Augereau with 18,000 men supported by Marmont with another 25,000, while the rest of the army crossed the Channel to Kent. The operation was to begin on 20 October. Yet he now shifted his attention to preparations for his coronation – even taking the trouble to have his wet-nurse, Camilla Carbon Ilari, brought from Corsica to see Paris, detailing Méneval to look after her.
His elevation had raised questions about the part his family were to play in the imperial structure. While they had for the most part been of little assistance to him, and felt no duty of obedience, they had all developed bloated ideas of their own worth, and exorbitant pretensions – Joseph actually believed that as the eldest brother he had a better claim to the throne. He was proving such a nuisance that Napoleon gave him a regiment to command and sent him off to Boulogne. But a more permanent solution was needed, and as Napoleon could hardly be president of the Republic of Italy as well as emperor of the French, he decided to turn that into a kingdom, and offered its throne to Joseph. Preliminary soundings in Vienna suggested such an arrangement might be acceptable. Joseph agreed, but kept laying down conditions, mostly concerning what he considered to be his right to succeed to the French throne.
Having been persuaded by Josephine that he was infertile, Napoleon had fixed on his step-grandson Napoléon-Charles, the two-year-old child of Louis and Hortense. He had a special fondness for Louis, whom he had largely brought up, and adored Hortense. But Louis had turned into a neurotic hypochondriac (among his bizarre 'cures' was bathing in tripe). His relationship with Napoleon was fraught, as Hortense explains: 'Brought up by him, perhaps too strictly, he conserved a kind of fear of him which robbed him of the strength to contradict him openly, as a result of which he had developed a habit of quiet defiance which hindered him in the expression of his wishes.' Matters were made no easier by the rumour circulating that Hortense's son was Napoleon's; he treated him as though he were his, sitting on the floor to play with him. Louis resented this, and did everything to thwart Napoleon's plans. So did Napoleon's other siblings. One evening when he was playing with Napoléon-Charles, who was sitting on his knee, Napoleon addressed him, saying, 'I advise you, my poor child, if you wish to live, never to accept any food offered by your cousins.' Not surprisingly, Louis and Hortense protested against their son being designated as the heir apparent. But Napoleon had decided that if he failed to produce a legitimate heir himself, the succession would pass through Joseph (who had only daughters) and then through Louis.
Letizia was given a court of her own, with an ancien-régime duke as chamberlain and Louis XVI's erstwhile first page as equerry. After much historical research, she was given the title of ' _Madame, mère de sa Majesté l'Empereur_ ', generally abbreviated to ' _Madame Mère_ '. She took the money Napoleon gave her, but was uncooperative, siding with her favourite Lucien against him. He had meant Lucien to marry the recently widowed queen of Etruria, but Lucien had secretly married another widow, by whom he had a son. Napoleon refused to recognise the marriage and tried to get him to divorce, but Lucien stood firm. He took his wife and his art collection off to Rome, where he was joined by Letizia.
Caroline Murat was in a rage at not having been given a title she regarded as due to her, and vented it on Hortense, whose children were princes while hers were not. She made such a scene, bursting into tears at table, that Napoleon relented and made her a princess. When Pauline realised that she was not going to be made one too, she stormed over to see her brother and screamed so much she actually fainted. Napoleon complied.
The youngest brother, Jérôme, was arrogant, vain and fatuous. He was destined by Napoleon for the navy, but was a reluctant sailor, enjoying only the pleasures of life in port. He did eventually learn his craft and take command of a brig, in which he sailed to the West Indies. He was stranded there by the end of the peace of Amiens, and aimed to return by way of the United States. In Baltimore he fell in love with Elizabeth Patterson, the daughter of a local merchant, and married. He had no right to do so, as French law required parental consent up to the age of twenty-five, and when he heard of it, Napoleon refused to recognise the union. He ordered him back to France, alone, as soon as possible, but Jérôme would not be parted from his wife. 'Inform your master,' she wrote to the French consul in Lisbon, where they landed, 'that Madame Bonaparte is ambitious and claims her rights as a member of the imperial family.'
As the coronation drew near, his siblings made a concerted effort to make Napoleon divorce Josephine. That the new etiquette demanded they curtsey and bow before her was bad enough, but the idea of her being crowned was too much. Matters came to a head in an unholy row on 17 November at Saint-Cloud as the final arrangements were discussed; when they were told they would have to carry her train, his sisters mutinied. Napoleon lost his temper, threatening to strip them of all their honours if they did not behave and treat his wife with the respect due to her.
'My wife is a good woman who has never done them any harm,' he said to Roederer. 'She's perfectly happy to play the empress, to have her diamonds, her fine dresses and the other consolations of her age! I never loved her blindly. If I made her empress it was out of a sense of justice. I am above all a just man. If I had been thrown into prison rather than mounting the throne, she would have shared my misfortune. It is only right that she should have a part in my greatness.' He had stopped nagging her about her spending on clothes and handing money out to friends in need, which was probably uncontrollable: even though she had a yearly clear-out, distributing discarded clothing to friends and servants, a surviving inventory of her wardrobe lists forty-nine grand court dresses, 676 dresses, sixty cashmere shawls, 496 other shawls, 498 blouses, 413 pairs of stockings, 1,132 pairs of gloves, more than a thousand heron feathers, and 785 pairs of shoes. He must have realised it was a compulsive disorder. According to Hortense, he was by then so exasperated by his siblings' attacks on Josephine that he asked her whether she would mind if he were to sire a child by another woman and pretend it was hers. He even consulted Corvisart on how this could be carried out, but the doctor refused to have anything to do with it.
Other arrangements may have cost him less annoyance, but no less time and effort. Historians rummaged through records of early French coronations, noting symbols and traditions. Some, such as the vigil of prayer, were deemed too religious; others, like the ceremonial robing, might diminish the new emperor. The actual crowning could not be done by the Pope, as that would have implied Napoleon held his power from him. For similar reasons the pontiff would not be borne into the cathedral on the _sedia_ , and would have to be in place by the time the emperor arrived. The question of what his throne should look like, and the design of the coronation coach and robes, were the subject of protracted discussion, as they had to be based on precedent but must not resemble anything pertaining to the previous dynasty. The result – a bizarre mishmash of the Graeco-Roman, the Merovingian and the Carolingian, with a dash of Henri IV – beggars description.
Napoleon had hoped to hold the coronation on 18 Brumaire, the anniversary of his seizure of power, but the Pope was not to be hurried, and the date was eventually set for 2 December. On 25 November Napoleon was at Fontainebleau and about to go hunting when news reached him that the Pope's coach was approaching. He mounted his horse and rode out to meet him, dressed as he was in his hunting clothes. When he sighted the Pope's travelling coach, he dismounted and walked over to greet the pontiff, who alighted. Shortly after, the imperial carriage drove up and took them the rest of the way to the palace. They spent three nights there, and on 28 November drove into Paris together. The Pope was installed in the Pavillon de Flore of the Tuileries, and as soon as word of his arrival spread, crowds of the faithful gathered outside. When he appeared at the window they knelt and held out long-concealed rosaries and images for him to bless. Napoleon rushed over to share the aura by appearing alongside him on the balcony.
There was a last-minute hitch when Josephine let slip to the Pope that she and Napoleon had never married in church. The coronation ceremony could not go ahead unless they were wed in the eyes of God, so that evening, much to Napoleon's discomfort, Fesch conducted a secret religious marriage in the Tuileries.
The ceremonial for the coronation was devised by Louis-Philippe de Ségur, grand master of ceremonies, assisted by the prefect of the palace, Auguste de Rémusat. The logistics were in the hands of the grand equerry General Armand de Caulaincourt, and the music was composed or selected by Paisiello and Lesueur. The cathedral of Notre Dame was decorated by Fontaine. To facilitate rehearsals, the painter Isabey drew floor plans of Notre Dame and painted a series of dolls to represent the principal figures. On 29 November he brought them to a delighted Napoleon, who began playing with them and then called over the major participants to rehearse their parts.
At eight o'clock on the icy morning of 2 December, while the capital resounded to the thunder of cannon and the pealing of bells, the legislative bodies arrived at Notre Dame and took their places. Two hours later the Pope arrived, in a gilded coach drawn by eight greys, preceded as custom demanded by a prelate mounted on an ass and bearing a processional crucifix. He took his seat and waited for nearly two hours in the freezing cathedral for Napoleon, who did not leave the Tuileries until eleven o'clock. He rode with Josephine in a gilded coach drawn by eight buckskin horses, escorted by several hundred cavalry with their bands blaring, followed by other members of his family and court in their carriages. The imperial couple and their attendants alighted at the archbishop's palace, where they donned their ceremonial robes, Napoleon's making him look even smaller than he was with its huge ermine cloak. He snapped furiously at his sisters when they staged a last-minute protest at having to carry Josephine's train.
By the time they entered the cathedral, to a bombastic fanfare, the Pope and most of those present were stiff with cold. To a twenty-year-old guardsman who had slipped in to watch, the ceremony was 'everything that the most fertile imagination could conjure up in the way of beauty, grandeur and magic'. Captain Boulart, a fervent admirer of the emperor, thought it resembled a masquerade, 'and Bonaparte as Commander of the army of Italy seemed to [him] greater than the Napoleon who was having himself anointed in order to reign by virtue of some pretended divine right'. He did not enjoy the ceremony, which he considered a load of 'humbug'. Republicans raged and Christians were appalled by what they saw as a cynical manipulation of the faith for political ends, and the humiliation of the Pope. Paisiello's music for the occasion echoed these contradictions: his usual light Neapolitan lyricism is in constant conflict with fanfares of brass and drums. Only Napoleon seemed sure of his purpose, though even he found it trying. The physician Joseph Bailly was seated quite close and had a good view of him. As he sat on the throne, with the crown on his head, clutching the orb in one hand and the sceptre in the other, Napoleon suddenly felt a sneeze coming on and made 'a singular grimace' as he attempted to quell it.
'There was, in this saturnalia, plenty to laugh at and to weep over, depending on one's taste,' remarked the royalist baron de Frénilly. The English caricaturists certainly had a feast. In France there were pamphlets critical of the ceremony, and scurrilous jokes and graffiti scrawled on walls opposite the Tuileries. Most of the population showed more curiosity than enthusiasm as they watched the gilded carriages and brilliant troops of cavalry clatter past, and made the most of the festivities and fireworks laid on for them that evening.
There was to have been a grand parade the following day at which regiments were to be presented with eagle finials for their standards, but it was delayed by two days as a result of Josephine's indisposition. On the evening of 4 December a relentless downpour soaked the painted canvas of the stand that had been prepared for the imperial couple and the dignitaries, whose seats were drenched. The following day, dressed in his carnivalesque coronation robes, Napoleon presided over a painful ceremony as his marshals distributed the eagles to the regiments, which paraded 'covered in mud and drenched in the coldest rain' with no crowd to watch them. Their clothes were soaked, their hats flopped over their faces, their plumes drooped. 'We were up to our knees in mud,' recalled one guardsman.
For once, the sun had let Napoleon down. Superstitious as he was, he might have reflected on this. He had radically altered his relationship to the French nation, a relationship which had brought him to power and restored its sense of identity. The invitations to the coronation proclaimed that Napoleon had been accorded imperial status by 'divine providence and the constitutions of the Empire'. When he received the members of the legislative bodies who had come to swear a new oath to him as emperor, in making a speech with more than his usual number of grammatical mistakes, he addressed them as 'My people' and his 'faithful subjects', which even his staunchest supporters did not consider themselves to be. In his pursuit of a national 'fusion' he had been sidetracked by the lure of aristocratic grandeur, which was leading him away from the republican spirit which had inspired and given him power. Far from reconciling French society as he had hoped, the implicit contradictions alienated republicans and royalists, agnostics and Christians, nobles and proletarians. And, as Cambacérès had foretold, they put him at odds with himself.
## 28
# Austerlitz
On 1 January 1805 Napoleon wrote to George III using the address ' _Monsieur mon frère_ ', customary between monarchs, proposing a new peace settlement based on a division of spheres of interest. France was not interested in overseas empire, and if allowed a dominant role in Europe would not contest Britain's dominion over the seas. The world was large enough for both nations, he argued. The offer was dismissed in a letter addressed to 'the head of the French government'. An unintended consequence of Napoleon's activities at Boulogne was to make the war popular in Britain for the first time since hostilities had begun over ten years before. The threat of invasion by 'Boney' struck a chord in all classes of the population, and the government now had the support of the country.
Napoleon had also written to Francis I of Austria, to inform him that he had magnanimously ceded all his rights over Italy to his brother Joseph, who would ascend the Italian throne and renounce his claim to that of France, thereby ensuring that the two countries would never be united under one ruler. He expressed the hope that this sacrifice of his 'personal greatness' would be reciprocated by goodwill on the part of Francis, urging him to reverse the Austrian troop concentrations in Carniola and the Tyrol.
The letter had hardly left Paris when Joseph declared that he would not, after all, renounce his right to the French throne. Napoleon then offered the crown of Italy to Louis, who also refused, equally jealous as he was of preserving his right to the imperial throne. Napoleon resolved to take the crown himself, and to appoint his stepson Eugène de Beauharnais as his viceroy. On 16 January a sick and depressed Melzi agreed to offer him the crown, and in a ceremony at the Tuileries on 17 March he was acclaimed by a number of Lombard nobles. On 31 March he left for Fontainebleau on the first leg of the journey to Milan for his coronation as King of Italy.
Marshalled by the grand equerry Caulaincourt, carriages, horses and three sets of court officials and servants leapfrogged each other along the way, so that when the imperial couple reached a stop everything was ready for them, with a full complement of staff, while the second set raced ahead to prepare the next stage, and the third waited to clear things up once they had left. Napoleon himself now had a travelling _berline_ , sometimes referred to as his _dormeuse_ , as he could sleep in it, which maximised his capacity to work. The vehicle could be turned into a study, with a tabletop equipped with inkwells, paper and quills, drawers for storing papers and maps, shelves for books, and a lamp by which he could read at night. It could also be turned into a couchette, with a mattress on which he could stretch out, and a washbasin, mirrors and soap-holders so he could attend to his toilette and waste no time on arrival, and, naturally, a chamberpot. There was only room for one other person – Berthier on campaign, Méneval at other times.
They left Fontainebleau on 2 April and stopped at Brienne the following day, staying the night at the château with the ageing Madame Loménie de Brienne and visiting the ruins of Napoleon's old school and other former haunts. On 14 March, Easter Day, they made an imperial stop at Lyon, where they attended mass celebrated by Fesch in the cathedral. By 24 March they were in Turin, and on 1 May reached Alessandria, from where Napoleon rode over to contemplate the field of Marengo. Four days later he reviewed 30,000 troops under Lannes on the battlefield, in the coat and bullet-holed hat he had worn during the battle.
The next day he met his youngest brother. Jérôme had reached the shores of Europe at Lisbon, but the French consul there refused to allow his wife ashore, and while he travelled on to plead with his brother she sailed to London. In July she would give birth in Camberwell to a son, Jérôme Napoléon, who would never be recognised by the emperor. 'There are no wrongs that genuine repentance will not efface,' Napoleon told his brother when they met at Alessandria on 6 May. Elizabeth Patterson was granted a pension on condition she went back to America, and Jérôme was given command of a frigate, with the mission to sail to Algiers and retrieve French and Italian subjects imprisoned there.
On 8 May 1805 Napoleon entered Milan. Although his entry was described by one French soldier as triumphal, with people weeping for joy in the streets, he was not satisfied. There followed nearly three weeks of receptions and festivities, culminating on 26 May, when he crowned himself with the iron crown of Lombardy once worn by Charlemagne, declaring, 'God has given it to me, woe to him that reaches for it!' The ceremony was greeted with enthusiasm by many who dreamed of a united Italy. It also made a lasting impression, with woeful consequences for much of South America, on a twenty-one-year-old Spanish creole who happened to be there, named Simón José Antonio Bolívar.
The coronation could only be viewed in Vienna as a provocation. With the aid of British subsidies, Austria had been arming over the past year, and had concentrated considerable forces in the Tyrol. They would be difficult to contain if other states on the peninsula were to join Austria. Napoleon had written to Queen Maria-Carolina, the power behind the throne of Ferdinand IV of Naples, warning her not to allow herself to be drawn into a coalition against him; she was the sister of the late Marie-Antoinette, and hated the French. He rightly suspected that a plan already existed to land British and Russian troops in Naples.
After the coronation he set off on a tour of the kingdom of Italy, inspecting fortifications and troops, meeting local authorities and nobles, going to the theatre and the opera, in a display of confidence and mastery. On 1 July he reached Genoa, which had been under French control for some time and was being administered, along with Liguria, Lucca and Piombino, by Saliceti, and now requested to be incorporated into the French Empire. The act was accompanied by elaborate celebrations, with Napoleon and Josephine towed out into the bay on a floating temple surrounded by gardens from which they watched a firework display. He went aboard the flotilla which Jérôme had commanded, greeting the 231 liberated slaves as they came ashore to universal applause.
A week later Napoleon was back at Saint-Cloud. He was expecting a new Russian envoy, Count Nikolai Novosiltsev, through whom he hoped to negotiate a separate treaty with Russia, but Novosiltsev had stopped in Berlin and sent back his French passports, on the grounds that Napoleon's encroachments in Italy had made negotiations pointless. The tsar had originally meant to avoid foreign entanglements and concentrate on reforming the Russian state. He secretly admired Napoleon, but had been shocked by the execution of Enghien – and mortified by Napoleon's retort to his protest. Supported by his anti-French foreign minister Prince Czartoryski, he now put himself forward as a champion of ethical politics, with a far-reaching vision for the remodelling of the political arrangement of Europe.
Napoleon affected to ignore the military preparations being made against him, and on 2 August he went to Boulogne. At the end of June he had given orders for the invasion force to be ready for embarkation by 20 July. He expressed frustration that his plan of drawing British ships off to the Indian Ocean and the Caribbean before sailing back to the Channel was proving difficult to implement. He was hoping to concentrate up to sixty-five ships of the line to protect the invasion craft. Impatient and accustomed as he was to overcoming any difficulty, he could not accept the delays imposed by the weather, blaming the admirals. They did indeed lack the dash he expected of them; hardly surprising, given the poor quality of the ships and the inexperience of the crews, which were no match for a Royal Navy in which Pitt had invested heavily during the late 1780s and early 1790s, and which had reached a peak of performance. The only French admiral with any initiative, Louis-René de Latouche Tréville, had died the previous summer. Napoleon urged Decrès to seek out younger men to command his fleets, but the real problem was, as he had already noted, lack of discipline among the crews, which could not be imposed in the British way, given his distaste for corporal punishment and the fact that, as he put it, 'for a Frenchman it is a principle that a blow received must be returned'.
He kept up the appearance of intending to go ahead with the invasion, even though eight months earlier, on 17 January 1805, he had told the Council of State that the concentration at Boulogne was a pretext to build up an army to strike against any of France's enemies at a moment's notice. On 3 August he instructed Talleyrand to warn Francis that he only meant to attack England, but might feel obliged to turn about and fight Austria if she supported Britain. Ten days later he instructed Talleyrand to send what amounted to an ultimatum to Francis, repeating that his invasion of England did not constitute a threat to Austria, but that if Francis persisted in rearming there would be war, and he would be spending Christmas in Vienna.
Throughout August Napoleon kept up a stream of instructions for the invasion of England, and on 23 August he wrote to Talleyrand saying that if his fleet arrived in the Channel in the next few days he would be 'master of England'. But on the same day he ordered supplies and rations to be stockpiled at Strasbourg and Mainz; two days later he sent Murat ahead along the Rhine to scout routes into southern Germany and gather maps of the area. 'The decisive moment has arrived,' he informed Berthier. A few weeks before, on 13 August, he had renamed the Army of England _La Grande Armée_. It was not only the name that had changed.
The army Napoleon had inherited was a mixture of regulars from the royal army and untrained volunteers and conscripts. Each unit had coalesced in wartime conditions around its most competent officers, and each of the armies around their commanding general. Given the soldiers' aptitude for desertion, it was impossible to impose discipline in traditional ways. Incompetent and disloyal officers had been purged and generals moved about, undercutting loyalties forged on campaign; demi-brigades had been re-formed as regiments; the men were paid, clothed and fed, and a sense of pride was instilled through parades. It nevertheless remained an unaccountable assemblage of men with idiosyncratic loyalties.
In May 1804 Napoleon had nominated fourteen marshals of the empire. While those singled out were all military men, this was in fact a civil rank, placing its bearer on a par with the ' _grands officiers_ ' of the empire and giving them a position at court, with the privilege of being addressed as ' _mon cousin_ ' by the emperor. The fourteen included close comrades such as Berthier and Murat, some awkward ones Napoleon needed to neutralise, such as Augereau and Bernadotte, as well as a number of capable generals whose loyalty he needed to capture. One such was Nicolas Soult, five months Napoleon's senior, the son of a small-town notary who had distinguished himself fighting under Moreau and later Masséna, a braggart and an opportunist who needed to be controlled. Another was the cooper's son from north-eastern France Michel Ney, seven months Napoleon's senior, who had also risen through the ranks under Moreau, brave but limited, and therefore in need of cousinly guidance; Josephine had taken the first step in 1802 by arranging his marriage to one of her protégées. A very different man was Louis-Nicolas Davout, the scion of a Burgundian family that could trace descent from Crusaders, who, being almost a year younger than Napoleon, had just missed him at the École Militaire and had served as a cavalry officer in the royal army. He had been introduced to Napoleon in 1798 by Desaix, who valued him highly, and although he too had served under Moreau he was not a man for factions; self-assured and professional, a strict disciplinarian and unflinchingly brave, he was devoted to the service of France. But whatever their origins, attitudes and sympathies, on receiving their marshal's baton such men became Napoleon's lieutenants, bound to him by far more than mere bonds of loyalty. They would allow him to operate in larger numbers on a wider theatre, and they would hold his army together.
The concentration of the greater part of the army at Boulogne for over a year transformed it. The idea of taking the war to the hated English aroused enthusiasm, and the rate of desertion dropped off. The cohabitation and frequent contact, both in drilling and exercises (although there was surprisingly little of either) and in off-duty activities, developed a wider esprit de corps and, in the words of one soldier, 'established relationships of trust between the regiments'. It had forged an army for Napoleon.
By 3 September he was back at Malmaison. A couple of days later he learned that Austria had invaded Bavaria, an ally of France. Over the next three weeks he attended to matters that needed to be despatched before he went on campaign, including an edict abolishing the revolutionary calendar and reinstating the Gregorian. On 24 September, having instructed the Senate to put in hand the raising of 80,000 more men, and leaving Joseph and Cambacérès in charge, he left for Strasbourg to join the Grande Armée, which had been on the march since the end of August.
While the 90,000 Austrians in Carniola and the Tyrol under Archdukes Charles and John moved into Italy, on 8 September General Karl Mack with a corps of 50,000 Austrians under the titular command of Archduke Ferdinand had marched into Bavaria and taken up position in the west of the country to await a Russian army under General Kutuzov which was to join him in invading France. The Grande Armée had left the Channel coast in seven corps, commanded by Bernadotte, Marmont, Davout, Soult, Lannes, Ney and Augereau, with a cavalry force of 22,000 under Murat, a total of some 180,000 men. They moved with astonishing speed, living off the land, allowing men to fall behind and catch up as best they could.
Napoleon left Strasbourg on 2 October in fine weather, cheered as he passed troops on the march, some of whom would present him with petitions. He would stop his horse or carriage alongside resting units and address the men; thanks to his extraordinary memory he could always name one or other of them and allude to their or their unit's battle records. On 4 October he was at Stuttgart with the elector of Württemberg, with whom he attended a performance of Mozart's _Don Giovanni_ , and from whom he had to borrow fresh horses as his were all spent. Three days later he was directing the crossing of the Danube at Donauwörth, far to the east of Mack's positions, which enabled him to sweep round and attack him from behind. From Augsburg on 12 October he wrote to Josephine that things had gone so well that the campaign would be one of his shortest and most brilliant yet: 'I am feeling well, although the weather is dreadful and it's raining so much I have to change clothes twice a day.' He was always in the thick of the action, and when Murat and Berthier took his horse's reins to pull him away from an exposed position in which bullets were whistling around their heads, saying it was not the place for him, he snapped at them, 'My place is everywhere, leave me alone. Murat, go and do your duty.'
'For the past eight days, rain all day and cold wet feet have taken their toll, but today I have been able to stay in and rest,' he wrote to Josephine from the abbey of Elchingen on 19 October, adding, 'I have carried out my plan: I have destroyed the Austrian army just by marching.' Archduke Ferdinand had managed to get away with a small force, but Mack had been checked by Ney at Elchingen and was left with no option other than to seek refuge in the town of Ulm, where he was bottled up with some 30,000 men while his cavalry fled back to join the Russians in Bohemia. On 19 October Mack had been obliged to capitulate, bringing the number of Austrian prisoners taken by the French in the space of two weeks to 50,000.
It was an extraordinary feat. Sébastien Comeau de Charry, a fellow artillery officer who had emigrated and ended up serving in the Bavarian army, now allied to the French, could barely believe what he witnessed. He had watched what looked like a rabble pour into Germany, shedding men and horses but streaming on, suddenly turn into a fighting force. On the Austrian side there were beautiful uniforms and fine horses, on the French 'not one unit in order, just a compact mass of foot-soldiers' pouring down the road. 'It is only a superior man, a sovereign, who can bring unity and harmony to such a crowd,' he reflected. A young French officer in Ney's corps thought he had dreamed it all when he reflected that he had been at Boulogne on 1 September and was taking Mack's surrender in Bavaria on 20 October.
Comeau de Charry had last met Napoleon at a mess table in Auxonne in 1791, when he had refused to sit next to him on account of his republican views, and was now astonished to see him adopt 'the tone and manner of an old, loved, esteemed comrade'. Attached to his staff, he was able to observe not only the emperor's extraordinary grasp of the situation, but also the unorthodox behaviour of the French army. Where another general would have wished and another army demanded a few days' rest and resupply after a victory such as Ulm, Napoleon pressed on along the Danube towards Vienna and his troops surged on, stopping in groups to cook up something to eat, then resuming their march, dropping behind their units, getting mixed up with others, going off on ' _la maraude_ ' in search of food and other necessities, but always ready at a moment's notice to form up columns, lines or squares, without having to be directed by their officers. Colonel Pouget, commanding the 26th Light Infantry, noted that on the march soldiers of various units would get together in groups to scavenge, mess and find comfortable overnight quarters, only rejoining their respective units in camp, but in an emergency they would integrate with the closest unit and fight as though they belonged to it.
On 24 October Napoleon entered Munich, and invited the elector of Bavaria to repossess his capital. On 13 November, after Murat, Lannes and Bertrand had managed to fool the unfortunate Austrian colonel guarding it to let them cross a bridge over the Danube, assuring him that an armistice had been signed, Napoleon entered Vienna. He took up quarters outside the city in the imperial palace of Schönbrunn. He was in an evil mood, to judge by a letter to Joseph written the next day in which he raged against Bernadotte, who had failed to act on his orders and missed a valuable opportunity. He was also displeased with Augereau, who had been slow, and with Masséna, who had failed to pin down the Austrians in Italy. His mood would not have improved three days later, when he received news that instead of sailing into the Mediterranean and harrying British ships supporting Naples, Admiral Villeneuve had left Cádiz with the combined French and Spanish fleets only to be disastrously defeated off Cape Trafalgar by Admiral Nelson. He took his displeasure out on Murat, who had allowed a Russian unit to give him the slip.
After Ulm, Napoleon had suggested peace negotiations to Francis, pointing out that Austria was bearing the brunt of the war and suffering on behalf of her British and Russian allies. Although he had lost an army, Francis remained sanguine, as Napoleon's position was precarious. In Italy, Masséna and Eugène had defeated the archdukes, but they could not pursue them as they had to turn about and face a Neapolitan attack supported by British and Russian troops. Forced out of Italy, the archdukes were now hovering on Napoleon's southern flank. Having been obliged to detach a force to head them off and leave men behind to cover his lines of communication, he was himself down to little over 70,000 men. A combined Russian and Austrian force of nearly 90,000 had gathered at Olmütz (Olomuc) to the north of Vienna, and there was a risk that Prussia might join the coalition and attack him from behind.
King Frederick William had been wavering between the option of joining France and acquiring Hanover as a reward, and that of joining the anti-French coalition. News of Trafalgar lifted the spirits of every enemy of France, and increased Napoleon's vulnerability. Tsar Alexander had visited Berlin on 25 October and, aided by the fiercely anti-French Queen Luise, managed to persuade the king to sign an accord promising to take the field against the French by 15 December at the latest. The pact was sealed by a night-time visit by the tsar and the royal couple to the tomb of Frederick the Great, where by the light of flaming torches they vowed to fight together and Alexander kissed the sarcophagus of the renowned warrior.
Napoleon's anxieties were compounded by the situation at home, where the fall-off in trade following the end of the peace of Amiens, a bad harvest and a budget deficit caused by military expenditure had precipitated a financial crisis and a run on the Bank of France, which Joseph was barely managing to contain. The first successes of the campaign, reported in fulsome Bulletins which were plastered on street corners and read out in theatres, had elicited enthusiasm and created a sense of national solidarity. But by the end of October there were scuffles outside the bank as people struggled to withdraw specie. By the beginning of November troops were being deployed to keep order outside the bank. Joseph and Cambacérès sent Napoleon daily pleas for good news to feed to the jumpy population. 'It is highly desirable that Your Majesty should send me news every day,' Joseph wrote on 7 November. 'You cannot imagine how easily anxiety rises when the _Moniteur_ does not give any news of Your Majesty and the grande-armée; in the absence of real news, anxiety forges false news.' Although the official reports played down its significance (Napoleon would dismiss it with talk of gales dispersing and wrecking some of the fleet), news of Trafalgar further undermined confidence. By 9 November, Joseph warned that 'we must either support the Bank or let it fail immediately'. Napoleon tried to ease the tension by sending back more mendacious Bulletins, but as he and his army marched further and further away, anxiety mounted, and by late November there was mild panic in Paris.
Napoleon needed a quick victory. He marched north to confront the Austro-Russian concentration at Olmütz, reaching Brünn (Brno) on 20 November. He rode out with his staff and spent a long time surveying the vicinity, noting various features of the terrain. 'Gentlemen, look carefully at this ground!' he said to his entourage. 'It will be a field of battle! You will all have a part to play on it!'
He was eager to bring on events, fearing the entry of Prussia into the war. Having ridden out and scouted the ground again, he began acting as though he wished to avoid an engagement. He withdrew units which had approached the enemy positions and instructed others to retreat if attacked, gradually drawing the enemy onto his chosen ground. On 26 November he sent a letter to the tsar through General Savary. Savary was snubbed at Russian headquarters by sneering aristocratic young aides, and although the tsar was more polite, his reply was addressed to 'the head of the French government'. Napoleon sent Savary back with a request for a meeting, to which Alexander responded by sending one of his aides, Prince Dolgoruky. Along with others in the tsar's entourage, the young man took these overtures as a sign of weakness, and when they met, out in the open, he looked down on Napoleon, whom he thought small and dirty, and declared that he must evacuate the whole of Italy and all Habsburg dominions, including Belgium, before any talks could take place. A livid Napoleon told him to leave. The exchange confirmed that Russian headquarters was dominated by inexperienced hotheads eager to prove themselves in battle, like the tsar himself, who would prevail over wiser counsels.
Two Austrian delegates arrived at Napoleon's headquarters requesting an armistice, and two days later, on 27 November, the Prussian foreign minister Count Christian von Haugwitz also turned up. Napoleon recognised these moves for the delaying tactics they were, and rudely sent them off to Vienna to confer with Talleyrand, to whom he wrote on 30 November saying he would be prepared to make far-reaching concessions to make peace with Austria. But he spent that day preparing for battle.
Impervious to the alternating rain and hail, he again carefully surveyed the terrain and observed the Austro-Russian army's movements. He seemed preoccupied, but rubbed his hands together with satisfaction. That night he slept in his carriage. After a final reconnaissance on 1 December, he settled into a small round hut which his grenadiers had built for him near a cottage in which his staff put up. He was joined by Junot, who had travelled from his embassy in Portugal to be at Napoleon's side and was overjoyed to have arrived in time for the battle. That night, after lecturing his staff over dinner on the subject of the deficiencies of modern drama when compared with the works of Corneille, Napoleon rode out for a last look at the enemy positions. He then walked among the campfires around which the troops huddled against the bitter cold. The supply train had, as usual, failed to keep up with the army, and they had little food. They had been read a proclamation in which he assured them that he would be directing the battle throughout, and would, if needed, be among them to face the danger. Victory on the morrow would mean a speedy return home and a peace worthy of them and him. As he walked through the bivouac, some soldiers lit his way with torches, and were soon joined by others with twists of straw or flaming branches, so that soon a torchlight procession snaked through the camp, to shouts of ' _Vive l'Empereur!_ ' 'It was magnificent, magical,' recalled one chasseur of what was now the Imperial Guard. The following morning seemed no less so.
It happened to be the anniversary of Napoleon's coronation. The troops were roused long before daybreak, and formed up in the thick mist of a wintry morning which muffled all sound. They stood to for some time in eerie silence. The sun rose, burning off the mist and temporarily blinding them before its rays glinted on the rows of bayonets and lance-tips facing them, giving the signal for the artillery to open up. The ' _soleil d'Austerlitz_ ' would go down in legend.
Napoleon's 73,000 men were outnumbered by the combined Russian and Austrian force of 86,000 facing them, and seriously outgunned with 139 pieces of artillery to their opponents' 270. But having surveyed the ground and taken up what appeared to be defensive positions, he had anticipated the direction in which they would be tempted to attack, and laid his plans accordingly. He instructed Davout on his right wing to fall back when the Russian left challenged him and to draw them on, off the high ground, in order to make their eventual retreat more difficult. The Russians responded as expected, and when they had overextended themselves, Napoleon launched a vigorous attack on the now exposed enemy's centre, while his left wing outflanked their right and forced it back, widening the gap at the centre. The manoeuvre worked as he had intended, and the enemy were thrown into confusion, with some units having to face about and others to fall back into the path of their advancing colleagues. But the Russians in particular fought doggedly, and there was a moment when a counter-attack by the Russian Guard threatened the outcome. It was countered by a vigorous cavalry charge led by Bessières and Rapp. The allied army crumpled, and while individual units stood their ground the majority took flight, with a humiliated Alexander galloping away from the field of battle.
'The battle of Austerlitz is the finest of all those I have fought,' Napoleon wrote to Josephine on 5 December; 'more than twenty thousand dead, a horrible sight!' As usual, he exaggerated the enemy losses and diminished his own, but it had been a triumph. The French army had taken forty-five enemy standards, 186 guns and 19,600 prisoners, and although the number of dead was considerably smaller than 20,000, the allied army had been diminished by at least one-third and its morale shattered. 'I had already seen some battles lost,' wrote the French émigré Louis Langeron, a general in Russian service, 'but I could never have imagined a defeat on this scale.'
The victorious troops lay down and slept around miserable smoking fires among the dead and dying, with nothing to eat except the odd crust they carried with them. Flurries of snow had made everything damp, and in the evening it began to rain. It was not until the following night that Napoleon himself slept in a bed for the first time in over a week, in a country house in the nearby village of Austerlitz, after which he named the victory. In his address to the troops he stressed that it had been entirely their work, and announced that he would adopt the children of all the French dead.
He only slept for a couple of hours. The Austrians had requested a ceasefire, and the following day he met the emperor, in the open at a prearranged place. Francis drove up in a carriage, from which Napoleon handed him down, and they spoke for over an hour as their aides watched. Francis conceded that the British were merchants in human flesh, and abandoned the coalition. Napoleon agreed to an armistice, on condition he expelled the Russians from his dominions. It was signed on 6 December.
Napoleon admitted to his secretary Méneval that he had made a mistake in agreeing to the meeting with Francis. 'It is not in the aftermath of a battle that one should have a conference,' he said. 'Today I should only be a soldier, and as such I should pursue victory, not listen to words of peace.' He was right. Davout, who had been in pursuit of the retreating Russians, had cornered them and was on the point of taking Alexander himself prisoner when he was informed by a note from the tsar that an armistice had been signed which included the Russians – which it did not. Davout retired and let them pass. On 5 December Napoleon had written to the elector of Württemberg, who was Alexander's brother-in-law, to use his good offices to persuade the tsar to lay down his arms and negotiate. But Alexander felt, according to one contemporary, 'even more thoroughly defeated than his army', and longed only for a chance to redeem his honour; he would fight on.
On 12 December Napoleon was back at Schönbrunn. Three days later, on the very day by which it was supposed to have joined the anti-French coalition, he signed a treaty of alliance with Prussia, sanctioning its annexation of the British king's fief of Hanover and thereby stealing one of Britain's potential allies on the Continent.
Talleyrand had been trying to persuade Napoleon to be generous to Austria and turn her into his principal European ally, which would give France tranquillity in Italy and the Mediterranean, a bulwark against Russia as well as a counterbalance to Prussian influence in Germany. But while Napoleon agreed with him that the only alternative, an alliance with Russia, was a poor prospect, qualifying the Russians as 'Asiatics', he had lost respect for Austria. He took no precautions as he moved about Vienna and its environs, and his soldiers noted that while the population was reserved, they treated them as tourists rather than enemies. On 17 December Napoleon had treated an assembly of Austrian generals and representatives of the estates to a two-hour admonition containing, according to the prince de Ligne, 'a little greatness, a little nobility, a little sublimity, a little mediocrity, a little triviality, a little Charlemagne, a little Mahomet and a little Cagliostro...' Napoleon did not consider them worthy allies.
True to his threat, he spent Christmas in Vienna. By the Treaty of Pressburg, dated 27 December, Austria ceded the Tyrol and Vorarlberg to Bavaria, other territories in Germany to Napoleon's allies Württemberg and Baden, and Venetia, Dalmatia, Friuli and Istria, gained by the Treaty of Campo Formio, to France. As well as losing Francis a sixth of his twenty-four million subjects, it destroyed what was left of the Holy Roman Empire. By the same treaty, Francis recognised Napoleon as King of Italy, the rulers of Bavaria and Württemberg were elevated to royal status, while that of Baden became a grand duke. Finally, Austria had to pay a huge indemnity to France to cover the cost of the campaign.
Napoleon could not afford to waste time in Vienna, as he had a country to rule, and he left the next day. On 31 December he was in Munich, where on 6 January he enjoyed a performance of Mozart's _La Clemenza di Tito_ with the newly-minted King of Bavaria, who was only too happy to give away his daughter Augusta in marriage to Eugène a week later. Josephine, who had come from Paris for the occasion, was 'at the height of happiness' according to Caulaincourt. The next stop was Stuttgart, where the new King of Württemberg, a man of legendary girth, laid on entertainments which included operas and a hunt. Wherever he went in southern Germany Napoleon was greeted with genuine enthusiasm. But he could not linger.
From the frantic letters of Joseph and Cambacérès it was clear that the French financial crisis had not subsided. News of Austerlitz eased the tension, but Cambacérès urged Napoleon to return as soon as possible, as there was 'a torrent of bankruptcies' undermining confidence in the government. People had come to identify stability and order so much with the person of Napoleon that his absence was in itself cause for anxiety. He was back at the Tuileries at ten o'clock on the evening of 26 January. Before retiring for the night he summoned the Council of State and a number of ministers to meet in the morning.
## 29
# The Emperor of the West
If the people of Paris were relieved to hear that their master was back, the same could not be said of those summoned to appear at the Tuileries on the morning following his return. They were going to have some explaining to do, and it was with a sense of foreboding that they gathered at the palace.
Faced with the necessity of going to war with Austria in the summer of 1805, Napoleon had instructed his treasury minister François Barbé-Marbois to raise money. This could only be achieved by unorthodox means which involved a group of Paris finance houses and merchants along with one of the principal military and civil victuallers, Joseph Vanlerberghe. It did not take long for them to become insolvent, and in the case of Vanlerberghe bankrupt, but they were kept afloat by the financier and speculator Gabriel Ouvrard. He had lent money to the Spanish government, in return for the contract to bring gold and silver coinage and bullion from Mexico and other American colonies to Europe. Since the Royal Navy had captured the Spanish treasure fleet in October 1804 and another treasure ship in July 1805, Ouvrard devised an ingenious scheme involving North American and Dutch partners, but this unravelled. In order to avoid the domino collapse of all the finance houses in Paris, Barbé-Marbois had extended credit to Vanlerberghe and his associates through the Bank of France, which precipitated a run on the bank.
Despite his distaste for 'men of business' and their ways, Napoleon had given his sanction to the operation before leaving to join the army. He now grilled his councillors and ministers in a session lasting a full nine hours, at the end of which he sacked Barbé-Marbois. 'I hope that Your Majesty does not accuse me of being a thief?' the minister asked, only to receive the reply, 'I would prefer it a hundred times if you were, for dishonesty has limits, stupidity has none.'
The man Napoleon appointed to take over at the treasury, Nicolas Mollien, was a brilliant administrator who shared his distaste for financial wizardry while understanding the need for subterfuge. He would rebuild the finances of the French state, at the same time allowing his master to pillage them secretly and manage his own parallel finances. The first step was to alter the statutes of the Bank of France, in order to bring it under closer government control; the second to salvage whatever could be from the Ouvrard operation. Vanlerberghe, Ouvrard and others were summoned and told they had to repay 87 million francs, but while some were forced to pay up, Ouvrard had enough connections among Napoleon's family and entourage to negotiate his way out. Mollien contrived to involve the London banking house of Hope, based in Amsterdam, and over a period of time most of the Spanish bullion would be brought to France – some of it in British ships.
Napoleon created a separate military treasury, under Pierre Daru, into which all the proceeds of war would be paid, beginning with the indemnity due from Austria under the Treaty of Pressburg. This provided him with a ready war chest of his own. In order to preserve it, he kept part of his army cantoned in Germany, at the expense of the local authorities, and he warned that he would still raise taxes in time of war. He also began building up a ' _Domaine extraordinaire_ ', a private treasury from which he could dispense pensions, grants and gifts. The cash was kept in a vault at the Tuileries and its contents closely monitored by means of two registers, one listing every source of income and its yield, the other every payment. Wherever Napoleon went, a ' _cassette_ ' went with him, full of rolls of gold coins, to be distributed at will.
When he returned from his first Italian campaign at the end of 1797 and discovered how much money Josephine had spent, Napoleon began investigating where it had all gone, and her continuing profligacy developed in him a reflex for checking bills and accounts. He would find out independently the cost of fabrics and ribbons in order to query the prices charged by her dressmakers and milliners. When he moved into the Tuileries, he began checking the numbers and cost of candles, firewood and food. He enquired how many of his household took sugar, how often, and then calculated how many kilograms that added up to, researched the price per kilo and finally checked the amount spent over the past month. In order to cut down on expenses he introduced vouchers, _bons de repas_ , with which members of the court were issued. The scheme was only abandoned after Hortense arrived for dinner and, as her ladies had forgotten to bring the appropriate vouchers, was denied coffee. He also issued regulations regarding candle-ends – if there were more than eight inches left, they were to be reused in the corridors, if between six and eight, they were to be sent to the private quarters of members of the court, and so on. He developed a quasi obsession when it came to linen, ordering Daru to make an inventory of the 12,671 pairs of bedsheets, 2,032 napkins, 500 'rags' and the other items. The cost of laundry did not escape his scrutiny either – not surprisingly, since he kept changing clothes himself: in the space of one month he sent thirty-six shirts, fourteen waistcoats, 137 kerchiefs and nine dressing gowns to be washed.
He began keeping notebooks in which he wrote down payments and expenditure in a given area, as well as decisions taken and observations on their execution. This helped him spot anomalies and fraud when checking accounts, and to catch out ministers, functionaries and officers. As he always wanted quick and precise answers to his questions they would sometimes invent facts or figures, but he would challenge them, often knowing more about their ministry or regiment than they did. Mollien noted that no amount of detail could overwhelm him, that he was always looking out for problems to solve, and that 'he was not content to reign or govern, he had to manage, and not as a prime minister, but more directly as any minister'.
The unsatisfactory conduct of affairs by those to whom he had delegated during his absence suggested the need to be better informed and have greater control of what was going on in Paris when he was away. He therefore set up a new system of communication, ' _estafettes_ ', whereby despatches contained in a briefcase to which only he and the director of posts, Lavalette, had a key were carried by postilions from one posting station to the next. They knew where they were going, they had fresh horses at their disposal, and they would write down the time of arrival and departure in a notebook that accompanied each briefcase. As there were sanctions for any delay, they acquitted themselves with diligence. This would permit him to control the administration in Paris more closely and to delegate less.
The Council of State met regularly when he was away, with his chair standing empty on its dais. Whoever was presiding, be it Cambacérès, Lebrun, Joseph or one of the other grand dignitaries or princes, sat in another chair beside it. According to councillor Jean Pelet de la Lozère, as Napoleon grew older business progressed more rapidly when he was absent, as he would suddenly fall into a reverie or go off on some digression which, fascinating as it might be, did not advance the matter in hand. Napoleon himself believed that things did not work properly unless he was present, and the members certainly paid greater attention when he was.
Among the matters addressed on his return from Vienna were education, prison reform, the judiciary, the status of the Jews, the provision of free funerals for the indigent, and subsidy for the opera and the national theatre. What comes through all his ideas on these and other subjects is that he was now more interested in building a society than just the state. On 10 May 1806 he founded the University of France, 'a body exclusively concerned with the education and instruction of the public throughout the Empire', with a special brief to 'direct political and moral opinions'. It was a pyramidal establishment crowning the entire educational system, bringing under a single management all existing institutions of learning. While Napoleon was particularly keen on developing the sciences, as he hoped to build up a large cadre of technocrats, he appeared more concerned with the morality of the teachers and the uniformity of the curriculum than anything else. 'I prefer to see the village children in the hands of a monk who knows nothing beyond his catechism and whose principles I know than of a half-educated man with no moral base,' he declared on the subject of primary schools. As for teachers in higher education, they should be incorporated along semi-military lines and make a ceremonial commitment, like a priest taking holy orders. 'When it comes to education, I feel that the Jesuits have left a great void,' he told the Council of State. 'I do not wish to bring them back, nor any other corporation subject to a foreign power, but I feel I should organise the education of the next generation in such a way as to be able to control its political and moral outlook.' He therefore felt that teachers ought to remain celibate until such time as they had proved themselves to be mature and reliable, but they should marry with time, as marriage was in his eyes the perfect social stabiliser, and they should then go on to achieve status, even as high as the Senate. 'I wish to create a corporation not of Jesuits who would have their sovereign in Rome, but Jesuits who would have no other ambition than that of being useful and no other interest than the public interest.'
A similar prejudice against individualism is manifest in his complaints about the members of the judiciary, whom he regarded as a kind of independent corporation. He wanted to see their sentencing standardised rather than left to their own judgement. He was also bothered by the Jews, of whose existence he had only become aware on his visits to north-eastern France and western Germany. Aside from his natural dislike of 'people of business', which prompted him to see Jews as usurers preying on the innocent poor like 'veritable flocks of crows', 'sucking the blood of real Frenchmen' and 'a vile, degraded nation capable of every baseness', he did not like the idea of them as a nation apart, and suspected them of disloyalty and spying. The fact that their presence was most notable in the border region of Alsace bothered him, and the best thing to do with them, he suggested, was to spread them more evenly over the territory of France. He would convene a great Sanhedrin, bringing together the rabbis and elders in a body, in consultation with which he would regulate their status.
Much of Napoleon's most cherished legislation was aimed at integrating people into society. He introduced the ' _livret_ ', which every worker had to carry, defining his profession. He was inordinately proud of having overseen the introduction of the ' _cadastre_ ', the land registry, which he described as being tantamount to a new constitution in itself, since it fixed everyone's rights to the property they possessed but also because it fixed their taxable status and therefore their position in society. They no longer needed to fear having their property seized, but in return had to submit to the state, in which they thereby gained a stake.
The gruelling workload he assumed was reflected in the routines he had adopted, which were carefully recorded by Agathon Fain, who now joined Méneval in Napoleon's private office as archivist. After his coronation Napoleon no longer shared a bedroom with Josephine. He did on occasion visit her for the night, and sometimes he would ask her to come and read to him before he went to sleep. This left him free to follow his own routine, which involved rising at around two o'clock in the morning to work with his secretary, who had to be on call at all hours of the day and night. After a couple of hours' work he would take a hot bath, and sometimes go to bed for an hour or two's sleep, before rising at seven to begin his toilette and dress. In Paris he always wore the blue uniform of a colonel of the grenadiers of the Guard, with white stockings and buckled shoes, or if he were going hunting, his green hunting dress, and only occasionally the ' _habit habillé_ ', the former court dress which he had reintroduced but hated wearing, referring to it as ' _cet accoutrement_ '. On campaign, he wore the green uniform of a colonel of the mounted chasseurs of the Guard, with high top-boots.
He had not moved his quarters in the Tuileries, but they had been altered. His inner study was, in the words of Fain, 'but a dependency of his bedroom', and he would work there in his dressing gown. The outer study or salon he only entered when fully dressed. Between the inner study and the bedroom was a room containing a store of maps and a large table on which they could be spread. At one end there was a partition with a hatch, behind which was a staircase and a station manned twenty-four hours a day by a _garde de portefeuille_ who passed incoming communications through it. There were two of them, working alternate shifts, eating and sleeping at their station, entering the private study only to tidy and to light the fire.
Napoleon's study was dominated by a table designed by himself, with two indentations facing each other on the long sides so he could sit at it facing his secretary with plenty of space for papers on either side. He would sit with his back to the fire, facing the door to the outer study or salon. The room had one window, opening on the gardens, in the embrasure of which stood a small writing table, at which the secretary would take dictation with his back to the room. At the other end of the room was a bookcase with a clock mounted in it, and in front of that a long mahogany table on which spread-sheets and maps could be unfolded. Beside the fire was a comfortable settee with a small round occasional table beside it.
Having dressed, Napoleon was usually back in his study by eight o'clock, ready to start work. His secretary would sit opposite him at the desk, passing him papers to sign. He would then go over to the fireplace and read the despatches and letters piled on the table next to the settee. He would dictate replies to some, dropping them on the floor for filing, and place those which needed reflection on the table to be dealt with later. He also read various reports and letters from his correspondents, the 'friends' all over the country who kept him abreast of opinion and gossip, which he would throw into the fire after reading, and would sometimes peruse a book, which also went into the fire if it displeased him. He would also look through the red morocco briefcase marked ' _Gazettes étrangères_ ', containing transcripts of letters intercepted by the _cabinet noir_ , the postal intercept and decryption office.
If there was need for a map, the emperor's cartographer Louis Albert Bacler d'Albe was summoned. After finding the requisite map in the cases of a room which was little more than a passage between the bedroom and the study, he would spread it on the large, sturdy table built for the purpose and produce a pincushion full of pins with different-coloured heads, together with coloured pencils and a pair of compasses to measure distances. If it was a large map, they would both climb onto the table and lie down on it. 'More than once I saw them both lying on that great table, interrupting their work with a sudden exclamation only when one of their heads hit the other too hard,' records Fain.
At nine o'clock the chamberlain of the day would scratch on the door to announce that it was time for the _lever_. Napoleon would pass into the larger study or salon, where the _chefs de service_ of the court would be waiting to receive their orders for the day, along with those of the ministers who had something to report or orders to receive. The room contained two tables covered in green cloth placed diagonally in the corners at the end nearest his private study, at which Napoleon would sit and interrogate a minister or make him sit and take dictation. But on the whole he would receive people standing up in order to save time. The minister of police and the prefect of the Seine were always there to regale him with the latest information and gossip on the night's doings. Unless he needed to discuss some matter at length, the _lever_ might last as little as five minutes, after which he would go back to his study to work. He breakfasted in a few minutes, taking only one cup of strong coffee. On Thursdays there was a _grand lever_ , to which all those who had entry would come, which included most of the court. The morning's work usually concluded in an interview with the secretary of state, Maret, a man some loathed but who was perfectly mannered and was one of the few who enjoyed Napoleon's complete confidence.
Napoleon dined at six or seven, usually with Josephine, and with members of his family on Sundays. The dinner consisted of no more than two or three dishes, and usually lasted closer to fifteen than twenty minutes. Sometimes not a word was uttered. After dinner he might go back to work or join the empress in her salon. At the end of the evening there was a brief _coucher_ , at which he would give the heads of the household services their orders for the next day. He was normally in bed by ten o'clock. 'In his private life, Napoleon was almost a military monk and everyone in his immediate service had to accommodate themselves to his rule,' recorded Fain.
The workload did not prevent the military monk from going to the theatre, hunting, planning new works and even philandering. The new sleeping arrangement gave him greater freedom, and he used it. He would take advantage of some of Josephine's young ladies-in-waiting, who were in no position to resist. He also liked going with Duroc to the public masked balls at the Opéra, where he acted as though nobody could recognise him, propositioning women and spreading salacious gossip. At one of these, early in 1806, he met Éléonore de la Plaigne, a nineteen-year-old protégée of Caroline Murat, newly married to a dragoon captain by the name of Revel, by all accounts an undesirable character. Shortly after Napoleon had noticed her, the captain was arrested, demoted and roughly dealt with by the police before being pressured into divorcing her. Éléonore was taken in by the Murats as a member of their household and lodged in a small pavilion of their house at Neuilly, where Napoleon visited her.
'He would sometimes spend a whole day without working, but without leaving the palace or even his study,' according to Méneval. 'He might go and spend an hour with the empress, then he would come back, sit down on his settee and either fell asleep or seemed to for a while. He would then come and perch on a corner of my desk, or on the arm of my chair, sometimes even on my knees. He would then put his arm around my neck and amuse himself by playfully pulling my ear or smacking me on the shoulder or on the cheek.' He would wander about the room, pull out a book, quote from it and discuss it, or declaim some verses by Corneille, and sometimes he would sing – horribly out of tune.
In the course of the past year Napoleon had defeated the combined might of the two greatest powers on the Continent, reducing one emperor to begging for peace and the other to ignominious flight. The experience cannot have failed to give him a sense of almost limitless power – his troops enthusiastically proclaimed that under his leadership nothing was impossible. He had also gained closer experience of the other states of Europe, at the diplomatic, administrative and military levels, and was not impressed. He had met rulers who were pusillanimous, ineffectual, corrupt, stupid, treacherous, weak or just lazy. He had seen for himself how poorly and nonsensically most of Europe was administered, and how people were ill-treated and resources wasted, and had come to view all rulers with varying degrees of contempt.
One who fully deserved it was the King of Naples. Back in September 1805 he had signed a treaty with France pledging to remain neutral on condition French troops withdrew from the Neapolitan ports which they had occupied against British and Russian landings. Knowing through his spies that the king had already signed treaties with Britain and Russia against France, Napoleon wrote to Queen Maria-Carolina warning her not to make any hostile moves. Three weeks after French troops started pulling out, in mid-October an Anglo-Russian squadron appeared and landed 12,000 Russian and 8,000 British troops which, along with the 40,000 strong Neapolitan army, began operations against the kingdom of Italy. On hearing news of Austerlitz, the Anglo-Russian contingent fell back and re-embarked. On 26 December Napoleon issued a proclamation from Schönbrunn declaring that by their faithlessness the Bourbons of Naples had forfeited their right to reign. On 6 January 1806 he put his brother Joseph in command of a French army with orders to occupy their kingdom. Maria-Carolina wrote an abject letter declaring that she had recovered from the blindness which had led her to act the way she had, and appealing to Napoleon's generosity to leave her husband his throne. But Joseph was already making his entry into Naples, and on 30 March Napoleon nominated him King of Naples – for the sake, as he put it, of the tranquillity of Europe. This, in Napoleon's view, required curbing British and Russian ambitions in the Mediterranean. With the whole of the Italian and Illyrian coasts now in French hands, and Spain as an ally, it seemed possible.
Following the death of Pitt on 23 January and the formation of a ministry under Lord Grenville with Charles James Fox as foreign secretary, an accommodation with Britain also seemed possible. On 6 March Talleyrand received a letter from Fox passing on intelligence about a planned royalist plot against Napoleon and suggesting peace talks. The British cabinet appeared willing to proceed, but nevertheless imposed a blockade on the coast of Europe from the Elbe in Germany to Brest in France. Napoleon took the precaution of pre-empting any discussion of the status of the Netherlands by converting the Batavian Republic into the kingdom of Holland, with his brother Louis as king.
Ten days after Louis ascended the throne, on 5 June 1806, the Earl of Yarmouth arrived in Paris to negotiate a peace treaty. The British were prepared to make peace, their only demand being that King Ferdinand be allowed to keep the Sicilian half of his former kingdom and that Joseph content himself with the mainland part of Naples. Napoleon declared that Joseph must also have Sicily, and promised to find Ferdinand a replacement kingdom in northern Germany or possibly Dalmatia. Oubril, who had been sent to Paris by Tsar Alexander to negotiate a treaty, suggested that Ferdinand be compensated with the Balearic islands. This set alarm bells ringing in London, where it was seen as a ploy to provide Russia with a naval base in the western Mediterranean. The new British negotiator, Lord Lauderdale, who reached Paris on 5 August, suggested Ferdinand be compensated somewhere in South America. For reasons that are hard to fathom, Napoleon kept changing his demands, undermining Talleyrand and eventually replacing him as negotiator with the less than diplomatic General Savary. Napoleon seems to have begun entertaining an entirely new vision of how Europe should be reordered, and of France's position in it.
A striking aspect of his elevation of 'Joseph-Napoleon' to the throne of Naples and Sicily was that it entirely bypassed the French Senate. So did the transformation of the Batavian Republic into a kingdom with Louis as king. The Senate was simply informed that 'We have proclaimed Louis-Napoléon, our beloved brother, King of Holland.' He went on to redraw the political map of Europe and transform the manner in which a great swathe of the Continent was governed. Having reduced Austria and enlarged Bavaria, Württemberg and Baden, he bound those three states, along with the remaining thirteen German political units, into the Confederation of the Rhine, of which he nominated himself protector. It was an updated version of the Holy Roman Empire, part of a Continental security system with each of the members obliged to provide a certain number of troops in the common defence: France 200,000, Bavaria 30,000, Württemberg 12,000, Baden, Cleves and Berg 5,000 each, Hesse-Darmstadt 4,000, and the rest 4,000 between them.
There was a logic to this arrangement, insofar as it protected the German heartland from outside interference and invasion; but the logic required the successor to the Holy Roman Emperor, this 'Emperor of the West' as people had begun to allude to him, to govern in the universal interest. Yet France was not actually a member of the Confederation, although it was clear that the whole enterprise was to function in her interest. The same went for the supposedly sovereign kingdoms. 'Do not ever cease to be a Frenchman,' Napoleon instructed Louis after making him King of Holland.
The internationalism of the Revolution had been gradually subsumed into the cult of the Nation, which had in turn been subjected by Bonaparte to that of the State, and this was now being transformed into a vision of empire. The terminology of the _Grande Nation_ had been superseded by that of the _Grand Empire_. Buried somewhere in this was the ideal of a Europe without frontiers, a common _patrie_ of the Enlightenment with a universal legal system and currency in which, as Napoleon put it, 'while travelling, everyone would never cease to be at home'. It was a dream that appealed to many and held out promise to millions, as most of the Continent was ruled in ways that were at best not benign, by corrupt and incompetent administrations geared to the benefit of the few.
'One of these days, I am convinced, we will see the Empire of the West reborn as tired peoples rush to place themselves under the rule of the best-governed nation,' Napoleon told his Council of State. In this, as in other things, he was ahead of his time. Yet as he started constructing his new pan-European system, he unaccountably began to look back. Not only did he base his diplomatic strategy on that of Louis XIV – his new 'Empire of the West' resembled a medieval system of personal vassalage.
He began at home, introducing statutes to govern the imperial family, of which he was 'head and father'. They were modelled on similar documents governing the ancient royal houses of Europe, but included concepts pertaining to Corsican family lore together with a dash of military discipline. They laid down rules of precedence, guidelines on conduct, restrictions on marriage and travel, so that nothing could be done or undertaken without his consent. They included a table of penalties, incarceration and exile among them.
The Continent was to be bound together not by a modern administration but by the Bonaparte dynasty and those established royal and ducal houses of Europe prepared to associate with it. Joseph was King of Naples, Louis King of Holland, Caroline's husband Murat Grand Duke of Berg, Élisa Bacciochi Duchess of Lucca and Piombino. Further layers of control were provided by those closest to the imperial throne, with Berthier becoming prince of Neuchâtel (a former Prussian fief), Bernadotte prince of Pontecorvo and Talleyrand prince of Benevento in the kingdom of Naples. Other fiefs, such as Dalmatia, Istria, Friuli, Cadora, Belluno, Conegliano, Treviso, Feltre, Bassano, Vicenza, Padua and Rovigo in what had been Venetian territory went to ministers and marshals.
In France itself, by a _senatus-consulte_ of 14 August 1806, Napoleon created an imperial nobility, granting titles of prince, duke, count, baron and knight. The language accompanying these acts and investitures was redolent of another age; the costumes, forms of address and fabulous endowments were an insult to the spirit of the Enlightenment and all that was dear to most Frenchmen about the Revolution. 'Dare I say it, when in a full council he posited the question of whether the institution of hereditary titles was contrary to the principles of equality which we professed, almost all of us replied in the negative,' admitted the old revolutionary butcher of nobles Fouché. 'In fact, the Empire being a new monarchy, the creation of grand officers and dignitaries and the bulwark of a new nobility seemed indispensible to us.' He became Duke of Otranto.
Human vanity had triumphed over the so-called Age of Reason. Murat, Louis and Joseph instituted new orders of chivalry, exchanged decorations, designed refulgent uniforms for themselves, their regiments of Guards, and court officials. They published etiquettes and granted titles of nobility to their friends. They sent ambassadors to each other's courts and played the part of monarch to a degree that even Napoleon found ludicrous. Marshals, ministers and generals, and particularly their wives, vied for titles and resented each other's, and former revolutionaries applied themselves to inventing arms to paint on their carriage doors. When Jérôme instituted an Order of the Union featuring the imperial eagle, a serpent eating its tail as a symbol of eternity, the lion of Hesse, the horse of Brunswick, and another eagle and lion, Napoleon told him there were 'too many beasts in that order'.
'Few people in his position would have retained such a degree of modesty and simplicity,' maintained the prefect of the palace, Louis Bausset, and there was a grain of truth in this. When a group of people declared the desire to open a subscription for an equestrian statue of him, Napoleon forbade it. 'Very simple in his way of being, he liked luxury in his surroundings only because it seemed to him that great show was a way of imposing, which made the business of government easier,' according to Fain, who saw in him 'a sure friend and the best of masters'. He spoiled his servants and made sure they did not lack for anything, even after they retired. If he did lose his temper with them, or upset them in any way, he would make up for it royally.
His view of himself and what he believed he embodied is reflected in his court ceremonial, which grew ever more ponderous, and in his artistic patronage, particularly his building programme and the monuments he erected. During his consulship, he wanted to celebrate soldiers. His early schemes included an ambitious rebuilding of the Invalides centred on a temple of Mars in which great French commanders would be suitably commemorated. Dead brothers-in-arms such as Desaix were immortalised in sculpture. In 1806 he laid the foundation stone of a triumphal arch to be built in front of the Tuileries on the place du Carousel, and of a column modelled on that of Trajan in Rome, to be cast from the bronze of the cannon captured at Austerlitz, on the place Vendôme. Another, larger, triumphal arch was also projected for the other end of the Champs Élysées. These works were balanced by a concurrent project to rebuild the church of La Madeleine as a temple to the glorious dead, but this was to be the last of the monuments dedicated to soldiers.
His next plan was for a vast palace on the heights of Chaillot, effectively a new imperial city with military barracks, a university, archives, a 'palace of the arts' and other buildings. His programme did continue to benefit the public: between 1804 and 1813 he spent 277 million francs on roads, 122 on canals, 117 on sea-ports, 102 on embankments, roads, squares and bridges in Paris, thirty on bridges elsewhere, and sixty-two on imperial palaces and buildings such as ministries and the stock exchange. Yet from 1806 onwards the monuments centred not on the nation, the army or even great victories, but on the person of the emperor. He does not, however, appear to have worked out in his own mind the ultimate purpose or the limits of the empire he was building.
## 30
# Master of Europe
The peace negotiations in the spring and summer of 1806 with Britain and Russia were bedevilled by mistrust on all sides. While professing its peaceful intent, the British cabinet not only issued Orders in Council putting France and much of Germany under blockade, it continued to support the Bourbon King of Naples against Napoleon's brother Joseph, landing troops in southern Italy and in July scoring its first mainland victory for a century at Maida. Napoleon was also stalling. He had negotiated a treaty with the tsar's envoy Peter von Oubril which had been sent to St Petersburg for ratification; he was probably hoping that this would put him in a stronger negotiating position vis-à-vis Britain.
It unsettled the King of Prussia, who feared that Napoleon would make a deal at his expense. He had acquired Hanover by a treaty with France in December 1805, and it seemed probable that an agreement between Britain and France would entail its loss. He also suspected that the price of peace between Napoleon and Tsar Alexander might be the cession of some of his eastern lands to Russia. Having marginalised Prussia, Napoleon had no wish to reduce it further, and tried to reassure the king, going so far as to order at the beginning of August the withdrawal of French troops still in Germany. Frederick William wanted nothing more than a preservation of the status quo, but he was being influenced by his belligerent queen and his minister Karl August von Hardenberg, who played to a body of public opinion which felt that Prussia had been humiliated, and an officer corps which believed its army was the best in Europe and longed to prove it. On 9 August, in response to a false report by General Blücher of French troop concentrations threatening Hanover, Prussia began to mobilise.
Although Napoleon responded with assurances of his desire for peace, he was outraged. When he learned of the publication in Bavaria of a violently anti-French pamphlet bemoaning the humiliation of Germany, he had its publisher Johann Philipp Palm tried by a military court and shot on 26 August. This provoked reactions among German nationalists and a surge of anti-French feeling in Prussia, where officers demonstratively sharpened their sabres on the stone steps of the French embassy in Berlin. Quick to take offence himself, Napoleon was seemingly incapable of appreciating that he could give it.
He also suspected there was more to Prussia's belligerence. 'The idea that Prussia can single-handedly engage against me seems to me so ridiculous that it is not worth discussing,' he wrote to Talleyrand. When on 3 September he learned that Tsar Alexander had rejected the treaty negotiated by Oubril he realised that Britain, Russia and Prussia had reached an understanding. Failing to grasp that he had pushed them into each other's arms, he could see only perfidy. 'These kings will not leave me alone,' he said to Caulaincourt. 'They seem determined to convince me that I will have no peace and quiet until I have destroyed them.'
He instructed Talleyrand and his ambassador in Berlin to assure Frederick William that he had no wish to make war, pointing out that it was not in his interests to disturb a peace he had just concluded. He may have been sincere in this, as it would have been difficult to see what advantages such a war could bring him. But he had taken umbrage at what he called 'a little kingdom like Prussia' defying him in front of the whole of Europe. It was, as he put it to Caulaincourt, ' _like some little runt impudently raising its leg to piss over a Great Dane_ '. By this stage, peace could only have been maintained if the runt lowered its leg, but that was not going to happen.
Buoyed by the prospect of 100,000 Russians marching to his aid, and anticipating that Austria, Bavaria and Sweden would seize the opportunity to join in the fight against France, the usually undecided Frederick William set his troops in motion. On 12 September they invaded Saxony in order to prompt its ruler into an alliance against the French. Two weeks later he issued an ultimatum to Napoleon to pull all his forces back behind the Rhine. 'They want to change the face of Europe,' Napoleon said to Caulaincourt. He went on to speculate that perhaps his 'Star' meant him to fight this senseless war which would, as he put it, 'open up a vast field for great questions'. He also intimated that since mere treaties could not guarantee peace, some new system would have to be put in place.
He wrote a last letter to Frederick William on 12 September professing his peaceful intentions and warning him not to start a pointless war. But he had ordered his _maison militaire_ to take the road two weeks earlier, and on 25 September he left Saint-Cloud for Mainz, accompanied by Josephine. On 2 October he was at Würzburg with his ally the King of Württemberg, aiming to confront the Prussians in Saxony.
On 10 October Lannes, commanding the advance guard, attacked and defeated a Prussian corps at Saalfeld. Its commander, the Prussian king's cousin Prince Ludvig, was cut down and killed by a French hussar. Napoleon sent one of his aides with a letter for Frederick William proposing peace talks, but on reaching the Prussian lines the aide was held back, and the letter never reached its destination.
The Prussian corps manoeuvred erratically, and Napoleon had some difficulty in guessing their intentions, but he reacted with extraordinary speed and attacked what he believed to be their main force at Jena on 14 October. In fact it was a body of about 40,000 men under Prince Hohenlohe. Not realising in the thick morning mist (he was shot at by his own pickets as he reconnoitred) that he outnumbered them heavily, possibly by as much as two to one, Napoleon operated cautiously and defeated them, putting them to flight by the early afternoon. Some fifteen kilometres to the north, Davout, with 30,000 men, who had been ordered to outflank what Napoleon took to be the left wing of the Prussian force, had run into the main Prussian army numbering some 70,000 men under the Duke of Brunswick and King Frederick William at Auerstadt. Bernadotte, who was marching alongside Davout with his corps, failed to come to his aid. But although he suffered heavy losses, in a brilliant action Davout routed Brunswick, who was mortally wounded, and as the retreating remnants collided with those fleeing from the battlefield of Jena, the Prussian army disintegrated. Entire corps and fortresses surrendered to advancing platoons of French cavalry, bringing Prussian losses in killed, wounded and captured to 140,000 in the space of a few days.
On 24 October Napoleon was at Potsdam, where like Tsar Alexander before him he visited the tomb of Frederick the Great, stealing his hat and sword to take back to the Invalides as trophies. He reported to Josephine that he was well and that he found Frederick the Great's renowned retreat of Sans-Souci 'very pleasant'. Davout made a triumphal entry into Berlin, where Napoleon joined him three days later, riding down Unter den Linden to take up residence at the royal palace, escorted by his Guard in parade-ground order.
Frederick William had written him a pathetic plea for a suspension of hostilities, but Napoleon was not in generous mood. He had been so incensed by Bernadotte's behaviour that he would have had him court-martialled and shot had he not been the husband of Désirée. He did order the execution of the governor of Berlin, Prince Hatzfeld, as a spy. After an amiable meeting with Napoleon, the prince had written to Frederick William's headquarters giving details of French dispositions, and the letter had been intercepted. The prince's wife came to beg for mercy, and Napoleon pardoned him. But his mood did not improve. Riding along with his Mameluke Roustam at his side, he drew a pistol from his saddle-holster and aimed at some crows. The gun did not go off, so he angrily threw it to the ground and berated Roustam in the foulest language. He was obliged to apologise after the Mameluke reminded him he had ordered a new safety-catch fitted to the pistol.
Napoleon was not impressed by Prussia. Its army had been little better than an eighteenth-century military machine, with the soldiers showing scant devotion to their officers or their country. 'The Prussians are not a nation,' he kept saying to Caulaincourt. He likened the desk of Frederick the Great at Sans-Souci to that of a French provincial notary, and having meant to take the four-horse chariot from the triumphal arch at Charlottenburg to adorn one in Paris, he was disgusted to discover that it was made of sheets of iron. He described Prussia and its monarchy as a tinsel stage-set hardly worth preserving, and began turning over in his mind various options regarding the reorganisation of its territory.
Count Metternich, the Austrian ambassador in Paris, believed that if Napoleon had made peace with Frederick William on the basis of a reduced Prussia incorporated into the Confederation of the Rhine, France would have been unassailable and Russian influence would have been entirely excluded from Germany. But Napoleon was slow to respond to Prussian overtures, and his conditions – that Prussia give up her possessions west of the Elbe, pay heavy war reparations and join France in alliance against Russia and Britain – were too harsh. Negotiations never got going before Frederick William took refuge in Königsberg to await salvation by Russia.
Meanwhile Napoleon decided to strike at the paymaster of all the coalitions against France. Like most Europeans at the time, he believed that the British economy, which was heavily reliant on credit, would implode if the trade supporting that credit were destroyed. Responding to the British Orders in Council of 16 May 1806, which decreed a blockade of French ports and seizure of French shipping, on 21 November he signed decrees which closed all European ports under his control to British ships, British goods and British trade. The aim was to deny British industry its markets and cut off vital supplies of grain, timber and raw materials, particularly from the Baltic. Napoleon would increase the pressure the following year, when he ordered that any ship which had docked at a British port could be confiscated, and then broadened this to include any vessel which had been searched by the Royal Navy, and to allow French corsairs to confiscate British goods on neutral ships. The British responded in kind.
The Berlin Decrees had far-reaching implications, since they made it essential that France control, directly or indirectly, every port in Europe. Allies would have to be forced and neutrals coerced into what Napoleon would call his Continental System. As a first step he ordered General Mortier to occupy the Hanseatic towns of Hamburg and Lübeck, and Swedish Pomerania. But enforcing the decrees was going to take a great deal more than a few regiments. Napoleon had entered into an open-ended commitment which he was never going to be able to fulfil. As if that were not enough, he now opened a Pandora's box.
On 19 November he had received a delegation of Polish patriots from Posen (Poznań), the capital of a Polish province annexed by Prussia a decade earlier. The collapse of Prussian might had raised hopes throughout Poland of the recreation of that country, which had been divided up by Russia, Prussia and Austria in 1795. The Prussian part of it was now effectively free, and the patriots had come to find out his plans for the area. He had none.
Like most western Europeans, Napoleon felt residual sympathy for the Poles following the loss of their country. During his first Italian campaign he had come to value several Polish officers, and particularly his aide Sułkowski. When he realised that among the Austrian prisoners there were Poles who had been drafted by the Austrians and were keen to fight against them, he formed them up into a legion which fought alongside the French. But when they were no longer of any use he felt no compunction in sending them off to Saint-Domingue, where most of them perished. Back in March 1806 he had instructed Fouché to insert articles in the press describing Russian repression and violence against the Poles, probably only to embarrass Russia, with which he was then negotiating a treaty.
Many Poles drafted into Prussian ranks had also deserted to the French, and Napoleon had them formed up into a legion under General Józef Zajączek, who had served under him in Italy and Egypt (1,500 were incorporated into a legion made up of Irish insurgents of 1798 who had been sold by the British government to the King of Prussia to work in mines, but had subsequently been pressed into the Prussian army). On 24 September Napoleon had instructed Eugène to despatch all Polish staff officers in the Italian army to join the legion under Zajączek. Less than a week after reaching Berlin, on 3 November, he wrote to Fouché in Paris instructing him to send the Polish general Tadeusz Kościuszko, the universally respected leader of a Polish national insurrection in 1794, along with any other Poles he could find in Paris, to join him in the Prussian capital. On 17 November, two days before his meeting with the delegates from Posen, he had given instructions for it to be said that he was intending to recreate a Polish state. Talleyrand was keen on the idea, and had been sounding out Austria on the possibility of her giving up her Polish province of Galicia in exchange for the richer Prussian one of Silesia.
By then the Grande Armée was marching through Poland to meet the oncoming Russians, and on 25 November Napoleon left Berlin to join it. Late on 27 November he drove into Posen, which was illuminated in his honour. He was greeted like a saviour, and young men rode in from the surrounding countryside hoping to fight for their country under his command. Murat, who rode into Warsaw on the following day, wrote that he 'had never seen such a strong national spirit'. The inhabitants were inviting officers and men into their houses, offering them food and drink. 'The Poles are all asking for arms, leaders and officers,' he went on. The following day, after talking to some of the locals, he wrote that he was convinced they were ready to rise and fight, and would be prepared to accept any ruler he chose to give them. He asked for instructions on how to proceed.
Napoleon wrote back from Posen that the Poles were superficial and unreliable, and telling him to offer nothing. 'Make them understand that I have not come to beg a throne for one of my people, as I do not lack thrones to give my family,' he warned Murat, who was already being lined up by Paris gossip as the next King of Poland. He had always been a dashing dresser, never conforming to regulation uniforms, preferring to swagger in skin-tight buckskin breeches adorned with ribbons, embroidered dolmans and turned-down buccaneer boots, but when he first saw traditional Polish noble dress, he stepped into another sartorial world. He had a new wardrobe run up in his version of the Polish model, with fur-trimmed velvet tunics, slashed hanging sleeves and fur cap, in a variety of colours. 'He had all the majesty of an actor trying to play a king,' commented one Polish lady, but she admitted that the Polish people would have accepted him as such if it had meant independence.
Napoleon meant to keep his options open as to how he would settle the 'great questions' raised by his victory over Prussia. While he encouraged Poles to join the ranks, in talks with local notables he did little more than demand supplies for his army. On 2 December he attended a ball given by the local nobility to mark the anniversary of his coronation, only to tell them they should be booted and spurred, not wearing stockings and pumps. After the ball he wrote to Josephine saying he loved and missed her, he found the nights long without her and he would soon be sending for her to join him. He was frustrated, as he had devised a sweeping manoeuvre designed to destroy the Russian army now in Poland under General Bennigsen. He had sent detailed instructions to his corps commanders, but while his plan looked straightforward on the map, it was proving difficult to implement, and he realised he needed to be closer to the theatre of operations.
On 16 December he left for Warsaw, which he reached on horseback, having had to abandon his carriage because of the state of the roads. He entered the city at night in order to avoid having to face a reception committee, spent four days there making arrangements for what he hoped would be a decisive battle, then left to take charge of operations, crossing the Vistula and the Bug to join his army at Nasielsk on Christmas Day. Intelligence on the whereabouts of the main Russian forces was confused, and while Lannes with 25,000 men attacked what proved to be Bennigsen's main force of 40,000 near Pułtusk, Napoleon marched towards Gołymin, where Davout, Augereau, Ney and Murat were engaged against other Russian units. By the time he realised what was going on and struggled back to join Lannes, it was all over. Lannes had beaten Bennigsen, who retired, but pursuit was out of the question due to atrocious conditions.
A sudden thaw had melted the snow and ice, turning the roads, mere tracks, into rivers of mud. The conditions were so bad that gun carriages sank into the sludge, dragging down their horse teams; even doubling the teams could not pull them free. Sunk to their bellies in mud overnight, the animals died, their crews helpless. Soldiers took off their boots and carried them, but it was not just boots that were swallowed up by the mud. According to the artillery officer Louis Brun de Villeret, 'in one single regiment, eighteen men drowned in this mud during a night march, their comrades being unable to help them without running the same risk'. Caulaincourt complained of 'mud up to one's ears', and Napoleon himself had to spend the night with only a few wisps of straw between him and the mud in an old barn. 'Regiments melted away by the day,' remembered Lieutenant Théodore de Rumigny.
Matters were not improved by a dire lack of supplies. 'No commander ever gave as many orders to provide victuals for his army as Napoleon,' remarked one infantryman, 'and none were more poorly executed.' What little supplies there were had got bogged down as well, and the under-populated, poor countryside provided scant resources. Men died of hunger and exposure, and some took their own lives out of despair. The mud of Poland entered French military lore alongside the burning sands of Egypt.
Napoleon's usual method, of moving fast and seizing opportunities as they offered themselves, proved useless in these conditions, but he had also fallen behind the army and could not coordinate operations. It is allegedly from this moment that he began to refer to his Guard as ' _grognards_ ' on account of their grumbles over the conditions and lack of food. They had learned the Polish for bread, ' _chleb_ ', and for 'There is none,' ' _Nie ma_.' Whenever he passed marching troops they would shout ' _Chleba, chleba!_ ' to which he would shout back, ' _Nie ma!_ ' They were not just grumbling over the lack of food; it was the first campaign on which he was not constantly in their midst. There was also criticism of his conduct of the campaign, and his prestige in the ranks was dented.
Back in Pułtusk on 29 December, given the impossibility of fighting on, he ordered his army to take winter quarters. On his return to Warsaw on 1 January 1807 he declared that since they could not fight, everyone should enjoy themselves. He was certainly meaning to do so himself. On 31 December news had reached him that Éléonore de la Plaigne had given birth to his son – proof that it was not, as Josephine had always maintained, he who was infertile. In his letters there was no further mention of her coming out to join him.
He spent the whole of January in Warsaw. There were parades, balls and concerts. Polish society fêted their French guests, and many women gave themselves to their putative liberators with patriotic fervour. 'The time we spent in Warsaw was magical,' recalled Savary. Major Boulart of the Guard Artillery remembered to the end of his days a pair of 'beautiful eyes' and the joy of flying around the sparkling, snowbound city in a sleigh.
Napoleon was viewed with respect, and in some cases with genuine awe. 'He seemed to have a halo,' noted the thirty-year-old Countess Potocka, who was 'bedazzled' by the sense of power he exuded. But if he was expecting to enjoy the privileges of a conqueror, he was to meet with disappointment. At a ball he spotted the beautiful Princess Lubomirska, and in the morning sent an aide to inform her he would call that evening. Fearing for her virtue, the princess ordered her carriages and left for the country, and when he called Napoleon found himself, as the Polish saying went, kissing the door handle. 'Silly woman,' he snapped.
Josephine, still in Mainz, was eager to join him in Warsaw, but he put her off, using the distance and the bad roads as a pretext. He urged her to return to Paris and enjoy herself, promising to let her know when she could join him. His letter of 18 January was a little more impatient: 'I am very well and love you very much, but if you keep crying I will begin to think you have no courage and no character.' He did add a saucy phrase about kissing her breasts, but it was not hers he was thinking of.
The evening before, at a ball given by Talleyrand in one of the Warsaw palaces, he had danced with a young woman he had spotted at a reception ten days earlier, and was smitten. Her name was Maria Walewska. She was twenty and married to a seventy-one-year-old, and though she did not love her husband, she had strong principles and believed in the sanctity of marriage. Her two brothers, both officers in the French army, and various other Polish patriots who had noticed Napoleon's interest, urged her to at least humour the man on whom the future of their country depended. She appears to have given him some hope, and the following day he sent her a note through Duroc. 'I saw only you, I admired only you, I desire only you,' he wrote, demanding a prompt response 'to calm the impatient ardour of N'. She refused to go with Duroc to the ardent Napoleon. He wrote again. 'Have I offended you, Madame? I had the right to expect the contrary. Your emotions have cooled, while mine have grown. Thoughts of you do not let me sleep! Oh! Give a little joy, of happiness to a poor heart which is ready to adore you. Must it be so difficult to obtain a reply? You owe me two.' She did come to him at the royal castle that evening, but left at four in the morning without having given herself to him. That morning he wrote Josephine a testy note ordering her to be 'merry, charming and happy', and stop nagging him.
Walewska's reticence was a novel experience for one who had grown used to submission. In his short, eager letters he cast himself as the lonely man at the top whose cares only she could dispel by allowing him to throw himself at her feet. 'Oh! Come to me, come to me! All your wishes will be granted. Your motherland will be dear to me if you take pity on my poor heart,' he cajoled, counting on her patriotism. The more she resisted him, the more loving the tone of his letters, the more he followed her around at receptions, watching her every move like a lovelorn teenager. At the same time his tone forbidding Josephine to even think of coming to join him grew imperious. Walewska did agree to call on him again, and after expending every argument he could, and faced only with her tears, he appears to have as good as raped her.
He had set up a council of prominent Poles as a provisional administration, but it was firmly supervised by Talleyrand and Maret, and its brief was limited to raising a Polish army and providing victuals and horses for his troops. At the same time, he ordered the setting up of a French-style administrative structure and even the introduction of his Civil Code. He would not make further commitments until the military situation had clarified.
He left Warsaw on 30 January, travelling north through Pułtusk, where he visited the sick Lannes, who told him the place was not worth fighting for and they should go home, a view echoed by many in his entourage. Three days later he watched a skirmish between Soult's corps and Bennigsen, who fell back, and on 4 February himself attacked Bennigsen at Allenstein, forcing him to retreat in a northerly direction and, on 7 February, to abandon the little town of Eylau. The weather had changed again, and it was snowing. The troops had not had any bread since leaving Warsaw a week earlier, and that evening Napoleon sat by a bivouac fire baking potatoes along with his grenadiers. Bennigsen counter-attacked in the morning, and there followed a chaotic battle fought in a blizzard, in which Napoleon himself was nearly captured. Both sides fought with determination, and although Bennigsen retired and his losses were greater, it could hardly be termed a French victory, and there was little doubt that Napoleon had not been fully in control.
'The victory was mine, but I lost many men,' he wrote to Josephine at three o'clock in the morning after the battle. 'The enemy's losses, which are even greater, are no consolation to me.' Many of his best troops had been killed, and the sub-zero temperatures meant that most of the wounded who could not move froze to death in the night. The sight of the battlefield the next day had a demoralising effect on the survivors: the dead lay so close that it was difficult not to walk over them. Napoleon himself was horrified by the carnage. 'This is not the pretty aspect of war,' he wrote to Josephine a couple of days later. 'One suffers and one's soul is oppressed by the sight of so many victims.' The army shared his feelings, and the men were anxious, knowing the losses could not be easily made good so far from home. The weather and the mournful landscape made them homesick, and morale plummeted as they once more went into winter quarters at Osterode. According to some accounts, over 20,000 men were suffering from dysentery.
As usual, the Bulletins proclaimed a decisive victory and minimised French losses, but letters from husbands, brothers and sons spread anxiety in Paris. Josephine expressed it and wished he would come home, not least because rumours of his romance were beginning to circulate. He wrote telling her she had no grounds for sorrow. 'I do know how to do other things than making war, but duty comes first,' he chided her. 'Throughout my life, I have sacrificed everything – tranquillity, interest, happiness – to my destiny.'
On 1 April Napoleon moved into the nearby castle of Finckenstein, where he was joined by Maria Walewska. She was delivered at night in an unmarked carriage by one of her brothers, and having been shown to her quarters would not leave them for the next six weeks. Her presence was supposed to have been a secret, and only Napoleon's valet Constant and his secretary Méneval were allowed to see her, but there was talk in the surrounding camps of ' _la belle polonaise_ ', and Warsaw society knew she was there.
She later admitted to a friend that her scruples had vanished, for Napoleon made her feel as though she were his wife. Innocent and uncomplicated, she was unlikely to have been critical of or dissatisfied with his sexual prowess, and seems to have fallen in love with him. They behaved as a married couple, even taking their breakfast together in her red-damask upholstered bed. He found the castle 'very fine', and its numerous fireplaces suited him, as he liked to see a fire burning when he got up in the night. He was in good health, he assured Josephine, noting that the weather was cold but fine. He inspected troops almost every day and took exercise on horseback, and in the evenings played cards.
His strategic position was not good. He had some 70,000 men at Osterode, but many were sick, the rest hungry and dispirited, and rates of desertion were alarming. He was facing a constantly growing Russian force. The last fortress in Prussian hands, Danzig, had fallen to Marshal Lefèbvre (who became duc de Danzig), but although the Prussian army had all but disintegrated, many of its officers were making their way to take service with Russia. On 26 April Frederick William signed the Convention of Bartenstein with Russia, by which both powers vowed not to make a separate peace. At his back, Napoleon had Austria, which was only being held in check by the presence of an Italian army under Eugène on its southern border. He had recently got wind of contacts between the Spanish minister Godoy and the British concerning the possibility of Spain joining the anti-French coalition. In May Napoleon concluded the Treaty of Finckenstein with Persia, which he hoped would result in military action on Russia's southern border. He was also encouraging the Turks to make a move that might divert Russian forces; he had received a Turkish envoy at Finckenstein in this spirit. But a British fleet had sailed into the Dardanelles, accompanied by a British invasion of Egypt, to pressure the Porte to make peace with Russia and expel the French ambassador.
At the beginning of June Bennigsen attacked Ney's corps, and with a couple of deft manoeuvres managed to sow confusion among the other French corps. Napoleon rallied them and followed Bennigsen, who fell back on the little town of Friedland in a curve of the river Alle, where on 14 June he was forced to accept battle. With no room to manoeuvre and no possibility of falling back when two of the three bridges over the river were destroyed by French artillery, his army was cut to pieces, losing by some estimates as much as 50 per cent of its effectives. It was the anniversary of Marengo, and Napoleon made much of this, saying the battle had been as decisive as Marengo, Austerlitz and Jena.
The tsar, who was close by, had no option other than to request an armistice, and Napoleon, who was keen to make peace and take his homesick army home, agreed to one on 21 June. Three days later, at his headquarters in the small town of Tilsit, he received a note from Alexander stating that for the past two years he had longed for an alliance with France, as only that could guarantee the peace and well-being of Europe, and requesting a meeting.
Alexander had been humiliated and lost an army at Austerlitz, and now another at Eylau and Friedland. He could raise more men, but his officer corps was not up to doing much with them. If he retreated he would be drawing the French into an area taken from Poland only ten years before, in which they would be welcome and he not. He was single-handedly supporting the crushed and ineffectual Frederick William and felt abandoned by his British ally; British gold had bought nothing but Russian blood and embarrassment. Something of a fantasist, he fancied he would be able to seduce Napoleon.
Napoleon for his part had begun to reflect on a possible alliance with Russia, against the advice of Talleyrand, who consistently pressed for a strategic alliance with Austria. On the day he received Alexander's note he had received a report from his ambassador in Vienna, General Andréossy, that Austria was hostile and only waiting for a chance to take revenge. The other news Napoleon had that day was that there had been a palace revolt in Constantinople, and the sultan Selim III, with whom he had been negotiating, had been deposed, so he could expect no support against Russia from that quarter. He agreed to Alexander's offer, and invited him to a meeting on the following day.
He ordered his sappers to construct a raft with a tented structure on it, decorated with the arms and ciphers of the two monarchs, and to moor it midstream on the river Niemen (Neman). When Alexander arrived with his suite on the opposite bank, he was rowed out to the raft, where Napoleon greeted him with an embrace as his troops, drawn up on the western bank, cheered. Frederick William, who had come with Alexander, was left sitting on his horse on the east bank, pointedly left out. Symbolism was the order of the day, and the showman in Napoleon had taken over.
'My Dear, I have just met the emperor Alexander,' he wrote to Josephine that evening. 'I am very pleased with him; he is a very handsome and good young emperor, he is more intelligent than is commonly thought. He is coming to stay at Tilsit tomorrow.' Over the next two weeks he entertained Alexander to dinner, had his troops parade before him, and held private conversations with him, sometimes lasting long into the night. As they strolled arm in arm he played the part of the great conqueror who appreciated the hidden qualities of the younger man and graciously treated him as an equal, taking him into his confidence as he discoursed on weighty matters of state. This was balm to the young tsar, a man of complexes, weak, unsure of himself, desperate to cut a figure as a military leader. He was intelligent enough to appreciate what Napoleon had achieved in rebuilding the French political edifice and society, something he dreamed of doing himself in Russia. Although a part of him resisted (strongly supported by his mother and his sister Catherine), he could not help falling under the spell of Napoleon, who tempted him with prospects of being able to play a part in the affairs of the Continent and even to fulfil the Russian monarchy's dream of conquering Constantinople, and of a combined march on India to expel the British and extend their own empires. This was accompanied by typically Napoleonic gestures, such as his asking the Russian guards parading before him to name their bravest, and presenting him with the Legion of Honour.
The troops of both sides fraternised, the French guards inviting their Russian counterparts to banquets in the open air. At a higher level, Murat teamed up with Alexander's younger brother Constantine in orgies of drunkenness and debauchery. When Murat appeared in his 'Polish' dress, Napoleon told him to go home and change, saying he looked like a comedian. More decorously, parades were held and uniforms inspected and compared – on one occasion two battalions of French infantry displayed the new white uniforms with which Napoleon was thinking of replacing the blue, on account of the shortage of indigo dye following the loss of France's West Indian colonies.
Although Alexander did persuade him to meet the King of Prussia and to admit him to the festivities, Napoleon continued to treat him as an irrelevance. He even failed to show much interest in the beautiful Queen Luise when she came to plead the Prussian cause. He adopted a tone both flirtatious and mocking, promised to do something for Prussia and then broke his word, reducing her to tears. He had already prepared the text of a proclamation dethroning Frederick William, and only relented at the request of the tsar.
The upshot was a treaty, signed on 7 July 1807, by which Russia lost nothing except its protectorate over the Ionian islands and gained in return a small piece of territory from Prussia, seemingly a miraculous outcome after having been roundly defeated. She also bound herself to withdraw from the Danubian principalities over which she was in conflict with the Turks, but was given licence to capture Finland from Sweden instead. Furthermore, Russia bound herself to bring Britain to the negotiating table by 1 November 1807, and if this proved impossible, to join France in alliance against her. In return, Russia endorsed all of Napoleon's arrangements in Europe, which included the dramatic reduction of Prussia, whose Polish possessions were turned into a Grand Duchy of Warsaw, ruled over by the King of Saxony, and the creation of a kingdom of Westphalia, mostly out of former Prussian provinces, with Napoleon's brother Jérôme as king.
The treaty effectively negated Russia's designs on Constantinople, excluded her from influence in Germany, and left in the shape of the Grand Duchy of Warsaw a French outpost on her border and an embryonic Polish state that might one day recover, or at least subvert, many of Russia's recent western conquests. The treaty humiliated Prussia, whose population was reduced from nearly ten million to less than five by the removal of its Polish conquests and provinces absorbed into the kingdom of Westphalia. It was obliged to join the war against Britain and pay a crippling indemnity to France – and to remain under French military occupation until that was settled. Furthermore, Denmark, Sweden and Portugal would be asked to close their ports to the British and recall their diplomats from London. If they refused, they were to be considered enemies of France and Russia.
Napoleon had got his way in everything, and there was now no state independent enough to act as proxy for Britain on the Continent. But by committing his allies to the trade war, he forced an unpopular and in some cases suicidal policy on them – and on himself the obligation to ensure that no port in any part of Europe remained beyond his control.
## 31
# The Sun Emperor
On his return to Paris Napoleon was greeted with a sixty-gun salute. When, on 15 August, his birthday, he drove across the city to Notre Dame he was cheered by people who believed they could now expect prolonged peace and prosperity. France had never seemed so great, and people began referring to him as _Napoléon le Grand_ , an epithet last bestowed on Louis XIV. There was by now much more of the Sun King about him than of the 'necessary dictator' whom so many had welcomed on his return from Marengo eight years earlier.
He had been away for nine months, but every couple of days he received an _estafette_ with most of the news and information he would have had in Paris, so he was able to hold the reins of government throughout that time, with Cambacérès regularly sending one of the _auditeurs_ of the Council of State off to his headquarters with a batch of papers for him to sign along with the relevant minutes and reports. Everything had functioned smoothly, and while enjoying the carnival in Warsaw or sitting by the fireside at Finckenstein he had been able to continue implementing public works and supervising projects such as the Commercial Code, which was to form part of the Civil Code. He was kept abreast of the meetings of the Grand Sanhedrin, which he had summoned to discuss the status of the Jews in the empire. He inspected accounts and queried the smallest expenses. His presence haunted Paris, if only by the never-ending stream of letters, instructing, admonishing, reproving, and always firm. This, combined with the institutions he had put in place contributed to a remarkable sense of stability. Few states could have survived, let alone functioned efficiently, with their absolute ruler so far away for so long. British naval bombardments of French ports and attempted landings had been seen off. News of Eylau had caused despondency and a recrudescence of anti-government and even royalist feeling in the west, but this had been contained, and although there was still much banditry on the roads, the country functioned normally. Cambacérès and Fouché had ensured that the press, the theatre and literature all followed the official line.
Yet on his return Napoleon felt a need to take matters more firmly in hand. He made a number of ministerial changes and named new senators, and on 19 August he abolished the Tribunate, allowing some members to retire and others to join the Legislative. The closing down of the 'chattering chamber' did not cause much surprise or alarm, and many felt the system would function better without it. Whatever people thought of it, the Napoleonic regime delivered stability and prosperity, and that was what most people wanted. Yet he seemed to be gradually losing sight of that crucial fact, and his vision was beginning to diverge from that of the majority of his subjects.
His latest victories had not produced the same effect on public opinion as earlier ones, partly because people no longer believed the Bulletins – the phrase 'to lie like a Bulletin' had entered common parlance – but mostly because they could see no point to them. As the Austrian ambassador put it, they felt no excitement at the news of a victory, only relief that it was not a defeat. Napoleon expressed disappointment when he was made aware of this, but did not reflect on the cause, which was that his role as the longed-for victorious hero and saviour of France had been played out; what the people now wanted was a strong ruler who could safeguard what had been achieved. That was not how he saw things.
His triumph over Russia and Prussia had opened up limitless new vistas to his imagination, in which mirages of eastern conquest now fought with concepts of a grand new arrangement of Europe. The exhilarating experience of Tilsit, and possibly also of knowing that he was not after all sterile, was not calculated to make him settle down to a quiet life. On 3 August Frederick William wrote him a letter, addressing him as 'the greatest man of the century' and begging for an alliance, but Napoleon did not answer; he preferred to bleed Prussia dry. Thanks to the huge sums she was forced to disburse, the war had largely paid for itself, and there was more to be squeezed out. Estates seized by the Prussian government when it had taken over its part of Poland were not returned to the government of the Grand Duchy of Warsaw but given to French marshals and dignitaries instead – part of a plan to bind Napoleon's growing imperium in a great web controlled by himself. He distributed titles of nobility to faithful servants and potential enemies alike, in the conviction that all men could be bought, creating 3,263 princes, dukes, counts, barons and knights by the end of the empire. Fifty-nine per cent of them were soldiers, and most of the rest either state functionaries or notables: 22.5 per cent were from the old nobility, 58 from the middle class, and 19.5 from the working classes.
Since they owed everything to him, he believed he was their master. Pontécoulant was struck by the change that had taken place in his manner during his absence, noting that 'there was in his deportment a kind of constraint, a sort of stiffness, which inspired fear rather than respect and seemed to put distance between him and those closest to him'. He also found his conversation less scintillating, and felt that in the Council of State he seemed 'more intent on imposing than convincing'. The court of the Tuileries reflected this process: 'it was no longer the tent of the hero crowned by victory, but the ridiculous show of an old-fashioned royal court with all the exaggerations of the past, without the politeness, the urbanity and the good manners'. As Josephine's lady-in-waiting Claire de Rémusat pointed out, the entire brilliant structure of Napoleon's power 'rested on an authority whose foundations were in opposition to the irresistible march of the human spirit'. Not only was he no longer in tune with the spirit which had brought him to power, he seemed to be regressing in time.
Perhaps the most significant change he made on his return was to remove Talleyrand from the Ministry of Foreign Relations. This was not a mark of disgrace or even displeasure, and he was honoured with the rank of vice-grand elector, which kept him at the heart of the court. It was a question of policy. Talleyrand may have been an opportunist by nature, but he was also a strategist. He had repeatedly and forcefully given Napoleon his opinion that he was moving in the wrong direction, and urged a reorientation of French foreign policy based on a strategic alliance with a strengthened Austria.
Napoleon wanted to direct foreign policy himself, and as Talleyrand's successor he appointed Jean-Baptiste de Champagny, previously minister of the interior, a conscientious executor of his will without much experience of the outside world. Unwilling or unable to take into account the interests and aspirations of others, Napoleon could not develop a fixed strategy. Most of his actions were henceforth dictated by a determination to bring Britain to book by destroying her economic power, while encouraging industrial development in mainland Europe by eliminating British competition, which was to be achieved by closing Russian, Prussian and Danish ports to her shipping. The Royal Navy would suffer for lack of supplies of Baltic timber, hemp and tar, there would be food shortages for lack of Polish wheat, and British industry would lose some of its most lucrative markets. With Louis reigning in Holland, Jérôme in Westphalia and Murat in the Grand Duchy of Berg, the entire coastline from St Petersburg to France was in theory secure, and Central Europe out of bounds to British commerce. This hurt the British economy, as some 36 per cent of exports had gone there.
An early setback in Napoleon's economic war came at the beginning of September 1807. Acting on intelligence that Denmark was being pressured by France to join in alliance against Britain with her large fleet, the British cabinet ordered an attack on Copenhagen which resulted in the capture of the entire Danish fleet. Fouché noted that he had not seen Napoleon react to any news with such fury since hearing of the assassination of Tsar Paul I. But he quickly realised he had to secure the other weak link in his alliance against Britain.
Ruled since 1700 by Bourbon kings descended from Louis XIV, Spain had been France's closest political and commercial partner. Along with the Bourbon kingdom of Naples and Sicily, it had formed part of the _pacte de famille_ , a defensive alliance against principally Austrian and British designs. This had been shaken by the outbreak of the French Revolution, and following the execution of Louis XVI his Spanish cousins invaded France. They were soon expelled, and fearing the contagion of revolution, Spain made peace, and by the Treaty of Basel in 1795 became an ally of France once more.
The King of Spain, Charles IV, was an amiable but foolish man more interested in hunting and making things – particularly shoes – than affairs of state. More interested in these was his wife, Maria-Luisa of Parma, commonly referred to as _la puta_ for her supposedly insatiable sexual appetite. She was governed by her favourite, the minor noble Manuel de Godoy, two years older than Napoleon, who had been showered with rank and honours, becoming virtual ruler of the country by 1792. Insofar as he had any principles beyond accumulating as much power and wealth as possible, he was a conservative and ill-disposed to France. He was widely hated. Most of his enemies and those of the status quo pinned their hopes on the heir to the throne, Ferdinand Prince of the Asturias, a dim-witted but treacherous twenty-four-year-old.
Because of its geographical position and colonial empire Spain was of immense importance to France, and Napoleon did not trust Godoy to keep the country from falling under British influence. When he reached Berlin after Jena he found letters from Godoy to the King of Prussia offering to attack France in support of Russia and Prussia. The risk of such an attack would not have worried Napoleon much, even when he was occupied in Central Europe, but the possibility of the British getting a foothold on the Iberian Peninsula did, because it would breach the commercial blockade. As an ally of France, Spain was committed to it, but Portugal was not.
In September 1807 Napoleon wrote to the regent of Portugal, Dom João, telling him to choose between France and Britain. He responded favourably and declared war on Britain, but he was too late. On 27 October an impatient Napoleon had concluded the Treaty of Fontainebleau with Charles IV, by which France and Spain would jointly take over Portugal.
To carry out the operation Napoleon had chosen Junot, telling him his marshal's baton was waiting for him in Lisbon. Among his reasons for sending him was that during Napoleon's nine-month absence Junot, who was military governor of Paris, had been having an affair with Napoleon's sister Caroline Murat (who some thought was thus positioning herself for the struggle over the succession were her imperial brother to meet with disaster on campaign). Napoleon did not wish Paris to witness the confrontation between Junot and a returning Murat. He could count on Junot, whose devotion since their first meeting at Toulon some compared to love. What he did not appreciate, or chose to ignore, was that the swashbuckling _bravoure_ , the hard drinking and the happy-go-lucky manner of the handsome, curly-headed Junot, concealed the beginnings of mental problems.
Junot crossed the border into Spain with 20,000 men on 17 October, with no maps and only a hazy idea of where he was going. His force was made up of young French conscripts unused to the rigours of war, supplemented by detachments of Swiss, Italians and Germans. They were inadequately equipped and supplied, and while they were unopposed by the bemused Spanish garrisons they passed on their way, they could not count on their assistance. Men soon began to fall behind and die, so that when he entered Lisbon on 30 November after a forced march of over a thousand kilometres, Junot had only 1,500 left, no cavalry and not one piece of artillery. It was a feat, but it misfired: the British had sailed into Lisbon, embarked the Portuguese royal family and taken them to their colony of Brazil, along with the Portuguese fleet which Napoleon had counted on seizing. Junot did not get his marshal's baton, only the title of duc d'Abrantès.
The situation in Spain itself was deteriorating rapidly as supporters of Ferdinand had begun plotting to overthrow Godoy, encouraged by the French ambassador in Spain, Josephine's brother-in-law François de Beauharnais, acting independently of Napoleon. Charles IV arrested his son on charges of treason, but then pardoned him and wrote to Napoleon asking on his behalf for the hand of a princess of the house of Bonaparte, something Ferdinand's supporters had been urging for some time.
At the end of November 1807 Napoleon began a tour of his Italian dominions, which were of key importance if he was to exclude the British from the Mediterranean and keep Spain allied to France. He had set in motion an ambitious shipbuilding programme which would over the next years produce seventy ships of the line, and while he had not given up hope of recovering some of France's colonies, his first priority was the Mediterranean, where he ordered the fleets at Brest, Lorient and Rochefort to join that of the Adriatic, based in Venice. He was already making new plans concerning the Middle East and India. Having, by the Treaty of Tilsit, recovered the Ionian islands, he was preparing to turn Corfu into a naval base to rival Malta. In the interests of making Italy secure against British interference, he pressed Joseph to invade Sicily and expel the British who were using it as a base. He dislodged the queen of Etruria, who did not apply the rules excluding British trade rigorously enough. He added her kingdom, which reverted to its name of Grand Duchy of Tuscany, to the French Empire as a fief for his sister Élisa, and gave the ex-queen a piece of Portugal in exchange (it was done quite amicably, and they went to the opera at La Scala together afterwards). Similarly, he annexed the papal province of Le Marche to the kingdom of Italy; that and the other Papal States had several strategic ports, and the Pope could not be relied on to deny use of them to the British or the Russians, as his relations with Napoleon had soured.
Napoleon's doings in Germany had affected the status of the Church by boundary changes and the introduction of French-style administration, not to mention financial extortion and outright looting of Church property. This was compounded by the extension in January 1806 of the Civil Code to Italy, which impinged on areas governed by the Church. The Code established the primacy of civil over religious marriage, and legalised divorce. The Pope's protests over this and over the French occupation of Ancona during the Austerlitz campaign angered Napoleon, who assumed he was siding with the allies at a moment when it looked as though they were winning. 'Your Holiness is sovereign in Rome, but I am its emperor,' he had reminded him in a brusque letter in February 1806. He insisted that 15 August, the feast of the Assumption of the Virgin, be henceforth celebrated as that of St Napoleon, and that the Imperial Catechism be taught in schools. At every opportunity he drove home the message that as temporal ruler of the Papal States, the Pope was vassal of the emperor of the French. He had not forgotten Rousseau's thesis that Church and state were in fundamental conflict.
Another point of discord was Napoleon's nomination of Joseph to the throne of Naples. Traditionally, the kings of Naples had been invested by the Pope, so Napoleon's action caused offence. When he insisted the Pope recognise the new monarch the Pope refused, prompting Napoleon to send troops in to occupy all the ports in the Papal States, purportedly to prevent communication between the Vatican and the exiled Bourbons, now in Sicily.
Napoleon kept making demands of the Pope as though he were one of his ministers, requesting, for instance, that he annul the marriage of Jérôme to Elizabeth Patterson. As the couple had never been married in church, the Pope could not oblige, which annoyed Napoleon, who was intending to marry Jérôme to Catherine of Württemberg and wanted to make him look as acceptable as possible to the family of the bride. On his return from Tilsit he sent more troops into the Papal States, and demanded the Pope withdraw his religious objections to his Code and apply it in his states.
As he sped around Italy, reviewing troops, inspecting fortifications and lecturing local authorities, Napoleon managed to fit in operas at La Scala and La Fenice, and to go to the theatre in smaller cities. Joseph came from Naples to confer with him in Venice, and on 13 December Napoleon had a six-hour-long meeting with Lucien at Mantua. He needed his younger brother to rejoin the family enterprise and offered him any kingdom he wanted, but, stuck in the rut of his self-inflicted conventions, he insisted Lucien must first divorce his wife, whom he deemed both too common and, as a divorcee, unsuitable. Lucien retorted that Napoleon had also married an unsuitable woman, adding, 'and at least mine isn't old and stinking like yours'. Napoleon undertook to recognise Lucien's daughters Lolotte and Lilli and make them princesses of France, but not his son, who was born out of wedlock. Lolotte would marry the prince of the Asturias and become queen of Spain. Lucien could carry on living with his wife, but she could only have the status of concubine. To sweeten the pill Napoleon offered to make her Duchess of Parma. But Lucien, who disagreed with the course Napoleon was taking, refused.
Three days later, in Milan, Napoleon signed yet another decree concerning the blockade. Britain had responded to his Berlin Decrees by ruling that any ship belonging to a neutral nation which had not put into a British port and had its cargo taxed (at 25 per cent) was liable to seizure. Napoleon reacted by ordering the seizure of any vessel that had conformed to the British decrees. This prompted President Thomas Jefferson of the United States to place an embargo on British and French vessels entering American ports.
Napoleon was back at the Tuileries on 1 January 1808. Three days later he visited David's studio to see the monumental painting of his coronation in progress. On 9 January he inaugurated the new theatre he had ordered Fontaine to construct in the Tuileries, with a performance of Paer's _Griselda_ , but at the second performance, of Corneille's _Cinna_ , the room was so cold the ladies in their scanty dresses had to flee at the interval, and he vented his rage on the unfortunate architect. In between hunting, attending performances of tragedies by Racine, presiding over the council of the university and inspecting public works, he fitted in visits to Maria Walewska, whom he had brought to Paris and installed in a discreet house. He also decreed the introduction of full military discipline into the navy, sent Joseph a plan for the invasion of Sicily, and gave orders for the military occupation of the Papal States.
In the course of a meeting with the Austrian ambassador, Metternich, he broached the subject of combined Franco-Austrian operations against Turkey. One can only wonder at how he thought he would represent this to his ally Alexander, given the Russian monarchy's age-old dream of conquering Constantinople. Napoleon wrote to him on 2 February dangling another prospect before him, presumably meant to distract him: 'An army of 50,000, Russian, French, perhaps even partly Austrian troops, marching into Asia through Constantinople would need to get no further than the Euphrates to make England quake and fall to its knees before the Continent.' But while he dreamed of dealing British power a blow in the east, he was going to have to defend himself against it closer to home.
By the beginning of 1808 it had become obvious that drastic action was required if Spain was not going to disintegrate. Aside from the struggles for power revolving around its dysfunctional royal family, there were broader tensions as well as local animosities simmering all over the country, between peasants and nobles, nobles and clergy, peasants and clergy, traditionalists and reformers, and within the clergy between those who supported the Inquisition and those who wanted it abolished; most historians agree that the manifold passions agitating Spanish society were about to boil over into extreme violence. France could ill afford to have a failing state on its border, particularly one open on three sides to seaborne British attack.
Along with most Europeans, the French viewed Spain as an archaic state ruled by an imbecile dynasty, populated by a lazy and decadent people marshalled by obscurantist priests – in a word, a society that badly needed the benefits of the Enlightenment. In the course of his recent tour of Italy, Napoleon had formed the impression that on the whole its inhabitants had accepted the new order he had imposed, and many had embraced it with enthusiasm. There seemed little reason to doubt that the same could be done in Spain.
His primary concern was to keep the British out, and he had been gradually sending troops into northern Spain under the pretext of guarding the supply lines of Junot in Portugal. By the beginning of 1808 Generals Dupont and Moncey had some 20,000 men each at Valladolid and Burgos respectively. In order to keep his options open, Napoleon deflected Charles IV's proposal of a dynastic marriage to Lucien's daughter on grounds of the disgraceful behaviour of the prince of the Asturias. On 20 February he sent Murat in with another 80,000 men while he considered what to do next.
Talleyrand argued that France would never be safe unless she could rely on the alliance with Spain, and that the solution imposed by Louis XIV a century earlier was the only sensible one: the throne of Spain should be occupied by a member of the same dynasty as that reigning in France. Cambacérès warned against getting involved in yet another country, but while Napoleon considered the options, events in Spain sucked him in.
On the night of 18 March 1808, supporters of Ferdinand stormed Godoy's palace at Aranjuez and imprisoned him, then forced Charles IV to abdicate in favour of his son, whom they proclaimed King Ferdinand VII. They assumed that they had the support of France, and were surprised when Murat, who had occupied much of the country by stealth and installed himself in Madrid, took the unfortunate Charles under his protection. Charles wrote to Napoleon informing him that he had been forced to abdicate and in effect placing himself at his disposal. Napoleon began to think his own presence in Madrid was necessary, and at the end of March he ordered horses, pages and cooks to be sent there. At the same time, he invited Ferdinand to France. It is difficult to deduce his ultimate goal, or whether he had one at this stage.
On 2 April he left Saint-Cloud, ostensibly on a tour of inspection of the south-west, stopping at Orléans, Bordeaux and other towns to inspect troops and meet local notables. Along the way he encountered three Spanish grandees sent by Ferdinand to announce his accession to the throne, but refused to receive them. On 14 April he reached Bayonne, and three days later took up residence nearby at the grim château of Marracq.
Massively built but small, it barely contained Napoleon and Josephine, who joined him there later with her _maison_ , which huddled uncomfortably in a series of small upstairs rooms. Napoleon's numerous staff were accommodated in nearby houses and cottages, while his military escort camped on the lawn in front of the house: a battalion of grenadiers of the Guard first, next to them a detachment of Basque _gardes d'honneur_ in red dolmans, black berets, breeches and stockings, and 500 metres away a fancily-uniformed squadron of the newly formed Polish chevau-légers of the Guard.
The day after taking up residence Napoleon wrote to Ferdinand, reserving his decision on whether to recognise him and inviting him to Bayonne. The same day he wrote to his brother Joseph warning him that in five or six days he might write again asking him to leave Naples and come to Bayonne. When Ferdinand arrived, on 20 April, Napoleon had a short interview with him and discussed matters with members of his entourage. Six days later Napoleon met Godoy, who had also arrived; he told him the Bourbons had lost all credit in Spain, and the people wanted Napoleon as their ruler. 'If I am not mistaken,' Napoleon wrote to Talleyrand, 'this play has reached its fifth act, and we are about to see the dénouement.' It began with the arrival on 30 April of Charles and Maria-Luisa, who trundled into the town in a convoy of magnificent state coaches of another age, 'huge gilded boxes with glass in front and behind as well as on the doors', suspended on wide leather straps attached to outsize gilded wheels. After dining with them that evening, Napoleon could begin to make his own assessment of the Spanish royal family.
He had taken little time to rule out Ferdinand. 'The Prince of the Asturias is very stupid, very wicked, very hostile to France,' he wrote to Talleyrand. As well as being an imbecile, he was untrustworthy – he had expressed regret that when forcing Charles to abdicate his partisans had not followed the example of Tsar Paul's assassins. He would also be easy for the British to manipulate. On the other hand, a couple of meetings with Charles and his consort sufficed to persuade Napoleon that he too was incapable of ruling effectively. 'King Charles is a good man,' he thought, while 'the queen has her heart and her past written all over her face; no more need be said'. He persuaded Charles to revoke his abdication and appoint Murat as his lieutenant pending a resolution of the crisis.
This had taken on a new dimension with the outbreak on 2 May of a riot in Madrid. Supposedly a protest against the departure for Bayonne of two more members of the royal family, it turned into an attack on all Frenchmen, principally soldiers, stationed in the capital, between 150 and 200 of whom were murdered. Murat restored order with savage repressions involving the execution of around a thousand rioters. When it reached Bayonne, the news contributed to a scandalous royal row in front of Napoleon, as Charles accused Ferdinand of treachery and Maria-Luisa urged Napoleon to have him executed. An exasperated Napoleon declared he could not recognise anyone as despicable as Ferdinand, and bullied him into renouncing his claim to the throne and acknowledging his father as king. Whether under pressure from Napoleon or not it is not clear, but Charles then renounced his own right to the throne, which he placed at the disposal of Napoleon, on the grounds that only he was in a position to restore order.
Napoleon returned to Marracq that evening in a state of agitation, and walked around the park with his chaplain, the Abbé de Pradt, discussing the diminishing options. He could see only one: 'The old dynasty is used up, and I have to rebuild the work of Louis XIV,' as he put it to General Mathieu Dumas. The next day he wrote to Talleyrand instructing him to prepare the château of Compiègne to receive the ex-king of Spain and his consort. The prince of the Asturias and his brother Don Carlos were to be put up at Talleyrand's château of Valençay, a punishment for Talleyrand, who was given the additional job of finding him a woman. 'I believe the most important part of the job to have been done,' Napoleon wrote, adding that although there might be a few disturbances, the firm lesson given by Murat in Madrid would prevent further trouble. He waited another four days before writing to Joseph instructing him to come and take the throne of Spain, encouraging him with the argument that while Naples was 'at the ends of the earth', 'In Madrid, you are in France.'
Another four weeks passed before Joseph arrived, and during that time Napoleon visited local garrisons and ports. At Biarritz he bathed in the sea, watched over by mounted chasseurs of the Guard. Presumably in consequence of a lack of reading matter, he gave orders for the creation of a thousand-volume travelling library, in the small duodecimo format with large print fit to be read in a carriage. It was to include sections on religion and the classics, a hundred novels, history, memoirs and the great classics of French drama. He also instructed his librarian to make extracts and précis of the campaigns of Crassus, Trajan and other Roman emperors against the Parthians on the Euphrates, and to have maps and plans of the area drawn up. When the weather grew warm, he and Josephine were plagued with flies and other insects, and slept together under a mosquito net. He was affectionate with her, and did everything to scotch the gossip about a possible divorce.
Joseph reached Bayonne on 7 June, and the two brothers began setting up the new monarchy. They drew up a constitution which enshrined many Spanish traditions and recognised Catholicism as the religion of state. Napoleon refrained from introducing the Code as he had insisted on doing in Italy. On 22 June, at Valençay, Ferdinand swore an oath of fealty to Joseph, who was proclaimed King José I on 8 July by a hastily convened Cortes consisting of ninety-one members. He was congratulated by the other members of the former dynasty, and began issuing proclamations styling himself 'Don José, by the Grace of God, King of Castille, Aragon, the Two Sicilies, Jerusalem, Navarre, Grenada, Toledo, Valencia, Galicia', and a sackful of other titles which had accrued to the Spanish monarchy, including sovereignty over the Canaries, the Eastern and Western Indies, those of Archduke of Austria, Duke of Burgundy, Brabant and Milan, and many others even more abstruse. Napoleon told him not to be so silly, and packed him off to Madrid the following day.
Joseph looked forward to his new role with confidence. In his two years on the throne of Naples he had proved himself a competent and generally popular king, displaying tact, behaving as a good Catholic and respecting local traditions. He had reformed the corrupt administration and modernised the army, cleared out gaols filled with people festering for forgotten crimes and suppressed much of the endemic banditry, eventually capturing the most notorious bandit, Fra Diavolo. He admitted that he had been naïve and idealistic in believing that people would respond well to reasonable and benign rule, and occasionally had to resort to firmness. But he did understand something Napoleon did not – that Naples could not be ruled as a colony.
Despite the apparent similarities, Spanish society and the Spanish political edifice differed fundamentally from those of Naples, and the cauldron of complex and contradictory hatreds had boiled over as a result of recent events inside and outside the country. The French military incursion had provoked resistance, to which the French responded with reprisals which in turn produced savage reactions, releasing a spiral of cruelty which spun out of control as the French razed villages and looted churches, and the inhabitants disembowelled or crucified French soldiers in retaliation.
The French Revolution, which had combined the destruction of the Catholic Church and religious persecution with that of the monarchy and the nobility, had branded all Frenchmen as enemies of Church and throne, while Napoleon's recent persecution of the Pope had turned him in the Spanish popular imagination into the Antichrist. Priests proclaimed that to kill a Frenchman was not a sin but a step on the path to heaven. Ferdinand on the other hand was miraculously transformed into a sacred symbol. Although he had not a drop of Spanish blood – of his sixteen great-great-grandparents, four were Bavarian, three French, two Polish, two Italian, one Austrian and the rest German (two of them Protestant) – he had become a national hero, _el Deseado_ , the Desired One.
Joseph's enthusiasm evaporated long before he reached Madrid. 'The fact is that there is not one Spaniard who is on my side apart from the small number of people who made up the junta and are travelling with me,' he wrote to his brother only three days after setting off from Bayonne. Even they began leaving him as he travelled on, and less than a week later he had to face the fact that 'I have not one single supporter here.' A couple of days later he made his solemn entry into Madrid: bells pealed and cannon saluted, but there was nobody in the streets or at the windows. 'I was not received by the inhabitants of this city as I was by those of Naples,' he reported.
In a succession of letters he assured his brother that they had been deluded, and that to pacify the country was an almost impossible task, given that he was facing an exasperated nation of twelve million people. He changed his approach, as in the circumstances 'kindness would appear as cowardice', and only overwhelming force could produce results, though he regarded it as 'a repulsive task'. He demanded an extra 150,000 troops and overall command of them – beginning with Murat, who had fallen ill with dismay at having been passed over, all the military commanders were ignoring him and acting independently of each other.
Napoleon made light of his brother's warnings. He had left Bayonne on 21 July after receiving reports of Bessières' rout of a Spanish army at Medina del Rioseco, confident in the effectiveness of French arms to deal with the situation. He made a stately progress, inspecting military units and attending receptions with the civil authorities as he went, and reached Bordeaux on 31 July. Joseph's literary pretensions had always annoyed him, and in his jeremiads he read only cowardice. He wrote back telling him the Spaniards were cowards, and he must show resolution and apply force. But his tone faltered after, on 2 August, he received news which profoundly shocked him.
A French force of 20,000 men under General Pierre Dupont was marching to relieve the remnants of the French fleet stranded at Cádiz after Trafalgar when it was itself encircled by a larger Spanish army under General Francisco Castaños at Bailén on 22 July. Dupont, whose mostly raw conscripts were suffering from severe shortages of food and supplies, capitulated on the promise that he and his men would be allowed to return to France with their arms and artillery. Once the act of capitulation had been signed, all but Dupont and a handful of senior officers were driven off as prisoners and treated with brutality.
The French setback gave heart to their enemies throughout the country, and on 31 July, after only twelve days in the capital, Joseph was obliged to evacuate it and fall back on Burgos. He wrote to Napoleon that he was not prepared to rule over a people who loathed him, and begged to be allowed to go back to Naples, arguing that Spain had become ungovernable. 'Your Majesty cannot have any idea, because nobody will have told him, to what extent the name of Your Majesty is reviled here,' he added for good measure. But Joseph had nowhere to go, as Napoleon had given his Neapolitan kingdom to Murat, who promptly declared himself Joachim-Napoleon, by the Grace of God King of Naples and Sicily. Two weeks later, Joseph wrote from Burgos giving his opinion that Spain could only be ruled 'by treating the Spaniards as they had treated the subjects of Montezuma', which would require 200,000 troops and 100,000 scaffolds 'to support the prince condemned to rule over them'.
Napoleon agreed, and on 5 August he directed half of the French troops still stationed in Germany to Spain, and sent Marshal Ney to take command. But the situation in the peninsula continued to deteriorate; in Portugal, Junot had attacked a newly landed British force under General Arthur Wellesley at Vimeiro on 21 August, only to be beaten and forced to capitulate. He was more fortunate than Dupont, and the terms of the capitulation were respected, his whole force being shipped back to France by the Royal Navy. With most of the peninsula cleared of French troops, Ferdinand VII was proclaimed king by a junta in Madrid.
Napoleon continued his tour of inspection, visiting the ports at Rochefort and La Rochelle, but he was in a bad mood. When, at Napoléon-Vendée, he discovered that his project supposed to revitalise a rundown village and transform it into an industrial town had barely got off the ground, he erupted. He had taken Bailén as an insult to French arms, and by extension to himself. When Mathieu Dumas reported to him at Saint-Cloud, he fumed at what he termed the cowardice of Dupont and, seizing Dumas's uniform by the facings, shook him, saying with concentrated rage that the French uniform would have to be washed in blood. He had determined to do that himself, but before he could send all available troops to Spain to drown it in blood, he had to parry a looming threat from another quarter.
## 32
# The Emperor of the East
On the day following his return to Paris, 15 August 1808, Napoleon held the customary audience for the diplomatic corps to receive their good wishes on his birthday. In the absence of a papal nuncio, the diplomats were headed by the handsome and urbane Austrian ambassador Count Metternich, who, in the interests of intelligence-gathering, was having an affair with Napoleon's sister Caroline, the new queen of Naples, having already consulted several other ladies in the same manner. Napoleon took him to task for over an hour on a quite different matter – that of recent Austrian armaments which had come to his notice. The Emperor Francis was also dragging his feet in recognising Joseph as King of Spain.
The harsh terms imposed after Austerlitz had left Austria smarting, while anti-French feeling had been growing throughout Germany, stimulated by a wave of nationalist literature and a folkloric revival, as well as French exactions and the arrogance of French officials; even within the Confederation of the Rhine Napoleon's high-handed treatment of his allies generated resentment. News of Bailén gave heart to all those who longed for revenge, and many felt it was time to rebel against French domination. Austria had been rearming in anticipation of war with France, assuming the rest of Germany would rise up and join it.
In the circumstances, Napoleon could not afford to denude Germany and the Grand Duchy of Warsaw of troops in order to send them to Spain unless he could cover his back, and the only way of doing that was to call on his ally Russia. Yet her reliability was open to question; his ambassador in St Petersburg, Caulaincourt, warned him that the Tilsit settlement was unpopular in Russia, being associated in the public mind with the defeats of Austerlitz, Eylau and Friedland, and the blockade was having a damaging effect on the economy.
Napoleon's inability to see things from another's perspective helped him ignore this and other warnings, as did his tendency to believe he could obtain results by dint of trying. When Alexander's ambassador was due in Paris after Tilsit, Napoleon bought Murat's sumptuous residence – pictures, furniture, silver, china, bedding and all – to provide him with a comfortable embassy, and went out of his way to honour him. But the ambassador, Count Tolstoy, remained aloof and barely concealed his dislike of Napoleon. In an attempt to revive Alexander's enthusiasm for the alliance, Napoleon had earlier that year returned to the subject of a joint expedition against the British in India, with the accompanying promise of an extension of the Russian empire in the east. Caulaincourt and the Russian foreign minister, Count Nikolai Rumiantsev, duly pored over maps, and General Gardanne calculated marching distances through Aleppo, Baghdad, Herat, Kabul and Peshawar. But while Napoleon never ceased dreaming of India, he had no intention of embarking on the venture, as Alexander probably realised.
Before parting at Tilsit, they had agreed to meet again the following year, and this encounter was to take place at Erfurt in Westphalia at the end of September 1808. Napoleon hoped that by deploying his usual mixture of charm and implied threat he would be able to reassert his ascendancy over the tsar. The meeting would also provide the opportunity to propose a dynastic marriage; such a union would kill two birds with one stone, as it would cement the alliance and at the same time provide Napoleon with an heir, which had become a pressing issue once again. The question had resurfaced when, on 5 May 1807, his nephew and adopted son Napoléon-Charles, the child of Louis and Hortense, died of croup. Now that he knew he could sire a child himself, many in his entourage, including Fouché and Talleyrand, urged him to divorce Josephine and marry a woman of childbearing age.
One day in November 1807, with the court at Fontainebleau, Fouché had called on Josephine in her apartment and suggested she go before the Senate and request a divorce in the interests of the empire. He even produced a prepared text of the speech she should make. She asked him whether he had been sent by Napoleon, which he denied, so she dismissed him, saying she would do only what her husband asked of her. When she informed him of Fouché's visit Napoleon made a show of rebuking his minister, though it seems unlikely Fouché would have acted without his knowledge. He also reprimanded him when he read a police report which mentioned that people were discussing the divorce as though it had been agreed. To Josephine it seemed as though it had. 'What sadness thrones bring!' she wrote to her son, foreseeing the inevitable.
Alexander had two unmarried sisters, and Napoleon did not see any reason why he should not embrace the idea if he could put it to him directly. 'An hour together will suffice, while the negotiations would last several months if it were left to the diplomats,' he said to Cambacérès as he left Paris. He had ordered Erfurt to be cleaned up, its buildings repainted and its streets lit, and he had sent out tapestries, pictures and china to adorn his apartments there. He had also arranged for the best actors and the prettiest actresses of Paris to be sent out to entertain the company in the evenings, and, if possible, to find their way into Alexander's bed.
To impress Alexander and lend weight to their meeting, he had also invited all the rulers of the Confederation of the Rhine and the King of Saxony. He had carefully selected the plays to be performed. According to Talleyrand, by staging heroic scenes he meant to disorient the ancient royals and aristocrats present and 'transport them in their imagination into other realms, where they would see men who were great by their deeds, exceptional by their actions, creating their own dynasty and drawing their origin from the gods'. The themes of immortality, glory, valour and predestination which recur in the plays he chose were meant to inspire admiration in all who approached him, and Corneille's _Cinna_ delivered the punchline in the phrase 'He who succeeds cannot be wrong.' Voltaire's _Mahomet_ treats of the need for a new faith and a new master of the world; its protagonist owes everything to his own qualities, and nothing to ancestry. Napoleon did not bring Josephine or a numerous suite, but as Talleyrand had been at Tilsit and was a good courtier who knew everyone in Europe, he brought him along. This turned out to be a mistake.
When Alexander announced his intention of going to Erfurt, most of his entourage expressed fears that he would allow himself to be cajoled by Napoleon into further engagements unfavourable to Russia, and even, given recent events at Bayonne, that he might never come back. In reply to his mother, who had written begging him not to go, he explained that despite the setbacks at Bailén and Vimeiro, Napoleon was still strong enough to defeat any power that defied him. Russia must build up her military potential while pretending to remain his ally. He must go to Erfurt to persuade Napoleon of his goodwill, and his presence there should send a signal to Austria not to try anything rash before time. To his sister Catherine, who had also implored him to have nothing to do with the Corsican ogre, he replied more succinctly: 'Napoleon thinks that I'm just a fool, but he who laughs last laughs longest.'
As soon as he heard that Alexander had set out, Napoleon left Paris, arriving at Erfurt on the morning of 27 September, and after dealing with some administrative business he called on the King of Saxony, who had preceded him. At two o'clock, having been alerted to Alexander's approach, he rode out to meet him outside the town. On seeing him ride up, Alexander alighted from his carriage and the two emperors embraced, after which they mounted up and rode into the town, greeted with full military honours, and spent the rest of the day together, only parting at ten that night.
Napoleon hoped to recreate what he called 'the spirit of Tilsit', having his troops parade before Alexander and spending hours in conversation with him on every subject that could flatter his vanity, while displaying his power over the other assembled sovereigns by ordering them about and telling them where to sit at table – 'King of Bavaria, keep quiet!' he snapped at one point.
As Alexander was hard of hearing in one ear, Napoleon had a dais built for the two of them close by the stage at the theatre. This meant that, as Talleyrand remarked, 'People listened to the actors, but it was him they were looking at.' During one performance, at the lines 'To the name of conqueror and triumphant victor, He wishes to join that of pacifier,' Napoleon made a show of emotion noticed by all. When, during a performance of Voltaire's tragedy _Oedipe_ , the actor spoke the line 'The friendship of a great man is a gift from the gods,' Alexander stood up and took Napoleon's hand in a gesture meant for the audience.
Napoleon acted the charming host one moment, running down the stairs to greet Alexander as he arrived for dinner, and putting him in his place the next. He arranged an excursion to the nearby battlefield of Jena, where, as one military man to another, he explained the battle to him, no doubt meaning to remind him of his own military prowess. He invited Alexander to a parade in the course of which he decorated soldiers with the Legion of Honour; since each man called forward had to give an account of his heroic exploit, and these had all taken place at Friedland against the Russians, the tsar was openly humiliated by having to listen to stories of his troops being beaten. Napoleon had even in the course of a discussion resorted to staging one of his rages, throwing his hat on the floor and stamping on it.
On 6 October there was a hunting party in the forest of Ettersberg, for which stags were driven into a funnel of canvas screens so that by the time they reached the hunters they were disoriented, and so close that even the inexperienced Alexander with his poor eyesight managed to bag one trotting past eight feet from him. The hunt was followed by a dinner, a short concert, a play and a ball. Napoleon did not dance because, as he put it in a letter to Josephine, 'forty years are forty years'. Instead, he had a two-hour discussion about German literature with the poet Wieland, whom he had invited for the purpose, showing off his knowledge to the surprised and flattered German literary men listening to him. He then walked over to Goethe and had a long conversation with him. One can but admire his stamina, given that all the while he was manipulating the various rulers of the Confederation of the Rhine, each of whom had to be cajoled and bullied by turns, running the government of France, and overseeing operations in Spain, not to mention fighting a severe cold. Goethe, with whom he had a long meeting over breakfast on 1 October, was overwhelmed by the power he sensed in Napoleon's gaze, and fascinated by his seemingly superhuman qualities.
One day, when Alexander had forgotten his sword, Napoleon handed him his own, at which Alexander declared, 'I accept it as a mark of your friendship, and Your Majesty may be quite sure that I shall never draw it against you.' He did not, as Napoleon had hoped, promise to draw it against Austria if she were to attack while he was occupied in Spain. Alexander adopted an attitude of stubborn neutrality, refusing nothing and promising nothing. Napoleon's position was identical, since he wanted to oblige Alexander to bind himself further while offering nothing in exchange, except for a vague promise to withdraw French troops from the Grand Duchy of Warsaw and Prussia and, in return for the tsar's acceptance of his doings in Spain, to allow his annexation of Finland. The lack of any mutual interest in their alliance was glaring. Yet it was crucial to Napoleon, not only to keep Austria in check, but also to maintain the blockade against Britain, which was beginning to take effect.
It was impossible to exclude British goods from the Continent entirely. Even while paying lip service, Russia had been contravening the terms of the blockade by allowing some neutral ships into its ports. British merchants had established entrepots at Heligoland, from where small ships could dart into creeks or minor harbours all over northern Europe, and at Malta, to do the same in the Mediterranean. British ships also defied the blockade by putting into the Austrian port of Trieste, from where their merchandise could reach Central Europe. There was plenty of clandestine trade, and there were even cases of French merchants from Bordeaux supplying the British forces in Portugal with wine and brandy. In Hamburg, the city authorities were surprised at a curious rise in the number of funerals, only to discover that coffins were being used to transport smuggled coffee and indigo – from which Bourrienne, now a commissioner there, was taking a cut. Even Napoleon's family flouted the blockade, Louis in Holland almost blatantly, Jérôme in Westphalia passing on goods, and Josephine buying smuggled silks and brocades. Cambacérès actually ordered the chief administrator of the Grand Duchy of Berg, Jacques-Claude Beugnot, to send him cured hams by clandestine means in order to avoid paying customs duties aimed to back up the blockade. On the march back from Germany following Tilsit, Captain Boulart of the Guard Artillery and his fellow officers and men happily bought quantities of English merchandise in Frankfurt and Hanover which they smuggled into France in their ammunition wagons, which they would not allow the customs officials at Mainz to inspect, arguing that the falling snow would soak the powder.
Nevertheless, by the first months of 1808 the blockade was having a crippling effect on the British economy, and, crucially, threatened to impinge on the political situation. Imports of much-needed cereals had plummeted by a staggering 93 per cent, and Napoleon calculated that if the pressure could be kept up, the country would not be able to feed itself and there would be bread riots which would force the government to its knees. He was therefore desperate to keep Russia within the system, and with Alexander visibly cooling the surest means of doing that seemed a dynastic alliance. The subject was broached, and the tsar gave all the appropriate signs of delight, but declared he had to obtain the assent of his mother before he could give a definite answer. He had no intention of going along with the idea, as he had already resolved to undermine Napoleon.
On the day after his arrival at Erfurt, Talleyrand had found a note from Princess Thurn und Taxis, a sister of the queen of Prussia, inviting him to take tea with her. There he met Alexander, who had set up the meeting. The two met there several times over the next few days, having quickly entered into an understanding – Talleyrand told Alexander that he was the only civilised ruler capable of saving Europe and France from Napoleon, and declared himself ready to serve him in this cause. Whether it was mentioned then or not, the service would not come free of charge.
On his return to Paris, Talleyrand would remain in touch through the secretary of the Russian embassy, Karl von Nesselrode. He was already in secret contact with the Austrian ambassador Metternich, who summed up Talleyrand's position thus: 'The interest of France herself demands that the powers capable of standing up to Napoleon must unite to oppose a dyke to his insatiable ambition, that the cause of Napoleon is no longer that of France, that Europe itself can only be saved through the closest possible alliance of Austria and Russia.'
'I am very satisfied with Alexander, and he must be with me,' Napoleon wrote to Josephine on 11 October, convinced that he had seduced the tsar. The following day they signed an agreement reaffirming their alliance, as well as a joint letter to George III professing their wish to make peace and appealing to him to enter into negotiations. Three days later, they rode out of Erfurt together to the spot on which they had met two weeks before, embraced and took their leave of each other. Napoleon then rode back, slowly, into town, apparently deep in thought. He had plenty to reflect on.
He had come to Erfurt to consolidate the alliance forged at Tilsit, only to see cracks developing in it. He had held court, surrounded by cringing monarchs, but, as he once confessed to his interior minister Chaptal, he felt they all despised him for his low birth and would gladly topple him from his throne. 'I can only maintain myself on it by force; I can only accustom them to see me as their equal by keeping them under my yoke; my empire is destroyed if I cease to be feared.' He was aware that the higher he rose the greater his vulnerability. It is tempting to think that the reason he was drawn to Alexander, the most unlikely and inconvenient ally for him, was that he sensed the tsar's insecurities and did not feel such a parvenu in his company. However much he may have boasted about them, Napoleon lacked faith in the value of his own achievements. 'Military glory, which lives so long in history, is that which is most quickly forgotten among contemporaries,' he admitted to one of Josephine's ladies. He also feared that his state-building and other achievements would not survive. Josephine remonstrated with him, maintaining that his genius gave him his title to greatness, to no avail. He was, according to Rapp, lamentably obsessed with what the aristocratic milieu of the Faubourg Saint-Germain thought of him, and ridiculously susceptible to gossip. It is ironic that while, as Talleyrand had noted, he used the theatre to drive home the message to the mostly idle and ineffectual sovereigns that he stood above them as the man of action, he lacked confidence in his own achievements and felt the need to adorn them with the trappings of royalty. 'Simplicity does not suit a parvenu soldier such as myself as it does a hereditary sovereign,' he said to one Polish lady.
To Chaptal, he complained that it was only ancient dynasties that could count on unconditional popular support, and while a hereditary monarch could lie around being dissolute, he could not afford to, as 'there is not one general who does not believe he has the same right to the throne as me', which was patently not true. Mollien was struck by 'his insatiable need to be the centre of everything', which he believed to be dictated by 'the fear lest any particle of power escape him'. He also noticed in Napoleon an obsessive need 'to represent himself as the only essential man, to establish in the public perception an exclusive superiority, to belittle anything that might threaten to share it', and he was convinced this was the result not of calculation, but of a kind of instinctive reaction – which suggests deep psychological insecurities. 'Don't you see,' Napoleon used to say to members of his family, 'that I was not born on the throne, that I have to maintain myself on it in the same way I ascended to it, with glory, that it has to keep growing, that an individual who becomes a sovereign, like me, cannot stop, that he has to keep climbing, and that he is lost if he remains still.' He could certainly not afford to remain still now.
The day following his arrival at Erfurt, he had received a special envoy from the Emperor Francis, General de Vincent. Although the audience had been courteous, with declarations of goodwill on both sides, it was obvious from Vincent's tone and the Austrian armaments that Vienna was preparing for war. Napoleon could not conceive that Francis would be foolish enough to make war on his own, and this led him to suspect the existence of a secret agreement between him and Alexander.
This made it all the more imperative to pacify Spain as quickly as possible. He was back at Saint-Cloud at eleven o'clock on the night of 18 October. On 22 October he visited the Salon (the painters who wished to submit had been given to understand that it would be desirable to show Napoleon visiting the battlefield of Eylau and casting a 'consoling eye' over it which would 'soften the horror of death'; the winner, Antoine Gros, evidently achieved this, having managed to 'give Napoleon an aura of kindness and majestic splendour'). In the course of the next few days he opened the session of the Legislative, held receptions, inspected public works, orphanages and hospices before leaving on 29 October. Travelling day and night, stopping only to dine briefly and meet officials along the way, sometimes taking to his horse, by 3 November he was at Bayonne, where in a letter to Joseph he admitted that he was 'a little tired'. That did not stop him sitting up all night with Berthier dictating orders. By the evening of the next day he was in Tolosa, where he delivered a tirade to a group of monks, telling them that if they meddled in politics he would cut their ears off, which, not knowing French they could only judge the gist of by his tone. Much the same was true when, at Vitoria two days later, Joseph presented his ministers to him; he harangued them in a mixture of Italian and French, accusing them of incompetence and their clergy of being in the pay of the British, and poured scorn on the Spanish army. He declared that he would pacify the whole country in the space of two months and treat it like conquered territory.
He took command of the Army of Spain, consisting of some 200,000 men spread across the country. While Marshal Soult on his right wing pushed back a British force of 40,000 under Sir John Moore, and on his left Lannes drove General Castaños back to Saragossa, Napoleon made for Madrid. On 12 November he reached Burgos, which had just been captured and was being put to the sack. One of his aides, Ségur, had been sent ahead, and selected the residence of the archbishop as the most suitable for his quarters. He was closely followed by Napoleon, accompanied only by Savary and Roustam. They went off in search of food and drink while Ségur lit a fire. Napoleon told him to open a window, and when Ségur pulled back the heavy curtains he was confronted by three Spanish soldiers, still fully armed, who had taken refuge there and now pleaded for their lives. Napoleon laughed at the danger he had run.
He spent ten days in Burgos inspecting troops and then pressed on, forcing strong Spanish positions at the pass of Somosierra on 30 November, and arrived before Madrid two days later. He ordered the attack for the next day, and on 4 December the city surrendered. Napoleon took up residence in a country house at Chamartin outside the city, leaving that to his brother to repossess. From the moment he had joined Joseph at Vitoria he had ignored him, and Joseph was reduced to following in the wake of the army. He complained, with some reason, that this undermined his authority in a country which was difficult enough to rule as it was, and on 8 December wrote to Napoleon renouncing his rights to the throne of Spain.
Napoleon did not reply for ten days, when he sent him a short note concerning finances, and a few days later a flurry of instructions through Berthier. He found time to write to Josephine frequently, mainly short affectionate notes assuring her that he was well, that his affairs were going splendidly and that she should not worry. In one, he discussed the wisdom of Hortense dismissing members of her domestic staff. He wrote to Fouché saying the Spaniards were not 'wicked' and the British only a minor irritant. He had a young virgin procured for himself, but according to his valet Constant she wore too much scent for his keen sense of smell, so he sent her away untouched – having paid her.
He issued decrees and orders for the administration of the kingdom as though Joseph did not exist, abolishing feudalism and the Inquisition, closing down convents and confiscating as much property as he could to pay for his campaign. He also attended to the administration of the empire, going into details and checking figures, and specifying, for instance, what quantities of quinine should be distributed to the health services of each of the empire's forty-two major cities.
He reviewed the main body of his army, and on 22 December set off to confront Moore, hoping to at last have an opportunity of fighting his British enemy in the field. 'The weather is fine, my health is perfect, do not fret,' he wrote to Josephine before leaving. The weather changed dramatically not long after he set off, and his march over the Sierra de Guadarrama in sleet and snow proved an ordeal for the troops, which not only grumbled but in some cases actually showed their feelings by shooting at him as he passed. He thought it best to ignore the incidents and pressed on, hoping that a battle would restore morale.
Moore retreated, making for the port of La Coruña, where the Royal Navy could evacuate his force, with Napoleon in pursuit. But on the evening of 1 January 1809, halfway between Benavente and Astorga, Napoleon was informed that an _estafette_ from Paris was trying to reach him, so he stopped and waited by the roadside until it arrived. When he had read the despatches, his mood grew sombre and he proceeded to Astorga in silence. Those around him noted with surprise that the urge to catch up with Moore at all costs had left him. After spending a day at Astorga and handing over command to Soult, he went back to Benavente and thence to Valladolid. The despatches confirmed that Austrian rearmament was proceeding fast, but that was not what troubled him.
He was aware that there was much discontent in France. At Bayonne in June he had been notified of an inept conspiracy involving a General Malet which had been uncovered and the plotters imprisoned. Bailén had emboldened his critics in the Senate and the Legislative, but he knew he only had to crack the whip to silence them. A slip made by Josephine while receiving a delegation of the Legislative, addressing them as the representatives of the nation, had annoyed him, but it had also given him his cue; he gave instructions for _Le Moniteur_ to carry a notice explaining that her speech must have been wrongly reported, since she was too well-versed not to know that 'In the order of our constitutional hierarchy, the prime representative of the nation is the emperor, and the ministers, who are organs of his decisions.' Now he was informed of what looked like an altogether more sinister machination – by two of his closest associates.
During a reception given by Talleyrand on 20 December, just as the guests had assembled, the usher announced the minister of police. It was no secret that Talleyrand and Fouché loathed each other and were seen under the same roof only when official functions required it, yet here was Talleyrand eagerly hobbling forward to greet the new arrival and then taking him, arm in arm, through the reception rooms for all to see, deep in conversation. News that two of the most consummate practitioners of the political pirouette had combined flew round Paris, and reached the emperor at Astorga.
What also reached him, thanks to postal intercepts by Lavalette, was an idea of what they were up to. With alarming reports of the exceptionally savage nature of the war in Spain reaching Paris, the possibility of Napoleon being killed had resurfaced, and this had drawn together the two men most concerned at the possible consequences for themselves. Both had for some time been in close touch with his sister Caroline, and were now preparing a contingency plan to put Murat on the throne if Napoleon were killed. Lavalette had passed the incriminating letters from Murat on to Napoleon.
His exasperation showed. When he heard soldiers of the Old Guard grumbling about conditions in Spain, he made a scene on parade, accusing them of laziness and of just wanting to get back to their whores in Paris. All officers passing through the town were obliged to call on him, and when one day General Legendre, who had been Dupont's chief of staff and signed the capitulation of Bailén, presented himself, he vented his fury on the man. He accused him of cowardice, of having defiled the honour of France, called the capitulation a crime as well as a crass show of ineptitude, and said the hand with which he had signed it should have withered. In a letter to Josephine on 9 January he urged her not to fret, but to be prepared to see him appear unexpectedly at any moment. A week later he raced back to Paris, at one stage covering 120 kilometres on horseback in five hours.
He reached Paris at eight o'clock on the morning of 23 January. That afternoon he visited the works on the Louvre and the rue de Rivoli, over the following days he received the diplomatic corps, went to the opera and, on 27 January, wrote to Talleyrand instructing him to hand his key of grand chamberlain over to Duroc. Talleyrand complied, and wrote Napoleon a letter brimming with sweetness and submission, expressing the extreme pain with which he had done so: 'My only consolation is to remain tied to Your Majesty by two sentiments which no amount of pain could overcome or weaken, by a feeling of gratitude and of devotion which will end only with my life.'
29 January was a Sunday, and after the usual parade, Napoleon held a privy council attended by Cambacérès, Lebrun, Gaudin, Fouché, Admiral Decrès and Talleyrand. Towards the end of the meeting he suddenly grew agitated and, turning to Talleyrand, who was leaning against a console, unleashed his fury. 'You're a thief, a coward, a faithless, godless creature; you have throughout your life failed in all your duties, you have deceived and betrayed everyone; nothing is sacred to you; you would sell your own father,' he ranted, pacing the room while Talleyrand remained perfectly still in his nonchalant pose, 'pale as death' according to one witness, his eyes half-closed. 'You, sir, are nothing but a pile of shit in silk stockings!' Napoleon concluded. Although he remained superciliously calm as he left the room, Talleyrand said quietly to grand master of ceremonies Ségur, who was just entering, 'There are some things one can never forgive.' And later he added, 'What a shame that such a great man should be so ill-bred.' He informed Metternich that he now felt free to act in the common cause. No doubt not wishing to give the impression of instability, Napoleon left Talleyrand with his rank of vice-grand elector. He did not penalise Fouché, whom he still needed, particularly as it was by now certain that he would have to go to war.
This was a war for which neither Napoleon nor France had any appetite. It also elicited little enthusiasm outside Austria, which was getting nowhere in its search for allies. Russia was opposed to it and Prussia fearful, as were most of the German states, however much they may have resented French dominance. Even Britain was only prepared to come up with a meagre subsidy. But Austria was eager to wipe out its humiliations of Ulm and Austerlitz. And despite the lack of interest in Germany, for the first time in its history the Habsburg monarchy was going to play the German national card. A powerful influence was the Emperor Francis's third wife, Maria Ludovica, a German nationalist with a hatred of all things French, whom he had married in January 1808. Another was the chief minister, Count Johann Philipp Stadion, who encouraged nationalist propaganda through the press and government-sponsored pamphlets, in which the coming war was represented as one of liberation and parallels were drawn with that raging in Spain.
The thirty-seven-year-old Archduke Charles had been reorganising the army, introducing conscription and giving it a more national character. In March 1809 he appointed the nationalist writer Friedrich Schlegel as his military secretary. His brother Archduke John also struck a national note, declaring himself to be 'German, heart and soul'. By the spring of 1809 Austria had mustered around 300,000 men. A force of 30,000 was deployed in Galicia under Archduke Ferdinand to check the Polish forces in the Grand Duchy of Warsaw and deter the Russians from supporting their French allies. Another 50,000 under Archduke John were poised to stop a French move out of Italy. The main army of nearly 200,000 under Archduke Charles invaded France's ally Bavaria on 10 April and entered Munich. This coincided with a planned insurrection in the Tyrol led by the partisan Andreas Hofer which forced the French and Bavarian troops stationed there to capitulate. The Austrian advance was accompanied by an appeal to the people of Germany to rise. It was answered by a Prussian officer, Major Schill, who led his regiment out to attack Westphalia, and by the Hessian Colonel Dornberg, an officer in Westphalian service who sallied forth at the head of 6,000 men to raise a general rebellion. With his main forces tied down in Spain, Napoleon could only muster 100,000 French troops, along with a total of 150,000 less reliable and certainly less motivated men supplied by his various allies. As soon as news came on the telegraph that the Austrians had invaded Bavaria, he went into action.
Although he still moved fast, travelling at all hours of the day and night, Napoleon had introduced a modicum of comfort into his campaigning, as his age no longer permitted subjecting himself to the rigours of sleeping out in all weathers and going without food. His travelling carriage was equipped with every comfort, and he kept adding resources. He loved _nécessaires_ of one sort or another, cases containing every conceivable utensil required for their purpose, be it washing or writing. He was followed or preceded by fourteen wagons and a train of mules bearing a set of five tents of blue-and-white-striped ticking – two of them, his bedroom and study, private; the other three also used by his staff. The wagons also carried everything else he might need, from spare uniforms and linen to dining silver and a supply of Chambertin. Closer to hand, one of his pages carried a telescope and another maps, which Napoleon would spread out on a table, or sometimes on the ground, and lie down on it, pincushion in hand, then stand up, surveying the picture and dictating orders briskly. His Mameluke was always in attendance, as was a small group of orderlies, _officiers d'ordonnance_ , some of them civilians, dressed originally in green and later pale-blue uniforms. Not far behind was a supply of spare horses, mostly Arabs. He was always escorted by a couple of dozen mounted chasseurs or chevau-légers of the Guard, while Berthier and the general staff were escorted by his own guards from his principality of Neuchâtel, uniformed in bright Serin yellow. Napoleon always seemed at his happiest when on campaign, spending much of the day in the saddle, surrounded by his staff and cheered by his troops, whom he would stop and talk to. The exercise invigorated him, and his high spirits were contagious. When he paused for something to eat, a picnic would be deftly spread out by his _maison militaire_ and all would share. 'It was really a party for all of us,' recalled his prefect of the palace Bausset.
In a series of three engagements between 19 and 21 April he tried to encircle part of the Austrian army, eventually scoring successes at Eckmühl and Ratisbon (Regensburg). He would later claim that Eckmühl was one of his finest manoeuvres, but these were not the victories he had been used to. The Austrians had learned to move and fight well, and retreated in good order. Riding over the battlefields, Napoleon was unpleasantly struck by the carnage involved in achieving victory. He had himself been lightly wounded in the foot by a spent musketball at Ratisbon. In his proclamation issued after the battle, he praised his troops for having once more demonstrated 'the contrast between the soldiers of Caesar and the rabble of Xerxes', and listed fictitious numbers of guns, standards and prisoners taken. To Cambacérès he wrote that it had been a finer victory than Jena. Few were fooled. Cambacérès replied that everyone was delighted by the news of the victories. 'Yet, Sire, in the middle of the general happiness your people are greatly alarmed at the dangers to which you expose yourself,' he wrote on 3 May.
Napoleon's attempts to outflank and cut off the retreating Archduke Charles came to nothing, and although he reached Vienna on 11 May and took up residence at Schönbrunn once more, he had little to rejoice over. His army had been bloodied and it had underperformed, largely because his seasoned troops and some of his best commanders, such as Ney and Soult, were in Spain, while Murat was in Naples. This time he had had to make a show of bombarding the city before Vienna opened its gates; the inhabitants nevertheless showed their admiration for him by cheering as he rode up to the walls. Archduke Charles had regrouped on the north bank of the Danube, and getting the French army across was not going to be easy.
Napoleon chose the stretch where the Danube divides into two narrower streams around the large island of Lobau, and on 19 May his engineers began building pontoon bridges. The following afternoon he was on Lobau, and began moving his troops across the second branch of the river. By the morning of 21 May some 25,000 to 30,000 had made it across and taken up positions in the villages of Aspern and Essling, facing about 90,000 Austrians. At this point the Austrians destroyed his bridges by floating heavily loaded barges down the river, which was in spate. The engineers struggled to repair them, but with more heavy objects being floated downriver Napoleon's army was stranded in three places, while Archduke Charles seized his chance and opened up on the French positions with heavy artillery. Fierce fighting developed as he tried to get between Masséna's corps at Aspern and the river, while Napoleon himself clung on at Essling. With the bridges repaired more men got across, bringing French numbers up to around 60,000 on the morning of 22 May. Napoleon launched an attack which was returned, and the two villages changed hands several times. Although the French had held their ground, the bridges at his back had been set alight by incendiary barges, preventing reinforcements from coming up, so at nightfall Napoleon pulled all his forces back onto the island. Both sides claimed victory, the Austrians naming it Aspern and the French Essling, but there was little to celebrate on either side. Losses had been heavy – more than 20,000 Austrians and upwards of 15,000 French.
A harrowing personal loss for Napoleon was that of Marshal Lannes, who had both legs crushed by a cannonball. Larrey amputated in an attempt to save his life, and the physicians struggled to keep him alive. Napoleon visited him every evening, but Lannes had been badly concussed. 'My friend, don't you recognise me?' Napoleon allegedly asked. 'It's your friend Bonaparte.' He died on 31 May. On hearing the news Napoleon hurried over and embraced the lifeless body. He was in tears, and had to be dragged away by Duroc. Lannes had been one of his closest and, according to Fouché, the only one of Napoleon's friends who was still able to tell him the truth. He ordered the body to be embalmed and taken back to France.
Napoleon was cheered by the news from the south, where Eugène had forced the Austrians out of Italy, and General Étienne Macdonald had ousted them from Dalmatia. He turned the island of Lobau into a fortress and a launchpad for his next offensive, and spent most of June bringing up reinforcements. He would go there nearly every day and often, donning a soldier's overcoat and carrying a musket, venture out to observe enemy positions. On 14 June Eugène and Macdonald defeated Archduke John at Raab and joined forces with Napoleon, giving him a comfortable superiority over Archduke Charles. On the night of 4 July, in a violent thunderstorm Napoleon began crossing to the north bank of the Danube.
## 33
# The Cost of Power
On the morning of 5 July 1809 a powerful artillery barrage opened what was to be the largest and longest-lasting battle Napoleon had fought. Over the next two days his forces, totalling nearly 190,000 men drawn from all over Europe, supported by more than 500 guns, fought it out with an Austrian army of up to 170,000 with 450 pieces of ordnance in what was more a battle of attrition than his usual decisive manoeuvre.
While the bombardment of their defences at Enzersdorf distracted the Austrians, the French army turned their left wing, forcing them to fall back on the village of Wagram. Archduke Charles managed to repel an attempt by Masséna's corps to outflank him on his right – helped by the fact that following a bad fall from his horse the day before, Masséna was commanding from a reclining position in his carriage. French attacks by Bernadotte, Eugène and Davout ground to a standstill in fierce fighting at close quarters which continued late into the evening and only died down at around eleven, when Bernadotte and then the others fell back.
Late that evening Napoleon conferred with Berthier, Davout, Oudinot and others, preparing a plan for the next day. The nature of war had changed, and so had his style; it was a far cry from the days of his first Italian campaign, when he told Costa de Beauregard that a council of war was a coward's resource. He went to bed in his tent at one o'clock in the morning, and rose at four. At five he was in the saddle, astride a fine grey called Cyrus on which he would cover almost the whole ten-kilometre stretch of the battlefield, often within range of enemy guns, which took a heavy toll on his staff. As one of his aides lifted his hat, which was the form on receiving an order, it was blown away by a cannonball, causing Napoleon to smile and say, 'It's lucky you're not taller.'
While Archduke Charles made a bold attempt to encircle Masséna, still in his carriage, on the French left, Napoleon ordered Davout to turn his left wing, while he himself launched a massed attack on his centre at Wagram. Ineptly led by Bernadotte, after having triumphed over stiff resistance the Saxon corps, which had led the attack, fell back, and all the advantage gained was lost. After exchanging vigorous words with Bernadotte (whom he later said he ought to have had shot for cowardice, but now just ordered back to Paris), Napoleon reorganised his forces. He combined a massive cavalry attack led by Bessières with a second assault on the Austrian centre, preceded by a heavy barrage, with the French artillery bringing over a hundred guns up to within a few hundred metres of the Austrian lines and pounding them at short range.
When he saw the attack drive home, Napoleon lay down on the grass to sleep for an hour, undisturbed by the thunder of nearly a thousand cannon. The exertions of the past two days were telling on his health, and he had what he called 'an overflow of bile' that evening. He was better in the morning. 'My enemies are undone, beaten and fleeing in complete disorder,' he wrote to Josephine. 'They were very numerous, but I crushed them.'
This was nonsense; the Austrians may have been defeated, but they withdrew in relatively good order, with most of their artillery. Assessments of the losses differ widely, but they were heavy both in men and horses, and greater on the French side. Although the French took as many as 15,000 prisoners, the Austrians lost fewer flags and cannon, and the battle had been neither tactically masterful nor decisive. Yet Napoleon's Bulletin claimed exactly that, and described the Austrian retreat as a 'rout', which it was not, since the French were too exhausted to pursue the advantage. When they did, two days later, they caught up with the Austrians at Znaïm, where after an inconclusive engagement on 11 July the Austrians proposed an armistice. Dismissing the wishes of his entourage, who were keen to finish them off decisively, Napoleon agreed to it, saying too much blood had been spilt already; he had been shocked by the heavy casualties incurred by both sides in the course of the campaign.
That was not his only worry as he returned to Schönbrunn on 13 July. Whatever he wrote in his Bulletins, he could see for himself that none of the battles he had fought over the past three months were in any sense decisive. Others could see it too. Even though it had earned him his marshal's baton, Marmont called Wagram 'a victory without consequence'. 'The days when swarms of prisoners would fall into our hands, as in Italy, at Ulm, at Austerlitz, at Jena, were past,' he reflected. In those days, when they encountered the lightning-bold tactics of the still young Napoleon and the dash of the French soldier fledged in the ranks of the Revolution, the Austrian or Prussian commanders and soldiers did not know what had hit them and threw up their hands in a natural reflex. But much had changed since then. It was not just that Napoleon and his generals had grown older, though that was certainly a factor.
Although Austria was obliged to sue for peace, Germany was by no means subdued. The indecisive nature of the battle of Aspern-Essling had reverberated through Europe in much the same way as news of Bailén the previous year, further denting the myth of Napoleon's invincibility. It had encouraged the Duke of Brunswick-Oels, whose father had been vanquished at Auerstadt, to march out in June at the head of his 'Black Legion of Vengeance' of 2,000 men raised with money from the Austrian government. He had joined up with a force of 5,000 Austrians and marched on Dresden and Leipzig before being seen off by Jérôme's Westphalians. The rising in the Tyrol had also revived at the news, forcing Napoleon to send Marshal Lefèbvre to pacify the area, but this only inflamed local feeling and fuelled a _guerrilla_ which would take time to put down.
Perceptions of Napoleon had shifted dramatically. From having been widely viewed as a liberator and a friend of the oppressed, he was now coming to be seen as the oppressor. The failure of his attempt to play the national card by calling on the Hungarians to rise up against the Austrians was eloquent evidence of this. They had good reason not to trust him: in order not to ruffle Russian sensibilities, he let down his own party in Poland. Commanded by the nephew of the country's last king, Prince Joseph Poniatowski, the army of the Grand Duchy of Warsaw had, after an initial defeat by Archduke Ferdinand, beaten the Austrians back and occupied most of their Polish province of Galicia. Instead of letting the Poles add it to the territory of the Grand Duchy, Napoleon ceded half of it to Russia, which had barely pretended to support him against Austria. He thereby forfeited the support of a large part of a nation prepared to be his most devoted ally.
The young Buonaparte, who had lived to hate the oppressor of his nation and dreamed only of liberating it, had grown out of his island patriotism and espoused the cause of a France that had embraced the progressive values of the day and offered greater promise to his people. Bearing the standard of that France, he had shattered the chains of feudalism and overthrown tyranny in northern Italy and subsequently bestowed the benefits of rational administration there and in western Germany, earning the gratitude and even love of millions. But a growing cynicism had led him to sacrifice the aspirations of those millions to what he had come to see as higher priorities. The dreams of a German emancipation which he had done much to foster were methodically doused by his arrangements within it, as well as his own and his agents' behaviour.
A prime example is Westphalia, which could serve as a microcosm of what was wrong with Napoleon's imperial policy. 'What the people of Germany ardently desire is that those who are not noble and who have talent should have an equal right to your respect and to employment, that all kinds of servitude and all other bonds separating the sovereign from the lowest class of the people should be entirely abolished,' Napoleon wrote to Jérôme as he took his throne. 'The benefits of the Code Napoléon, the openness of procedures, the establishment of juries will be among the distinguishing marks of your monarchy. And if I am to be quite open with you, I am counting on such measures more than on the greatest victories to extend and establish your monarchy. Your people must enjoy a liberty, an equality and a well-being unknown to the people of the rest of Germany, and may this liberal government in one way or another lead to the most salutary change in the whole Confederation and the enhancement of your monarchy.'
The kingdom, which had a population of two million, was made up of territory taken from Prussia and eighteen minor German principalities. With its capital at Kassel, it was organised in departments along French lines and given a constitution drawn up by Cambacérès and Regnaud de Saint-Jean d'Angély based on that of France but incorporating local law. Although at the outset it was run by ministers brought in from Paris, the administration was gradually taken over by locals. But while the kingdom was supposed to be independent, Napoleon could not help treating it as a department of France. He demanded from it a tribute of forty-nine million francs per annum, and awarded estates there to French generals and officials who sucked another seven million francs a year out of it.
The twenty-four-year-old Jérôme was not lacking in intelligence or other qualities, but he was lazy, vain and dissolute. His career as a naval officer had been a fiasco and his military role as commander of an army corps in Silesia during the campaign against Prussia of 1806–07 was less than brilliant; in Breslau in January 1807 he and his staff had kept themselves warm with eighteen bottles of champagne and 208 of other wines each day. He was married to the plain and plump Catherine, daughter of the King of Württemberg, and although he was copiously unfaithful to her, he developed real love for his 'Trinette'.
He established a court modelled on Napoleon's, created a new nobility and instituted an order of chivalry. Palaces were rebuilt and hung with state portraits of the new royal couple, splendid uniforms were designed for royal guards, and even a new unit of currency, the Jérôme, was introduced – to be spent lavishly on court entertainments, jewellery and the trappings of royalty. He ordered a statue and over fifty busts of himself, and twelve of his wife, from Carrara. He nevertheless managed, with the help of a few competent French officials, to rule not much worse than most monarchs. As Countess Anna Potocka put it, 'With a little more legitimacy and a little less puerile vanity, he would have passed for a distinguished ruler.' But as well as making endless demands for more money and troops, many of which were sent to Spain, Napoleon kept interfering in his conduct of affairs, undermining his authority. He also kept rearranging the territory of his kingdom along with his changing plans; provinces were shunted between vassal states or incorporated into the French Empire, which not only disorganised the administration but also sapped any feelings of loyalty that might have developed to the new state and its ruler. Therein lay much of the weakness of Napoleon's system: he undermined the authority of the siblings he placed on thrones by treating them as his lieutenants, yet out of a combination of fondness, family solidarity and the inability to put anyone more trustworthy in their place, was unable to control or discipline them.
There was an inherent contradiction at the heart of the whole Napoleonic imperium: its mission was to enlighten, liberate and modernise. Feudalism was swept away, along with all disabilities imposed by guilds and corporations, Jews were liberated, and all forms of servitude abolished, yet new hierarchies were created, and political constraints imposed on the economy. Since most of the inhabitants of the Continent recognised only monarchy as a principle of government, Napoleon abandoned republican models in favour of imperial and royal ones, with all their trappings of titles, honours, decorations and courts. In August 1811 he would institute an _Ordre de la Réunion_ , intended to bind prominent people from all parts of the French dominion into a confraternity – which necessarily excluded all the inhabitants of Napoleonic Europe who did not belong to his newly created elite.
What undermined the whole enterprise, particularly in Germany, was that while the benefits of emancipation, equality before the law and a functioning administration based on a solid constitution, not to mention the spread of education for all, were generally appreciated, those who had bestowed them were increasingly resented for their arrogance and their financial demands. As Jacques Beugnot, who had been sent to Düsseldorf to run the Grand Duchy of Berg after the generally popular Murat had moved to Naples, noted, he and other French officials in Germany were in the same positions as proconsuls in the Roman Empire. 'Do not forget that in the states of the King of Westphalia you are the minister of the Emperor,' the finance minister Gaudin reminded Beugnot as he set off on his mission in 1807. 'His Majesty is very keen that you should not lose sight of that.'
The situation was not much better in those states of the Confederation of the Rhine ruled by their own sovereigns. While the people were emancipated and constitutions brought in, the process allowed the rulers to sweep away anachronistic rights and exemptions, and gave them far more power than they had enjoyed hitherto. Liberated from their Habsburg overlords, they now had armies, and many had been promoted in status, while their subjects gained little. And with time, the rulers too began to resent the constant demands from Napoleon for money and troops. Something which affected all the areas outside France, whether they were kingdoms governed by one of Napoleon's siblings or allied states, was Napoleon's stationing of French troops there. The commanders tended to behave as though they were in conquered territory, helping themselves to what they needed, behaving badly and ignoring or even browbeating local officials. As Rapp once said to Napoleon, 'Unfortunately, Sire, we do a lot of damage as allies.'
They did a great deal more damage in the case of Prussia, which was not an ally, and which had been subjected after Tilsit to humiliating conditions. It was obliged to pay a levy of 600 million francs to France in penalties for having started the war, and to support a French army of occupation numbering 150,000 men and 50,000 horses. French military authorities supervised the administration of the country, sucking more money out and reducing much of the population to poverty and even starvation. Houses in towns and villages were abandoned, thousands of beggars wandered the land, and suicides were common. Originally welcomed as a liberator, by 1809 Napoleon was seen as an oppressor. Resentment of all things French grew, and the ribbon of the Legion of Honour was referred to as 'the sign of the Beast' in some quarters. Young men dreamed of revenge.
All those who for one reason or another hated French rule or Napoleon looked to Spain, where the outbreak of variously motivated violence provoked by French intervention coalesced around the symbols of God and Ferdinand. Wishful thinking turned the 'little war', _guerrilla_ , waged by small regular units and armed bands against the French into an archetype; in the popular imagination all over Europe as far as Russia, the figure of the heroic _guerrillero_ assumed mythical proportions, arousing the enthusiasm of conservative Catholics and revolutionaries alike, who dreamed of emulating him. In Prussia many young men joined the _Tugendbund_ , the 'League of Virtue', to prepare themselves and Prussian society for the struggle to liberate Germany from the Napoleonic stranglehold. The extent to which Napoleon's credibility as a liberator had fallen can be gauged from the failure of Augereau's attempt to play the anti-Spanish card in Catalonia, usually open to suggestions of separatism.
The situation in Spain had actually shifted in favour of the French. Joseph had re-entered Madrid on 22 January, and ignoring his brother's advice to act with firmness, he played to Spanish national feelings by attending mass every day, appointing Spaniards to key posts and indulging local customs. He created a functioning administration and gradually built up a body of adherents among Spaniards who wished to modernise their country. He even managed to raise Spanish regiments which demonstrated a modicum of loyalty to him. The area under his control expanded, and the first burst of insurgency subsided. Saragossa had fallen to the French on 20 February, and Soult had taken Oporto on 27 March. Victor defeated a Spanish army at Medellín on the following day, and Suchet managed to pacify Aragon.
But there was no unity of command, as none of the commanders in the field paid any attention to orders issued by Joseph or his commander-in-chief General Jourdan. Napoleon had encouraged a spirit of emulation among his marshals which had turned into rivalry, and they were not disposed to cooperate, as each tried to wrongfoot the other. The situation was particularly bad between Ney and Soult, whose mutual animosity dated back to their service on the Rhine in the 1790s. General Wellesley outmanoeuvred Soult and Victor, broke out of Portugal and marched into Spain. He scored a minor success at Talavera at the end of July before being forced to retreat back into Portugal. After a French victory at Almonacid two weeks later, things began to look good for the French. A victory by Soult at Ocaña in November would open up Andalucia, and by the following spring the French were in control of most of the country.
Wellesley showed himself to be the equal of Napoleon in terms of propaganda, sending home a report of Talavera representing it as a great victory which was printed in the British press. This came to Napoleon's notice in Vienna, and he fumed at the incompetence of his brother and the commanders in the field. An officer sent by Joseph explained that the report in the British press was exaggerated, listing as regimental colours and eagles what were only _guidons_ , and pointed out that all the eagles were still in French hands, but Napoleon would have none of it. He had little faith in his brother's capabilities. His ambassador in Madrid, Antoine de Laforêt, disliked Joseph and retailed what he knew his imperial master would like to hear. Each of the commanders also criticised Joseph, as well as each other, in their reports. Joseph's attempts to explain the realities of the situation and justify his policy make painful reading. Napoleon dismissed his arguments, ignored his request to be allowed to abdicate, and stopped answering his letters altogether.
This silence should have been caused by a period of reflection. Cambacérès had written after Essling informing Napoleon, with all the emollient tact that had kept him in office so long, that public opinion in Paris did not reflect his triumphs, and that people did not feel they were worth the cost in blood. He added that there was anxiety at the possibility of his being killed, but made it clear that there was much discontent at the continuing war, the dispiriting news from Spain and a deteriorating economic climate. He received in reply what he described as 'a rather dry letter' demanding more specific information. In his next report Cambacérès could not hide that there was also much criticism of his treatment of the Pope.
It had long been Napoleon's conviction that France's security rested on denying other powers influence in Italy and the Mediterranean, and that the Papal States represented a strategic security risk for the kingdoms of Naples and Italy. As all subsequent rulers of Italy would accept, logic demanded they be liquidated. Logic was reinforced in Napoleon's view by the fact that the College of Cardinals was mostly made up of aristocrats sympathetic to every anti-Napoleonic coalition, and that Rome had become a refuge for many of his enemies.
He also believed that the clergy should be loyal citizens of the state and politically neutral. Since most of them were his subjects they should obey him, yet the Pope exercised a rival authority over them, inspiring them to resist some of his arrangements, which he found intolerable. He could not or would not see that there were some measures which the Pope could not sanction on theological grounds, which is why he opposed the introduction of the Code into the Papal States. As Napoleon saw it, the Pope was using spiritual weapons in defence of his temporal interests, which justified disarming him by confiscating these.
Shortly after reaching Vienna, on 17 May, Napoleon ordered the Papal States' incorporation into the French Empire. He justified this by arguing that the Pope had only acquired temporal power through the generosity of Napoleon's 'august predecessor' Charlemagne, and that he now no longer required it.
In response, on 10 June the Pope issued a bull excommunicating all the despoilers of the Holy See. Just in case he might be in any doubt, two days later he wrote to Napoleon informing him that he had been excommunicated and anathemised. Napoleon made light of this, but sent orders to the commander on the spot, General Miollis, to deal severely with the pontiff, without specifying what he meant. On the night of 6 July Miollis sent General Radet to Rome. Radet entered the Castel Sant'Angelo, seized the Pope, bundled him and Cardinal Pacca into a travelling coach and drove them off under escort of gendarmes to Genoa and thence to Grenoble, where they were held incommunicado. Napoleon was annoyed when he heard of this, saying the Pope should have been left in peace in Rome, but concluded that 'what is done is done'; he was not going to back down. On the pages of _Le Moniteur_ he lectured that Christ had preached poverty and rejected temporal power, quoting His saying that His kingdom was not of this world, and the passage about rendering unto Caesar. But the good work of the Concordat had been undone, and royalist sentiment revived in France. His actions also alienated public opinion throughout Catholic southern Germany, which included his allies Bavaria, Baden, Württemberg and Saxony, in Poland and Italy, and inflamed the situation further in Spain.
Many of Napoleon's oldest supporters were growing anxious at the turn events were taking, and some of his closest collaborators, even among the military, were beginning to have their doubts. There was criticism of his conduct of the last campaign, and particularly of Wagram, as well as anxiety at the cost in life. Napoleon relied more and more on brute force and artillery – an estimated 96,000 shots were fired by the French at Wagram.
As he relied for his successes on tactics and movement, Napoleon saw little reason to innovate equipment. While other armies perfected theirs – the Prussians brought in a slicer on their muskets which saved the time taken biting off the top of the cartridge with one's teeth and increased firepower, the British brought in rifles which increased accuracy – the French stuck with the musket model of 1777. While the British developed rockets and the Russians sophisticated gunsights, the French stuck with the Gribeauval cannon designed in 1765. Although Napoleon founded officers' schools at Fontainebleau, La Flèche and Saint-Germain-en-Laye, promotion still operated on the revolutionary principle of peer selection, with Napoleon nominating officers after a battle on the recommendation of their comrades, which often yielded poor results. And, as the commander of one light infantry regiment noted, awarding the Legion of Honour was often counterproductive, as it gave the recipient a pension to protect, an incentive to avoid danger.
While his enemies learned from him, Napoleon failed to learn from them. After the battle of Heilsberg in 1807, Lannes commented that the Russians were beginning to fight better, and Napoleon agreed, allegedly adding that he was teaching them lessons that would one day make them his masters. It was not just a question of weapons and tactics. Many on the French side were astonished as they surveyed the battlefield of Eylau to see Russian dead lying in ranks as they had stood and fought, and at Friedland Russian soldiers were seen to throw themselves in the river and risk drowning rather than surrender. Napoleon paid no attention to this, nor to the other lessons of the campaign of 1806–07.
He failed to take into account that the tactics he had used in his Italian and south German campaigns, where the theatre was relatively small, densely populated, rich in provender and easily crossed on relatively good roads, were entirely inappropriate to the open spaces and quagmires that passed for roads in Poland and Russia. More important, he had failed to take stock of another factor which he had not encountered before.
Until then he had commanded troops motivated by national feeling or local loyalties against imperial or royal armies of drafted peasants or professional soldiers who differed little from mercenaries. This had gradually been reversed. By 1807 the Grande Armée contained contingents of Poles, Germans and Italians, and even the French soldiers were beginning to question what they were doing so far from home, while the Russian army he faced was composed of determined Russian peasants doggedly defending theirs. This reversal became more pronounced over the next two years, in the fighting against a more nationally conscious Austrian army, and above all against the Spanish regulars, not to mention the _guerrileros_. Just as he had mutated from liberator into oppressor, so his troops had become agents of imperial power while their adversaries had changed roles from being the upholders of feudalism to that of defenders of the people.
According to one member of the Council of State, Achille de Broglie, at Vienna after Wagram all the generals and marshals longed for peace, 'cursing their master' and contemplating the future with 'great apprehension'. Many were astonishingly outspoken. 'He's a coward, a cheat, a liar,' General Vandamme burst out in front of his comrades. Admiral Decrès did not mince his words either. 'The Emperor is mad, completely mad, and he'll send us all, every one of us head over heels and it'll all end in an appalling catastrophe,' he said to Marmont. There were plenty more who shared such views.
Napoleon ignored them, resorting as he increasingly did to cynicism. During the Wagram campaign he turned to General Mathieu Dumas, who had fought for the American as well as the French Revolution, and asked him whether he was 'one of those idiots who still believed in liberty'. When Dumas affirmed that he was, Napoleon told him he was deceiving himself, and that he must be driven by personal ambition like everyone else. 'Look at Masséna,' he went on. 'He has acquired enough glory and honours, but he's not content: he wants to be a prince like Murat and Bernadotte, he's ready to go out tomorrow and get himself killed just to be made a prince.' Masséna did accept the title of prince of Essling, but he and his fellow marshals were appalled when Napoleon floated the idea of instituting a new military order of the Three Golden Fleeces.
Napoleon spent the next two months at Schönbrunn, where he made himself at home, even erecting a couple of obelisks capped with imperial eagles at the entrance. He held parades which people would drive out of Vienna to watch, as they were both splendid and theatrical. Napoleon would speak to the soldiers, inspect their knapsacks and question them about their experiences. While reviewing a pontoon company he went up to one caisson, asked what was inside, and after having its contents listed in detail, had it opened and personally counted the axes, saws, bolts, nails and other equipment, even climbing up onto the wheel to inspect the inside, to the delight of soldiers and onlookers. He would make regiments execute various manoeuvres and adopt battle formation, praising or criticising, and personally correcting. When the splendidly uniformed Polish chevau-légers of the Guard broke ranks around a pile of building materials blocking the entrance to the parade ground, he flew into a rage and ordered them off, snapping, to the delight of onlookers, 'That lot are good for nothing except fighting!'
In the evenings there were theatrical performances, usually Italian opera, which Napoleon found 'rather mediocre'. There was also more intimate entertainment. Soon after reaching Schönbrunn, before Essling, he had written to Maria Walewska inviting her to join him. While he waited, he distracted himself with what was noted down in the accounts of his _cassette_ as 'Viennese adventures'. When Walewska arrived, Duroc installed her in a cottage in the village of Mödling a short distance from Schönbrunn, and Napoleon's valet Constant would come to collect her at night. In mid-August he developed a persistent rash on his neck, so he summoned Corvisart from Paris. The rash had largely cleared up by the time he arrived, and it may be that the reason for the summons was not the rash, but to check whether, as Maria thought, she was pregnant, which Corvisart confirmed. Yet in his letters to Josephine, Napoleon made out that he was bored and looked forward to getting back to Paris, and to her, expressing himself with his usual hints of intimacy.
During one of the parades at Schönbrunn, on 12 October, a young man approached him and managed to get quite close before Rapp, noticing that he had a hand in his pocket, ordered a gendarme to arrest him. He was found to be clutching a kitchen knife with which he meant to murder Napoleon. When questioned, he said he would only talk to the emperor himself. Intrigued, Napoleon interviewed him. Friedrich Staps, the seventeen-year-old son of a pastor, had decided to assassinate Napoleon for the harm he was doing to Germany. Napoleon could not understand him, and concluded that he was mad. He passed him to Corvisart, who examined him and declared him to be quite sane. Napoleon told him that if he apologised he would be forgiven and allowed to go free, but the young man said that would be a mistake, as he would only try again. Napoleon was nonplussed, and had him shot.
On 16 August Cambacérès wrote reporting that Napoleon's birthday had been celebrated in Paris with 'prodigious' attendance. But his letter crossed one from Vienna with a stricture on his behaviour over something he had viewed as no more than a local difficulty, but which had caused alarm in his unquiet master.
While Britain had only contributed a modest subsidy to Austria's war effort, it did attempt to take advantage of Napoleon's absence, and on 7 July, just as the battle of Wagram was drawing to a close, a British force of 1,000 men landed at Cuxhaven at the mouth of the river Weser. It was quickly contained and forced to re-embark by Westphalian troops, but on 30 July a larger force landed on the island of Walcheren in the Scheldt estuary, took the port of Flushing and threatened Antwerp.
As the minister of the interior Emmanuel Crétet was ill and Cambacérès dithered, it fell to Fouché to deal with the threat. He called out the National Guard and delegated the only marshal of France at hand, Bernadotte, to take command of the troops in the area, which he did, arriving at Antwerp on 13 August. Bernadotte had left the battlefield of Wagram in disgrace, and on hearing of the nomination a furious Napoleon despatched Bessières to take over from him. The British, incompetently led and suffering from swamp fever, re-embarked a few days after his arrival and sailed away.
As minister of police, Fouché was aware of the discontent simmering in various quarters, and worried by the continuous landings in France of royalist agents from England. There were also occasional raids by the British on coastal forts, possibly rehearsals for an invasion to coincide with a royalist rising. News of the substantial landing on Walcheren may have caused him to overreact in calling out the National Guard. To Napoleon in Vienna it looked as though he was providing himself with the necessary force to take over Paris, and the connection with Bernadotte conjured sinister thoughts, but what seems to have particularly annoyed him was the ineffectual role of Cambacérès in the crisis.
The Treaty of Vienna was signed on 14 October. The terms were harsh, but not as drastic as Napoleon had originally intended. His first thought had been to force Francis to abdicate in favour of his brother Ferdinand, and to break up the empire by creating an independent kingdom of Hungary and using other provinces to cement his failing alliance with Russia. The negotiations, conducted by Metternich and Champagny, resulted in Austria losing access to the sea by the cession of Trieste, Ragusa, Istria, Fiume and Carniola, which were added to French possessions along the Dalmatian coast to make up the new department of Illyria. Austria also lost Salzburg, which went to Bavaria, and Galicia, which was divided between the Grand Duchy of Warsaw and Russia. In all, Austria lost about three and a half million subjects. She also had to reduce her army to 150,000 and pay a heavy indemnity. Two days after the signature of the treaty, Napoleon left Schönbrunn for Paris.
He travelled by easy stages, pausing for two days at Nymphenburg to go hunting with a grateful King of Bavaria and flirt with his wife, to whom he had taken a fancy. He also stopped at Stuttgart to visit the King of Württemberg, though his visit there was more Napoleonic – he arrived at seven o'clock in the morning and left at ten the same evening, after having attended a play in the court theatre. On the evening of 26 October he was back at Fontainebleau, where the following morning he gave Fouché a dressing-down. He spent the best part of the next three weeks there, stag-hunting on horseback and shooting, and enjoying a dalliance with a plump little blonde lady-in-waiting to Pauline, Christine Ghilini. She had only recently been married to a Piedmontese nobleman, so she resisted his advances at first, but Pauline wore her down, and although she could be difficult and moody, the affair would go on for a couple of months. Never ungenerous, Napoleon granted her father a title.
He had for some time been coming round to the view that he must divorce Josephine, but hesitated to make the move, perhaps because he had got used to her and feared being alone. She was always sensible when he sought her advice. She understood him, and the world they lived in – and from where they had come. He was a man of habit, and he had passed his fortieth birthday. There had been no more talk of divorce during the first half of 1808, although he was already considering marrying a Russian princess. Josephine's letters reveal that their relations had been particularly close during the time they spent at Bayonne and in the autumn of 1808. It was not until a full year later, on the evening of 30 November 1809, that he openly broached the subject with her at the Tuileries. She burst into tears, then collapsed, writhing in a paroxysm, and appeared to lose consciousness. Napoleon called Bausset, who had been in the next room, and together they carried her down to her bedroom.
The process of divorcing Josephine was not going to be easy. The Code Napoléon permitted divorce by mutual consent only up to the age of forty-five, which she had passed, while the Statutes of the Imperial House which he had invented himself forbade it outright. The matter was handed over to Cambacérès to sort out, which he accomplished with the legal acrobatics he excelled at. Louis, who had taken the opportunity to seek permission to divorce Hortense, was told he could not as there were no grounds for it.
Meanwhile, life went on as usual, and the morning after her fainting fit Josephine presided over a reception in honour of the kings of Naples, Württemberg and Holland who had come to Paris to celebrate the peace with Austria. On 3 December there was a _Te Deum_ at Notre Dame, the following day a reception at the Hôtel de Ville followed by a banquet, a concert and a ball at the Tuileries. The banquet was a tense affair, with Napoleon in full coronation robes with his plumed hat on his head looking uneasy and impatient, while Josephine sat opposite covered in diamonds looking as though she might faint at any moment. She would not have enjoyed the presence of Letizia, Caroline and Pauline, who had never looked happier. Whether she received much comfort from her husband is doubtful, as he spent the night of 5 December with another. Once he had decided on the divorce, he had begun to philander more, which Hortense saw as a means of both making himself more interesting to women and of fortifying himself against the forthcoming separation. 'His mind was made up, but his heart still hesitated,' she wrote. 'He was trying to distract it elsewhere.' He had broken down and wept when he had informed her of his intention to divorce her mother. On 8 December Eugène arrived in Paris and the divorce was discussed with him and Josephine by Napoleon. Three days after that she had to take her place at Napoleon's side at a party at Berthier's estate of Grosbois.
On 15 December, at a special meeting attended by all the family members currently in Paris – Letizia, Louis and Hortense, Jérôme and Catherine, Joseph's wife Julie, Eugène, Murat and Caroline, and Pauline – in the presence of Cambacérès and the secretary of state for the Imperial House, Regnaud de Saint-Jean d'Angély, Napoleon and Josephine each read out prepared texts announcing their wish to divorce, and stating their reasons. The minutes of the meeting taken by Regnaud were signed by those present and passed to the privy council, which that same evening drew up the project of a _senatus-consulte_. This was presented to the Senate the following day by Regnaud. The meeting was presided over by Cambacérès, and Josephine's son Eugène read out the family's wish that 'the founder of this fourth dynasty should grow old surrounded by direct descendants'. There was no debate, and the _senatus-consulte_ was passed by seventy-six votes, with seven against and four abstentions. The same day, Josephine left the Tuileries.
There then arose the delicate matter of annulling the religious marriage. There could be no question of involving the Pope, who was in solitary confinement at Grenoble. Cambacérès argued that the ceremony conducted by Cardinal Fesch had been 'clandestine', since there had been no witnesses present, and was therefore invalid. This could be attested by the diocesan authorities in Paris, and the marriage being invalid, there was no need of an annulment. The diocesan council ruled accordingly, fining Napoleon six francs (to be distributed to the poor) for having contracted an illegal marriage. The ruling was endorsed by a bishop who had no authority, since he had not been approved in office by the Pope.
Two days after she drove away from the Tuileries, Napoleon dined with Josephine at Trianon. 'My love, I found you weaker today than you should be,' he wrote afterwards. 'You have shown courage, and you must find enough to support you and not to let yourself go to a fatal melancholy, and to be content, and above all to keep up your health, which is so precious to me.' He wrote frequently, expressing his concern and professing his enduring love for her. He visited her at Malmaison on 24 December, and she dined with him at Trianon the following day. She could barely eat, and looked as though she were about to faint. Hortense, who was present, saw Napoleon wipe away his tears more than once. When he returned to the Tuileries three days later he found the palace empty without her, and wrote saying he felt lonely there.
He was determined to treat her well. She retained her titles and arms as Imperial Majesty. He gave her the Élysée Palace in Paris, Malmaison, and the château of Navarre near Évreux. She had a settlement on the civil list of two million francs per annum, and he threw in another million from his private chest. When it came to his notice that people were keeping away from her he made it plain that such behaviour would incur his displeasure.
## 34
# Apotheosis
The question of whom Napoleon should marry had resolved itself. Tsar Alexander had no intention of cementing his alliance with him, let alone letting him marry one of his sisters. Even if he had, he would have been powerless to do so. Shortly before his death his father Paul I had issued an _ukaz_ giving his consort power to decide over his daughters' marriages. The dowager empress loathed the very idea of Napoleon, and as soon as she heard of his intention she encouraged her elder daughter to marry Prince George of Holstein-Oldenburg. Alexander's other sister Anna was two months short of her fifteenth birthday when, at the end of November 1809, Napoleon instructed Caulaincourt in St Petersburg to make the request for her hand. Alexander made a show of pleasure, but did nothing. When pressed a few weeks later he asked for two weeks to consider the matter and gain his mother's approval. At the end of the two weeks he asked for another ten days, then for another week. He was still stalling at the beginning of February 1810, by which time Napoleon, fearing the snub of a refusal, had changed his mind.
A meeting of his privy council at the Tuileries on Sunday, 28 January had reviewed the three possible candidates: the Grand Duchess Anna, the twenty-eight-year-old Maria Augusta of Saxony, and the eighteen-year-old daughter of the emperor of Austria, Marie-Louise. Napoleon never seriously considered the Saxon option. His first choice would have been the Russian, as it would have cemented his alliance with Russia against Britain – and it would have tickled his vanity that his heirs could then claim descent from the Paleologue rulers of the Roman Empire of the East. Cambacérès, Murat and Fouché also favoured the Russian, but given the difficulties being made by Alexander, they concurred with Talleyrand and the others, who supported the no less grand Austrian candidate, who was descended from Louis XIV and Charles V. Informal talks had been taking place between Talleyrand and Metternich, now Austria's chancellor, and both had come to the conclusion that such a match might distract Napoleon from his pursuit of dominion. Metternich had authorised his ambassador in Paris, Prince Karl von Schwarzenberg, to accept the offer if it were made. A week later, during a shoot at Fontainebleau, Eugène went up to Schwarzenberg and formally requested the hand of the archduchess on Napoleon's behalf. Napoleon ordered the marriage contract to be drawn up that very day, taking as a template that between Louis XVI and Marie-Antoinette.
The news was greeted with horror by Louis XVIII in England and with delight in Austria. 'What a joy for mankind!' exclaimed the ultimate Habsburg courtier the prince de Ligne, expressing a view held by many that the match would 'settle' Napoleon and that, by joining him to a descendant of the 'real Caesars', 'his edifice will become stable at last'. As well as promising peace and stability, the forthcoming union would go some way to restoring Austria's position among the great powers, even though Napoleon did not envisage returning any of the territory he had taken. Public opinion in Vienna was not even put out when Berthier, recently named Prince of Wagram, arrived there to marry the archduchess by proxy. The news had also gone some way to soothe anti-French feeling elsewhere in Germany.
Reactions in France were more mixed. The aristocracy, which had rallied to Napoleon, were delighted. Many welcomed the promise of a lasting peace settlement. But many were haunted by memories of that other Austrian marriage and its unhappy end. Others did not like the idea of what looked like yet another step back to the ancien régime. The army mostly disapproved, not so much for ideological reasons as out of sympathy for ' _la vieille_ ', 'the old girl', whom they saw as a good French wife to Napoleon and whom many even considered to have brought him luck – old soldiers could be highly superstitious.
The proxy marriage took place in Vienna on 11 March 1810, and two days later Marie-Louise left for France. Napoleon was in a state of childlike excitement in anticipation of her arrival, and insisted on overseeing down to the last detail the arrangements for her reception at Compiègne. He went there a week before she was due, followed by his sisters Caroline and Pauline, Joseph's wife Julie and, later, Murat, Fesch and others. They were joined over the days by members of the court and Austrian dignitaries. To keep fit, Napoleon went hunting, enjoyed the favours of his current mistress, and took dancing lessons from Hortense, whom he asked to help him appear less grave.
Following the protocol of 1770, Napoleon had Davout's engineers run up a building on the frontier with three chambers representing, respectively, Austria, neutral territory, and France. When she arrived there on 16 March, Marie-Louise entered the first room, in which she shed everything associated with her Austrian past and changed into a dress of gold brocade. She then entered the central chamber with her Austrian attendants and seated herself on a dais. A French reception party entered from the other side, bringing the number of those present to around a hundred. An act of translation was read out and signed, after which her Austrian attendants departed one by one, kissing her hand as they took their leave. She was then ushered into the French chamber, where Caroline Murat took charge and she was dressed in the French fashion.
Taking things one step further than the Bourbons, Napoleon had invented another ceremony, to take place in a specially designed tent at Soissons not far from Compiègne, in the course of which Marie-Louise was to kneel before him. But his impatience was such that it never took place. Taking only Murat with him, he drove out to meet her, and had reached the village of Courcelles when one of his coach wheels broke. It was pouring with rain, so he and Murat took shelter in the porch of the village church, and when the carriage bringing Marie-Louise drove up the coachman, recognising him, stopped. Napoleon rushed up to the carriage, opened the door and leapt in. Dripping wet in his grey overcoat, he sat down next to his astonished bride and kissed her. He then told the coachman to drive straight to Compiègne, where they arrived at half past nine in the evening.
The little town had been illuminated, but the rain had extinguished most of the lights. There was to have been a banquet, but Napoleon decided otherwise. They supped lightly together with Caroline, after which, having ascertained from Fesch that they were actually married, instead of retiring to his prescribed quarters he quickly freshened up with eau de cologne, changed into a dressing gown, and followed Marie-Louise into hers, where he exercised his marital rights. In the morning they took breakfast and lunch in her bedroom, and were hardly parted for the next forty-eight hours. Both appeared ecstatically happy, and Napoleon later reminisced that she kept asking for more. In a letter to her father she confessed that the Corsican ogre was 'very engaging and very eager, and almost impossible to resist'. On the evening of 29 March, only forty-eight hours after she arrived, during a concert at which La Grassini sang for them accompanied by Paër, Napoleon kept falling asleep. 'From time to time, the empress would wake him up by saying something to him, he would give her a sweet look, adopt a serious air to reply, and then fall asleep again,' according to an Austrian courtier present.
The next day the couple transferred to Saint-Cloud, where on 1 April they were married in a civil ceremony (the irony of the date did not go unnoticed). The following day, in bright sunshine, they drove into Paris in two separate coaches, each drawn by eight horses, followed by another thirty-eight carriages drawn by six horses each. Escorted by detachments of all the mounted regiments of the Imperial Guard, they drove under two specially erected wood and canvas triumphal arches, one of them covering the half-built Arc de Triomphe at the Étoile, and down the Champs-Élysées to the Tuileries. The onlookers showed little interest.
Napoleon wore a white satin version of court dress designed by himself, with a black velvet toque covered in diamonds topped by three white plumes, making him appear even shorter and fatter than he was, looking, according to one witness, like the king of diamonds from a pack of cards. Beaming with satisfaction he led his bride down the long gallery, lined on either side by the ladies of the court standing on three tiers. There had been the usual family rows, with his sisters balking at being made to carry Marie-Louise's train, and Pauline took her revenge by pulling faces behind her back. Delighted as they were to see the end of Josephine, they did not welcome a new interloper. The grand salon with a ceiling depicting Apollo had been converted into a chapel, and there Cardinal Fesch married them, after which he performed the traditional royal ceremony of blessing the bed.
By then, Napoleon was furious. Thirteen of the cardinals he had brought to Paris by force in January had failed to attend the ceremony, on the grounds that his marriage to Josephine had not been annulled. When the ceremony was over, he was heard threatening to have them shot. The following day, when he and Marie-Louise seated on their thrones received the compliments of the Senate, the Legislative, the marshals, the diplomatic corps and all the other bodies, and the cardinals' turn came, he had them thrown out. He ordered them to be exiled to provincial towns where they were forbidden to wear their robes.
That night Paris was illuminated and decorated as never before. Public buildings were adorned with painted canvas panels or, like the seat of the Legislative across the bridge from the place de la Concorde, turned into a 'Temple of Hymen', with an allegorical figure representing Peace blessing the newlyweds. Trees were decked with lanterns and private houses with candles in every window and braziers outside. But the festivities did not live up to the décor. In preparing the public fête for the people of Paris Napoleon had deliberately abandoned the tradition of having food served in the street and fountains running with wine, on the grounds that it led to brawls, and replaced it with more organised celebrations, including having food and wine delivered to the poor in their houses. But, as one contemporary noted, even the public festivals Napoleon gave were somehow stilted, and people were beginning to be made to feel their station. Those who were admitted to the more august festivities felt little different. Thibaudeau found the marriage ceremony 'as cold and sad as a funeral', while Captain Coignet, who had been present at the banquet, commented that 'It may have been grand, but it was not fun.'
Having dealt with the essentials in a session of the Council of State, on 5 April Napoleon took his bride back to Compiègne, where they spent the next three weeks. He hunted and occasionally received someone on business, but otherwise devoted all his time to his wife, petting her and showering her with presents. Aside from the fact that she liked to sleep with the window open and he with it closed, they were well suited, and he particularly appreciated her innocence and truthfulness, which contrasted with Josephine's depravity and deviousness, which had both excited and annoyed him.
On 27 April 1810 the imperial couple set off on a tour of Belgium and the Low Countries, inspecting canals, public works and factories along the way. In Antwerp they launched a ship of the line and watched the Festival of the Giant, which included a carnivalesque procession with a huge dummy whale squirting water, a chariot of Neptune and an outsize elephant. On 5 May they attended a reception given by Louis, King of Holland. But in the course of a conversation between the two brothers Napoleon learned something that enraged him.
He had been aware that for some time the banker Ouvrard had been in contact with the British government through his associate Pierre-César Labouchère's cousins, the Barings of London; he had used the connection to make informal peace proposals himself. When these were rejected he lost interest, but his brother Louis did not, as he was desperate for some kind of settlement with Britain; the Dutch economy was heavily dependent on overseas trade and banking, and was crippled by the state of war. Another who was keen for an end to the conflict with Britain was Fouché. He had been sending out feelers through his own contacts in London, and sometime in 1809 he had also begun to use the Ouvrard/Labouchère channel. One of his agents had been received at the Foreign Office by Lord Wellesley. This came to Napoleon's notice at Antwerp, and he jumped to the conclusion that Fouché was plotting behind his back. 'Not only has the man been meddling in my family affairs without my permission [a reference to the minister's bringing up the subject of divorce with Josephine], he now wants to make peace behind my back,' he raged. The next day he vented his ill-humour on a deputation of Belgian clergy which had come to greet him, for having dropped regular prayers for him from the liturgy.
He ordered Savary to investigate, and continued on his tour, taking in Breda, Berg-op-Zoom (where he boarded a yacht after a copious lunch and was seasick) and Flushing, where he made his displeasure felt that the town had capitulated to the British the previous year. They visited Middleburg, Brussels, where they attended a grand reception, Ghent, Bruges, where they visited the cathedral, Ostend, Dunkirk and Lille, and then went via Calais, Boulogne, Dieppe, Le Havre and Rouen back to Paris, where they arrived on the night of 1 June. Napoleon held a council of his ministers in the morning, and the following day sacked Fouché.
As Napoleon had left the capital for Compiègne immediately following his marriage, it was only now that the various festivities that would normally have accompanied it were held. Marie-Louise was awkward and did not possess Josephine's charm. Unlike Josephine, she could not remember people or their names, which led to embarrassing situations. Her awkwardness was contagious, and a sense of constraint reigned whenever she was present.
The city of Paris gave a fête at the Hôtel de Ville for the notables of the capital to meet the new empress, but it was a joyless occasion, spoiled as much by Napoleon's evident impatience and inability to enjoy such events as by her manner. More successful was a fête given by Pauline at her property in Neuilly, in the grounds of which she arranged magical tableaux and illuminations. Actors of the Théâtre-Français acted out a play in one part, dancers executed a ballet in another, both vying for the attention of the guests. Two orchestras placed at opposite ends of the park played as though one were the echo of the other. There were temples with goddesses, a hermitage with a hermit, and a cherub who offered the empress a garland. At the end of the park there was a replica of Schönbrunn, with fountains and dancers in Tyrolean costume, at which point Marie-Louise burst into tears, whether out of homesickness or exhaustion nobody could tell.
Two weeks later, on 28 June, while they were at dinner in the Tuileries, Eugène was announced and Napoleon rose from the table while Marie-Louise was still eating her ices. She protested, but he ignored her, sensing the news was important. It was: Louis had decided to give up the Dutch throne. Napoleon expostulated, gesticulating 'like a real Corsican' according to one witness, but the news should not have come as a surprise.
While he too enjoyed festooning himself with trappings of monarchy, Louis had taken his job as King of Holland seriously. He worked hard to mould the disparate and traditionally republican elements he was given into a modern constitutional monarchy with a national identity. He introduced fiscal and administrative reforms, and a new educational system. Holland was economically devastated by the blockade, yet with its innumerable estuaries, creeks and islands it was impossible to seal against smuggling, so goods still got through, but the state could not control or tax them. In December 1808 Napoleon closed its frontier with France in order to keep them out, compounding the problem for Holland. He demanded that Louis supply another 40,000 troops over and above the 12,000 already serving France in Germany and the 3,000 fighting in Spain. In 1809 he refused to allow him to introduce a version of the Code he had painstakingly adapted to Dutch conditions, and insisted on imposing his own.
Using the pretext of the British landing on Walcheren the previous year, Napoleon had sent French troops to take control of the coastal areas and then annexed the provinces of Brabant, Zealand and Guelders to France. In March 1810 he had forced Louis to place all Dutch troops under French command, and in June Marshal Oudinot set off for Amsterdam, where Louis was instructed to put on a triumphal ingress for him. Napoleon had made his younger brother's position untenable, yet he was upset by his decision to abdicate and took it as a personal affront. 'The folly of the King of Holland has upset me,' he wrote to Josephine, 'but I have grown used to the ingratitude and the fickleness of my brothers; they serve me poorly, as they have little love for France or me.' He had been stung by the behaviour of Lucien, who had ignored his wishes, set off for America but been caught by the Royal Navy and taken to England as a prisoner of war.
Louis abdicated formally on 2 July in favour of his son Napoléon-Louis and fled, taking refuge at Gratz in Austria. A week later Napoleon decreed the incorporation of Holland into France, arguing that 'it is complementary to the empire, the estuary of its rivers; its navy, its ports, its commerce and its finances can only prosper if combined with those of France'. The move went down badly with public opinion in France, as people feared it might provoke another war and could see no point to it.
Paris was in sombre mood. On 1 July the Austrian ambassador Prince Schwarzenberg had given a ball in honour of the newlyweds. After they had watched 'a charming ballet' performed on a lawn against the backdrop of a _trompe-l'oeil_ of the gardens at Laxenburg, when the ball had started and the dancing was in full swing one of the marquees caught fire. Panic ensued as people rushed for the exits and men tripped over their swords while struggling to carry out fainting ladies. Napoleon managed to lead Marie-Louise out and drive her to safety, and then returned to help, earning praise for his handling of the situation. 'Heart-rending cries of pain and despair could be heard on all sides as mothers called out to daughters and husbands their wives,' in the words of one officer. 'The garden lit up as though it were daylight, filled instantly with people shouting as they searched for each other and running to extinguish their clothes which were on fire.' The ambassador's sister-in-law Princess Schwarzenberg rushed back into the marquee in search of her daughter, but died as it collapsed on her. Several others died of burns, and many were permanently scarred. People did not fail to draw analogies with the celebrations of the marriage of Louis XVI and Marie-Antoinette in 1770, when a firework display went wrong, precipitating a panic in which over 200 people were crushed to death.
Analogies with the ancien régime were not out of place. A new court etiquette was introduced, consisting of 634 articles, based on that of 1710. Colonel Lejeune was astonished when he came with reports from Spain to find himself instructed by the ballet master from the Opéra on how to perform three courtly bows when introduced into the imperial presence. The efforts of broad-shouldered proletarian warriors to submit to the new etiquette often ended in ridicule. The eighteenth-century silk _habit habillé_ obligatory for court balls looked absurd on men with a military gait and scarred faces, sometimes still bandaged or with an arm in a sling.
Having married a niece of the last King of France, Napoleon began referring to his 'uncle Louis XVI', and adopted a kind of walk he had been told the Bourbons had affected, which in his case turned into an unflattering waddle. He had the slogan ' _Liberté, Égalité, Fraternité_ ', which had been painted over the entrance to every public building in Paris during the Revolution, effaced. He considered going back on his plan to refashion the Madeleine into a Temple of Glory dedicated to French heroes and turning it instead into an expiatory chapel dedicated to the guillotined Louis XVI. He carried his policy of social fusion to bizarre lengths, at one point issuing a circular to all prefects to draw up lists of nubile girls from noble families suitable for marriage to soldiers and officials – the purpose was not so much to conjoin as to subsume and legitimise. Yet it had not worked in his own case, and he had lost nothing of his social awkwardness. 'It is difficult to convey how gauche he was in a drawing room,' recalled Metternich, who had come to Paris to represent Francis I at the marriage.
'The court had grown rigid and lost everything it still conserved of social ease,' recalled Victorine de Chastenay, adding that Marie-Louise made people regret Josephine. She had possessed a grace and an ancien-régime _savoir-vivre_ tempered by all the experiences of the Revolution, and created an atmosphere in which all could feel at ease. She had also exerted a humanising influence on Napoleon, often bringing him down to earth from his flights of fancy. Now Napoleon was grander and more distant, and even more prudish. In Josephine's day he would banter with the ladies and on occasion talk of past conquests. Now, young men were afraid of addressing ladies in his presence for fear of being ticked off for what he assumed were salacious proposals, or even just frivolous talk. 'I do not think there could have been a court where the morals were more pure,' recalled Hortense. The notoriously homosexual Cambacérès was instructed to pay regular ostentatious visits to an actress in the Palais-Royal, which fooled nobody and only provoked ribaldry.
Napoleon's civil list and other sources of income (he was not averse to diverting some taxes and state revenues to his private treasury) made him the richest monarch in Europe, with a vast stack of gold in the vault of the Tuileries which allowed him to adorn his court with unprecedented splendour. His views of himself and of France were well reflected in his public works and monuments, which were increasingly grandiose and closely bound to his person. He had been so struck by the magnificent royal palace in Madrid that on his return he instructed Fontaine to draw up plans for the aggrandisement of the Louvre, which he wanted 'to equal in magnificence everything he had seen', and to incorporate a church dedicated to St Napoleon. He also gave instructions for the former royal residences of Rambouillet, Meudon and Chambord to be restored to splendour, along with more than forty other palaces around the empire. When Fontaine came up with a plan for the Louvre which involved linking up the two extended wings, Napoleon protested. 'What is great is always beautiful,' he declared, 'and I cannot agree to dividing a space whose principal feature is its extent.' Instead, the space was embellished with the triumphal arch of the Carrousel, on which were placed the four horses of St Mark's in Venice, drawing a Roman chariot in which the spirit of flattery had led to a statue of himself being placed. Even he balked at this, and had it removed. No such restraint was in evidence when, as soon as it was known that Marie-Louise was pregnant, he put in hand plans for a monumental palace complex for his presumed son on the heights of Chaillot.
This infatuation with all things aristocratic and the accent on grandeur worried most of those who had helped bring Napoleon to power and worked with him at rebuilding a France that would incorporate the best of all worlds. Even Cambacérès, despite being bedecked with imperial and Austrian decorations, was uneasy. The country seemed to them to be drifting back to a mongrel version of the ancien régime. Yet those who had come of age under the empire did not share such reservations, and the symbols of Napoleon's power and glory made them feel proud to be French and to serve him.
The departure of Fouché from the centre of political life broke yet another link with the Revolution, and not just because of his Jacobin past, which had acted as a sort of guarantee against a Bourbon restoration. As had been the case with Talleyrand, his presence at the centre of public affairs and his ability to act as a restraining influence on Napoleon had provided a dose of wisdom to his conduct. Cynical and often perfidious as it was, his method of policing had been based on surveillance rather than punishment, on making people behave because they thought they were being watched rather than on the detention of suspects. This light touch changed overnight with the appointment in his place of Savary, who admitted to being astonished on taking over at how little real power he found at his disposal. He also found very little information, as Fouché had deftly removed or destroyed all his more sensitive papers.
'I inspired fear in everyone; people started packing their bags and talking of exile, imprisonment and worse still,' wrote Savary. 'I do not think that an outbreak of the plague on one of our coasts would have caused more fear than my appointment to the ministry of police.' This was hardly surprising. He was a strict executor of Napoleon's wishes, which were growing increasingly despotic. On his return from Vienna after Wagram, he had reorganised the workings of the courts in the interests of what he saw as efficiency, and in March 1810 he re-established prisons of state in which people could be locked up without trial, in effect reinstating the infamous _lettre de cachet_ and creating half a dozen new Bastilles. According to Savary, there were just over 600 inmates, a significant number of them 'deviants' of one kind or another whose families preferred to avoid the publicity of a trial.
The Penal Code, introduced that year, made assemblies of twenty or more illegal, although religious confraternities and Freemasonry were exempt. There was also a growth of scientific societies around the country. But the number of theatres, where the themes of plays could only too easily suggest unfavourable parallels and provoke discussion, was reduced. Although he supposedly instructed Savary to 'treat men of letters well', Napoleon tightened censorship. His reactions to any disorder or infraction had grown more peremptory, and included in one case ordering soldiers to be shot for no more than a drunken brawl. Yet when a young man from Saxony turned up in Paris and after being arrested confessed to the intention of assassinating him, Napoleon instructed that he be locked up with plenty of books to read so he could cool off, and released him after a few weeks.
Napoleon was still capable of showing his human side – usually with people of the lower orders. When they were caught by rain during the tour of the Low Countries the imperial party took shelter in a farmhouse whose owner, not knowing who his guests were, sat in his armchair while Napoleon and the others perched on benches, and proceeded to talk freely, dispensing old man's wisdom. The emperor chatted with him affably, and it was only as they were leaving that he gave an inkling of who he was, by offering to provide a dowry for the man's daughter. He often did this when travelling, dispensing gifts to astonished serving girls and grooms at wayside inns.
Nor did he forget those he loved. He set up Maria Walewska in a townhouse in Paris elegantly furnished in the Empire style, gave her a villa in Boulogne, and provided for their son by giving him estates in the kingdom of Naples. 'No sovereign has ever given more than the Emperor, yet none has left so many resentful,' remarked Chaptal, explaining that the manner in which he gave smacked of charity or reward rather than generosity, but the former minister was by then ill-disposed to him. Josephine turned to Napoleon whenever she needed help or money with the plea, 'Bonaparte, you promised never to abandon me; now I need your advice', and he never failed her. 'He would charm everyone around him whenever he let himself go to his bonhomie,' recalled Hortense. Even Metternich had to admit that in private or in intimate company, Napoleon's conversation 'possessed a charm difficult to define'. He could also be clear-sighted and candid. One day, he asked those around him what people would say when he died. As each began saying something flattering, he interrupted them. 'People will just say: Ah! at last we can breathe! We're rid of him, what joy!' He also admitted that his becoming emperor was really something of 'an accident'.
But that did not correspond to any sense of humility. Napoleon noticed that when writing to her father his wife addressed her letters to 'His Sacred Imperial Majesty', and he asked Metternich about this form he had not come across before. Metternich explained that it was accepted usage when addressing the Holy Roman Emperor. 'It is a fine and fitting custom,' said Napoleon with a solemn air. 'Power derives from God, and it is only on account of that that it can be placed beyond the reach of men. In time, I shall adopt the same title.'
Metternich had attempted to resolve the conflict with the Pope, but Napoleon's views had hardened. To the sculptor Antonio Canova, whom he had brought to Paris to make a bust of Marie-Louise, he said irritably that 'these priests want to control everything, meddle in everything and be masters of everything'. He reasoned that St Peter had chosen Rome rather than Jerusalem because that was the metropolis of the time, but Rome had fallen, and the papacy had ended up being a minor state subject to the temporal requirements of the rulers of 'a very small corner of Italy', and that it was the resulting political entanglements which had led to the Reformation. He argued that the Pope should move to Paris, and in preparation began rebuilding the archiepiscopal palace beside Notre Dame, moving the Vatican archives and, in January 1810, forcing the cardinals of the Sacred College to take up residence in the new Rome.
Meanwhile, in the former Papal States the French authorities dissolved monasteries and convents, rationalised parishes, and expelled recalcitrant priests and monks. The text relating to their incorporation into the French Empire underlines 'the independence of the imperial throne from any authority on earth'. The custom among Catholic monarchies which maintained the belief that they ruled by the grace of God had been to defer to His vicar on earth, the Pope. Napoleon had paid lip service to this by insisting on the Pope being present at his coronation, even though he then still based his right to rule on the will of the nation. Now he needed neither the Pope nor the nation. Arguing the point with Fesch at Fontainebleau one evening, Napoleon led him out onto the terrace and, pointing to the heavens, asked him whether he could see God, to which the cardinal replied in the negative. 'Well, then, you had better keep quiet,' snapped the emperor. 'I can see my star, and that is what guides me.'
## 35
# Apogee
Napoleon would later blame his marriage to an Austrian archduchess for his downfall, referring to her as 'that bank of roses obscuring the abyss'. There was something in that, as its joys did distract him and its fruits deceived him, with fatal consequences. He was besotted with his new bride, and seemed to revel in the possession of this fresh, young, submissive yet lusty girl with her imperial blood.
In a report to his emperor, Metternich had characterised Napoleon as a 'good family man, with those accents which one finds most often in middle-class Italian families', but the Latin paternalism had given way to deference and become tinged with Austrian _Gemütlichkeit_. He ordered paintings of battles fought against the Austrians to be removed from the imperial palaces, and commissioned views of Schönbrunn and Laxenburg, where Marie-Louise had grown up. Where he had chided Josephine for being late, he waited obsequiously for his new bride. He who had never spent more than twenty minutes at table now sat patiently as she munched her way through seven courses. She was bored by the tragedies of Corneille and Racine that he loved, so he sat through comedies that he despised. He was so deferential that she confessed to Metternich that she thought he was a little in awe of her.
He went hunting more often than before, mainly to get some exercise and exhaust himself; he dashed about on his horse wherever his fancy took him, to the exasperation of Berthier, who as grand huntsman planned the hunt with his usual thoroughness. It did not prevent him putting on weight, and those around him felt he had slowed down and declined physically. He was not eating more than usual, so there must have been another cause to his slide into obesity. It has been convincingly argued that it was probably the failure of his pituitary gland, which can affect men around the age of forty, leading to weight-gain and genital shrinkage, from which he also suffered according to post-mortem examinations.
His workload remained impressive, but less strenuous. In the past he had been continually on the road, obsessed as he was with taking matters in hand and judging on the spot before making decisions. He was now travelling less; he had never before spent such a long time in Paris and its environs. Many saw in this an encouraging development. At the marriage banquet in April 1810, Metternich had proposed a toast 'To the King of Rome!' – the title traditionally borne by the heir to the Holy Roman Empire. The Austrian chancellor's toast suggested that the Habsburg monarchy had ceded its rights to the new emperor of the West, and the age-old struggle between the House of Austria and France was at an end. It implied that the birth of a King of Rome would seal a lasting peace, and as soon as it was confirmed that the empress was pregnant people began to pray for it.
As she went into labour on the evening of 19 March 1811, the court gathered at the Tuileries, while doctors Corvisart and Dubois took charge, attended by two surgeons. Expectation gripped the city. The stock exchange closed, and many employers gave their workers the day off. The birth would be announced, as were victories and major events, by the firing of cannon: twenty-one shots for a girl and one hundred for a boy. On the esplanade in front of the Invalides, the gunners of the Imperial Guard primed their pieces and waited for the order to fire.
They had to wait all night, as the birth proved a difficult one. Napoleon remained at his wife's bedside from the moment the labour started at about seven in the evening, showing signs of distress at her pain. This subsided at around five o'clock in the morning and she fell asleep, so he went to have a bath. It was not long before a nervous Dr Dubois came hurriedly up the hidden staircase to tell him that there were complications, as the baby was presenting itself badly. Napoleon asked whether there was any danger, and the doctor replied that the empress's life was threatened. 'Forget she is the empress and treat her as you would a shopkeeper's wife from the rue Saint-Denis,' Napoleon interrupted him, adding, 'And whatever happens, save the mother!' He dressed and joined the doctors at her bedside, calming her as Dr Dubois took out his forceps. The baby came out feet first, and it took some time to get the head clear, during which Marie-Louise screamed so much Napoleon was in tears. At around eight in the morning the child was born. Having satisfied himself that the mother was out of danger, Napoleon took the child in his arms and stepped into the adjoining salon where the dignitaries of the empire were waiting, bleary-eyed after their long vigil. 'Behold the King of Rome!' he declared. An aide ran through the rooms and out to his waiting horse, to give the gunners their orders.
At the first shot, the city came to a standstill. People opened their windows and came out of shops, carriages and wagons pulled up, pedestrians stopped. The first twenty-one were fired at intervals of several seconds so everyone could count them. When the twenty-second was heard, 'there rang out across the town a long shout of joy which ran through it like an electric current', in the words of one lady. It was accompanied by the remaining seventy-eight shots delivered in quick succession, and the pealing of bells from every church in Paris. A police report noted that two porters at Les Halles who were on the point of coming to blows paused at the first shot, and embraced at the twenty-second. Even opponents of the regime and enemies of Napoleon felt joy. To many it seemed as though the future was secure, and a _pax gallica_ would descend on Europe. In a poem dedicated to Marie-Louise, Goethe represented her union with Napoleon in cosmic terms, referring to her as 'the beautiful bride of peace'.
That evening, while the people of Paris celebrated, the child was baptised according to the rites of the French royal family – he had already been assigned as governess the same comtesse de Montesquiou who had brought up the children of Louis XVI. The next morning, seated on his throne, Napoleon received the congratulations of the Senate, the Legislative and other bodies of the government and administration, the diplomatic corps and the municipal authorities, after which they accompanied him to view the infant as he lay in a cradle donated by the city of Paris, featuring a figure of Glory holding a crown, with an eagle ascending towards a star representing Napoleon. Over the next days congratulations poured in from every corner of the empire, and from every foreign court except that of St James's.
Aside from the satisfaction he felt at the birth of an heir, Napoleon was as moved as any man by the experience of fatherhood; he immediately sent a page to inform Josephine of the birth. He may even have taken the child later to Malmaison for her to see. He still felt deep affection for her, and every year after the divorce he would send her a million francs in addition to her settlement. When Mollien informed him that she wanted three more officers to attend her, Napoleon told him 'not to make her cry' and let her have them. He had hoped that Marie-Louise would come to accept her as a friend, and that he would be able to accommodate them both in his life, and was, according to Hortense, put out by the younger woman's jealousy.
The notion that the blessings of peace were about to descend on France was enhanced by numerous depictions of Napoleon as a father figure of the nation and a pacific family man. An engraving published in Vienna showed a nativity scene, with Marie-Louise as the Virgin, Napoleon's son as the infant Christ, the kings of Saxony, Bavaria and Württemberg as the three wise men and the other rulers of the Confederation of the Rhine as the shepherds, and, hovering on a cloud, Napoleon himself as God the Father declaring, 'This is My Son, in whom I am well pleased.'
On 9 June 1811 Napoleon and Marie-Louise drove in the coronation coach to Notre Dame for the ceremonial christening of their son. The two-month-old baby was baptised by Cardinal Fesch in a church packed with marshals, members of the court, the public bodies, representatives of all the cities of the empire, foreign princes and the diplomatic corps. This was followed by a banquet at the Hôtel de Ville at which Napoleon, his consort and the royals present sat at table wearing their crowns. There followed a court ball and, in the Champs-Élysées, fireworks and free food, wine and dancing for the people of Paris.
'Now begins the finest epoch of my reign,' Napoleon declared shortly after the birth of his son, and appearances seemed to bear this out. Miot de Melito, who came to Paris for the baptism after an absence of five years, was astonished at the change the city had undergone. Everywhere he saw new buildings, bridges and monuments, he drove down elegant _quais_ and across open spaces, visited the Louvre and other museums, and was overwhelmed by the city's magnificence.
Paris, with its wide streets, grand buildings, fountains and gardens was only the centre, from which fourteen grand imperial roads and as many improved lesser ones, supported by 202 subsidiary ones, radiated to the furthest points of the empire. Travel time was cut by at least half in the course of Napoleon's rule, and with a network of 1,400 posting stages and 16,000 horses, the _Messageries impériales_ could carry people and post at unprecedented speed. The telegraph had been extended to Amsterdam, Mainz and Venice. There was a plan to link the river Seine to the Baltic with a new canal. Decrees had been issued for the cleaning of the Roman Forum and the dredging and banking of the Tiber, and, after the birth of the King of Rome, for a new imperial quarter on the Capitol. Antwerp, Milan and other cities throughout the empire were improved or, as in the case of La Roche-sur-Yon, built from scratch in deprived areas. Paris boasted the greatest library on earth, but dozens of public libraries had sprung up in medium-sized towns, each the seat of a literary and/or scientific learned society. The empire and its allied states had seen spectacular industrial growth, encouraged by the blockade which excluded outside competition, with the development of metallurgical industries in north-eastern France, Belgium and Saxony, of textile industries in France and northern Italy, and of the sugar-beet industry across northern Europe.
The French empire, with its 130 departments stretching from Amsterdam to Rome and its population of 40 million out of a European total of 170, was the greatest power on the Continent, and to the outside observer looked set to remain so. But in effect, it was a deeply flawed structure with profound problems.
While it had continued to grow on the Continent, it had been shrinking overseas, losing its last colonies to the British: La Petite Terre in 1808, La Désirade, Marie-Galante, Guyana, Saint Louis, Santo Domingo, Saint Lucia, Tobago, Martinique and the Danish Antilles in 1809, Réunion (renamed Bonaparte in 1806), Guadeloupe and Île de France in 1810, and Mauritius, Tamatave and the Seychelles in 1811. Napoleon planned to build up to a hundred ships of the line, but in the hurry to achieve this poor timber was used, while the cannon were of such poor quality, and so prone to explode, that the British did not use captured guns. French privateers did prey on British shipping, taking 519 prizes in 1806, and 619 in 1810, but that was only a pinprick to the British sailing stock, and with the introduction of convoys even that was reduced.
The real problems were economic: Napoleon's grand projects and imperial splendour required money, and his need kept growing. His budget went up from 859 million francs in 1810 to 1,103 million the following year. The cost of the land army rose from 377 to 500 million. His court was taking a greater share of government income than that of Louis XVI before the Revolution. He raised taxes, and imposed customs duties and other means of indirect taxation (these had more than doubled in the past five years), while looking for economies by eliminating imagined waste. He spent hours inspecting accounts, adding up figures and delighting in discovering a discrepancy of a few francs, discussed the necessity of every expense and quibbled with architects, engineers and builders, accusing them of trying to cheat, and insisting that any, even the smallest, extra-budgetary expense be authorised by himself, even in dependent territories such as the Grand Duchy of Berg. He went through the court accounts looking for waste, and haggled with suppliers. He kept lists in his notebooks of everything he had authorised and referred to them to check that nothing had been slipped in without authorisation. At the same time, the published budgets and accounts were as fictitious as his Bulletins.
His military expenditure was enormous. In the past, war had paid for it, and the treaty signed after Wagram had yielded a huge sum in indemnities. Part of the reason for the harshness of its terms was that the campaign had been more costly than previous ones on account of the size of the armies and the quantity of ordnance involved. It had also been more costly in terms of casualties. The war in the Iberian Peninsula was proving equally costly, and brought in nothing. Napoleon had raised a loan on the income of the Grand Duchy of Warsaw to finance his foray into Spain in 1808 ('Bayonne-like sums' is still a proverb in Poland today to denote untold riches), looted whatever he could and sold off as much Church property as he could lay his hands on. He sent as many non-French units as possible to fight there in order to reduce the expense – Westphalian, Dutch, Polish and Italian troops were equipped and paid by their respective governments, and their casualties did not have an impact on public opinion in France. But the war dragged on, and the cost to his treasury was growing.
He had meant to return to Spain in the autumn of 1809 to take charge, drive out the British and impose order. But his divorce and remarriage had distracted him, and when, in the spring of 1810, he discovered the joys of life with his new bride, he put off going. There seemed to be no urgency, as the military situation did not look bad: Joseph and Soult had occupied Andalucia and Seville, where they recovered all the standards lost at Bailén, Suchet had taken control of Aragon, and Masséna had pushed Wellesley, now Viscount Wellington, back into Portugal. But Napoleon's policy of sending German, Dutch and Italian troops to serve in Spain had a deleterious effect, as many of them took the first opportunity to desert, creating a climate which communicated itself to their French comrades who also went over to the enemy.
Joseph had no control over the French troops supposed to support his rule. Berthier was nominally in command of the Army of Spain, but remained in Paris. In February 1810 Napoleon divided Spain into military provinces whose commanders had extraordinary powers, which, since there was nobody in overall command, only dispersed the military effort further. The administration put in place by Joseph was undermined, taxes collected by his officials were seized, and his attempts to impose his authority were ineffectual. By the middle of 1810 he was in conflict with every one of the commanders operating in Spain, and Napoleon ignored him, not bothering to reply to his letters.
Joseph was so exasperated that one day in August he emptied a pair of pistols at a portrait of Napoleon. He wrote to his wife Julie saying he had decided to leave Spain, sell Mortefontaine and find a place far from Paris to retire to. He begged Napoleon to allow him to abdicate, arguing that his health could no longer stand the strain. He came to Paris unbidden for the christening of the King of Rome to plead his case, only to be told to go back to Madrid and wait for Napoleon to come and take things in hand.
But the possibility of his doing so was receding, as other financial and political problems loomed. One was a severe economic crisis at the beginning of 1811 which caused a recession across northern Europe and hit France badly, with multiple bankruptcies, a rise in unemployment and strikes, along with riots against conscription and anti-war slogans daubed on walls. Napoleon took measures to provide emergency food for the poor, but he had to look further for additional sources of income, which aggravated an already difficult international situation.
The economic war with Britain was damaging both sides while failing to deliver a result. Just as Britain began to suffer, the French intervention in Spain provided her with a lifeline; the Spanish colonies in Central and South America took advantage of the change of dynasty in Madrid to declare independence and open their ports to British shipping, creating a market for British manufactured goods. And if Britain was economically damaged by the Continental blockade, the effect on France was hardly better: maritime trade had withered, French ships rotted in port and the treasury was starved of customs revenue. Under pressure to find new sources of income, in 1809 Napoleon allowed merchants to purchase licences to trade with Britain, and not long afterwards the British government did the same with regard to France, as the country was running short of grain. Thus, by the end of the year France was exporting brandy, fruit, vegetables, salt and corn to England, and importing timber, hemp, iron, quinine and cloth. This made a mockery of the Continental System, and had profound political consequences, as it was an insult to France's principal ally, Russia.
As soon as his marriage to Marie-Louise had been agreed, Napoleon had written to Alexander tactfully announcing his intention. His letter crossed one from Alexander informing him that while he still hoped their two houses would one day be united, the dowager empress had ruled out his marrying the Grand Duchess Anna for another two years on the grounds of her age. It was a polite refusal, and it should have been Napoleon who felt affronted. Yet it was Alexander who was made to look foolish; he had championed the entente with France in the face of hostile public opinion at home, and it now looked as though his ally had snubbed him. The announcement of the Austrian marriage also suggested that Napoleon had been conducting parallel negotiations with Austria, which raised the question of what else might have been agreed. 'Russia acts only out of fear,' Metternich had said to Napoleon during his visit to Paris for the wedding in March 1810. 'She fears France, she fears our relations with her, and, with fear generating more fear, she will act.' He judged right.
At Tilsit, Napoleon had declared to Alexander that there were no points of friction between the interests of France and those of Russia, and that he had no wish to extend French influence beyond the Elbe, adding that the area between that and the Niemen should remain a neutral buffer zone. Yet he had established a French satellite there, and a provocative one at that; the creation of the Grand Duchy of Warsaw in 1807 was seen in Russia as the first step in a restoration of the kingdom of Poland, which raised the possibility of Russia having to give up some if not all of the 463,000 square kilometres, with a population of some seven million, acquired when Poland was liquidated. Many Poles, whether they were citizens of the Grand Duchy or not, did see it as the nucleus of a restored Poland. When Austria went to war with France in 1809 and the Polish army of the Grand Duchy invaded Galicia, the part of Poland ruled by Austria, local patriots rose in support. In the peace settlement, Napoleon allowed only a small part of the liberated territory to be added to the Grand Duchy, and awarded the greater part to Russia. It was a typically Napoleonic compromise: it disappointed the Poles without pacifying Russian public opinion, which saw it as a second step in the restoration of Poland.
Napoleon never intended to restore Poland. All his statements to the contrary date from later, when he was trying to keep the Poles on his side or salvage his reputation. At the time he dismissed the idea firmly and frequently; he regarded Poland as 'a dead body', and did not think the Poles capable of reviving it as a viable state. But he could not deny himself a vast pool of soldiers (most of them to fight in Spain), so he encouraged the Poles in thinking he favoured their cause.
Alexander wanted Napoleon to sign a convention pledging not to allow the restoration of Poland, and to take up arms against the Poles should they attempt it. Napoleon replied that while he could declare his opposition to such a revival, he would and could not undertake to hinder it. To sign the text suggested by Russia would 'compromise the honour and dignity of France', as he put it to his foreign minister Champagny; tens of thousands of Poles had fought alongside the French for over a decade, inspired by hopes of a free motherland and convinced of France's sympathy for their cause.
On 30 June 1810, when he received a communication from St Petersburg with a list of complaints and a renewed demand that he sign the convention on Poland, and hinting that Russia might not be able to keep up the blockade against Britain without it, Napoleon lost his temper. He summoned the new Russian ambassador, Prince Kurakin, a ridiculous and ineffectual man known in Paris as ' _le prince diamant_ ', since he never appeared otherwise than covered in decorations and jewellery, who was eloquent testimony to how little Alexander valued developing good relations with France. 'What does Russia mean by such language?' Napoleon demanded. 'Does she want war? Why these continual complaints? Why these insulting suspicions? If I had wished to restore Poland, I would have said so and would not have withdrawn my troops from Germany. Is Russia trying to prepare me for her defection? I will be at war with her the day she makes peace with England.' He then dictated a letter to Caulaincourt in St Petersburg telling him that if Russia was going to blackmail him and use the Polish question as an excuse to seek a rapprochement with Britain, there would be war. It was an idle threat, as war with Russia was the last thing he wanted.
Alexander, on the other hand, was coming to see war as inevitable. Russian society resented the alliance with Napoleon as it associated him with the Revolution and godlessness, as well as fearing that he intended to restore Poland. Orthodox Russian traditionalists regarded the Catholic Poles as the rotten apples in the Slav basket, and the Polish inhabitants of what were now the empire's western provinces as a fifth column of western corruption within it. Such feelings turned to paranoia when, in the summer of 1810, the Swedish people elected a Frenchman as their crown prince and de facto ruler.
The Swedish king, Charles XIII, was senile and childless, and in their search for a successor, the Swedes looked for a distinguished French soldier who might help them recover Finland, lost to Russia in 1809. They turned to Napoleon, who suggested Eugène. He declined, not wishing to abandon his Catholic faith, so, encouraged by Champagny, they suggested Bernadotte. Napoleon was not best pleased, realising that he might prove less than cooperative, but assumed that he would behave as a Swedish patriot if not a Frenchman – Sweden's natural enemies were Russia and Prussia, and France her traditional ally. The Swedes' friendly feelings towards France were strained by the Continental System, but their long coastline and their Pomeranian colony on the northern coast of Germany permitted them to breach it. It would also have been a relief to Napoleon to have Bernadotte out of the way.
In Russia, Bernadotte's election was greeted with uproar. 'The defeat of Austerlitz, the defeat of Friedland, the Tilsit peace, the arrogance of the French ambassadors in Petersburg, the passive behaviour of the Emperor Alexander I with regard to Napoleon's policies – these were deep wounds in the heart of every Russian,' recalled Prince Sergei Volkonsky. 'Revenge and revenge were the only feelings burning inside each and every one.'
Such feelings were reinforced by the economic hardships caused by the Continental System. Russia had little industry, and was dependent on imports for a variety of everyday items. These now had to be smuggled in via Sweden or through smaller ports on Russia's Baltic coastline. Her exports – timber, grain, hemp and so on – were bulky and difficult to smuggle. The Russian ruble fell in value against most European currencies by as much as 25 per cent, which made the cost of foreign goods exorbitant. Between 1807 and 1811 the price of coffee more than doubled, sugar became more than three times as expensive, and a bottle of champagne went from 3.75 to 12 rubles. This cocktail of wounded pride and financial hardship produced ever more violent criticism of Alexander's policy, and the only way he could deflect it was to break free of Napoleon. He had been building up and modernising his army since Tilsit, and back in December 1809, while still pretending to favour Napoleon's marriage to his sister, he began trying to subvert the Poles with promises of autonomy under Russian aegis.
The summer of 1810 yielded a poor harvest in England, which coincided with a dramatic fall in the value of sterling. Napoleon tightened the economic screw by raising tariffs further on licensed imports. Britain was struggling economically, and he was convinced he could bring her to the negotiating table (on his terms). He therefore, in October 1810, instructed Caulaincourt to order Russia to raise tariffs too. This left Alexander with little option but to defy the system openly. On 31 December he opened Russian ports to American ships, and imposed tariffs on French manufactured goods imported overland into Russia. British goods were soon pouring into Germany from Russia; the Continental System was in tatters.
Napoleon could not accept it. 'The Continental System is uppermost in his mind, he is more taken up with it than ever,' noted his secretary Fain. In his determination to control all points of import, Napoleon annexed the Hanseatic ports. In January 1811 he did the same with the duchy of Oldenburg, whose ruler was the father of Alexander's brother-in-law. He did offer him another German province as compensation, but this was refused. Alexander was outraged, and felt personally insulted – his supposed ally was now despoiling members of his family. He had to act, if only to save face. 'Blood must flow again,' he told his sister Catherine.
At the beginning of January 1811 he renewed attempts to win over the Poles, or at least ensure their neutrality, while his minister of war General Barclay de Tolly drew up plans for a strike into the Grand Duchy followed by an advance into Prussia. Alexander had 280,000 men ready, and calculated that if the Poles and the Prussians were to join him, he could be on the Oder with a force of 380,000 before Napoleon could react. Napoleon was well informed, and took the threat seriously. He ordered Davout, in command of the French forces in northern Germany, to prepare for war, and ordered the Poles in the Grand Duchy of Warsaw to mobilise. 'I considered that war had been declared,' he later affirmed. In a report to Francis on 17 January 1811, Metternich stated his opinion that war between France and Russia was inevitable.
In the same report, he argued that the restoration of Poland would be desirable if, in return for giving up the rest of Galicia, Austria were to recover the Tyrol, part of Venetia and Illyria. That would strengthen her position in the Balkans, improve her defences in the south and give her Trieste and access to the sea, while a restored Poland would act as a buffer against Russian aggression. Austria rejected Russian diplomatic overtures aimed at securing support against France, fearing Russian expansion in the Balkans and increased influence in Central Europe; a strategic alliance between Austria and France was on the cards. The treaty Austria would sign with France on 14 March 1812 had as its aim the return of the Danubian Principalities to the Porte, and left open the possibility of recreating a kingdom of Poland. In Paris, gossip had it that Murat would be made King of Poland.
'I have no wish to make war on Russia,' Napoleon declared to the Russian Count Shuvalov during an interview at Saint-Cloud in May 1811. 'It would be a crime on my part, for I would be making war without a purpose, and I have not yet, thanks to God, lost my head, I am not mad.' To Colonel Chernyshev, whom the tsar had sent to Paris with letters for Napoleon, he repeatedly stated that he had no intention of fatiguing himself or his soldiers on behalf of Poland, and 'he formally declared and swore by everything he held holiest in the world that the re-establishment of that kingdom was the very _least_ of his concerns'. But such professions of goodwill would not suffice.
When Caulaincourt returned to Paris from St Petersburg on the morning of 5 June 1811, he drove straight to Saint-Cloud, and within minutes of arriving was ushered into Napoleon's presence – in which he spent the next seven hours in a discussion whose course he noted down that evening. He explained Alexander's position, and warned that the tsar would fight to the end rather than submit to Napoleon's demands. Napoleon dismissed this as bravado, asserting that Alexander was 'false and weak'. He could not believe Russian society would accept the implied sacrifices – the nobles would not want to see their lands ravaged for the sake of Alexander's honour, while the serfs would as likely revolt against them as fight for a system of slavery.
He viewed the Russian abandonment of the Continental System as a betrayal, and her troop build-up as a threat to his influence in Central Europe. He had convinced himself that Alexander was using the Polish question and the subject of trade as excuses to break out of the alliance and draw closer to Britain, and that he would invade the Grand Duchy of Warsaw the moment an opportunity presented itself.
Caulaincourt pointed out that Napoleon had only two options: he must either give a significant part, if not the whole, of the Grand Duchy of Warsaw to Alexander, or go to war with the aim of restoring the kingdom of Poland. He advised him to take the first course, which in his opinion would guarantee a stable peace. Napoleon declared that such a betrayal of the Poles would dishonour him and lead to further Russian expansion into the heart of Europe.
He wanted to maintain his alliance with Alexander, yet would not pay the necessary price, and wanted to keep the Polish question open without committing to it. But this was no longer possible. By making his alliance with her the linchpin of his plan to defeat Britain, Napoleon had inflated Russia's significance, and his continued attempts to make Alexander do his bidding had spurred the tsar to assume an even greater role in European affairs.
Napoleon's exasperation erupted on 15 August 1811, his forty-second birthday. At midday he strutted into the throne room at the Tuileries, filled with court officials and diplomats perspiring in their uniforms and ceremonial dress on what was a particularly hot day. After receiving their good wishes, Napoleon stepped down from the throne and walked among the guests. When he reached the Russian ambassador, he accused Russia of massing troops with the intention of invading the Grand Duchy of Warsaw, describing it as an open act of hostility. The unfortunate Kurakin kept opening his mouth to reply, but could not get a word in edgeways, while sweat poured down his face. After bullying him for a while, Napoleon walked away, leaving him in a state of shock.
The following morning, after a conference with Maret, who had succeeded Champagny as foreign minister, in the course of which they reviewed every document concerning Russia since Tilsit, Napoleon concluded that France wanted Russia as an ally against Britain and had no wish to fight her, since there was nothing she wanted from her, but that she could not buy Russia's friendship by betraying the Poles. France must therefore prepare for war in order to prevent Russia from going to war. Caulaincourt's successor in St Petersburg, General Lauriston, was instructed to explain this.
Napoleon could not see that he had put Alexander in an impossible situation, and he would not believe what he did not wish to see – that unless he stepped back, war was inevitable. Nor did he wish to face the fact that Russia was strategically invulnerable, as it was too vast to overrun and subdue. France on the other hand was highly vulnerable, since it was already engaged in a war in the Iberian Peninsula and was open to attack from Britain along its entire coastline. French possessions in Germany and Italy were unstable, as Napoleon kept moving boundaries and rearranging their administration, and satellites such as Naples were not dependable. Nor were his allies in the Confederation of the Rhine loyal other than by necessity. The whole Napoleonic system was a work in progress, whose final arrangement was contingent on an outcome with Britain, which now depended on solutions in both Spain and Russia. Acting tactically, without an overall strategy, Napoleon had got himself into an impasse from which the only way out was back – not a step he was used to contemplating.
'It would have been difficult to imagine any new obstacle to the Emperor's prosperity, and, whatever he undertook, people expected of the magician what no man would have undertaken,' wrote Victorine de Chastenay. Surrounded by his _maison_ , which had grown to include 3,384 people, he was cut off from the real world. Beugnot, who had returned to Paris after an absence of three years, was struck by the luxury of the court, but noted that at Napoleon's table and those of his ministers, which were 'sumptuously served and attended by valets shimmering with gold', boredom reigned, as nobody discussed matters of state as they had in the past. Although there were few guards in evidence at the Tuileries, and security surrounding the emperor was light, fear and self-censorship proclaimed despotism; people whispered or kept silent, and Napoleon could ignore unpleasant truths. He must have read, as he always did, the police report from Lille relating to 2 December 1811, the anniversary of Austerlitz and his coronation, one of the major national feast days of the Napoleonic calendar, which found that 'the inhabitants appeared not to know for what reason' the city was illuminated and festivities were taking place. But it clearly made no impression deep enough to make him reflect. From where he sat, his power seemed limitless. On 3 November 1811, the fourteen-year-old Heinrich Heine watched him ride into Düsseldorf. He thought 'his features were noble and dignified, like those of ancient sculptures, and on his face were written the words: "Thou shalt have no other gods beside me."'
He was defying God himself; when, back in June, the Council of French bishops, headed by Fesch, had sworn allegiance to the Pope, Napoleon had closed it down and imprisoned a number of its members in the fortress of Vincennes. On 3 December he issued another ultimatum demanding the acquiescence of the Pope, whose behaviour had 'wounded' his imperial authority, and imprisoned or exiled more clerics. The Pope himself would soon be dragged off in a closed carriage, travelling by night to house arrest at Fontainebleau, and even Fesch would be exiled.
By that time, troops were on the move all over Europe, recruits were being drilled, arms, uniforms and supplies of every kind stockpiled. Yet Napoleon still denied he intended to make war. To Metternich and many others it now seemed inevitable, and the only question was what the outcome would mean for Europe. 'Whether he triumphs or succumbs, Europe will never be the same again,' Metternich wrote to Francis. 'This terrible moment has unfortunately been brought on us by the unpardonable conduct of the Russians.'
## 36
# Blinding Power
Napoleon still had no fixed policy at the beginning of 1812. 'I am far from having lost hope of a peaceful settlement,' he wrote to Jérôme on 27 January. 'But as they have adopted towards me the unfortunate procedure of negotiating at the head of a strong and numerous army, my honour demands that I too negotiate at the head of a strong and numerous army. I do not wish to open the hostilities, but I wish to put myself in a position to repulse them.'
Yet to one of his aides he explained that he was 'propelled into this hazardous war by political reality', as the fertile and civilised south of Europe would always be threatened by uncivilised ravenous hordes from the north, and 'the only answer is to throw them back beyond Moscow; and when will Europe be in a position to do this, if not now, and by me?' According to some in his entourage, he feared that his military talents and powers of endurance were in decline, and felt he must deal with Russia while he still had the energy. 'One way or another, I want to finish the thing,' he said to General Vandamme, 'as we are both getting old, my dear Vandamme, and I don't want to find myself in old age in a position in which people can kick me in the backside, so I am determined to bring things to a conclusion one way or the other.' As he began regrouping his forces and preparing for war, the soldier seems to have awoken in Napoleon. And according to Mollien, he even thought that, as in the past, a war might refill his coffers. In effect, he did not really know what to do. 'I feel myself propelled towards some unknown goal,' he admitted to his aide Philippe de Ségur, adding that his fate was 'written'.
He had assembled the largest army the world had ever seen. The Frenchmen in its ranks were outnumbered by Poles, Germans, Austrians, Belgians, Dutchmen, Swiss, Italians, Spaniards, Portuguese and Croats, all of whom had differing interests and loyalties. Yet military instinct and the spirit of emulation bound them together. French rabbis exhorted young Jews: 'You will fight and vanquish under the command of the God of armies. Go, and return covered in laurels which will attest to your valour.' Valour, as tested in battle, was considered the prime virtue at the time, and young men felt a strong urge to prove their worth. 'Whatever their personal feelings towards the emperor may have been, there was nobody who did not see in him the greatest and most able of all generals, and who did not experience a feeling of confidence in his talents and the value of his judgement,' in the words of one aristocratic German officer. 'The aura of his greatness subjected me as well, and, giving way to enthusiasm and admiration, I, like the others, shouted " _Vive l'Empereur!_ "' A Piedmontese cavalry lieutenant to whom Napoleon had addressed a few words during a parade felt the same. 'Before that, I admired Napoleon as the whole army admired him,' he wrote. 'From that day on, I devoted my life to him with a fanaticism which time has not weakened. I had one regret, which was that I had only one life to place at his service.'
The size of the army obscured its quality. In March 1812 an inspection of the cavalry revealed that a third of the horses were too weak to carry a man. Only about the same proportion of the men were fit for action in most of the contingents. Napoleon made light of this. 'When I put 40,000 men on horseback I know very well that I cannot hope for that number of good horsemen, but I am playing on the morale of the enemy, who learns through his spies, by rumour or through the newspapers that I have 40,000 cavalry,' he argued. 'Passing from mouth to mouth, this number and the supposed quality of my regiments, whose reputation is well known, are both rather exaggerated than diminished; and the day I launch my campaign I am preceded by a psychological force which supplements the actual force that I have been able to furnish for myself.'
Buoyed by the enthusiasm of the younger men, he chose to ignore the state of mind of many of those with greater experience. Much of the revolutionary ardour that had fired the French armies of the 1790s and early 1800s had been quenched by 1812. 'From the moment Napoleon came to power, military mores changed rapidly, the union of hearts disappeared along with poverty and the taste for material well-being and the comforts of life crept into our camps, which filled up with unnecessary mouths and numerous carriages,' in the words of General Berthezène. 'Forgetting the fortunate experiences of his immortal campaigns in Italy, of the immense superiority gained by habituation to privation and contempt for superfluity, the Emperor believed it to be to his advantage to encourage this corruption.' He had given his marshals and generals titles, lands and pensions; they became less willing to forsake their warm beds and palaces, their wives and families for the rigours of the bivouac and the uncertainties of war. Many were entering middle age; they could hardly expect to win greater glory, but could lose everything they had and leave their families destitute.
Napoleon's marshals, senior generals and entourage were mostly opposed to the war for specific reasons: the distances involved, the terrain, the nature of the enemy, the pointlessness, the lack of any advantage to be gained from it, and the possible consequences on the political situation back in France. Even the commander of the Polish contingent, Poniatowski, warned him against invading Russia. Yet such was Napoleon's extraordinary aura that even the most sceptical submitted to the spell and believed in his 'star'. 'It was so sweet to abandon oneself to that star!' reminisced Ségur. 'It blinded us, it shone so high, so brilliant, it had worked such miracles!'
While Napoleon was involving half the states of Europe in the forthcoming war, he was determined not to enlist them as real allies, because he meant to keep his options open. Nor did he bother to prepare the ground at the diplomatic level – quite the contrary. On 27 January 1812, under the pretext that the Continental System was not being enforced rigorously there, he sent his armies into Swedish Pomerania and took possession. He followed this up with a demand to Sweden for an alliance against Russia and a contingent of troops. When this was rejected, he offered to return Pomerania, and threw in Mecklemburg as well as a large subsidy. But it was too late. His high-handed seizure of Pomerania had been taken as an insult in Sweden, and within two weeks of the news reaching Stockholm, Bernadotte's envoy was in St Petersburg asking for a treaty with Russia, which was duly signed on 5 April.
Napoleon failed to encourage the Turks to carry on fighting the Russians in the Balkans, with the result that they would soon make peace, allowing Russia to transfer troops from there to face him. His treatment of Austria and Prussia meant he had two disgruntled allies at his back only waiting for a chance to abandon or even turn against him. This was careless in view of the rising tide of anti-French feeling in Germany. Throughout 1811 reports from French commanders and diplomatic agents there alerted him to the growing danger. In Prussia, the king was barely able to contain the national feeling, particularly strong in the army. 'The ferment has reached the highest degree, and the wildest hopes are being fostered and cherished with enthusiasm,' reported a nervous Jérôme from neighbouring Westphalia in December. 'People are quoting the example of Spain, and if it comes to war, all the lands lying between the Rhine and the Oder will be embraced by a vast and active insurrection.'
Napoleon's lack of contingency planning accords with other evidence that he was confident war could be avoided, and that the military build-up was aimed principally to cow Alexander into submission. In this he misjudged the situation catastrophically; he knew Alexander was weak and stubborn, and with his wide experience of men he should have known that stubborn men, however weak, grow more stubborn when pushed. Alexander could not step back from the brink without discrediting himself forever in the eyes of his subjects, thereby exposing himself to a fate like his father's. By now, even a face-saver over Poland would not have sufficed, as the tsar had rallied to his side an impressive array of Napoleon's enemies, representing a spectrum of causes. They included Germaine de Staël, who lent him the intellectual credibility of supporting liberalism, the fiercely anti-French German nationalist Baron Karl vom Stein, who hoped to bring about the regeneration and unification of Germany, and Napoleon's old enemy Carlo Andrea Pozzo di Borgo, pursuing his vendetta. Alexander also dreamed of playing a grand part on the world stage, and was beginning to see his duel with Napoleon as not just a challenge, but an opportunity.
If it did come to war, Napoleon needed to inflict such a shattering blow that the Russian army would lose all ability and will to resist, as the Prussian had following Jena. But his campaign of 1807 had shown that speed was not achievable in this part of the world, and that of 1809 had revealed that his enemies had got wise to his tactics and become deft at slipping out of the traps he set for them. In a sparsely populated area where he had no spies, he would be operating in the dark. And by concentrating such a huge force he cancelled out any possibility of swift manoeuvring.
The enterprise presented a logistical nightmare. Napoleon had read every book he could lay his hands on regarding the topography, climate and characteristics of the theatre of operations. He had pored over maps, calculating distances and imagining the conditions in which he would have to operate. The starting point, the Russian frontier on the Niemen, was some 1,500 kilometres from Paris, and the two principal Russian cities, St Petersburg and Moscow, were respectively 650 and 950 kilometres beyond that. The stretch of 300 kilometres on the western side of the border and 500 beyond it was very poor, sparsely populated country with rudimentary roads and bridges, few towns, numerous rivers, bogs and forests to get lost in, and scant resources. The Grande Armée would have to take with it everything it needed.
Perhaps more important than any of these considerations was that a change had taken place in the nature of war, and the kind of brilliant victories he had achieved in the past would no longer yield the same results; the verdict of the battlefield had ceased to be decisive. Napoleon still believed that if an enemy's army was defeated and its capital occupied, it would be forced to sue for peace and then to abide by its terms, however onerous, even though Spain had revealed this not to be so. And although he had seen the Russian soldiers let themselves be hacked to pieces at Eylau and Friedland rather than surrender, he had not drawn the conclusion that, given the size of the country, there would always be more to take their place, and he was therefore bound to lose a war of attrition.
There were only two areas in which the Russian state was vulnerable. Having recently conquered a huge amount of territory and not had time to absorb or fully pacify its indigenous populations, it could be challenged by multiple national insurrections. And, based as it was on serfdom, it could be destabilised by revolution. Yet these were two options that Napoleon did not wish to use, since they would undermine his preferred outcome – a renewal of his alliance with Alexander.
On 24 April Kurakin delivered a letter from Alexander in which the tsar declared that no more talks could take place unless Napoleon withdrew all his troops west of the Rhine, which was tantamount to a declaration of war. In his reply, delivered three days later, Napoleon expressed regret that the tsar should be ordering him where to station his troops while he himself stood at the head of an army on the frontiers of the Grand Duchy. 'Your Majesty will however allow me to assure him that, were fate to conspire to make war between us inevitable, this would in no way alter the sentiments which Your Majesty has inspired in me, and which are beyond any vicissitude or possibility of change,' he ended.
He could delay no longer. He had to go and take command of his armies. Before doing so, he made arrangements for the defence and the administration of France. Although he had, as a long shot, made a peace offer to Britain, suggesting a bilateral withdrawal of French and British troops from the Iberian Peninsula, with Joseph remaining King of Spain and its former rulers being allowed back into Portugal, he expected nothing to come of it. He therefore strengthened France's coastal defences and organised a national guard of 100,000 men who could be called out in an emergency. To remind people of their duty, he had the man who had capitulated at Bailén, General Dupont, retried and given a stiffer sentence. He also put in hand public works projects including five abattoirs, two aqueducts, three fountains, a canal, eleven markets, three bridges, a granary, a university, an observatory, a college of art, and refurbishments to or further work on an opera, a conservatoire, the national archives, a ministry, several palaces, a temple, a church, cemeteries, embankments and streets.
At their last meeting, on the eve of Napoleon's departure, the prefect of police Étienne Pasquier voiced fears about the possibility of an attempt by his enemies to seize power while he was so far away. 'Napoleon seemed to be struck by these brief reflections,' recalled the prefect. 'When I had finished, he remained silent, walking to and fro between the window and the fireplace, his arms crossed behind his back, like a man deep in thought. I was walking behind him, when, turning brusquely towards me, he uttered the following words: "Yes, there is certainly some truth in what you say; this is but one more problem to be added to all those that I must confront in this, _the greatest, the most_ difficult, enterprise I have ever undertaken; but one must accomplish what has been undertaken. Goodbye Monsieur le Préfet."'
Napoleon knew how to hide any anxiety he may have felt. 'Never has a departure for the army looked more like a pleasure trip,' noted Fain as the emperor left Saint-Cloud on Saturday, 9 May with Marie-Louise. At Mainz he reviewed troops and received the Grand Duke of Hesse-Darmstadt and the prince of Anhalt Coethen, who had come to pay their respects. At Würzburg, where he stopped on the night of 13–14 May, he found the King of Württemberg and the Grand Duke of Baden waiting for him like faithful vassals.
On 16 May he was met by the king and queen of Saxony, who had driven out to greet him, and together they made their entry into Dresden by torchlight as the cannon thundered salutes and the church bells pealed. His _lever_ the next morning was graced by several ruling princes. The queen of Westphalia and the Grand Duke of Würzburg arrived later that day, and the emperor and empress of Austria the next. They were joined a couple of days later by Frederick William of Prussia and his son the crown prince.
Napoleon had taken over the royal palace, obligingly vacated by the king, in which he held court attended by all the crowned heads present, 'whose deference to Napoleon went far beyond anything one could imagine', in the words of his aide Boniface de Castellane. After they had cringed at his _lever_ every morning, they followed him to attend the _toilette_ of Marie-Louise. They watched her pick her way through an astonishing quantity of jewellery, trying on and discarding one piece after another, and occasionally offering one to her barely older stepmother the Empress Maria Ludovica, who simmered with shame and fury; she loathed Napoleon for the upstart he was, and for having thrown her father off his throne of Modena some years earlier.
In the evenings they dined off the silver-gilt dinner service Marie-Louise had been given as a wedding present by the city of Paris, which she had thoughtfully brought along. The company assembled and entered the drawing room in reverse order of seniority, each announced by a crier, beginning with mere excellencies, going on to the various ducal and royal highnesses, and culminating with their imperial highnesses the emperor and empress of Austria. A while later, the doors would swing open and Napoleon would stride in, with just one word of announcement: ' _L'Empereur!_ ' He was also the only one present who kept his hat on. 'Napoleon was indeed God at Dresden, the king amongst kings: it was on him that all eyes were turned; it was to him and around him that all the august people brought together in the King of Saxony's palace gathered,' in the words of one observer.
There were balls, banquets, theatrical performances and hunting parties, all focused on Napoleon in a choreographed display of power intended to remind his allies of their subjection to him. He was still hoping that when he saw himself isolated and faced with such an array of power Alexander might agree to negotiate. He still felt what Méneval described as 'an extreme repugnance' for going to war, and clung to the delusion that the tsar's resolve would crumble. 'Never have the reason and judgement of a man been more deceived, more led astray, more dominated by his imagination and his passions than those of the Emperor in some matters,' noted Caulaincourt after one of their meetings.
Napoleon had convinced himself that Alexander was being manipulated by his entourage, and believing that if only he could talk to him directly or through some trusted third party they would reach an understanding, he despatched his aide Louis de Narbonne to the tsar's headquarters at Vilna (Vilnius). Alexander received him coolly, and sent him back to Dresden. Napoleon then sent a courier to Lauriston in St Petersburg, instructing him to go to Alexander at Vilna and talk sense into him, but he was denied permission and told to leave Russia.
Napoleon had left himself with no option other than to fight, and he put on a brave face. 'Never has an expedition against them been more certain of success,' he said to Fain, pointing out that all his former enemies were now allies. 'Never again will such a favourable concourse of circumstances present itself; I feel it drawing me in, and if the Emperor Alexander persists in refusing my proposals, I shall cross the Niemen!' Yet he had no fixed idea as to what he would do after that.
'My enterprise is one of those to which patience is the key,' he explained to Metternich. 'The more patient will triumph. I will open the campaign by crossing the Niemen, and it will end at Smolensk and Minsk. That is where I shall stop. I will fortify those two points, and at Vilna, where I shall make my headquarters during the coming winter, I shall apply myself to the organisation of Lithuania, which is burning to be delivered from the Russian yoke. I shall wait, and we shall see which of us will grow tired first – I of making my army live at the expense of Russia, or Alexander of nourishing my army at the expense of his country. I may well myself go and spend the harshest months of the winter in Paris.' And if Alexander did not sue for peace that year, Napoleon would mount another campaign in 1813, into the heart of Russia. 'It is, as I have already told you, only a question of time,' he assured Metternich. He said much the same to Cambacérès, whom he assured that he would restore Poland up to the river Dnieper, and would go no further.
He was nevertheless open to every possibility. 'If I invade Russia, I will perhaps go as far as Moscow,' he wrote in his instructions to one of his diplomats. 'One or two battles will open the road for me. Moscow is the real capital of the empire. Having seized that, I will find peace there.' He added that if the war were to drag on, he would leave the job to the Poles, reinforced by 50,000 French.
He still refused to see Alexander as an enemy to be defeated, thinking of him as an ally to be brought back to heel, which he wished to do with as little unpleasantness as possible and a minimum of damage. 'I will make war on Alexander in all courtesy, with 2,000 guns and 500,000 soldiers, without starting an insurrection,' he explained. But he still clung to the hope that he would not have to do even that. 'I may even not cross the Niemen,' he wrote to Cambacérès; his aide Dezydery Chłapowski was convinced that he was only bluffing, and had no intention of invading Russia at all.
Talleyrand, Narbonne and Maret were among those who advocated creating a Polish state as a bulwark against Russian expansion, and Napoleon did not rule this out. He did have to keep the Poles on his side, and he needed to prime, even if he did not come to fire it, the weapon of Polish national insurrection in Russia's western provinces. In order to do this, he must send a clever man to Warsaw as an unofficial personal ambassador. He had originally selected Talleyrand for this purpose, but his choice now fell on the Abbé de Pradt, Archbishop of Malines. He was to encourage the Poles to proclaim the resurrection of the Polish state, without committing himself or his imperial master to backing it.
Napoleon gave some thought to the question of whom to put on the Polish throne if he did decide to restore the kingdom. It would be too important a place for Murat or Eugène, both of whom believed themselves to be in line for the job. He did consider Davout, a good soldier and administrator popular with the Poles, but the example of Bernadotte raised questions as to future loyalty – and Napoleon never entirely got over his jealousy at having been outshone by Davout's feat at Auerstadt. 'I'll put Jérôme on it, I'll create a fine kingdom for him,' he told Caulaincourt. 'But he must achieve something, for the Poles like glory.' He duly put Jérôme in command of an army corps and directed him to Warsaw, where he was supposed to win the love of the Poles.
Thrilled at being given a command, Jérôme kitted himself out with helmet and breastplate emblazoned with the insignia of his Order of Union, with its eagles, lions and serpents. He made a regal entry into the Polish capital and announced that he had come to spill his blood for the Polish cause. He sent back the mistress he had brought from Kassel and took a Polish one. The Poles found him overbearing and ridiculous, and were put off by the behaviour of his troops. More important, most reasoning Poles sensed the lack of commitment, and indeed of purpose, in Napoleon's policy. He had assembled the greatest army the world had ever seen, with no specific goal; by definition, aimless wars cannot be won.
After thirteen days in Dresden, where he had achieved little more than blind himself with his own display of power, Napoleon bade an affectionate farewell to the King of Saxony and a tearful one to Marie-Louise, and climbed into his travelling carriage. Two days later he was in Posen, which he entered under an arch inscribed with the words _Heroi Invincibili_ , greeted deliriously by its Polish citizens, who had illuminated the city and festooned it with flags and garlands. But after a conference with Daru, who was overseeing the provisioning, he had to face up to the fact that his preparations had proved ineffective, and as he continued his journey he could see for himself the dire supply situation. There was a shortage of draught horses, which meant that supplies could not be brought forward fast enough, and men and horses were dying in large numbers. The situation was growing worse with every passing day; the ground was burning under his army's feet, and Napoleon had to move fast before it starved.
The Russian forces were divided into three armies, positioned so as to be able to either defend Vilna or move out and attack. The First, deployed in advance of the city under General Mikhail Bogdanovich Barclay de Tolly, numbered about 160,000 men. The Second, under General Piotr Ivanovich Bagration, consisted of just over 60,000. It was poised to either support an advance by the First by outflanking the enemy, or to assist its defence by threatening the enemy's flank. A Third Army consisting of nearly 60,000 men under General Tormasov was positioned south of the Pripet Marshes, guarding the approaches to the Ukraine.
Napoleon proposed to attack Barclay's First Army while Eugène's and St Cyr's corps drove a wedge between that and Bagration, and further south, Jérôme took him on with three other army corps. The attack was to be spearheaded by Murat with a huge body of cavalry, a great battering-ram of four divisions. In the north, Marshal Macdonald with the Prussian contingent was to advance on Riga with Oudinot in support. South of the Pripet, Schwarzenberg's Austrians were to mark Tormasov. 'The wings of our army were thus entrusted to the two nations which had the greatest interest in seeing our enterprise fail,' remarked an officer on Berthier's staff.
It is impossible to determine the real strength of the Grande Armée. In theory, it consisted of 590,687 men and 157,878 horses, with another 90,000 or so men in various parts of Poland and Germany. On 14 June Napoleon issued a circular insisting that the commanders of every corps provide honest figures on the able-bodied, the sick, deserters, as well as the dead and the wounded. 'It has to be made clear to the individual corps that they must regard it as a duty towards the Emperor to provide him with the simple truth,' ran the order. But Napoleon reacted angrily when provided with dwindling figures, particularly if these could not be explained by battle casualties, so unit commanders concealed losses from him. 'He was led astray in the most outrageous way,' wrote General Berthezène. 'From the marshal to the captain, it was as if everyone had come together to hide the truth from him, and, although it was tacit, this conspiracy really did exist; for it was bound together by self-interest.' According to him, the true strength of the Grande Armée was no greater than 235,000 when it crossed the Niemen. That was still a considerable force, and this added urgency to the need for a quick victory; every day increased the difficulty of feeding it.
In two Bulletins, on 20 and 22 June, Napoleon explained how, since Tilsit, he had bent over backwards to accommodate Russia, but she had been taken over by 'the English spirit' and begun arming against him and the whole of Europe. 'The vanquished have adopted the tone of the conquerors,' he concluded. 'They are tempting fate; let destiny take its course.'
## 37
# The Rubicon
Omens of destiny were not in short supply. Having reached the furthest outposts, in the early hours of 23 June Napoleon borrowed a Polish lancer's cap and cloak and rode out, with his staff similarly disguised as a regular patrol, to scout the river Niemen for a good crossing point. A hare started from under his horse's hooves and he was thrown. Instead of cursing and blaming the horse as he usually did, he remained tight-lipped and remounted without a word. Berthier and Caulaincourt, who were in attendance, took it as a bad omen, and said they should not cross the river.
Napoleon spent the rest of the day working in his tent, in sombre mood. This contrasted sharply with the elation he normally displayed at the start of a campaign, and his entourage noted it with apprehension. He issued a proclamation to the army which announced the commencement of 'The Second Polish War', assuring his men that as well as being 'glorious for French arms', it would bring about a lasting peace and 'put an end to that arrogant influence which Russia has been exerting on the affairs of Europe over the past fifty years'.
At three on the morning of 24 June he was in the saddle once more, mounting a horse named Friedland, and as the sun came up he could see three pontoon bridges which had been thrown across the river, and one division taking up defensive positions on the other side. He took his place on a knoll overlooking the scene and watched, a telescope in his right hand and his left behind his back. The huge army, dressed as for a parade, was crossing the river, the morning sunshine glinting on the helmets and breastplates of cuirassiers and dragoons, and on every polished cap badge and belt buckle, and lighting up the blue, white, yellow, green, red and brown uniforms of the various allied contingents. He seemed in a good mood, and hummed military marches as he contemplated what one witness described as 'the most extraordinary, the most grandiose, the most imposing spectacle one could imagine, a sight capable of intoxicating a conqueror'.
' _Vive l'Empereur!_ The Rubicon has been crossed,' noted a captain of grenadiers of the Guard in his diary at a bivouac outside Kowno (Kaunas) on 26 June, adding that some 'fine pages' would be added to the annals of the French nation. Four days later Napoleon entered Vilna, which had just been evacuated by the Russians. He was greeted by a municipal delegation, but the inhabitants had not had time to prepare the usual trappings, and his entry into the city was anything but triumphal. And as he bedded down for the night in the former archbishop's palace, where Alexander had slept the night before, a primeval storm burst on the area to the south and west of the city.
Men and horses exhausted by lack of food and fodder, as well as by the intense heat of the past weeks, were suddenly drenched by a downpour of cold rain which lasted through the night. The morning sun revealed a landscape littered with dead or dying horses and men, of wagons, guns and gun carriages mired in mud, and those still alive struggling to get free. Some artillery units lost a quarter of their horses, and the cavalry did not fare much better, but it was the supply services which suffered the most; at a conservative estimate the French army lost around 50,000 horses that night.
The psychological damage was hardly less significant. As the men trudged on through the quagmire that had replaced the dusty roads, they could see dead and dying men and beasts by the roadside, and rumours of grenadiers having been struck by lightning passed from rank to rank. Had they been Greeks or Romans in ancient times they would undoubtedly have turned about and gone home after such an augury, quipped one of Napoleon's aides.
Napoleon was baffled by the behaviour of the Russians, who had shown every sign of meaning to defend Vilna, yet decamped at his approach, leaving behind stores accumulated over months. It made no sense, and he instructed his commanders to proceed with caution, expecting a counter-attack. He need not have bothered. Barclay was a fine general, but although he was also minister of war, Alexander had not given him overall command, and hovered at his side limiting his freedom of action. In the absence of any fixed plan, he thought it best to fall back.
On 1 July Napoleon received an envoy from Alexander, General Balashov, who brought a letter proposing negotiations conditional on a French withdrawal. 'Alexander is making fun of me,' Napoleon retorted: he had not come all this way in order to negotiate, and since Alexander had refused to do so before, it was time to deal once and for all with the barbarians of the north. 'They must be thrown back into their icy wastes, so that they do not come and meddle in the affairs of civilised Europe for the next twenty-five years at least.'
Balashov could hardly get a word in as Napoleon paced the room, venting his frustration in a monologue which veered from whining complaints to squalls of anger. He professed his esteem and love for Alexander, and reproached him for surrounding himself with 'adventurers'. He could not understand why they were fighting, instead of talking as they had at Tilsit and Erfurt. 'I am already in Wilna, and I still don't know what we are fighting over,' he said. He shouted, stamped his foot and, when a small window which he had just closed blew open again, tore it off its hinges and hurled it into the courtyard below. But in the reply to Alexander which he handed to Balashov he professed continuing friendship, peaceful intentions, and a desire to talk, without accepting the precondition of a withdrawal behind the Niemen.
'He has rushed into this war which will be his undoing, either because he has been badly advised, or because he is driven by his destiny,' he declared after Balashov had gone. 'But I am not angry with him over this war. One more war is one more triumph for me.' On 11 July he issued a mendacious Bulletin announcing great military successes, achieved at the cost of no more than 130 French casualties.
On the same day as Napoleon's interview with Balashov, the Polish patriots of Vilna had held a _Te Deum_ in the cathedral, followed by a ceremony of reunification of Lithuania with Poland. Napoleon had hoped that he would be able to defeat the Russians and reach an agreement with Alexander before he had to confront the Polish question, since that would probably have been part of the deal. But now he was being pressed to commit himself. In an attempt to duck the issue, on 3 July he set up a government for Lithuania, to administer the country, gather supplies and raise troops, and instructed his foreign minister Maret, whom he had brought to Vilna, to string them along.
On 11 July, eight delegates from the national confederation which he had called for in Warsaw arrived in Vilna. The emperor kept them waiting three days, then listened impatiently to their request that he announce the restoration of the kingdom of Poland. 'In my position, I have many different interests to reconcile,' he told them, but added that if the Polish nation arose and fought valiantly, Providence might reward it with independence. With this speech, he cooled the ardour of the Poles and robbed himself of what would have been a powerful weapon; the investigation conducted by the Russians after the war revealed that the population of the area in which he was operating was on his side, yet he would not engage its support or even sanction popular initiatives to act behind enemy lines lest it hinder chances of a reconciliation with Alexander.
In his proclamation launching his 'Second Polish War', he had written that he was taking the war into Russia, giving his troops the impression that from the moment they crossed the Niemen they were in enemy territory, and therefore licensed to behave as they liked. 'All around the city and in the countryside there were extraordinary excesses,' noted a young noblewoman of Vilna. 'Churches were plundered, sacred chalices were sullied; even cemeteries were not respected, and women were violated.' With no fighting to do and no palpable purpose to the campaign, tens of thousands of men had deserted and were roaming the countryside in gangs, attacking manor houses and villages, raping and killing, sometimes in collusion with mutinous peasants. 'The path of Attila in the age of barbarism cannot have been strewn with more horrible testimonies,' in the words of one Polish officer. In view of their numbers there was no way of enforcing the law, and those rounded up deserted again at the first opportunity. Officials were not safe, and _estafettes_ were attacked.
Apart from cooling the ardour of the local patriots, this complicated what was already a challenge. Napoleon was operating with huge army corps at distances that would have presented a problem in well-mapped areas with good roads. Couriers and staff officers struggled to find their way down sandy tracks, through boggy wildernesses and interminable forests. It was difficult for them to locate the commanders they were seeking, as these were themselves on the move, and many of the troops encountered along the way were not familiar enough with the marshals and generals to recognise them, while many could not speak French. Napoleon could not act or react as fast as he was wont to, which frustrated his plans.
He had managed to drive a wedge between Barclay's First Army and Bagration's Second, and had sent Davout with two divisions and Grouchy's cavalry corps to cut Bagration's line of retreat and crush him against Jérôme's advancing corps. But Jérôme had got off to a slow start, and failed to pin down Bagration, who was able to swerve south and get clear before the French pincers closed. Napoleon berated him, reprimanded Eugène and insulted Poniatowski, both of whom were under his orders.
The failure to destroy Bagration was his own fault; it had been his idea to give Jérôme such an important role. He had quickly come into conflict with his corps commanders and his own chief of staff. Napoleon had instructed Davout to oversee the combined operation but had failed to notify Jérôme, so Davout and Jérôme also fell out. Jérôme decided to go home, and, taking with him his royal guards and his only trophy of war, a Polish mistress, on 16 July began his march back to Kassel. 'You have made me miss the fruit of my cleverest calculations, and the best opportunity that will have presented itself in this war,' wrote a furious Napoleon. For good measure, he reproved Davout for his handling of the situation.
'I am very well,' Napoleon wrote to Marie-Louise that day. 'Kiss the little one for me. Love me, and never doubt my feelings for you. My affairs are going well.' They were not. Having himself wasted two weeks at Vilna, he had allowed the Russians to retreat in good order to a previously fortified camp at Drissa. When he got news of this, he decided to sweep round into their rear and trap them in it. But by the time he set off they had changed their plan and abandoned the camp, robbing him of his chance of a battle. On 21 July he nevertheless wrote a triumphant letter to Cambacérès announcing the capture of the camp.
He resumed his pursuit, and took heart when Murat engaged the Russian rearguard at Ostrovno. 'We are on the eve of great events,' he wrote to Maret on 25 July, and sent off a note to Marie-Louise brimming with optimism. Two days later he caught up with Barclay, who was preparing to give battle before Vitebsk. It was midday, and he could have engaged him immediately. Instead he decided to wait for all his troops to catch up, and postponed the attack to the following morning. That evening Barclay received news that Bagration, whom he had been expecting, could not make it, so he decided to strike camp silently in the night and resume his retreat. The French rose early and prepared for battle only to find the Russians had vanished.
Napoleon was baffled, and spent a day scouting the surrounding area before deciding to pause and give his army a rest. The men had marched under scorching sun, in temperatures recognised only by the veterans of the Egyptian campaign, along dusty roads through swarms of mosquitoes and horseflies, suffering agonies of thirst, since wells were few and far between. Many had wandered off in search of victuals and never been seen again, some had died of heatstroke or dehydration, others had fallen ill from drinking from brackish puddles or even horses' urine. The cavalry had been concentrated in a great body under Murat, which meant that even when they did find water, the tens of thousands of horses could not all be watered, and as there was no forage, they were lucky to find some old thatch to eat off a cottage roof. Some units were down by a third, and Napoleon had lost as many as 35,000 men without a battle since leaving Vilna.
He took up quarters in the governor's residence at Vitebsk, where he spent the next two weeks, undecided as to what to do next. He contemplated stopping there and turning Vitebsk into a fortified outpost. He wrote to his librarian in Paris requesting 'a selection of amusing books'. It was still extremely hot, and while his troops bathed in the river Dvina he sweated as he worked at tidying up his army. He issued confident-sounding Bulletins, wrote to Maret in Vilna instructing him to publicise non-existent successes, and blustered in front of the men, but in the privacy of his own quarters he was irritable, shouting at people and insulting them. He received news of the treaty between Russia and Turkey, and details of that between Russia and Sweden signed in March. What he did not know was that Russia had also signed a treaty of alliance with Britain on 18 July. But he was cheered by the news of the outbreak of war between Britain and the United States of America.
He had been greeted in Vitebsk by local Polish patriots, and evaded their questions as to his intentions by heaping abuse on Poniatowski and the alleged cowardice of the Polish troops, which, he claimed, was largely responsible for the failure to catch Bagration. 'Your prince is nothing but a c—,' he snapped at one Polish officer. To Maret in Vilna he sent contradictory instructions regarding the Polish question. Many argued that this was the moment to send Poniatowski south into Volhynia. This would have raised an insurrection in what had been Polish Ukraine, which would have yielded men and horses as well as supplies. More important, it would have tied down the Russian forces in the south, under Chichagov and Tormasov. But, as he admitted to Caulaincourt, he was more interested in using Poland as a pawn than in restoring it.
Unusually for him, Napoleon consulted a number of generals on what to do next. Berthier, Caulaincourt, Duroc and others felt it was time to call a halt. They cited losses, provisioning difficulties and the length of the lines of communication, and expressed the fear that even a victory would cost them dear, on account of the lack of hospitals and medical resources in the area. But Napoleon hankered after a battle to show for his pains, and hoped that now they were on the borders of Russia proper, Barclay would have to fight. 'He believed in a battle because he wanted one, and he believed that he would win it because that was what he needed to do,' wrote Caulaincourt. 'He did not for a moment doubt that Alexander would be forced by his nobility to sue for peace, because that was the whole basis of his calculations.' Leaping out of his bath at two o'clock one morning he suddenly announced that they must advance at once, only to spend the next two days poring over maps and papers. 'The very danger of our situation impels us towards Moscow,' he said to Narbonne. 'I have exhausted all the objections of the wise. The die is cast.'
He marched out of Vitebsk on 13 August, meaning to cross the Dnieper and take Smolensk from the south before the Russians could prepare a defence, and then use its bridges to recross the river into Barclay's rear. As a result of confused manoeuvring caused by differences between Barclay and Bagration, who had now joined forces, Smolensk was full of Russian troops. There was no value in taking this thickly-walled fortress, and Napoleon could have recrossed the river further east and forced Barclay to give battle by coming between him and Moscow. He nevertheless decided to storm it. The murderous battle cost him 7,000 casualties and reduced Smolensk to a scorched charnel house strewn with the corpses of the defenders and citizens who had died in the bombardment and fire that engulfed it.
Barclay resumed his retreat, with Ney in pursuit. Napoleon had sent Junot to cross the river further east, and he was in a position to cut the Russian line of retreat, but Junot had a mental blackout and his generals could not get an order out of him, and since Napoleon did not bother to ride out to see what was going on, the manoeuvre came to nothing. Ney, supported by Davout and Murat, fought hard but could not stop the Russians from making good their retreat.
The following morning Napoleon rode out to the scene. 'The sight of the battlefield was one of the bloodiest the veterans could remember,' according to a lancer of his escort. The troops paraded on the field of battle, and he awarded the coveted eagle that topped the colours of regiments which had earned it to the 127th of the Line, made up largely of Italians, which had distinguished itself the previous day. 'This ceremony, imposing in itself, took on a truly epic character in this place,' in the words of one witness. Napoleon took the eagle from the hands of Berthier and, holding it aloft, told the men, their faces still smeared with blood and blackened by smoke, that it should be their rallying point, and they must swear never to abandon it. When they had sworn the oath, he handed the eagle to the colonel, who passed it to the ensign, who in turn took it to the elite company, while the drummers delivered a deafening roll. Napoleon dismounted and walked over to the front rank. In a loud voice, he asked the men to name those who had distinguished themselves in the fighting. He promoted those who were named and gave the Legion of Honour to others, dubbing them with his sword and giving them the ritual embrace. 'Like a good father surrounded by his children, he personally bestowed the recompense on those who had been deemed worthy, while their comrades acclaimed them,' in the words of one officer. 'Watching this scene,' wrote another, 'I understood and experienced that irresistible fascination which Napoleon exerted when he wished to.' By this means he managed to turn the bloody battlefield into one of glory, consigning those who had died to immortality and caressing those who had survived with words and rewards. But many asked what, if anything, had been achieved by the past four days of bloodletting.
Napoleon had beaten the Russians and taken a major city, but while he had inflicted heavy losses, he had lost as many as 18,000 men in the two engagements, with nothing to show for it. According to Caulaincourt, over the next few days he behaved like a child who needs reassurance. 'In abandoning Smolensk, one of their holy cities, the Russian generals have dishonoured their arms in the sight of their own people,' he claimed. He fantasised about turning it into a base, from which he would attack either Moscow or St Petersburg the following year. But the burnt-out city represented no military value. Yet to retreat now was politically unthinkable. He had walked into a trap from which he could see no viable issue.
He vented his frustration on anything that came to hand. He blamed the Lithuanians for failing to raise enough troops and supplies, he reprimanded the corps commanders, and when he came across some soldiers looting one day, he attacked them with his riding crop, yelling obscenities. In his desperation to find a way out, he tried to persuade a captured Russian general to write to the tsar. 'Alexander can see that his generals are making a mess of things and that he is losing territory, but he has fallen into the grip of the English, and the London cabinet is whipping up the nobility and preventing him from coming to terms,' he lectured Caulaincourt. 'They have convinced him that I want to take away all his Polish provinces, and that he will only get peace at that price, which he could not accept, as within a year all the Russians who have lands in Poland would strangle him like they did his father. It is wrong of him not to turn to me in confidence, for I wish him no ill: I would even be prepared to make some sacrifices in order to help him out of his difficulty.'
Most of his entourage begged him to go no further, but he felt he could not return home without a victory. Moscow was only just over two weeks' march away, and the Russians would surely make a stand in its defence. 'The wine has been poured, it has to be drunk,' he told Rapp. When Berthier nagged him once too often on the subject, he turned on him. 'Go, then, I do not need you; you're nothing but a... Go back to France; I do not force anyone,' he snapped, adding a few lewd remarks about what Berthier was longing to get up to with his mistress in Paris. The horrified Berthier swore he would not dream of abandoning his emperor, but the atmosphere between them remained frosty, and Berthier was not invited to the imperial table for several days.
While senior officers shook their heads, the younger ones were excited by the prospect of a march on Moscow. 'The whole army, the French and our foreign auxiliaries, was still full of ardour and confidence,' according to the twenty-one-year-old Lieutenant de Bourgoing. 'If we had been ordered to march to conquer the moon, we would have answered: "Forward!"' recalled Heinrich Brandt of the Legion of the Vistula. 'Our older colleagues could deride our enthusiasm, call us fanatics or madmen as much as they liked, but we could think only of battles and victories. We only feared one thing – that the Russians might be in too much of a hurry to make peace.'
As they penetrated Russia proper, the character of the war changed. The retreating Russians adopted a scorched-earth policy, forcing the population out of their homes and burning them, along with standing crops and anything that might provide shelter or provender to the advancing army. 'At night, the whole horizon was on fire,' in the words of one soldier. They poisoned wells with dead animals. They felled trees and left overturned carts in the road, and, as their retreat grew less orderly, corpses of men and horses, which rotted in the sweltering heat. Yet the men marched on, confident in what one soldier called 'the vast genius' of their 'father, hero, demi-god'.
Napoleon was uneasy at the sight of the burning villages, but concealed his feelings by heaping ridicule on the Russians and calling them cowards. 'He sought to avoid the serious reflections which this terrible measure raised as to the consequences and duration of a war in which the enemy was prepared to make, from the very outset, sacrifices of this magnitude,' explains Caulaincourt. He nevertheless continued to clutch at every straw; on 28 August he seized an opportunity to write to Barclay, hoping to open up a channel of communication with Alexander.
Two days later, when he and his entourage stopped for lunch by the roadside, Napoleon walked up and down in front of them, holding forth about the nature of greatness. 'Real greatness has nothing to do with wearing the purple or a grey coat, it consists in being able to rise above one's condition,' he declaimed. 'I, for instance, have a good position in life. I am emperor, I could live surrounded by the delights of the great capital, and give myself over to the pleasures of life and to idleness. Instead of which I am making war, for the glory of France, for the future happiness of humanity; I am here with you, at a bivouac, in battle, where I can be struck, like any other, by a cannonball... I have risen above my condition...' But the following day an _estafette_ from Paris brought news that in Spain Marmont had been defeated by Wellington at Salamanca on 22 July. 'Anxiety was clearly visible on his usually serene brow,' according to General Roguet, who lunched with him that day.
The Russians were as desperate as Napoleon for a battle, but the speed of the French advance had prevented Barclay from getting his troops into position. Under pressure from public opinion Alexander replaced him with the popular Mikhail Ilarionovich Kutuzov, a sly, gout-ridden, fat sixty-six-year-old with a talent to rival Napoleon's for falsifying facts to build up his image. It was not until 3 September that Kutuzov chose a defensive position in which to stand and fight, in front of the village of Borodino.
Napoleon reached the scene two days later. He ordered an exposed Russian redoubt to be captured, then spent a day reconnoitring and preparing for battle. Kutuzov had built a formidable earthwork redoubt on a slight rise at the centre of his line, covered on his left with three _flèches_ , earthworks in the shape of chevrons. Napoleon decided to deliver a frontal assault on the redoubt while Ney, Davout and Junot took the _flèches_ and penetrated into the Russian rear, and Poniatowski made a deeper flanking movement in support. Davout suggested that his corps be added to the Polish one so as to drive deeper into the Russian rear, but Napoleon feared engaging such a large force too deep. He had between 125,000 and 130,000 men, so he was outnumbered by the Russians with their 155,000 (about 30,000 of whom were poorly trained militia), and he was outgunned, in calibre as well as in numbers, by the 640 Russian guns to his 584.
Napoleon was unwell. He was suffering from an attack of dysuria, an affliction of the bladder which made it almost impossible for him to urinate, and when he did only a few dark drops came out, heavy with sediment. He may also have had a fever, as he was coughing, shivering and breathing with difficulty. His spirits were lifted by the arrival of Bausset with a case containing a portrait of the King of Rome just painted by Gérard, which he immediately had unpacked. 'I cannot express the pleasure which the sight gave him,' noted Bausset. The proud father had the picture displayed outside his tent so his generals and soldiers could come up and admire it, and wrote a tender note to Marie-Louise thanking her for it.
A less welcome arrival was Colonel Fabvier, who had come from Spain with details of Wellington's victory over Marmont at Salamanca and of the worsening military position of the French in the Peninsula. News of the French defeat would give heart to all Napoleon's enemies – not just those facing him, but, more alarmingly, those at his back. He slept badly, waking several times. At three in the morning he got up and drank a glass of punch with Rapp, who was on duty and had spent the night in his tent. 'Fortune is a fickle courtesan,' Napoleon suddenly said. 'I have always said so and now I am beginning to feel it.' After a while he added, sighing, 'Poor army, it is much reduced, but what is left is good, and my Guard is intact.' He then rode out to show himself to the troops.
The army had spent the previous day buffing up, and some said it looked as fine as on a parade before the Tuileries. The men were read a proclamation which exhorted them to fight and assured them that victory would lead to a prompt return home. It contained a reference to Austerlitz, which was not out of place, since that was the last time the Grande Armée had faced Kutuzov, and when the sun came up Napoleon exclaimed, ' _Voilà le soleil d'Austerlitz!_ ' He then rode up to a vantage point from which he could see almost the whole field of battle, where a tent had been pitched for him, surrounded by his Guard in formation. He took the folding chair that had been set out for him, turned it back to front and sat down heavily, his arms on its back.
At six o'clock the French guns opened up and the attack began. Assault followed assault as the Russian positions fell, only to be retaken in fierce hand-to hand fighting. The _flèches_ were murderous traps for the troops who took them, as their only escape was forward, into the next Russian line of defence. Napoleon listened impassively as officers rode up to report. He refused all offers of food, only taking a glass of punch at around ten o'clock. He watched two assaults on the great redoubt at the centre, but failed to reinforce the successful one, while his cavalry stood idle. 'We were all surprised not to see the active man of Marengo, Austerlitz, etc.,' noted Louis Lejeune, an officer on Berthier's staff. Napoleon appeared curiously remote.
His state of health undoubtedly played a part, but so did his state of mind; unsettled by an unexpected sortie by Russian cavalry on his left wing and afraid of playing his last card so far from home, he would not commit the Guard when Davout reported that the way was open for it to sweep into the rear of the Russian army and destroy it completely. He hesitated for a couple of hours before ordering the general assault. When he did, his cavalry, which was being gradually shot to pieces by the Russian guns, surged forward and, charging up the hill, swarmed into the great redoubt, and the Russian line crumpled. Napoleon then rode over the battlefield, which presented what one of his generals describes as 'the most disgusting sight' he had ever seen. Russian casualties were around 45,000, including twenty-nine generals, the French 28,000 and forty-eight generals. The bodies of nearly 40,000 horses littered the ground.
The French victory was complete; Russian losses were such that most of the units had ceased to be operational, and nothing stood between the French and Moscow. But there had been no trace of Napoleonic genius in evidence in what had been little more than a slogging match. The Russians did not flee, and there was no pursuit, as the French cavalry was exhausted. At dinner that evening with Berthier and Davout Napoleon said little and ate less. He did not sleep that night.
Kutuzov badly needed to get the remnants of his army out of the path of the French and to fall back to the south, where he could be fed and resupplied. Instead of doing so directly, he cleverly retreated to Moscow and out the other side, guessing that the city would act as a 'sponge' which would absorb the French and permit him to get away. He was right. Napoleon followed, and on the afternoon of 14 September from the Poklonnaia Hill he surveyed his prize – a huge and beautiful city glittering with its many gilded onion-shaped domes. But it was empty, and no delegation came out to submit to him. 'The barbarians,' he exclaimed. 'They really mean to abandon all this? It is not possible.'
## 38
# Nemesis
The following morning, 15 September, Napoleon rode into Moscow and took up residence in the Kremlin. 'We were surprised not to see anyone, not even one lady, come to listen to our band, which was playing _La Victoire est à Nous!_ ' a disappointed Sergeant Bourgogne noted as they marched in. Some two-thirds of the city's inhabitants had left, and the remainder, including many foreign tradesmen, servants and artisans, cowered in their homes. Even members of the several-hundred-strong French colony kept out of the way. The shops were closed, and what little traffic there was in the streets was mainly Russian stragglers.
The surrender of a city was normally negotiated so that the authorities assigned the occupying troops billets and made arrangements for feeding them, but in this case there was a free-for-all to obtain the necessities of life. Generals and groups of officers selected aristocrats' palaces and noblemen's townhouses, while their men settled in as best they could in the surrounding houses, stables and gardens. Napoleon had appointed Marshal Mortier governor, with orders to prevent looting, and the occupation began in a relatively civilised manner. But as the shops were closed and most of the houses abandoned, the men helped themselves to whatever they needed, and chaos ensued, aggravated by the action of the Russian governor of the city, Count Rostopchin, who had ordered it to be put to the torch and removed the fire pumps before leaving. By nightfall large parts of it were on fire, and as a significant proportion of the houses were made of wood, it proved impossible to bring under control. By the following morning the flames came dangerously close to the Kremlin, and Napoleon thought it prudent to leave the city with his Guard and move to the nearby palace of Petrovskoe. The city turned into an inferno in which French looters were joined by local criminals, Russian deserters and others eager to save something for themselves from the flames. A drunken bacchanalia accompanied the pillage, rape and murder, shattering the bonds of military discipline.
Once the fire had abated, on 18 September Napoleon rode back into Moscow, but the smouldering remains of the city no longer represented much of a prize, and he began to make plans to leave. The question was where to go. A withdrawal to Vilna would mean losing face and admitting that all the exertions since crossing the Niemen and the deaths of Borodino had been in vain. He considered leaving the main body of his army in Moscow and marching on St Petersburg with Eugène's corps and a few other units, which might persuade Alexander to treat. Eugène was apparently keen on the plan, but others raised objections, and according to Fain, 'they managed for the first time to make him doubt the superiority of his own judgement'. Some wanted to fall back and take winter quarters in Smolensk, others suggested a march south on the industrial cities of Tula and Kaluga, followed by a foray through the Ukraine. But that would mean abandoning his bases at Minsk and Vilna.
Napoleon tried to make contact with Alexander, in the hope that the fall of Moscow might have made him more amenable. In his letter, sent through a Russian gentleman who had remained in the city, he castigated Rostopchin's burning of Moscow as an act of barbarism; in Vienna, Berlin, Madrid and every other city he had occupied the civil administration had been left in place, which had safeguarded life and property. 'I have made war on Your Majesty without animosity,' he assured him, saying that a single note from him would put an end to hostilities. He sent another letter through a minor civil servant, and on 3 October suggested sending Caulaincourt to St Petersburg. Caulaincourt excused himself, on the grounds that Alexander would not receive him. Napoleon then decided to send Lauriston. 'I want peace, I need peace, I must have peace!' Napoleon told him as he set off two days later. 'Just save my honour!'
According to Caulaincourt, Napoleon realised his repeated messages would, by showing up the difficulty of his position, only confirm Alexander in his purpose. 'Yet he kept sending him new ones! For a man who was so politic, such a good calculator, this reveals an extraordinary blind faith in his own star, and one might almost say in the blindness or the weakness of his adversaries! How, with his eagle's eye and his superior judgement could he delude himself to such a degree?'
He may have been trying to pressure Alexander by giving the impression that he was prepared to sit it out in Moscow and spend the winter there if necessary; he talked of bringing the actors of the Comédie-Française to entertain him and his men through the winter months. But lingering in Moscow only undermined his own position; although enough had survived in cellars and buildings that had escaped the flames to feed and clothe his army for some months, and there were large quantities of arms, shot and powder left in the city's arsenal, there was no fodder for the horses, and without horses he would be able neither to keep his lines of communication open nor to launch a fresh campaign in the spring. The whole area in his rear had been ravaged in the advance and was awash with deserters, many settled in bands along the way. The behaviour of these, and of foraging parties sent out from Moscow, was beginning to turn an originally indifferent population against the invaders; isolated French soldiers and even small units were being attacked.
While Kutuzov gradually rebuilt his forces in his fortified camp at Tarutino south of Moscow, Murat's corps, camped nearby to check him, wasted away. The 3rd Cavalry Corps, consisting of eleven regiments, could only muster 700 horsemen. The 1st Regiment of Chasseurs could only field fifty-eight, and that only thanks to some reinforcements that had reached it from France. Some squadrons in the 2nd Cuirassiers, usually 130 strong, were down to eighteen men. The backs of many of the horses were so worn through that in some cases when riders dismounted and unsaddled they could see their entrails. 'We could see that we were slowly perishing, but our faith in the genius of Napoleon, in his many years of triumph, was so unbounded that these conversations always ended with the conclusion that he must know what he is doing better than us,' recalled Lieutenant Dembiński.
Napoleon's apartment in the Kremlin overlooking the river Moskva and part of the city consisted of a vast hall with great chandeliers, three spacious salons and one large bedroom, which doubled up as his study. It was here that he hung Gérard's portrait of the King of Rome. He slept on the iron camp bed he always used on campaign, his desk had been set up in one corner and his travelling library laid out on shelves. He had two burning candles placed at his window every night, so that passing soldiers would see he was watching and working.
He had set up a skeletal administration of the city, and a semblance of normality was established. People travelled 'as easily between Paris and Moscow as between Paris and Marseille', according to Caulaincourt, if it took them a little longer. The post took up to forty days, but the _estafette_ only fourteen. Its arrival was the high point of Napoleon's day, and he would grow restless if, as happened once or twice, it was a couple of days late.
News from Paris was welcome, particularly when it flattered Napoleon's vanity. He read with pleasure that his birthday, which he had spent before Smolensk, had been celebrated by the laying of foundation stones for the Palais de l'Université, a new Palais des Beaux-Arts and a building to house the national archives. He was informed that 'the enthusiasm of the Parisians, on hearing of the emperor's entry into Moscow is tempered only by their fear of seeing him march out of it in triumph on a conquest of India'. News that Wellington had taken Madrid was less welcome.
Napoleon attended to affairs of state as well as those of his army with a punctiliousness that may have helped him avoid facing up to the realities of his situation. He badgered Maret to put pressure on the American minister, the poet Joel Barlow, who had just arrived in Vilna, to negotiate an alliance with the United States against Britain. He gave instructions for horses to be sent from France and Germany and for rice to be purchased and shipped to Moscow. He held parades on Red Square before the Kremlin, at which he awarded crosses of the Legion of Honour and promotions earned at Borodino. He was not looking forward to a winter away from home. 'If I cannot return to Paris this winter,' he wrote to Marie-Louise, 'I will have you come and see me in Poland. As you know, I am no less eager than you to see you again and to tell you of all the feelings which you arouse in me.'
While he reviewed the troops stationed in Moscow, he showed little interest in those elsewhere. When Murat sent his aide-de-camp to inform him of the dire state of the cavalry, Napoleon dismissed him, saying his army was 'finer than ever'.
Each day he spent in Moscow made it harder to leave without loss of face, and the usually decisive Napoleon seemed paralysed by the need to choose between an unappealing range of options on the one hand, and belief in his star on the other. He only really had one option, and he was reducing the chances of its success with every day he delayed. The weather was unusually fine, and he teased Caulaincourt, accusing him of telling tales about the Russian winter. 'Caulaincourt thinks he's frozen already,' he quipped, dismissing suggestions that the army provide itself with gloves and warm clothing. As soon as they reached Moscow, all the Polish units had set up forges to produce horseshoes with crampons in preparation for winter. A few Dutch and German officers followed their example, but not the French. Luckily for Napoleon, Caulaincourt had the horses of his _maison_ properly shod.
On 12 October the _estafette_ from Moscow to Paris was captured, and the following day that coming from Paris was intercepted. General Ferrières, who had travelled all the way from Cádiz, was captured almost at the gates of Moscow. These events shook Napoleon, as did the first shower of snow, on 13 October. 'Let us make haste,' he said on seeing it. 'We must be in winter quarters in twenty days' time.' It was not too late. Smolensk, where he had some supplies, was only ten to twelve days' march from Moscow, his well-stocked bases at Vilna and Minsk only another fifteen to twenty from there. If he could reach these, his army would be fed and supplied, safe in friendly country and able to draw on reinforcements from depots in Poland and Prussia.
His chances of an orderly withdrawal were reduced by his hope that he might sway Alexander by appearing to occupy Moscow indefinitely; instead of sending the lightly wounded of Smolensk and Borodino back to where they could safely convalesce, he had left them where they were or had them brought to Moscow. Rather than send the thousands of horseless cavalrymen back to Poland where they could be remounted, he kept them in Russia. He did not send back unnecessary members of his _maison_ or other civilians, and did not evacuate the trophies – banners, regalia and treasures from the Kremlin, and the great silver-gilt cross he had had wrenched from the dome of the tower of Ivan the Great. It was not until 14 October, the day after the first snowfall, that he gave orders that no more troops were to be sent forward to Moscow, and that the wounded in the city be evacuated, a pointless and fatal decision; the badly wounded, possibly as many as 12,000, should have been left where they were, as Dr Larrey intended (he had organised medical teams to care for them).
Napoleon could go back the way he had come, which had the advantage of being familiar, guarded by French units and punctuated with supply depots, as well as being the most direct route. But that would smack of retreat. He considered marching north-westward, in a sweep back to Vilna, and defeating a Russian army on the way. This option had the merit of threatening St Petersburg, which might just cause Alexander's nerve to snap. Or he could march southwards, strike a blow at Kutuzov, and then go back to Minsk another way. He did not make up his mind until the last moment, further delaying preparations.
Having decided to strike at Kutuzov, he still entertained the option of returning to Moscow. He therefore left part of his _maison_ there, and gave orders to stockpile three months' worth of rations, to improve the defences of the Kremlin, and to turn all the monasteries into strongpoints. He overruled General Lariboisière, inspector-general of the artillery, who wanted to start evacuating equipment; as a result 500 caissons, 60,000 muskets and quantities of powder, not to mention a large number of cannon, were left in the city. Napoleon seemed incapable of committing to any course, as though he were waiting for some chance to present itself. He ended a letter to Maret in which he sketched out his probable plans with the words: 'But in the end, in affairs of this kind, what takes place in the event is sometimes very different from that which is foreseen.' He affected a confidence which had seen him through in the past. 'Today is 19 October, and look how fine the weather is,' he said to Rapp as he set out from Moscow. 'Do you not recognise my star?' Rapp felt this was no more than bravado, and noted that 'his face bore the mark of anxiety'.
His forces numbered no more than 95,000, and probably less, but they included a nucleus of tested troops, including the Guard, which had not been blooded during the campaign. They marched out singing, but while they looked martial enough, their baggage carts were loaded down not with military supplies, but with loot. Behind them came less disciplined troops, stragglers and civilians driving carriages and carts loaded with booty, looking like a grotesque carnival. The high spirits flagged three days later when a downpour transformed the road into a morass. Vehicles had to be abandoned, cumbersome objects jettisoned from knapsacks, and the line of march lengthened as stragglers fell behind.
They marched south, but found the road blocked by Kutuzov at Maloyaroslavets. After fierce fighting in the course of which the town changed hands several times, Eugène and his Italians drove out Kutuzov. Losses were heavy, with at least 6,000 casualties, and that night, in a squalid cottage whose single room was divided in two by a dirty canvas sheet, Napoleon asked his marshals for their views on what to do next. He listened in silence, staring at the maps spread before him. At dawn he rode out to reconnoitre. He narrowly missed being captured by cossacks, and after riding through the burnt-out ruins of Maloyaroslavets, whose streets were strewn with corpses, many of them hideously mutilated by the wheels of guns or shrivelled in grotesque poses by the blaze, he was visibly shaken. He decided to retreat by the most direct route, and sent orders to Mortier in Moscow to abandon the city, bringing all the wounded, and make with all speed for Smolensk. Before he left he was to blow up the Kremlin and torch the townhouses of Rostopchin and Count Razumovsky, the Russian ambassador in Vienna, as well as destroying all the stores left in the city.
Mortier also brought with him two prisoners, General Wintzingerode and his aide-de-camp, who had unwisely ridden into Moscow to verify that the French had left, only to be captured. When Napoleon saw Winzingerode, a native of Württemberg in Russian service who seemed to epitomise the _internationale_ that was forming against him, he erupted into a rage. 'It is you and a few dozen rogues who have sold themselves to England who are whipping up Europe against me,' he ranted. 'I don't know why I don't have you shot; you were captured as a spy.' That did not exhaust his anger, and on seeing a country house that had escaped destruction, he ordered it burnt down. 'Since _Messieurs les Barbares_ are so keen on burning their own towns, we must help them,' he raged (he soon countermanded the order).
When they passed Borodino, he was annoyed to find many wounded still in the makeshift hospitals. Against the advice of Larrey and the medical teams caring for them, he insisted they be placed on every available vehicle, including gun carriages. The order killed many who might have lived; they were in no condition to survive the jolting and buffeting, and those who were not killed by it soon either fell off or were thrown off. Progress was slow due to lack of horsepower. Shortage of fodder had debilitated the horses – guns normally drawn by three pairs were now hitched to teams of twelve or more, and even these had to be helped up inclines by infantry. Powder wagons were blown up and shells jettisoned to lighten the load. Private carriages and loot-laden wagons were seized and burnt by the artillery, which commandeered the horses, but this did not solve the problem. As the nights grew colder more horses died, and the artillery took those that had been drawing wagons with wounded men.
Napoleon saw himself as carrying out a tactical withdrawal rather than a retreat, so although his generals advised abandoning some of the guns in order to free up horses with which to draw the rest and save time, he would not hear of it, fearing the Russians would claim the abandoned guns as trophies. The same went for the 3,000 or so Russian prisoners, who only encumbered the army.
The army corps were marching one behind the other, so only the leading one had a clear road; the others had to move through the mess left behind by preceding ones. Their path was churned by tens of thousands of feet, hooves and wheels into a sea of mud if it was wet, and into a sheet of ice when it froze. Such supplies as there might have been along the way were devoured, and any available shelter was dismantled for firewood by those who had gone before. The road was littered with abandoned vehicles, dead horses and jettisoned baggage, and clogged by slow-moving stragglers and civilians – French and other foreign inhabitants of Moscow who feared the return of the Russians; Russians, particularly women and petty criminals, who had thrown in their lot with the French or been forcibly enlisted as wagoners or bearers; functionaries attached to the army; and officers' servants. Soldiers fell behind and became separated from their units by a mass of people, horses and vehicles. After a time, most of them threw away their weapons and joined the crowd of stragglers, demoralised and guided by herd instinct, easy prey for pursuing cossacks.
The new moon on the night of 4 November brought a drop in temperature, and by the morning hundreds of undernourished men and horses had frozen to death. The men began adapting their dress to the cold: furs, shawls and costly textiles brought along as gifts for wives or sweethearts were put on over uniforms, giving the retreating army a carnivalesque aspect. It did not protect them from frostbite, and as the inexperienced inhabitants of warmer climes had no idea of how to restore circulation, many lost fingers, toes, ears and noses. Cavalrymen had to dismount to prevent their feet freezing, and Napoleon, who had abandoned his uniform for a Polish-style fur-lined green velvet frock-coat and cap, got out of his carriage at intervals and tramped alongside his troops, with Berthier and Caulaincourt at his elbow.
On 6 November he was met by an _estafette_ from Paris which brought news of an attempted coup aimed at overthrowing him. It had been quickly foiled, but it brought home to him the frailty of his rule, and he began to contemplate leaving the army and racing back to Paris. When he reached Smolensk on 9 November, the blanket of snow concealing the charred ruins allowed him to entertain for a while the feeling that he had reached safety. He set about organising winter quarters for the army, but found only a fraction of the stores he expected, barely enough for the 15,000 sick and wounded left behind after the storming of the city. Bad news poured in from all sides. Vitebsk had been taken by the Russians, a division had been forced to surrender south of Smolensk, and Eugène's Italian corps had lost almost a quarter of its effectives and fifty-eight guns while crossing a river. As his columns trudged in he could see how depleted they were; there were now no more than about 40,000 left with their colours.
He took out his frustration on his marshals. 'There's not one of them to whom one can entrust anything; I always have to do everything myself,' he complained, refusing to accept responsibility for his predicament. 'And they accuse me of ambition, as though it was my ambition that brought me here! This war is only a matter of politics. What have I got to gain from a climate like this, from coming to a wretched country like this one? The whole of it is not worth the meanest little piece of France. They, on the other hand, have a very real interest in conquest: Poland, Germany, anything goes for them. Just seeing the sun six months of the year is a new pleasure for them. It is they that should be stopped, not me.'
The retreat would have to go on, and fast, as two Russian pincers were converging in his rear, and Kutuzov was overtaking him to the south. Schwarzenberg had fallen back, not on Minsk, where he would have joined forces with Napoleon, but westwards, back into Poland, leaving Napoleon's line of retreat exposed. Desperate not to lose face and not wishing to withdraw further than he absolutely had to, he refused to accept that he would not find winter quarters in Russia, and so put off until the last minute every decision to retreat further. He only left Smolensk on 14 November. Eugène, Davout and Ney were to follow at one-day intervals.
As they set off the temperature dipped further, to as low as minus twenty degrees, and conditions deteriorated. Those who were still with their colours managed to provide themselves with food and shelter; when they could not get hold of rations they ate horses, then dogs and cats, and anything else they could lay hands on; sometimes no more than hot water with some axle-grease. But the growing number of stragglers were caught up in a desperate struggle for survival; they began to steal food and clothing from each other, callously stripping those too weak to resist. The cold was such that what food could be obtained froze so hard it could not be eaten, so horses were sliced up while still alive.
Napoleon himself had a regular supply of food and wine. An officer would ride ahead to select a place to stop for the night, sometimes a country house, sometimes a hut. The iron camp bed would be set up, a rug spread on the floor and the _nécessaire_ containing razors, brushes and toiletries brought in. A study would be improvised, in the same room if no other could be found, with a table covered in green cloth, his travelling library in its case and the boxes containing maps and writing instruments. A small dinner service would be unpacked, so he could eat off plate. Even though he did have the luxury of a change of clothes, and despite the resources of the _nécessaire_ , he was infested with lice like the rest of his army. And despite the comforts of his camp bed, he suffered from insomnia. The night after leaving Smolensk, he called Caulaincourt to his bedside and discussed the necessity of his going back to Paris. He had just heard that the Russians had cut the road ahead near Krasny, and he could not rule out the possibility of being taken prisoner, so he had his physician Dr Yvan prepare him a dose of poison, which he kept in a black silk sachet around his neck.
He fought his way through to Krasny, where he paused to allow the other corps to catch up, keeping the Russians at bay. 'Advancing with a firm step, as on the day of a great parade, he placed himself in the middle of the battlefield, facing the enemy's batteries,' in the words of Sergeant Bourgogne. Eugène's and Davout's corps got through, but Ney was still some way behind. Napoleon could not afford to wait any longer, as Kutuzov was by now threatening to cut his line of retreat to Orsha, and set off at the head of his grenadiers. 'The shells which flew over were bursting all round him without his seeming to notice,' recalled one of the few cavalrymen left in his escort. That morning he had told Roguet it was time he stopped playing the emperor and became the general once more.
On reaching Orsha on 19 November, he set about rallying the remains of his army. He ordered everything surplus to requirements to be burnt – including the portrait of the King of Rome. He forced stragglers to rejoin their regiments and distributed the supplies stored in the town. He was overjoyed when Ney, who had cleverly circumvented the Russian force blocking his path, rejoined him at Orsha. The five days of fighting around Krasny had cost him possibly as many as 10,000 of his best remaining soldiers and more than 200 guns, but he refused to give in to despair.
'Although this man was rightly regarded as the author of all our misfortunes and the unique cause of our disaster,' wrote Dr René Bourgeois, who held profoundly anti-Napoleonic political views, 'his presence still elicited enthusiasm, and there was nobody who would not, if the need arose, have covered him with their body and sacrificed their lives for him.' One of his aides, Anatole de Montesquiou, explains that they owed everything to Napoleon's ability not to show his feelings. 'In the midst of the overwhelming horrors which seemed to be pursuing or rather enveloping us with the perseverance of fatality, we recovered peace of mind and hope by turning our eyes on the Emperor,' he wrote. 'More unfortunate than any of us, since he was losing more, he remained impassive.' He represented their best chance of getting out of the mess they were in, and his stoicism gave them comfort. 'His presence electrified our downcast hearts and gave us a last burst of energy,' wrote Captain François. Whatever their nationality and their political attitude, men and officers alike realised that only he could keep the remains of the army together, and snatch some shreds of victory from the jaws of defeat.
Napoleon's glory was their common property, and to diminish his reputation by denouncing him would have been to destroy the fund they had built up over the years, which was their most prized possession. According to the British General Wilson, who was attached to the Russian army, even when taken prisoner, they 'could not be induced by any temptation, by any threats, by any privations, to cast reproach on their emperor as the cause of their misfortunes and sufferings'. These were about to increase dramatically.
On 22 November Napoleon learned that his supply base at Minsk had fallen to the Russians. He was momentarily 'struck with consternation', and sat up all night talking to Duroc and Daru, admitting that he had been foolish to invade Russia. Another piece of bad news came two days later: the only bridge over the river Berezina at Borisov had been burnt, and a Russian force held the far bank. 'Any other man would have been overwhelmed,' wrote Caulaincourt. 'The Emperor showed himself to be greater than his misfortune. Instead of discouraging him, these adversities brought out all the energy of this great character; he showed what a noble courage and a brave army can achieve against even the greatest adversity.'
Having learned of a ford some twelve kilometres north and upstream from Borisov, he made a feint to the south and managed to convey false intelligence to the Russians on the opposite bank that he was aiming to make a crossing there, then marched north to the ford at Studzienka. 'Our position is impossible,' Ney said to Rapp. 'If Napoleon succeeds in getting out of this today he is the very Devil.' Napoleon had regained his composure, and inspired his shattered army to one last act of heroism. He stood on the bank as his sappers dismantled the wooden houses of the village, and 400 Dutch engineers began building a trestle bridge across the river. Stripping off, they worked up to their necks in the icy water, battling the current and avoiding the large blocks of ice being carried along by it. They completed one bridge, a hundred metres long and four wide, and began work on a second as units still capable of fighting crossed and took up defensive positions on the opposite bank, shouting ' _Vive l'Empereur!_ ' as they marched past. He himself crossed on 27 November, along with most of the units still with their colours. The infantry and cavalry used the first bridge, while the artillery, baggage train and carriages carrying the wounded took the second. The crush of men and horses on the frail structures resulted in many ending up in the water, and when the Russian guns on the eastern bank opened up that afternoon, confusion and panic added to the casualties. Over the whole of that day and the next, the remnants of the army, followed by the mass of stragglers and civilians, struggled across while Marshal Victor's depleted but still battleworthy corps held off the converging Russian armies. But it could not prevent them from shelling the crush of people and vehicles on the bridges and those waiting their turn to cross, turning the scene into one of indescribable horror, with people being shot, trampled or pushed into the icy water. The Russian forces on the western bank had also come up by now, but they were held off by units of Swiss, Dutch, Poles, Italians, Croats and Portuguese under Oudinot and Ney. That night, Victor crossed with his corps, and in the morning the bridges were destroyed, leaving a considerable number of stragglers and civilians to their fate.
Napoleon's bold manoeuvre had extricated him and most of the remaining army from a seemingly fatal trap. Over the three days of the crossing the French had lost up to 25,000, many of them civilians or non-combatant stragglers, and inflicted losses of at least 15,000 on the Russians, all of them soldiers. The operation was not only a magnificent feat of arms; it was an extraordinary demonstration of the resilience of the Napoleonic military machine and of his ability to inspire men of well over half a dozen different nations to fight like lions for a cause which was not theirs.
Buoyed by the miraculous escape and the feeling that they had once more triumphed over the odds, the remnants of the Grande Armée made a dash for Vilna, where they would be safe and where there were abundant victuals. But at this point the temperature sank to a new low, recorded by some as minus thirty-five and a half degrees. Many froze to death during this last march, and those who did not walked in a state described by some as akin to drunkenness, while others were struck with snow-blindness and had to be led.
Napoleon instructed Maret to send away any foreign diplomats, so they should not see the condition of his army, and badgered him for news from Paris, demanding to know why no _estafette_ had reached him for eighteen days. Maret was to spread news of a victory at the Berezina, in which the French had taken thousands of prisoners and twelve standards. Ironically, the next day Alexander held a service of thanksgiving in St Petersburg, having been informed by Kutuzov that he had won a resounding victory on the Berezina. Napoleon could no longer hope to fool people, and on 3 December he dictated the 29th Bulletin of the campaign, in which he described the disaster, finishing off with the phrase: 'His Majesty's health has never been better.' He had to stop playing the general and become emperor once more – which meant he must get to Paris as quickly as possible to reassure his subjects.
Against the advice of Maret, who said the army would fall apart without him, he decided to leave immediately. Ignoring advice to put Eugène in command, he chose Murat, fearing that his brother-in-law would not obey him and would seize the perceived insult as an excuse to march back to Naples. Napoleon set off on the evening of 5 December, with Caulaincourt, Duroc and a couple of other officers, Roustam, Constant and Fain, escorted by Polish and Neapolitan cavalry. The cold was intense, shattering the wine bottles in Napoleon's carriage as their contents froze, and cutting a swathe through the escort, which lost all of its Italians along the way. At one point they narrowly missed being intercepted by marauding cossacks. Napoleon had a pair of loaded pistols with him, and instructed his companions to kill him if he failed to do so himself in the event of capture.
Two days later, having recrossed the Niemen, he felt safe. He transferred to an old carriage mounted on runners, and chatted to Caulaincourt as they sped along, with snow blowing in through the cracks around the ill-fitting doors. He went over the events that had led up to the war, which he repeatedly insisted he had never wanted. 'People do not understand: I am not ambitious,' he complained. 'The lack of sleep, the effort, war itself, these are not for someone of my age. I love my bed and rest more than anyone, but I have to finish the work I have embarked on.' His conversation kept drifting back to the subject of Britain, the one obstacle to the desired peace; he was fighting the fiendish islanders on behalf of the whole of Europe, which did not realise that it was being exploited by them.
He had talked himself into a good mood by the time they reached Warsaw on the evening of 10 December, and in order to stretch his legs he got out at the city gate and walked through the streets to the Hôtel d'Angleterre, where the sleigh had been sent on. Nobody took any notice of the small, plump man in his green velvet overcoat and fur hat, which covered most of his face. He seemed almost disappointed.
He continued to talk with animation while dinner was prepared and a servant girl struggled to light a fire in the freezing room they had taken. Caulaincourt had been sent to fetch Pradt, who was struck by the jolly mood of the emperor when he arrived. Dismissing his own failure with the phrase 'From the sublime to the ridiculous there is but one step,' he berated Pradt for having failed to galvanise Poland, raise money and furnish men. He said he had never seen any Polish troops during the whole campaign, and accused the Poles of being ineffectual and cowardly.
His tone changed with the appearance of the Polish ministers he had summoned. He admitted to having suffered a major reversal, but assured them that he had 120,000 men at Vilna, and that he would be back in the spring with a new army. In the meantime, they must raise money and a mass levy in order to defend the Grand Duchy. They stood around getting progressively colder as he paced up and down, warmed by his fantasy. 'I beat the Russians every time,' he told them. 'They don't dare to stand up to us. They are no longer the soldiers of Eylau and Friedland. We will hold Wilna, and I shall be back with 300,000 men. Success will make the Russians foolhardy; I will fight them two or three times on the Oder, and in six months' time I will be back on the Niemen... All that has happened is of no consequence; it was a misfortune, it was the effect of the climate; the enemy had nothing to do with it; I beat them every time...' And so it went on, with the occasional self-justificatory 'He who hazards nothing gains nothing,' and the frequent repetition of the phrase he had just coined, and which he appeared to relish: 'From the sublime to the ridiculous there is but one step.'
Having had dinner, Napoleon climbed back into his sleigh and set off for Paris. When he realised they were passing not far from the country house of Maria Walewska, in a sudden surge of gallantry he decided to call on her. Caulaincourt had the greatest difficulty in convincing him that not only would this delay their arrival in Paris (and increase the danger that some German patriot might get to hear of their passage and ambush them), it would be an insult to Marie-Louise, and public opinion would never forgive him for going off to indulge his lust while his army was freezing to death in Lithuania.
As they sped on, Napoleon turned over the whole political situation again and again, as though he were trying to convince himself that the Russian campaign had been only a minor setback. 'I made a mistake, _Monsieur le Grand Écuyer_ , not on the aim or the political opportunity of the war, but in the manner in which I waged it,' he said, giving Caulaincourt's ear an affectionate tug. 'I should have stopped at Witepsk. Alexander would now be at my knees. [...] I stayed two weeks too long in Moscow.'
This was true. Two weeks before Napoleon left Moscow, Kutuzov had no more than about 60,000 men, and was in no condition to engage him; he could have withdrawn down any road he chose. He would have been able to evacuate his wounded and equipment, and get back to Minsk and Vilna before the temperature dropped. Most Russians at the time, as well as observers such as Clausewitz, agreed that the French defeat had nothing to do with Kutuzov and everything to do with the weather. 'One has to admit,' wrote Schwarzenberg, who referred to the field marshal as ' _l'imbécile Kutuzov_ ', 'that this is the most astonishing kick from a donkey any mortal has ever had the whim to court.'
## 39
# Hollow Victories
Napoleon reached Dresden in the early hours of 14 December 1812, and stopped at the French minister's lodgings. He dictated letters to his German allies, and sent an officer to the royal palace to summon the King of Saxony. Frederick Augustus dressed hurriedly and arrived by sedan chair at the French minister's residence. Napoleon, who had managed to snatch an hour's sleep, was sitting up in bed. He reassured the astonished king that he would be back in the spring with a new army and asked him to raise more troops. He also borrowed a comfortable carriage from him in which he resumed his journey, pausing only to change horses. At some stops he would not even leave the carriage. At Weimar he leaned out of the window to ask someone to convey his respects to ' _Monsieur Gött_ '. At Verdun he bought some sugar-coated almonds, the regional speciality, for Marie-Louise, saying that one could not return to one's sweetheart without a gift. He asked the serving girl whether she had one, and on hearing that she did, asked what was locally considered to be a respectable dowry, promising to send her the sum once he reached Paris.
Four days after leaving Dresden his carriage trundled up to the Tuileries. It was a few minutes before midnight, and although he was unshaven and barely recognisable in his fur overcoat and cap, he marched into the apartment of Marie-Louise, who was preparing for bed. Before allowing Caulaincourt to go home and rest, he ordered him to call on Cambacérès, to inform him of his return and tell him to announce that there would be a regular _lever_ in the morning.
The 29th Bulletin had been published three days earlier. For over a decade these had contained only tidings of victory, and people were stunned to read an admission of failure. Before they could recover from the shock or start drawing conclusions, on the morning of 19 December the cannon of the Invalides notified them with an imperial salute of Napoleon's return. The master was back, behaving as though the events of the past few months had been no more than a minor difficulty. 'I am very pleased with the mood of the nation,' he wrote to Murat, addressing the letter to Vilna. But by the time he was writing out that address, Vilna was in Russian hands and Kutuzov was attending a gala organised in his honour by the nervous inhabitants.
On leaving the Grande Armée, Napoleon calculated optimistically that he still had some 150,000 men holding the eastern wall of his imperium, with 60,000 under Murat at Vilna, 25,000 under Macdonald to the north, 30,000 Austrian allies to the south under Schwarzenberg, Poniatowski's Polish corps and the remainder of the Saxon contingent covering Warsaw, and over 25,000 men in reserve depots or fortresses from Danzig on the Baltic down to Zamość. He was confident of being able to raise 350,000 men and come to their aid in the spring.
The fiery Murat was magnificent when given a tall order on the battlefield, but, as Berthier pointed out, 'The King of Naples is in every respect the man least capable of overall command.' He had failed to hold Vilna, declaring to Berthier before leaving that he was not going to let himself be besieged in that 'pisspot'. The resulting confusion had prevented an orderly evacuation even by those units still capable of action, and a couple of days later not many more than 10,000 men recrossed the river Niemen. For political reasons it was expedient to keep the King of Naples onside, so instead of a reprimand, Napoleon sent him a friendly note saying that the mood in Paris was positive and reinforcements were on their way.
He told anyone who would listen that the outcome of the campaign was due to extraneous factors. 'My losses are substantial, but the enemy can take no credit for them,' as he put it in a letter to the King of Denmark. The losses were more than substantial, since some 400,000 French and allied troops had perished or gone missing during the campaign – less than a quarter of them combat casualties. Among those losses were some of the most experienced soldiers, NCOs and officers, the backbone of the army, without whom it would be difficult to rebuild a new one. They included cavalrymen whom it had taken years to train, not only to fight on horseback but also to look after horses. It would take years to replace the more than 100,000 horses, along with the hundreds of thousands of muskets and swords, not to mention the cannon, gun carriages, ammunition wagons, and the vast quantity of harness and other essential equipment.
The losses did not end there. Méneval's constitution had been so undermined that he could no longer work, Junot returned a broken man, and many others were badly maimed, mentally as well as physically. It had required all his powers of self-possession, Napoleon explained to Molé, to repress all signs of emotion, but he too had been tried by the experience. 'I showed a serenity, I might even say gaiety throughout, and I do not think anyone who saw me then could deny it,' he said to Molé. But it had cost him. 'Without such command over myself, do you think I could have achieved all I have done?'
To Hortense, who saw him shortly after his return, he seemed 'tired, preoccupied but not crestfallen'. Mollien was astonished when he called at the Tuileries: a few days before Napoleon left for Russia, Mollien's wife had fallen dangerously ill, and Napoleon's first words to him on his return were to enquire of her health. Another who was struck by the emperor's serenity was Frederick William's envoy Prince Hatzfeld. 'In general, I can assure Your Majesty on my honour that on no other occasion when I have been with the Emperor have I found him so gay, so affable and so pronounced in his opinions and his hopes than on this,' he reported.
Napoleon meant to show that nothing had changed, so he rode out inspecting public building works with Fontaine, and insisted that the carnival go ahead as usual, even though tens of thousands were mourning their dead or anxiously waiting for news of loved ones who had gone missing. The balls were not calculated to spread merriment, as so many of the dancers had no arms, wooden legs, or lacked noses, ears and fingers lost to frostbite. His feeling did show on occasion, and as he took leave of him in March, the prefect Joseph Fiévée noted 'a dark sadness' in his eyes.
While the immediate reason for leaving his army and returning to Paris was to muster fresh forces with which to march out in the spring and relieve those he had left behind, what really preoccupied Napoleon on his return was something entirely different.
On the night of 23 October, as he was beginning his retreat from Moscow, General Claude-François Malet and a handful of others had made an audacious attempt to seize power by calling on key officials, announcing that the emperor was dead and brandishing faked documents authorising them to take over. They had managed to fool a number of people, including the prefect of Paris Nicolas Frochot, and arrested the minister of police Savary before they were stopped. They were promptly tried, and twelve were shot, before Napoleon even came to hear of the attempted coup, which made some wonder whether the speed had not been dictated by the wish to prevent further investigations, a suspicion fuelled by the enmity between the two ministers conducting them, Clarke and Savary. Malet had already conspired to mount a coup in 1808, but had been caught and sent to a madhouse. When asked by the general presiding over the court martial whether he had any accomplices, he had replied, 'The whole of France and you yourself, if I had been successful.' The police had stumbled on another conspiracy in the Midi, which involved a number of republicans, among them Barras, and there was undoubtedly much discontent with Napoleon's rule. But that was not what shocked and disturbed him.
On hearing the news of his death in Russia, those who believed it had not reacted in the appropriate manner, which, he pointed out to the Council of State and the Senate when they came to greet him, would have been to proclaim the accession of his son. 'Our fathers rallied to the cry: " _The king is dead, long live the king!_ "' he reminded them, adding that 'these few words encompass the principal advantages of monarchy'. The fact that they had not been uttered on the night of 23 October spelled out to him that for all its trappings, the monarchy he had created lacked credibility. It was a severe blow to his self-esteem as well as to his political edifice, calling into question the very basis of his right to rule.
From Dresden on his way back to Paris, Napoleon had written to his father-in-law asking him to double the contingent of Austrian troops defending the Grand Duchy of Warsaw and to send a reliable ambassador to Paris. Francis sent General Ferdinand Bubna, whom Napoleon knew and liked. At their first meeting, on the evening of 31 December 1812, Bubna made an offer on the part of Austria to mediate in peace negotiations between France and Russia. Napoleon debated with Cambacérès, Talleyrand, Caulaincourt as well as Maret on whether it would be better to accept this offer or to try and strike a deal directly with Russia, over the heads and possibly at the expense of Austria and Prussia. He listened to their opinions without committing to either course.
He wanted peace, probably more than any of his enemies. He was forty-three years old. 'I am growing heavy and too fat not to like rest, not to need it, not to regard the displacements and activity demanded by war as a great fatigue,' he confessed to Caulaincourt. He knew that Austria, Prussia and all his other German allies also longed for peace, and that they feared the involvement of Russia in German affairs even more than they disliked his dominance. From certain statements it is clear that he had come to appreciate that the terms of Tilsit were too hard on Russia, and that he might be prepared to make concessions, particularly if a general settlement including Britain could be agreed. But he had an innate reluctance to negotiate from anything other than a position of strength. He also believed, as he explained to Mollien, that if he were to sign a peace he himself had not dictated, nobody would believe in his sincerity. Perhaps more important, he felt a need to restore his credentials as a ruler, called into question by the Malet affair, and as he believed these were based on military glory, the only way to do so was to re-establish his reputation as a general.
The Senate agreed to raise 350,000 fresh troops, 150,000 of them to be conscripted in advance from those normally eligible in 1814, another 100,000 from those who had been eligible in previous years but had not been called up, and a further 100,000 from the ranks of the National Guard. In the event, probably no more than two-thirds of that number would join the colours, many of them of doubtful quality. They could not all be provided with uniforms and arms, and despite enormous effort, no more than 29,000 horses could be found, which would not provide for the needs of cavalry, artillery and transport. The improved situation in Spain allowed Napoleon to withdraw four Guard regiments, the mounted gendarmerie and some Polish cavalry from the Peninsula.
'Everything is in motion,' he wrote to Berthier on 9 January 1813. 'There is nothing lacking, neither men, nor money, nor good will.' He appears to have elicited more sympathy than blame for what had happened in Russia, and he received many marks of support. Not all were of much use: Louis, who had just published a crass novel entitled _Marie, ou les peines de l'amour_ , wrote to his brother from his retreat in Gratz offering to return to Holland and galvanise the Dutch. Lucien, who had settled in England to write a new version of the _Odyssey_ , had approached the foreign secretary Lord Castlereagh with a proposal to broker an alliance between Britain and Joseph in Spain. Jérôme had whiled away his time since leaving Napoleon in Russia with his three mistresses, and in November unveiled a nine-foot-tall statue of himself on the Place Royale of Kassel.
The perceived danger threatening France helped the mobilisation. There was much discontent and grumbling about the call-up, but, as even a declared enemy of Napoleon had to admit, once conscripted the young men marched out shouting ' _Vive l'Empereur!_ ' The conscripts, known as ' _les Marie-Louise_ ' (as she had signed the call-up decree in Napoleon's absence), were kitted out in a simplified uniform, with trousers rather than breeches, and no waistcoat. There were not enough officers to lead them, but Napoleon hoped to find these among the surviving officers and NCOs of the Grande Armée, who were recuperating in Poland and Germany.
He worked tirelessly, not only forming up the new army, but also shoring up his authority and tidying up affairs neglected during the retreat from Moscow. More than a thousand letters of his survive from the first four months of 1813, most of them long and detailed. Quite a few of them relate to the situation in Spain, where although the military position had stabilised, Joseph and Soult were at loggerheads. A more pressing issue was that of finance: juggle the figures as he might, he could not find enough money for his needs, and military expenditure was now absorbing around 65 per cent of state revenue. He put on a brave face, but the situation was not good, and on his return from a performance at the Théâtre-Français on the evening of 9 January 1813 he received more unwelcome news.
On 30 December 1812 General Yorck von Wartemburg, commander of the Prussian corps in the Grande Armée, detached it from the French units and effectively signed his own alliance with Russia. Following fast on this news came the assurance that Frederick William had denounced the move and dismissed Yorck, but that was a meaningless gesture, since he and his men had already joined the Russian army.
Frederick William was in an unenviable position. The French garrison in the fortress of Spandau paraded through Berlin, reminding him that there were more French than Prussian troops in the country. The probability was that Napoleon would be back in the spring with a fresh army with which he would crush the Russians. In the circumstances, both he and his chancellor, Baron August von Hardenberg, agreed that alliance with Napoleon was the lesser of two evils. He sent Prince Hatzfeld to Paris with the proposal of a closer alliance against Russia, to be sealed by the marriage of the Prussian crown prince to a princess of the house of Bonaparte. But Napoleon did not mean to tie himself to Prussia.
He believed that his father-in-law the Emperor Francis would stand by him: Napoleon was so besotted by Marie-Louise and his son that he assumed Francis must share those feelings for his favourite daughter and grandson. 'Our alliance with France is so necessary that if you were to break it off today, we would propose to re-establish it tomorrow on the very same conditions,' Metternich had told Napoleon's ambassador in Vienna, explaining that only France could counterbalance the threat presented by Russia.
Kutuzov and most senior Russian officers were against carrying the war into Germany, and most of the Russians around the tsar felt that Russia should do no more than help herself to East Prussia and much of Poland, providing herself with some territorial gain and a defensible western border. But Alexander had undergone a spiritual awakening, and had come to see himself as an instrument of the Almighty destined to free Europe from the spirit of Godlessness, of which Napoleon was the epitome. He pressed on, occupying East Prussia and the Grand Duchy of Warsaw, bringing in his wake a bevy of German nationalists bent on raising the whole of Germany against Napoleon.
In the absence of any encouragement from Napoleon, and as most of his army was by then operating in defiance of him, Frederick William was obliged to accept Alexander's offer of an alliance, and on 16 March declared war on France. The two monarchs accompanied this with a proclamation calling on Germans everywhere to rise up and help them overthrow the Confederation of the Rhine, and warning its German rulers that if they did not join in this venture they would lose their thrones.
Nobody was more alarmed by this than Metternich. While he and Francis were eager to exclude French influence from Germany, they did not wish to see it replaced by a Russian hegemony, and the proclamation threatened to arouse revolutionary and nationalist passions that could undermine the Habsburg state. Although Metternich had lamented the abolition of the Holy Roman Empire, he could appreciate the usefulness of the Confederation of the Rhine. And he did not agree that Napoleon must be got rid of at any cost.
He hoped the Russian campaign had sobered him enough to make him realise his best option was to make peace – a peace Metternich would broker, with attendant advantages to Austria. First, he had to extricate Austria from her alliance with France. Only then could he cast Austria in the role of honest broker (and forestall the possibility of Russia and France reaching a deal over his head). To strengthen his position, he ordered the mobilisation of Austria's armed forces.
Metternich had been in secret communication with the Russian court throughout the past year, and although obliged to send an Austrian corps into Russia as part of Napoleon's invasion force, he had instructed its commander, Schwarzenberg, to avoid fighting. When the Russians began to advance, Schwarzenberg pulled back into Poland, and in January 1813 began evacuating the Grand Duchy of Warsaw, which he was supposed to defend in common with Poniatowski's Polish army. Schwarzenberg signed a secret convention with the Russians and withdrew from their path, forcing Poniatowski to fall back, opening Poland and the road west to the Russians.
Metternich also wanted to involve Britain, and in February 1813 he sent an envoy to London to sound out the British cabinet on whether it would agree to participate in negotiations under Austrian mediation. Since Marie-Louise's marriage to Napoleon, the view in London was that Austria was a close ally of France, and Metternich's move was viewed as some kind of intrigue. What neither Metternich nor Napoleon appreciated was that Alexander was on a mission; negotiations were far from his mind, and his troops were on the move.
Before he could march out to face them, Napoleon needed to prepare the ground at home. At the opening of a new session of the Legislative Assembly, he astonished its members with an extraordinary speech asserting that he had 'triumphed over every obstacle' during his Russian campaign. He assured them that he desired peace, and would do everything to further it, but would never make a dishonourable one. He painted a reassuring picture of the state of affairs: the Bonaparte dynasty was secure in Spain, and there was nothing alarming about the situation in Germany. 'I am satisfied with the conduct of all my allies,' he stated. 'I will not abandon any of them; I shall defend the integrity of their possessions. The Russians will be forced back into their horrible climate.' For good measure, he nominated a dozen new members solidly loyal to him to keep an eye on the others.
Having at last accepted that his treatment of the Pope was alienating people all over Europe and undermining his standing in France, on 19 January he went to Fontainebleau, where the pontiff had been confined. After a preliminary meeting at which good intentions were professed on both sides, he returned on 25 February with a protocol which amounted to a partial climbdown, the details of which were to be determined at a later date. The Pope was ill and in no condition to resist, so he agreed to it. Napoleon promptly announced that a new concordat had been signed. The Pope abrogated the agreement three days later, and issued a formal retraction on 24 March, but Napoleon ignored it, and since the retraction was not published his version stuck.
He then turned his attention to the coming campaign. Following his failure to rally the remnants of the Grande Armée at Vilna and then at Königsberg in East Prussia, on 16 January Murat had left his post and gone back to Naples. He had already opened secret negotiations with Austria as, sensing the possibility of further French defeats, he was determined to ensure the survival of his own throne; when Davout tried to stop him, reminding him that he had only acquired it 'by the grace of Napoleon and French blood', Murat retorted that he was king by the Grace of God.
Eugène, who had taken his place, managed to stabilise a front along the Vistula, but was gradually obliged to pull it back to the Oder and then the Elbe, leaving behind French garrisons in fortresses such as Danzig, Modlin and Magdeburg. They would be of use to Napoleon, who planned to take French forces back across the Niemen into Russia. On 11 March he sketched a bold plan for a sweep through Berlin and Danzig into Poland. From Krakow, Poniatowski supported by the Austrians would strike northward and cut the Russian army's lines of communication.
These plans were disrupted but Napoleon's confidence was not shaken when, on 27 March, the Prussian ambassador in Paris announced Prussia's declaration of war. Napoleon's reaction was to instruct his ambassador in Vienna, Narbonne, to offer Austria the Prussian province of Silesia (which the Prussians had captured from Austria in 1745) as a prize if she stood by France. Metternich could do without Silesia, and did not mean to go to war again at the side of France. In order to persuade Napoleon to negotiate, he sent Schwarzenberg to Paris with instructions to make clear that while Austria would support France in pursuit of a fair peace, she did not feel bound to do so unconditionally, and that Napoleon's marriage to Marie-Louise counted for nothing. Napoleon ignored these warnings as he prepared to restore his position by military means before entering into any negotiations.
How sure of himself he felt is open to question; unnerved by the implications of the Malet coup, he had set the Council of State the task of devising a mechanism that would ensure the survival of his dynasty if anything were to happen to him. Accordingly, a _senatus-consulte_ of 5 February 1813 gave Marie-Louise the status of regent for the King of Rome, with a Regency Council made up of the principal grand officers of the empire.
Schwarzenberg, who had a long interview with Napoleon at Saint-Cloud on 13 April, found him less belligerent than in the past, and genuinely eager to avoid war. 'His language was less peremptory and, like his whole demeanour, less self-assured; he gave the impression of a man who fears losing the prestige which surrounded him, and his eyes seemed to be asking me whether I still saw in him the same man as before.' Thirty-six hours later Napoleon left for the army, which he joined at Erfurt on 25 April. He was hoping to defeat the Russians and Prussians before tackling negotiations with Austria, and instructed Marie-Louise to keep her father from making a move prematurely. 'Write to Papa François once a week,' he wrote to her from Mainz, 'inform him of the military situation and assure him of my fondness for him.'
Alexander and Frederick William had already taken the offensive. With the Prussian army under General Gebhard Blücher in the van, they invaded Saxony, denouncing its king as a tool of Napoleon and a traitor to their cause. As Alexander was intending to hold on to Prussia's former Polish provinces, he had promised to compensate Frederick William with territorial 'equivalents' at the expense of Saxony. Both therefore hoped that Frederick Augustus would not declare for the allies.
Frederick Augustus was one of the few European monarchs endowed with a sense of honour, and was genuinely attached to Napoleon. He was both unwilling to cast off his alliance with him and afraid of doing so. He sidestepped the issue by taking refuge in Austria, which promised to protect him and his kingdom. Not long after he left his capital, Dresden was occupied by Alexander and Frederick William, who marched in at the head of their troops, some 100,000 Russians and Prussians commanded by the Russian General Wittgenstein and the Prussian Blücher. They then moved out to face the French forces concentrating around Erfurt.
Napoleon's appearance there exerted the old magic on the troops. 'The joy of the army was extraordinary and each of us, forgetting the sufferings we had experienced, was already looking forward to victory and, after that, to the longed-for peace,' recalled a lieutenant of the Lancers of the Vistula. 'The army is superb,' General Bertrand wrote to his wife Fanny. Colonel Pelleport found his men 'confident, looking forward to meeting the enemy'.
Napoleon advanced swiftly, making for Leipzig. The allied army attacked his right flank at Lützen on 2 May, where Ney held it off while Napoleon doubled back to take charge and lead the young conscripts into the attack. They showed remarkable enthusiasm and advanced on the enemy guns fearlessly, throwing the allies back in disorder. The victory was not decisive, as shortage of cavalry prevented Napoleon from pursuing the enemy and turning it into a rout. Although he trumpeted the news of a great victory for propaganda purposes, he was not satisfied. To Eugène he admitted that in view of the insignificant number of prisoners taken it was no victory at all.
Alexander, who had been present along with Frederick William, made light of the defeat, but it cast a pall over the allied army. The Prussians had suffered painful losses, and mutual recriminations followed, as they blamed the Russians for not holding firm and vice-versa. Although the retreat was orderly, Alexander and Frederick William had to abandon Dresden and take refuge in Silesia. The King of Saxony hurried back to his capital to greet Napoleon. 'I am once more the master of Europe,' Napoleon declared to Duroc.
Metternich assumed that their defeat would have sobered the allies and made them realise they needed the support of Austria, while its limited nature would not have given Napoleon enough confidence to make him intransigent. This raised the Austrian chancellor's hopes, but he believed the only way he could persuade Napoleon to agree to negotiate was by suggesting he would only have to make minor concessions to obtain peace. Narbonne correctly surmised that Metternich was hoping to get Napoleon to agree to negotiations in principle, and then start upping the terms, thereby forcing him to either accept these or break off the negotiations, which would allow Austria to declare their alliance null. Sensing that he was getting nowhere with Narbonne, Metternich resolved to address Napoleon through Bubna.
Napoleon fortified Dresden, which he intended to use as the base from which he would strike at the allied armies converging on the Elbe. Wishing to dispense with etiquette, he put up not in the royal palace but in the Marcolini Palace, set in extensive gardens on the outskirts of the city. Here he could behave as though he were on campaign, working and resting to a rhythm set by the demands of war and diplomacy. A daily _estafette_ from Paris brought news of everything that was going on not merely in the capital but throughout his realm. Agents all over Germany reported on events and morale.
Bubna arrived on 16 May with Metternich's suggested bases for negotiation: Napoleon should give up the Grand Duchy of Warsaw, cede German territory east of the Rhine, and return Illyria to Austria. The interview quickly turned into a harangue as Napoleon accused Austria of duplicity, of arming and negotiating with France's enemies while pretending to remain her ally. He pointed out that Schwarzenberg's withdrawal from Poland had been a betrayal of their alliance; at their last meeting in Paris, Schwarzenberg had sworn that the 30,000-strong Austrian auxiliary corps was still at his disposal, only to withdraw it when the Russians appeared.
As for the suggested bases for negotiation, Napoleon declared that they were both insulting to him and obviously too minimal to satisfy his enemies. Narbonne had warned him that there was 'an underground connection' between Vienna and the Russian headquarters, and he realised a trap was being set for him. He told Bubna that he regretted having married Francis's daughter, and declared that he would not give up a single village.
At one point during the five-and-a-half-hour meeting, Napoleon launched into a diatribe about the importance of maintaining his honour, arguing that if the people of France were to conclude he had failed them, or worse, betrayed them as Louis XVI had done under the influence of his Austrian consort, he and Marie-Louise might end up just as they did; hinting at the possibility of her and her son being murdered by the Paris mob. While this may have been a crude attempt at blackmailing Francis, he does appear to have worked himself into a genuine frenzy on the subject. Less than two months later, when berating the Leipzig authorities over their poor handling of some anti-French disturbances in the city, he mentioned the September massacres of 1792 in language which suggests that he still feared the mob.
Although he blustered at Bubna, he was far from confident, and realised that if he refused to go along with the proposed negotiations he would be isolating himself, so at a final interview he told Bubna he was prepared to make peace, on terms to be discussed. As soon as Bubna had left Dresden, Napoleon despatched Caulaincourt to the Russian front lines with the request for an immediate ceasefire and for one-to-one talks between France and Russia. If he were going to be forced to give up the Grand Duchy of Warsaw, he might as well use it to bribe Russia into ditching Prussia and Austria. His instructions to Caulaincourt were to offer to 'destroy Poland forever'; his Polish aide Chłapowski, who escorted Caulaincourt and stole a glance at them, was so appalled he resolved to leave Napoleon's service as soon as the fighting was over.
The offer was rejected, so on 20 May Napoleon struck again. He outflanked the new allied defensive positions behind the river Spree around Bautzen, forcing them to abandon the field and beat a retreat. Had Ney not wasted an hour getting into position in the allied rear, their army would have been all but annihilated. Once again Napoleon had demonstrated that he was still the greatest general in Europe. The sureness of his touch impressed everyone, as did his decision to take a two-hour nap in the middle of the battle. 'Lulled by the sound of artillery and musketry the Emperor lay down on a cloak laid on the ground and gave orders that he was not to be woken before two hours, and in the calmest way went to sleep before us,' noted one of his aides. He did not even wake when a shell landed and burst close by. Although his shortage of cavalry once again prevented him from exploiting his victory, morale on the allied side plummeted as the Russians and Prussians trudged back into Silesia.
The Russian army, some of whose units were down to a quarter of their nominal strength, was in poor condition. The rank and file, mostly drafted in 1812 to resist the foreign invader, had been promised they could go home once the fatherland had been liberated. Only junior officers avid for glory and promotion wanted to take the war into Germany. As far as the rest were concerned the conquest of Poland was enough of a prize. Tensions were mounting between them and their Prussian allies, and there were instances of individual commanders refusing to carry out orders given by allied superiors.
If Napoleon continued his advance, the Russians would be forced to fall back into Poland while the Prussian forces would have to retreat northwards, as Oudinot operating on Napoleon's left flank threatened Berlin. This would split the allied army in two, making it easy to defeat separately. Although the French lines of communication would be stretched by such an advance, that would be made up for by the troops Napoleon would release from fortresses in Poland. Morale in the Russian army might well be tipped over the edge. The retreat would also dampen the enthusiasm of the German nationalists. As it was, the number of volunteers coming forward to fight for the liberation of Germany was disappointing; it was proving difficult to raise troops, and desertion was on the rise, even among officers.
But Napoleon was worried by the state of his own forces. French losses had been heavy. Shortage of cavalry restricted reconnaissance as well as pursuit. Paucity of draught animals meant there was a shortage of food and supplies. To add to the misery, the spring of 1813 was unusually cold and wet. Rates of desertion rose, particularly in the contingents contributed by Napoleon's German allies. Most of his marshals had had enough. 'What a war!' Augereau complained. 'It will do for us all!'
At a more personal level, Napoleon had been deeply saddened by the death, during the opening shots of the battle of Lützen, of Marshal Bessières, one of his most loyal and capable commanders. He had been profoundly shaken three weeks later when his old friend Duroc was killed at Bautzen. Napoleon sat at his bedside for hours that night until Duroc breathed his last. Those two deaths revived muttering in the army that Napoleon had forfeited his 'star' when he divorced Josephine. 'When will it all end? Where will the Emperor stop? We must have peace _at any cost_!' was a common refrain.
Instead of pursuing the allies, Napoleon decided to call a halt and wait for reinforcements, so he sent an envoy to allied headquarters with the offer of an armistice of seven weeks. The offer was eagerly accepted and the armistice concluded at Plesswitz on 4 June. The armistice 'saved us and condemned him', as one Russian general put it. Hardenberg agreed. Not only did Napoleon save the allies from almost certain defeat, he threw away the initiative, which he would never regain.
## 40
# Last Chance
News of the armistice was greeted with joy throughout the empire; from every department prefects reported that people were desperate for peace. The pursuit of glory no longer held any appeal outside some sections of the army, and most of Napoleon's marshals and senior officers were begging him to conclude peace at almost any price. 'You are no longer loved, Sire,' General Belliard told him frankly, 'and if you want the whole truth, I would say that you may be cursed.' He assured Napoleon that if he were to make peace he would be blessed. Napoleon listened but said nothing.
Even Poniatowski, who had been obliged to evacuate Poland and had joined Napoleon at Dresden with his Polish corps, told him he should make peace now on the best terms available in order to be able to make war from a better position in the future. 'You may be right,' Napoleon replied, 'but I will make war first in order to make a better peace.' In similar vein, Berthier suggested that Napoleon take advantage of the armistice to pull out his far-flung garrisons and concentrate all his forces on the Rhine. But Napoleon saw the presence of his troops in places such as Hamburg, Stettin and Danzig, and his own in Dresden, as an indication of his determination to stand by his German allies, and any retreat as a sign of weakness that would give heart to his enemies. In letter after letter Cambacérès urged him to make peace, saying that everyone was desperate for an end to the war, and that his reputation would not suffer if he were to make concessions. But Napoleon clung to his conviction that the people of France would not respect him if he failed to come up with something which could be dressed up as a victory, and what he called his ' _magie_ ' would be dispelled, as he explained to Fouché.
It was a measure of his insecurity that he had drawn Fouché out of retirement and was sending him to take up the post of governor of Illyria – in Paris he might be tempted to engineer a coup against him; in Trieste he was safely out of the way. The post had become vacant as its previous holder, Junot, had begun displaying dramatic symptoms of neurosyphilis dementia and had to be retired.
Metternich arrived in Dresden on 25 June. When he went to the Marcolini Palace the following day, he was struck by the look of despondency on the faces of the senior officers in the emperor's anterooms. He found Napoleon standing in a long gallery, his sword at his side and his hat under his arm. The emperor opened the conversation with cordial enquiries about Francis's health, but his countenance soon grew sombre. 'So it is war you want: very well, you shall have it,' he challenged Metternich. 'I annihilated the Prussian army at Lützen; I beat the Russians at Bautzen; and now you want to have your turn. I shall meet you at Vienna. Men are incorrigible; the lessons of experience are lost on them.' He accused Austria of treachery, and said he had made a mistake in marrying Francis's daughter. When Metternich tried to make him see that this was his last chance to make peace on favourable terms, Napoleon declared that he could not give up an inch of territory without dishonouring himself. 'Your sovereigns, born on the throne, can afford to let themselves be beaten twenty times and still return to their capitals; I cannot, because I am a parvenu soldier,' he said. 'My authority will not survive the day when I will have ceased to be strong, and therefore, to be feared.'
He did not trust Metternich, and saw the bases for negotiation suggested by him as a trick, since they would not be acceptable to Russia, let alone Britain, so that in agreeing to them he would be entering an open-ended negotiation. He was right, as although Metternich was sincere in trying to salvage what he could for Napoleon, his prime concern was to disengage Austria from alliance with him and give himself freedom of action. Napoleon tried to browbeat him, accusing him of treachery and of being in the pay of Britain, ridiculing Austria's military potential and threatening to crush her. He lost his temper more than once, threw his hat into a corner of the room in a rage, only to resume the conversation on polite, even friendly terms. The meeting lasted more than nine hours, and it was dark outside when Metternich left.
He returned that evening at Napoleon's invitation to see a play put on by the actors of the Comédie-Française, who had been brought over from Paris. He was astonished to find himself watching the famous Mademoiselle Georges (with whom he had had an affair in Paris) playing Racine's _Phèdre_. 'I thought I was at St Cloud,' he wrote to his wife before going to bed, 'all the same faces, the same court, the same people.' The weather had turned fine, and there was a festive atmosphere in the baroque city. The armistice had cheered all those who longed for peace, and there were balls and parties for the French officers and Napoleon's entourage.
Further meetings having proved fruitless, Metternich was about to leave, on 30 June, when he received a note summoning him for an interview with Napoleon. He ordered his horses to be unharnessed and went to the Marcolini Palace, dressed as he was, expecting to have to listen to the same complaints and threats. To his surprise, Napoleon agreed to a peace congress under Austrian auspices, to be held at Prague in the first days of July. He suggested including Britain, the United States of America and Spain, but Metternich demurred, seeing this as an unnecessary complication.
A few days after his departure, Napoleon received unwelcome news from Spain. Wellington had gone over to the offensive at the end of May, and Joseph had been forced to abandon Madrid. The British caught up with him and the retreating French army at Vitoria and routed it on 21 June. It was a humiliating defeat, rendered all the more shameful to French arms by the loss of over a hundred cannon as well as all the army's and the king's baggage. Napoleon gave Soult overall command of the Army of Spain, and ordered Joseph to go to Mortefontaine and not show himself in Paris.
He did not put much faith in Metternich's mediation, but hoped he might be able to strike a deal with Alexander. 'Russia has the right to an advantageous peace,' he told Fain. 'She will have bought it with the devastation of her lands, with the loss of her capital and with two years of war. Austria, on the contrary, does not deserve anything.' Yet Alexander was the one monarch least likely to treat with Napoleon on any terms, while Metternich did still favour a peaceful outcome.
The armistice was extended to 10 August; if terms were not agreed by midnight on that date hostilities would resume, with Austria in the allied camp. But the congress, which convened at Prague, never got beyond procedural questions. 'At heart, nobody truly wanted peace,' wrote Nesselrode, adding that the congress was a 'joke' which Alexander and Frederick William had opposed from the start, and the tsar sabotaged the proceedings by sending an envoy who would not be acceptable to Napoleon. Caulaincourt and Narbonne struggled to get negotiations going, but they were hamstrung; Caulaincourt had done everything to avoid being nominated to represent Napoleon, whose intransigence would make it impossible for him to negotiate. When he suggested making concessions, Napoleon burst out, 'You want me to pull down my trousers to get a whipping,' and stormed out of the room. Caulaincourt was instructed to take the line that Napoleon had never been beaten in Russia, and only 'sustained some losses through the inclement weather'. He was so exasperated that he appears to have told Metternich he wished Napoleon would lose a battle, as only that could bring him to his senses.
Napoleon was determined to brazen it out, and in a show of nonchalance set off on 25 July for Mainz, to spend ten days with Marie-Louise. It was not a joyous occasion. He arrived to find her tired out by her journey, and nursing a cold. The weather was bad, with heavy rain. After reviewing the troops in Mainz, he took her with him as he reviewed those camped in the vicinity. He made a show of confidence, putting in hand works for the refurbishment of the imperial residence in the city and declaiming about the apparent success of the negotiations going on in Prague. He also made elaborate plans for her to attend the flooding of the new harbour at Cherbourg, which was to provide a large sheltered basin for the fleet that would threaten Britain. But he was often silent and moody at dinner, and on one occasion even snapped at her.
He was back in Dresden on 4 August, only to discover that the negotiations in Prague had not begun. He wrote to Metternich asking him to state his terms, and received the answer on 7 August: the Grand Duchy of Warsaw should be divided between the three allies, Austria should recover Illyria, Hamburg and Lübeck should regain their independence, and France should give up her protectorate over the Confederation of the Rhine and her other German conquests.
Given Napoleon's position, the terms were acceptable; there was no mention of Holland, Belgium or Italy, which left plenty of room for manoeuvre when peace talks began in earnest. His acceptance would have prevented Austria from joining the allies in the war against him, which was important, since he continued to entertain thoughts of defeating the Russians and Prussians before then, which would, he believed, allow him to split the allies and play them off against each other. But, determined not to appear too keen, Napoleon delayed his reply accepting the terms.
The showman was determined to keep up his act. As his birthday fell after the end of the armistice, he had ordered the festivities to be brought forward by five days to 10 August, and it was celebrated with pomp in every unit, and imperially in Dresden itself, with a parade, a ball, a banquet and fireworks. 'One could not imagine anything under the sun more martial; everything exuded confidence, ardour, enthusiasm,' wrote one of the actors of the Comédie-Française who had been performing in Dresden. 'My God, what a show!' It did not impress his generals, many of whom saw disaster looming.
'The great moment has arrived at last, my dearest friend,' Metternich wrote to his wife the same day. That evening, while fireworks lit up the sky above Dresden, the Russian and Prussian negotiators had gathered at his residence in Prague. Watches were consulted with impatience, and when the chimes of midnight rang out over the sleeping city Metternich announced that the armistice was over and Austria was now a member of the alliance. He ordered a beacon to be lit which, by a chain reaction, carried the news to allied headquarters in Silesia. By morning, Russian and Prussian troops were on the march to join the Austrian army outside Prague.
On 12 August, just as Caulaincourt and Narbonne were preparing to leave Prague, a courier arrived from Dresden with Napoleon's instructions to accept Metternich's terms. Caulaincourt called on Metternich without delay, but was told it was too late; Austria had issued her declaration of war. Napoleon instructed him to delay his departure in the hope of being able to obtain an interview with Alexander, who was due a couple of days later. On 18 August Maret wrote to Metternich arguing that the congress had not been given a chance, and proposing a fresh one to be convoked in some neutral city to include all the powers of Europe, great and small. But Metternich had by then ruled out peace, and Alexander had been against it all along. The tsar had gone so far as to conceal Britain's agreement to join the negotiations, knowing it would have strengthened Austria's case for peace and encouraged Napoleon to take the negotiations seriously – he would probably have been prepared to make concessions in such circumstances; a general peace with the participation of Britain, involving as it would not only huge economic relief but also the return of French colonies, could have been dressed up as a victory and allowed Napoleon to claim that he was making peace with honour.
The only victory he could hope for now was on the battlefield, and that was going to be difficult to achieve. Facing him was the main allied army under Schwarzenberg, consisting of 120,000 Austrians, 70,000 Russians under Barclay de Tolly and 60,000 Prussians under General Kleist, a total of 250,000. Behind it stood Blücher's army of Silesia, consisting of 58,000 Russians and 38,000 Prussians. In the north Bernadotte commanded an army of 150,000 Swedes, Russians and Prussians. That added up to well over half a million men, and did not include Wellington's Anglo-Spanish army, which was approaching France's south-western frontier. More significantly, the allies had agreed a plan which consisted in refusing battle to Napoleon and only taking on individual corps commanded by his marshals. The idea was to wear down his forces without risking defeat. His resources were diminishing, while theirs were on the increase; the vast war effort Alexander had put in motion as soon as the French had been expelled from Russia was beginning to produce spectacular results in men, equipment and, crucially, horses.
'I have an army as fine as any and more than 400,000 men; that will suffice to re-establish my affairs in the North,' Napoleon boasted to Beugnot, but later in their conversation he complained that he was short of cavalry and needed more men, particularly seasoned troops. His forces were in fact greatly inferior to those of the allies. His garrisons in Germany and Poland accounted for 100,000 of his calculation, and they were beyond his reach. His best marshal, Davout, was stuck in Hamburg with a body of seasoned troops, Rapp was besieged in Danzig with over 20,000 veterans, many of them officers and NCOs, while the bulk of the 300,000 or so men at Napoleon's immediate disposal were mostly conscripts with rudimentary training. Much the same was true of the Army of Italy which Eugène had been forming up to threaten Austria's southern flank.
Morale was surprisingly good among the troops as they marched out of Dresden on 16 August, boosted by the arrival of Murat, whom Napoleon had persuaded to come from Naples and take command of the cavalry. Napoleon's plan was to drive back Blücher and then, leaving Macdonald to cover him, veer south and outflank the main allied army under Schwarzenberg, which was moving on Dresden. The first part of the operation went according to plan, but at Lowenberg on 23 August, as he was taking a hurried lunch standing up, a courier arrived with a message from Gouvion Saint-Cyr, whom he had left to hold Dresden, warning that the main allied army under Schwarzenberg was threatening the city from the south. Napoleon smashed the glass of wine he was holding against the table as he read the despatch. The fall of Dresden would have political repercussions, so he turned about and marched back, detaching a force under General Vandamme to move south into the allies' rear while he took them on at Dresden.
He arrived outside the city on 26 August, and the next day, in pouring rain with mud up to their knees, his forces began pushing the allied forces back and eventually put them to flight. It was a fine victory; he had inflicted around 15,000 casualties, taken 24,000 prisoners, fifteen standards and a number of guns. But he failed to follow it up as he would have done in the past. He marched back to reinforce Vandamme, who was now in a position to cut off the allied retreat, but unaccountably stopped and turned back. The result was that Vandamme was himself caught in a trap and forced to capitulate at Kulm with around 10,000 men. If Napoleon had come to his assistance he would have destroyed the allied army and probably captured all three allied sovereigns and their ministers.
Napoleon's sluggish behaviour has been variously blamed on a bout of food poisoning and on the depressing news he received on 30 August. Oudinot, whom he had ordered to march on Berlin, had been defeated by the Prussians at Grossbeeren. 'That's war,' Napoleon said to Maret that evening after hearing of the disaster of Kulm. 'Up there in the morning, down there in the evening.' He was increasingly prone to making fatalistic comments and quoting lines of poetry about destiny; it was as though he were giving himself up to it rather than, as in his youth, trying to forge it. News of the death of Junot, who had leapt out of a window and killed himself on 29 July, would not have helped. In his last letter he had compared his worship of Napoleon to that of 'the savage for the sun', but begged him to make peace. In Lannes, Duroc and now Junot, he was losing men who had served him with devotion since Toulon, nearly twenty years before.
A curious twist of fate had brought two of his long-standing rivals out against him. Moreau had been persuaded to return from America and had joined the tsar's headquarters, entertaining dreams of a military and perhaps political comeback. These were shattered by a French shell outside Dresden on 27 August; he died four days later. To the north, as Sweden had joined the coalition, Bernadotte was leading a combined Swedish and Prussian corps, entertaining more clearly stated dreams of succeeding Napoleon as ruler of France. To that end, he avoided coming face to face with French troops and badgered the allies to allow him to attack Denmark instead. The allies did not trust him (Blücher only ever referred to him as 'the traitor', and Hardenberg described him as 'a bastard that circumstances have obliged us to legitimise'), and kept a wary eye on him.
A couple of days after hearing of the defeats of Kulm and Grossbeeren, Napoleon received news that Macdonald had been repulsed with heavy losses by Blücher on the river Katzbach, and not long after, that Ney had been defeated at Dennewitz on 6 September. He was breaking his own golden rule, never to divide his forces but always to concentrate them at the decisive point. And while 'the Bravest of the Brave', as Ney was referred to, was a fine cavalry commander with all the panache one could hope for on the field of battle, he lacked judgement and, like most of the marshals, was not up to operating on his own. It did not help that Berthier was showing signs of age and despondency, which affected his management of operations. Napoleon too hesitated and kept changing his mind, meaning to march on Berlin one moment and into Bohemia the next. With the Austro-Russian army of Schwarzenberg licking its wounds in Bohemia, he decided to take on Blücher, but the Prussian refused to give battle, and Napoleon was obliged to trudge back to Dresden; the allies had drawn him into a game of blind-man's-buff as he lunged at one and then another.
Soon after hostilities began, the weather turned wet and cold. The roads were morasses of mud, reducing his mobility as well as the effectives of every unit with each march. Communications were impeded by shortage of cavalry and by the large numbers of cossacks roaming the country; staff officers were reluctant to carry orders and proceeded with caution when carrying out reconnaissance for fear of being captured. The persistent rain often rendered muskets useless, so the troops had to resort to the bayonet. The marches and counter-marches exhausted the men and depleted the ranks. 'Whenever we left a bivouac in the morning, having spent the night either only partially or not at all sheltered from the rain, the wind and the cold, we almost always left behind exhausted men, undermined by fever, hunger and misery, and that was almost always so many men lost, as in our incessant marches we did not have the possibility of having them moved,' wrote Sergeant Faucheur. Dresden was filling up with sick and wounded soldiers and the supply situation was dire. 'Never had my duties been more difficult or my efforts less fruitful,' recalled the man in charge, General Mathieu Dumas.
Morale dipped, particularly among senior officers, who could see the situation growing desperate. None felt that more than Napoleon, whose exasperation was evident; he alternated between spells of lethargy and sudden bold decisions which his marshals considered too rash. He also lost his temper, calling into question their competence and their loyalty. When he accused Murat of treason (with good reason), Berthier tried to intervene, only to have Napoleon tell him to mind his own business and snap, 'Shut up, you old fool!'
He could no longer hold on to his exposed position at Dresden, and on 13 October decided to fall back on Leipzig, where Frederick Augustus had preceded him. Political considerations made him commit a fatal error: fearing that abandoning Dresden would make a poor impression, he left Saint-Cyr there with more than 30,000 men, thus depriving himself of a significant number of troops at a moment when the allies were gaining in strength. Reaching Leipzig two days later, he repelled an attack by Schwarzenberg, and the following day scored significant success, at one point coming close to capturing the three allied monarchs. But towards the end of the day Blücher, whom he had assumed to be far away, appeared in his rear, and he was forced to call off the attack.
By then the allies had some 220,000 men facing his 150,000 on three sides, and outgunned him with over a thousand pieces of artillery. He had lost the initiative, and admitted as much by sending an Austrian general captured the previous day, with an offer to negotiate – which was rejected out of hand. Their recent successes had buoyed the allies, and the tensions between them had been worked out by the signature on 9 September of the Treaty of Töplitz, which committed them to the common struggle. The only thing that could have saved Napoleon would have been a rapid withdrawal of all his forces in Germany and a concentration on the Rhine, but he continued to put strategy second to what were by now entirely irrelevant political considerations. The allies held off on 17 October as they prepared their concerted attack, but he did not seize the opportunity to make good his escape or even prepare for it; he did not evacuate the wounded or supplies of ammunition, or even have adequate crossings prepared over the rivers.
On 18 October, by which time they outnumbered the French by well over two to one with some 360,000 men and a vast artillery, the allies launched their attack. The French fought with determination, but the sheer numbers facing them told, and matters were not helped when the Saxon contingent in the French army suddenly turned around while advancing on the enemy and began firing on its French comrades who were coming up in support. Other German contingents also defected, sowing confusion and affecting morale. The number of men and guns on the field of battle meant that the slaughter was unprecedented. The corps commanders who could see the pointlessness of the situation were also losing heart. 'Does that b— know what he's doing?' Augereau fumed to Macdonald two days later. 'Haven't you noticed that in the recent events and the catastrophe which followed he lost his head? The coward! He abandoned us, he sacrificed us all...'
Napoleon really did not appear to know what he was doing. On the evening of 18 October he gave the order to withdraw, and columns of troops began a disorderly retreat through the narrow streets of Leipzig. The allies stormed the city the following morning, sowing confusion. A sergeant left guarding the single bridge over the river Elster with orders not to blow it until the rearguard had crossed panicked and lit the fuses too early, cutting off at least 12,000 men with eighty guns, and leading to the death of Poniatowski, who drowned trying to get across the river despite being severely wounded. Napoleon had been asleep in a windmill outside the city, and was woken by the explosion. Macdonald, who had managed to get across, reported the event. Napoleon seemed stunned as much as distraught, and apparently unaware of the extent to which his lack of foresight had been to blame for a debacle of monumental proportions. The losses of the Grande Armée in the fighting around Leipzig were 70,000 men and 150 guns, not counting the 20,000 German allies who had changed sides. Allied losses were 54,000.
Before leaving Leipzig Napoleon went to the palace and offered Frederick Augustus refuge in France, but the Saxon king declined the offer, saying that he could not leave his subjects at such a time. Frederick Augustus sent officers to each of the allied monarchs, but received no response. Alexander snubbed him when he rode into Leipzig, and after some argument the unfortunate Saxon royal couple were bundled into a carriage and sent under armed escort to captivity in Berlin. Murat on the other hand was allowed to sneak off to Naples, where he had an army of around 25,000 men, magnificently uniformed but inadequately trained and led. Metternich, who may also have been influenced by fond memories of the affair with Caroline he had enjoyed in Paris a couple of years before, seems to have believed that his forces were stronger and to have been impressed by his military reputation. He thought it politic to detach him from Napoleon by offering to leave him on the Neapolitan throne.
Napoleon fell back on Erfurt, where he spent two days, in the same rooms in which he had held talks with Alexander less than five years earlier, 'in an attitude of deep meditation', in the words of Macdonald. He briefly thought of making a stand there, but his marshals balked at this, pointing out that the Bavarians, who had now joined the coalition, were about to cut them off from France. Listless and undecided, he had to be urged to move on by his marshals, and made for the Rhine. Aside from the Guard, which was still disciplined, most of his remaining forces were no more than a crowd marching without order; one officer was reminded of the retreat from Moscow. No effort was made to rally the troops, and many were abandoned to die by the roadside.
At Hanau, their road was barred by 50,000 Bavarians. The Guard managed to defeat their erstwhile allies, but Napoleon barely directed the action, sheltering in a wood and seeming to those around him to have lost his nerve. Ségur, who had arrived from Paris and had not seen him for six months, was shocked by the change that had taken place in him. 'The impression he made on me was so strong and so painful that I still feel it today,' he wrote more than a decade later. When Napoleon addressed the remnants of Poniatowski's Polish corps, releasing them from their oath but begging them to stay with him, promising to fight again one day for their country's cause, many were so moved to pity that they did.
He crossed the Rhine on 30 October with no more than 30,000 men and some 40,000 stragglers. He spent two days at Mainz, from where he sent optimistic reports and captured standards to Paris, assuring Marie-Louise that people in Paris were 'unnecessarily alarmed': 'My troops have a decisive superiority over the enemy, who will be beaten sooner than he thinks.' To Savary, he wrote that the alarmist talk in Paris was ridiculous and made him 'laugh'. But the situation was nothing short of catastrophic.
His empire was crumbling. The network of control over Germany built up since 1806 unravelled. As other rulers of the Confederation of the Rhine joined the allies, Jérôme fled Kassel, 'accompanied by his ministers of foreign affairs and war, and still surrounded by all the tattered trappings of royalty', in the words of Beugnot, who saw him pass through Düsseldorf, escorted by 'lifeguards whose theatrical uniforms heavy with gold were wonderfully inapposite to the situation' and a court which 'resembled nothing so much as a troupe of actors on tour rehearsing a play'. The 190,000 or so French troops still holding out in fortresses such as Dresden and Hamburg, not to mention points further east, were now beyond Napoleon's reach and isolated in a hostile sea, and would capitulate one by one. Private scores were settled as his regime imploded, unruly Prussian and Russian troops bent on rapine swarmed over the area, and a typhus epidemic spread rapidly as people fled in all directions, turning military hospitals into morgues and striking down exhausted and underfed stragglers.
The situation further south was little better. Austrian troops had invaded the Illyrian provinces, forcing the weak French garrisons to evacuate them. Eugène could do little to stem their advance, and fell back on Milan. In November he was approached on behalf of the allies by his father-in-law King Maximilian of Bavaria, who urged him to safeguard his future by changing sides, but he refused and remained loyal to Napoleon, firmly supported by his wife.
As he contemplated the defence of France itself, Napoleon did what he could to improve her defences by closing off potential points of entry. He pressed the Diet of the Helvetic Republic to declare its neutrality (without going so far as to recall the Swiss troops in his own ranks), withdrew all French forces and renounced his role as Mediator.
He also belatedly tried to lance the Spanish ulcer, instructing Joseph to abdicate (which he at first refused to do, waxing indignant about being forced to 'sacrifice' sacred rights to 'his' throne, and complaining that he was not accorded the honours due to his royal rank), and freed Ferdinand, still a guest of Talleyrand at Valençay. He was to return to Spain, having first married Joseph's twelve-year-old daughter Zenaïde and signed an alliance with France promising to expel British troops from the Peninsula. By the time Ferdinand set off, in March 1814, he could no longer be of any use to Napoleon, even if he had wished to be. Soult at Bayonne and Suchet further south, with 50,000 and 15,000 men respectively, faced a combined Anglo-Spanish force three times that number.
Eugène was only just holding out in Italy, with 30,000 troops of questionable quality and allegiance against a more numerous Austro-Bavarian army. Only Augereau's reserve of about 20,000 stationed in the region of Lyon stood between that and Paris. In the north-east, apart from the troops besieged in fortresses in Holland, Belgium and along the Meuse, Napoleon had only around 70,000 men. They faced at least 300,000 allies who had reached the Rhine and threatened to cross it at any moment.
While he was still at Dresden he had instructed Cambacérès to make the Senate bring forward the call-up of 1815, and on 12 November, after his return to Paris, it voted the conscription of another 300,000 men. Napoleon estimated that he would soon have 900,000 under arms, but his calculations were as fictitious as those concerning available funds. As the area under his control shrank, so did his manpower pool, and resistance to conscription increased; the number evading it by going into hiding rose drastically, and according to some estimates reached 100,000. Few of the class of 1815 ever reached the ranks. Even if they had, they would not have been of much use, as there was nothing to arm them with. Given an annual production of 120,000 muskets, the losses of 500,000 in 1812 and 200,000 in 1813 could not easily be made up. At the end of 1813, the 153rd Regiment of the Line had 142 muskets for 1,100 men, the 115th regiment 289 for 2,300 men. The situation in the cavalry was no better, with the 17th Dragoons having to share 187 sabres and even fewer horses between 349 men.
Napoleon was back at Saint-Cloud on 10 November. The following day he held a Council of State during which he complained that he had been betrayed by everyone, venting particular rage against King Maximilian of Bavaria and vowing vengeance. 'Munich shall be burned!' he ranted repeatedly. He put on a brave face, and only a few days after getting back to Paris he went hunting. Ten days later he rode around with Fontaine inspecting the new post office and corn market, and progress on the extravagant project of a palace for the King of Rome at Chaillot. Nobody was fooled. 'Despite his efforts to hide them, it was evident to all those accompanying him that other thoughts were occupying him more than these grand building projects,' noted Bausset. Napoleon relieved his stress with outbursts against people, and also used his feigned rages to show that he was still the roaring lion. He tried to bully the Pope into accepting his 'new concordat'; when he refused, the old man was bundled off back to detention in Savona. Seeing Talleyrand at the first _lever_ , Napoleon threatened him that if he were brought down, Talleyrand would be the first to die. On 9 December at the opening of the Legislative Body he lectured it on the need for more men, more money and more determination. Court life continued as usual; the receptions were as glittering and crowded as ever, but Joseph and Jérôme were kept away, as Napoleon did not want dethroned monarchs spoiling the show.
'The master was there as always, but the faces around him, the looks and the words were no longer the same,' recorded one official who attended the imperial _lever_ at the Tuileries. 'There was something sad and tired about the demeanour of the soldiers, and even the courtiers.' The mood in Paris was despondent. 'People were anxious about everything, foreseeing only misfortune on all sides,' wrote Pasquier. 'The court was gloomy,' wrote Cambacérès. 'With the exception of a very small number, all the men with positions anticipated the impending catastrophe and were secretly occupied in trying to avoid it and secure their political existence.' Many were expecting a change of regime.
Napoleon only confided in a very few. 'In the evenings, he would call me to his apartment, as he sat in his dressing gown warming himself by the fire,' recalled Lavalette. 'We would chat (I can find no other word for this hour-long talk which preceded his sleep). The first days I found him so prostrate, so despondent, that I was horrified.' Marmont, who saw him often, noted that he was 'gloomy and silent', but would always buoy himself up with hopes that the allies would pause on the Rhine long enough for him to raise a new army; he could envisage no other means of salvation.
'Come back to France, Sire, identify yourself with the French and every heart will be yours, and you will be able to do what you wish with them,' Josephine had written to him on hearing news of Leipzig. But Napoleon could not bring himself to trust the French people. He knew that Bernadotte had contacted his Jacobin friends in the hope of taking power, and saw the despair to which his entourage had given way as weakness at a moment when the state they had all laboured to build was about to crumble like the Bastille. He was convinced that only he could safeguard the new order he had created, and that only by a show of force.
He desperately wanted peace, but he had based his right to rule so exclusively on glory and his supposedly miraculous 'star' that he felt he would be betraying it by making what he saw as a humiliating peace. 'In that, he underestimated the generosity of the French and was not able to trust in a quality which was alien to his own character,' commented Pasquier. 'He did not even do himself justice, for he possessed, in the memory of his brilliant record, and even in his mistakes and his reversals, an _éclat_ and a grandeur that would always have sustained him.' He could envisage only one way of reasserting his right to rule, by redeeming himself on the battlefield, and as a result threw away his last chance of keeping the throne of France.
## 41
# The Wounded Lion
Up to now, the allies had concentrated on forcing Napoleon out of Germany, and only envisaged military operations as far as the Rhine. Having reached that, they hesitated; to carry the war into France would lend their enterprise a different character. Alexander was keen to keep going and take Paris, but neither his ministers nor his generals were, and his troops were more interested in going home. Frederick William was also wary of continuing, and although Blücher was bent on dealing further damage to the French, his army was in poor condition. Metternich, who was now in Frankfurt with the other allied ministers, did not wish to weaken France further and was wary of the tsar's plans, while Francis wanted peace.
Through a returning French diplomat, the baron de Saint-Aignan, Metternich sent Napoleon a peace proposal on the basis of France giving up her conquests in Italy, Spain and Germany, and returning to her so-called natural frontiers on the Rhine, the Alps and the Pyrenees, thereby keeping Belgium and Savoy as well as the left bank of the Rhine. The status of the rest of the Netherlands was left unspecified, and there was talk of negotiation on the subject of colonies and maritime matters. Although the British representative in the allied camp, Lord Aberdeen, was aware of it, the initiative was taken by Metternich and Nesselrode, so it had only a semi-official character.
Saint-Aignan reached Paris on 14 November, and the following day presented these proposals to Napoleon. He was quick to spot that as there was no mention of maritime matters, and as Belgium was left in French hands, they would not be acceptable to Britain. They therefore represented an opportunity to split the allies, so he responded positively; but, not wishing to appear too eager, and encouraged by Maret, one of the few who still trusted that his 'genius' would triumph, he did so in the vaguest terms, suggesting a peace congress and bringing up additional points.
It did not take him long to realise that this was a mistake. He moved Maret back to his old job as secretary of state and, after briefly considering Talleyrand, replaced him with a reluctant Caulaincourt. Caulaincourt spent the best part of a week persuading Napoleon to accept the Frankfurt proposals as they stood, and it was not until 2 December that he was able to write to Metternich that he had. His letter arrived too late. On 19 November the allies had agreed a plan of campaign, and on 7 December they published their 'Frankfurt Declaration', which suggested that the 'natural frontiers' were no longer on offer, and, more ominously, that they were fighting not France but Napoleon.
Had he accepted the proposals immediately, the allies would have been obliged to halt their offensive and a peace conference would have been convened, at which he could have bargained and played for time. It would have given him the breathing space he needed to rebuild his forces, and even if he did not manage to get his way at the conference (he had already drawn up all his demands, which were extensive) he would be in a position to start extending his influence again once peace had been made. Above all, he would have avoided the crucial development of his fate being separated from that of France.
'The strange thing is that Napoleon, whose common sense was equal to his genius, could never discern at which point possibility ended,' noted Mathieu Molé, who had worked closely with him since 1809. He went on to say that on encountering an obstacle Napoleon would look no further than surmounting it, seeing in the process a test for his will, and thinking only of the present, not the future. These characteristics were on display in the speech he made on 19 December, opening the session of the Legislative. He described the 'resounding victories' he had won in the recent campaign, which had only been annulled by the defection of his German allies. Ten days later, in the course of a debate on the unfortunate outcome of the Frankfurt negotiations, one member made a speech suggesting that peace should be made on the basis of the interests of France, not those of the emperor. An outraged Napoleon wanted to close down the assembly. 'France needs me more than I need France,' he ranted. Cambacérès managed to calm him, but a number of members were invited to leave Paris.
The allied advance had resumed: in the north Blücher's Prussians crossed the Rhine between Mainz and Cologne, in the south the Austrians moved against Eugène in Italy, and in the centre Schwarzenberg with the main Austro-Russian forces crossed into France from Switzerland to deploy on the plateau of Langres. Metternich, who hoped to avoid unnecessary fighting, had suggested fresh talks, with the participation of Britain, whose foreign secretary Lord Castlereagh was on his way, and Napoleon had agreed; only the venue still needed to be fixed. As the allied advance had not been halted, Napoleon meant to strengthen his hand with a military victory. On 4 January 1814 he decreed the _levée en masse_ in the departments threatened with invasion, mobilising customs officials, police officers, gamekeepers, foresters and veterans to organise a territorial defence. He showed a degree of reluctance to call up the Paris National Guard, as he was no longer sure whom he could trust.
A few days later, on 7 January, unbeknown to Napoleon, Murat signed a treaty of alliance with Austria. As recently as 12 December 1813 he had written asking for instructions, assuring the emperor that 'I will for the rest of my life be your best friend'. Napoleon had been aware of Murat's contacts with the Austrians, but he realised that he and Caroline had only been hedging their bets, and would revert to him in the event of a change in his fortunes. Murat was being pressed by Austria to take the field openly, but delayed as long as he could. Napoleon had sent Fouché to Naples in November to keep an eye on him, but Fouché was looking to his own future, and advised Murat to join the Austrians. The decision was probably made by Caroline, who was more intelligent and hard-nosed, as was Élisa, who did her best to hang on to Lucca by breaking off relations with France. Meanwhile, Eugène continued to give Napoleon assurances of loyalty but resisted his suggestion that his pregnant wife come to Paris – where she would have been a hostage to his good behaviour. Napoleon asked Josephine to write to him, which she did, enjoining him to remain loyal to Napoleon and to France.
On Sunday, 23 January, after attending mass, Napoleon made his way to the Hall of Marshals in the Tuileries. There he presented the King of Rome to the officers of the Paris National Guard. The same day he signed letters patent naming Marie-Louise regent in his absence. The next morning he nominated Joseph Lieutenant-General of the Empire, and that evening, after burning his most secret papers, he embraced his wife and son; at six in the morning on 25 January he rode out of Paris to join the army. 'He appeared in a good mood, determined and in perfect health,' noted Lavalette. To Pontécoulant he declared that unless a cannonball struck him down, within three months there would not be a single foreign soldier on French soil. He rebuked those around him who thought the war lost. 'They think they can already see cossacks in the streets,' he had quipped over dinner a few days earlier. 'Well, they're not here yet and we haven't forgotten our trade.' He assured his wife that he would defeat the allies and dictate peace to her father. 'I'll beat Papa François again,' he repeated as he hugged her for the last time. 'Don't cry, I'll be back soon.' He would never see her or his son again.
Before leaving Paris he dictated a letter to his father-in-law suggesting that he make a separate peace. He pointed out that if the allies were to lose, Austria would lose more than the others, while every allied victory only diminished her influence, since it increased that of the other allies disproportionately. He meant to drive the point home with a victory, and having narrowly escaped being killed on the way by a patrol of cossacks, he took command of the 45,000 men camped at Châlons-sur-Marne. 'Despite the disasters of the campaign in Saxony, despite the allies' passage of the Rhine, the army was convinced that it would defeat the enemy,' recalled the colonel of one of the Guard regiments, noting at the same time that the senior commanders were more sceptical. They had good reason to be: while the allied generals could be defeated, the allied statesmen had become accustomed to defeat, and each new one confirmed them in their conviction that the only way to obtain a lasting peace was to be rid of Napoleon. He was sanguine that he could rout the allies and drive them back, and thereby recover the 90,000 men stuck behind their lines in fortresses along the Rhine or just beyond the borders of France.
Blücher had drawn ahead of the other allied forces, and Napoleon attacked him near Brienne, where he had begun his military career. He dealt him a heavy blow and drove him back, but, reinforced by Schwarzenberg, Blücher counter-attacked and, outnumbered by more than two to one, Napoleon was defeated at La Rothière on 1 February. He fell back on Troyes behind the Seine.
This emboldened the allies, and when Caulaincourt met their plenipotentiaries at Châtillon for negotiations a week later, he was flatly told that the best he could expect was France's pre-revolutionary frontiers. When Napoleon heard of this on the evening of 7 February he protested that he could never agree to such terms, as he would be breaking his coronation oath and giving his enemies grounds to dethrone him. He was in desperate mood, and did not sleep. When, in the early hours, a messenger brought news that Blücher had drawn away from Schwarzenberg and was marching on Paris, he decided to take him on a second time. Maret, coming in with a letter to Caulaincourt for him to sign, found him lying on a map with a pair of compasses, all thoughts of negotiation banished. Napoleon moved fast, gathering up every unit he could find along the way. On 10 February he defeated Blücher's advance guard at Champaubert, the following day another of his corps at Montmirail, and the day after that a third at Château-Thierry. On 14 February he defeated Blücher himself at Vauchamps. He was in fine spirits, and all who saw him took heart. On 18 February he scored another victory at Montereau, in the course of which he aimed a cannon himself.
'They thought the lion was dead and it was safe to piss on him,' he exclaimed. He sent instructions to Caulaincourt at Châtillon to settle for nothing less than France's 'natural' frontiers, to hold out for Italy, to give as little ground as possible, and above all to refer back before agreeing to anything. He wrote to Francis once again, hoping to persuade him to make a separate peace, but he himself had only thoughts of war. On 21 February he wrote to Augereau, chiding him for dragging his heels: 'If you are still the Augereau of Castiglione, keep your command; if your sixty years weigh on you, leave it and hand over to the most senior of your general officers. [...] we must recover our boots and our resolve of '93!'
Blücher's defeat had come as a shock to the allies, and panic spread through some units. Schwarzenberg fell back and requested an armistice as the allied monarchs and their ministers raced for safety. Bernadotte was in contact with his French friends, raising fears of his defection. Morale on the French side soared, despite the heavy losses and the exhausting forced marches in the atrocious conditions of the winter campaign, and in the countryside in which he operated Napoleon was greeted with enthusiasm. The behaviour of the German troops, seeking revenge for years of humiliation, had aroused the anger of the locals, and there was some spontaneous partisan resistance in the areas affected by the war. But while Napoleon made sure that the cannon of the Tuileries thundered out the good news of every victory and enemy prisoners were paraded through the streets along with captured standards, the Parisians were increasingly fatalistic. 'Everyone is hiding their most precious possessions, burying them in the ground, sealing them up in the thickness of walls or up their chimneys,' noted the architect Fontaine. The director of the Louvre was badgering Joseph to have its treasures safeguarded.
Napoleon bombarded Joseph with instructions on how to manage public opinion, sending him material, such as accounts of atrocities committed by foreign troops, to be inserted in _Le Moniteur_. He was furious when he heard that Marie-Louise, remembering what she had done in Vienna when it was being bombarded by him, proposed holding public prayers for the success of the campaign. He was alert to anything that might weigh in the propaganda war, and, realising that detachments of cossacks were roaming the countryside, instructed Joseph to have the silver, the portraits of the imperial family, and 'anything that could be made to look like a trophy' at Fontainebleau packed up and removed to a place of safety.
Napoleon agreed to Schwarzenberg's request for an armistice, but when negotiations opened on 24 February he tried to use them to affect the subsequent peace talks by suggesting a demarcation line close to France's 'natural frontiers', and after days of fruitless talks, on 5 March the negotiations broke down. By then he was in a much weaker position.
On 20 February he received news of Murat's defection. Ten days later he heard that on 27 February Soult had been beaten at Orthez by Wellington, who was marching on Bordeaux. Assuming that Murat might be swayed by news of his recent successes, Napoleon instructed Joseph to send someone to talk to him. He also suggested he make a renewed effort to bring Bernadotte over to the French side. He wanted Eugène to forget about defending Italy, which could be easily reconquered at a later stage; instead, he should march into France, collect the 5,000 men at Chambéry, another 8,000 at Grenoble and Augereau's force at Lyon, which would give him at least 50,000 men with which he could sweep into the enemy rear and up into Lorraine.
The negotiations had resumed at Châtillon, but they were ineffectual, since Caulaincourt did not have a free hand and Napoleon was in no mood to give way. The situation had revived his deepest insecurities, and he could not face Paris otherwise than as a victor. Molé records him saying that he was in bond to his glory: 'If I sacrifice that, I am nothing, it is from her that I hold all my rights.'
The desperate situation also brought out his finest qualities as a tactician and a leader of men, and galvanised his faculties. General Ricard was astonished when he called at headquarters to hear Napoleon tell Berthier, 'Sit down and write!' and proceed to dictate orders enumerating the strength and giving the position of nineteen different units, and the time it would take each of them to concentrate at a given point, without referring to a single note.
Spotting a chance to defeat Blücher, who was moving away from Schwarzenberg, he pursued him and attacked him at Craonne on 7 March, and after one of the bloodiest battles of the campaign drove him back. He was able to exploit intimate knowledge of the terrain by seeking out his old friend from Auxonne, Belly de Bussy, who lived nearby. Two days later he came up against Blücher's main force at Laon. He had underestimated the Prussian's strength, which was twice his own, and was forced to retreat after an inconclusive engagement. He refused to accept the hopelessness of his situation, and accused those who advised suing for peace of cowardice. 'Today, I am the master, like at Austerlitz,' he wrote to Joseph on 11 March. That was not how it looked in Paris, where those who had supported him in the interests of rebuilding France were growing disenchanted as they watched him bring her to her knees.
'The situation is grave, and becomes worse with the passing of every day,' Cambacérès wrote the same day. 'We are in dire poverty and surrounded by people who are either spent or angry. Elsewhere it is even worse; official reports and private correspondence alike make it clear that we can no longer defend ourselves, that despondency has become general, that signs of discontent are evident in various quarters and that we are about to witness the most sinister events if the strong arm of Your Majesty does not come promptly to our aid.' Like some frantic gambler, Napoleon clung to the hope that another throw of the dice could still reverse the situation; now, more than ever, he needed to establish his right to rule.
Two days earlier, on 9 March, the allies had signed the Treaty of Chaumont, which bound Britain, Russia, Prussia and Austria, henceforth identifying themselves as 'the Great Powers', to fight Napoleon to the end and oversee the reorganisation of Europe after his removal. They were divided as to who should succeed him, Britain and Austria favouring the Bourbons, Alexander supporting Bernadotte, who now made a dash for Paris, adopting an equivocal pose that left it open for him, if he failed to gain the throne, to become an enabling lieutenant either for a republic or for a Bourbon restoration – either a Cromwell or a Monck.
On 13 March Napoleon routed an isolated Russian corps at Reims. He then went after Schwarzenberg and caught up with him at Arcis-sur-Aube, but when the Austrian turned about and brought his 90,000 men to bear against Napoleon's 20,000 the following day, Napoleon had to withdraw. He saved the day when retreating French cavalry had threatened to cause panic in the ranks; when a shell landed in front of them and they drew back, he rode forward and stopped his horse over it, and although the horse was killed he escaped unscathed. Some believed he may have been seeking death; there were other moments in this campaign when he led from the front, sword in hand, apparently courting a glorious end.
On the retreat, 'discouragement overwhelmed our spirits', recalled General Boulart. On 25 March Marmont and Mortier were mauled at La Fère Champenoise; Augereau had surrendered Lyon. The troops were still capable of flashes of enthusiasm, but the mood in the higher ranks was defeatist, and generals talked openly of the hopelessness of further action. According to one police source there was even a plot by a group of generals to do away with Napoleon.
Cambacérès' advice that he return to Paris was based on sound calculation: the inhabitants of the poorer _quartiers_ were overwhelmingly loyal and patriotic, and the allies would not have dared attempt to storm the city, with its huge population and its revolutionary legacy (and no Bourbon would be mad enough to agree to ascend a throne over the bodies of the capital's defenders). More important, as it turned out, his presence would have prevented his enemies from making a deal with the allies behind his back. But Napoleon did not heed it.
Instead, he decided to slip past the allied armies, penetrate into their rear, disorient them and oblige them to halt their advance, collect troops from the fortresses along France's eastern border and strike at them from the rear. It was a bold plan which would have worked back in 1797, but the allies did not panic, and when a messenger carrying a note to Marie-Louise which revealed his plan was caught, along with others carrying various orders, they immediately moved on Paris. Realising his mistake, Napoleon hastened back, racing ahead on horses and vehicles borrowed along the way, leaving his troops to follow. He could hear the sound of guns in the distance as he hurried on, but he was too late.
Paris had been without news of him since 25 March, and as the enemy drew near Joseph grew nervous. Marmont's and Mortier's corps were on their way, but all the city's military governor General Moncey could muster in its defence was a mixed bag of troops, veterans, national guards, armed firemen and gendarmes totalling no more than about 25,000. On 28 March Joseph held a meeting of the Regency Council to decide whether the empress and the King of Rome should leave the capital for a place of safety. Most of those present felt they should remain, fearing the instability that might follow their departure. Joseph then read out letters he had received from Napoleon in February instructing him to make sure that his wife and child did not fall into enemy hands. ' _Do not leave my son_ , and remember that I would prefer to see him drowned in the Seine than in the hands of the enemies of France; the fate of Astyanax as a prisoner of the Greeks has always seemed to me the most unhappy one in history,' he had written on 16 March, adding that every time he watched Racine's tragedy _Phèdre_ he wept over the fate of the grandson of the King of Troy. In the light of this, most of those present gave way and agreed that the empress should leave. She protested, but was persuaded, and on the following day she and her son left for Rambouillet, accompanied by Cambacérès and other members of the Regency Council, as well as a number of other dignitaries and ministers, and most of her _maison_.
Joseph, who remained in Paris, issued a call to arms and went to the heights of Montmartre to oversee the defence of the city, which began with the first allied attacks in the early morning of 30 March. It soon became evident that the situation was desperate, and he conferred with Marmont and others on what to do. The troops were determined to defend the city to the last man, and were joined by volunteers from every class of the population, and a stiff resistance was put up at various points. At the same time, ladies in carriages drove out to watch as though going to a day at the races. Late that afternoon, judging the situation to be hopeless, against the advice of Lavalette, who expected Napoleon to arrive at any moment, Joseph sent Marmont to allied headquarters to negotiate a capitulation. He then left to join Marie-Louise and the rest of the Regency Council. Not long afterwards, news arrived from Napoleon announcing that he was on his way, so Marmont asked for a twenty-four-hour ceasefire, but Alexander, who was at headquarters, refused and threatened to sack the city unless it capitulated immediately. Terms were agreed, and Marmont's units began withdrawing in the direction of Fontainebleau while his aides attended to the formalities.
At ten o'clock that evening at La Cour de France, a couple of hours' drive from Paris, Napoleon met General Belliard, leading Marmont's cavalry, who informed him that Paris had capitulated. He was stunned. His immediate reaction was to go on, but after a short distance he turned back. He walked up and down along the road, giving way to conflicting emotions, raging against the 'coward' and 'cunt' Joseph, against his marshals and against fate, alternating between exaltation and despair, between the determination to march on Paris and to negotiate peace. He then went back to the post house, where he sat down with his head in his hands and remained motionless for some time.
Around three o'clock in the morning he roused himself, wrote to Marie-Louise and despatched Caulaincourt to Paris to see the tsar. He then drove to nearby Fontainebleau, where over the next few days he was joined by the remnants of his army. Along with the units that had come out of Paris, they amounted to no more than 40,000 operational troops, but wishful thinking inflated their number in his mind (he kept writing down Marmont's corps, which now amounted to no more than 5,200 effectives, as being 12,400 strong). On 1 April he held a council of war to consider the options. Most of those present were for withdrawing behind the Loire, linking up with the remains of Soult's Army of Spain and Augereau's corps, and joining the empress and the King of Rome. Napoleon again wanted to march on Paris, convinced that his appearance would galvanise the population, and ordered Marmont, whose corps was camped in forward positions at Essonnes, to prepare for action. The following morning, as he was reviewing troops in the great courtyard of the palace, Caulaincourt returned from Paris with a gloomy countenance. Napoleon dismissed the parading troops and went inside to hear his news.
Manipulated deftly by Talleyrand, who had avoided leaving the capital with the rest of the Regency Council, Alexander had accepted that the Bourbons should be reinstated. Talleyrand was forming a provisional government, and, fearing any resurgence of Napoleon's influence, was exploring the possibility of having him assassinated. The tsar had succumbed to his influence and was determined not to negotiate with Napoleon, but did give assurances that he would be provided with a refuge in which he could continue as a sovereign, mentioning Corfu, Sardinia, Corsica and Elba as possibilities. All that afternoon and late into the night Napoleon listened impassively as Caulaincourt went over every detail of his interviews with Alexander and everything he had seen and heard in Paris, where most people were busy looking to their future under the new regime, without a thought for him. 'I do not care about the throne,' Napoleon said. 'Born a soldier, I can, without feeling sorry for myself, become a citizen again. My happiness is not in grandeur. I wanted to see France great and powerful, and above all happy. I prefer to leave the throne than to sign a shameful peace. I am glad that they did not accept your conditions, as I would have been obliged to subscribe to them, and France and history would have reproached me for such an act of weakness. The Bourbons alone can accommodate themselves to a peace dictated by the cossacks.' Caulaincourt told him his only option was to abdicate, warning him that he was about to be toppled.
Napoleon was outraged, and the next day, as the Old Guard paraded before him, he told them that traitors had handed over Paris to the enemy and they must go to its rescue. The men shouted 'To Paris!' and appeared keen to fight, so he began making plans. That evening news arrived that Talleyrand had assembled a rump of the Senate, sixty-four members out of 140, which had voted his deposition on the grounds that he had violated the constitution and subjected the interests of France to his own. It had also approved the formation of a provisional government under Talleyrand, whose first action was to release all Frenchmen from their oath of loyalty to the former emperor.
The following morning, 4 April, after the usual parade he conferred with Marshals Berthier, Ney, Lefèbvre, Moncey, Oudinot and Macdonald, along with Caulaincourt and Maret. He kept bringing up the possibility of marching out and inflicting a stinging defeat on the allies, if only to be in a better position to negotiate. They all frankly told him the troops were no longer up to fighting, and that even if they had been, a victory would yield nothing. They were unanimous that he should abdicate. He told them he would think about it and give them an answer the next day, but afterwards in conversation with Caulaincourt he again suggested carrying out military operations alongside peace talks. In the end he was persuaded to sign a proposal to present his abdication to the Senate once the Powers had recognised the succession of his three-year-old son as Napoleon II, with Marie-Louise as regent. The proposal was to be carried to Alexander by Caulaincourt as foreign minister, assisted by Marshals Ney and Macdonald to make it clear to Alexander that the army was behind the Bonaparte dynasty and opposed to the Bourbons. The three of them set off, accompanied by a numerous escort of senior officers.
Along their way, at Essonnes they called on Marmont, only to discover that he had been engaged in negotiations of his own. Having been fed misinformation by Talleyrand and others, he had been in touch with the Austrian commander, Schwarzenberg, to arrange the defection of his corps from Napoleon's side to that of the allies. The operation was to be carried out that night. He pretended that it had merely been discussed, and gave instructions for nothing to be done, while volunteering that he join Caulaincourt and his two comrades on their mission to Paris, where they arrived late that night.
Despite efforts on the part of Talleyrand to prevent it, they were accorded an audience with Alexander at three o'clock on the morning of 5 April. He listened for half an hour to their arguments and showed some sympathy, as he despised the Bourbons and felt no enthusiasm to reinstate them. He told them to come back after noon the next day, which would give him time to consider the matter, and they left in positive mood, enhanced by the worried looks of Talleyrand and his colleagues whom they encountered on the way out (Alexander had put up at Talleyrand's residence). They went off to sleep, and agreed to meet for breakfast at eleven at Ney's house.
As the four of them began their breakfast they were interrupted by the arrival of a breathless Colonel Fabvier, who announced that during the night Marmont's corps had gone over to the enemy. Marmont went pale, jumped up and, seizing his sword, blurted out that he must go and 'repair' things. He then rushed out, leaving his colleagues gaping with astonishment. By the time they called on Alexander the whole of Paris knew of Marmont's defection, and their argument that the army was solidly behind Napoleon no longer held. The tsar told them that Napoleon must abdicate unconditionally. In return he would be given the Mediterranean island of Elba to rule in full sovereignty, and generous provision would be made for him and his family.
As Alexander was speaking, Napoleon was making alternative plans. He had attended his usual parade that morning, and the sight of his troops had filled him with military ardour once more. He began dictating orders for a withdrawal behind the Loire, where he would join the empress and the King of Rome, who had taken up residence in the Renaissance château at Blois with her _maison_ and enough silver to fill a palace, as well as the entire imperial treasure from the Tuileries. Napoleon's brothers were also lodged in the castle, while Cambacérès, Molé, Clarke, Montalivet, Regnaud and other members of the Regency Council and various dignitaries accommodated themselves as best they could in the small town.
Cambacérès valiantly kept up his standards, sticking to his official dress and having himself carried around the old town, whose streets were too narrow for carriages, in a sedan chair. The others tried as best they could not to show that they realised they had been outmanoeuvred and sidelined by their former colleague Talleyrand. Savary had already entered into negotiations with him regarding his own future. Marie-Louise was hoping to join Napoleon, and wrote to him asking for guidance and support, and to her father for help. The Buonaparte men reverted to their native instincts as they contemplated a future in which they would not be able to rely on their brother for a life of grandeur and luxury. Joseph attempted to play the head of the family and make all the decisions, seconded by Jérôme. Napoleon had for some time suspected him of wishing to seduce Marie-Louise, and he now seized the opportunity to try and rape her. For his part, Louis added a sudden surge of religious zeal to his neurotic behaviour.
Napoleon was woken at two o'clock on the morning of 6 April by Caulaincourt, Ney and Macdonald, who had just returned from their mission to Alexander. After listening to their report he announced that he would never abdicate unconditionally, and dismissed them. But nobody slept much; at six o'clock in the morning Caulaincourt was back with him, and the two of them talked at length. Napoleon had been taken aback by Marmont's defection, and deeply hurt by such an act of treachery by one of his oldest friends. More than that, it had undermined his position by calling into question his hold on the army.
On that morning of 6 April, Napoleon wrote out the four and a half lines of his abdication in his own hand, making a large ink-stain in the process. He then dictated the formal instructions for Caulaincourt and the two marshals, empowering them to negotiate the details of the settlement. What he did not know as they took their leave that evening was that, persuaded by his ardently royalist wife, Ney had already written to Talleyrand pledging his submission to the new government. As Caulaincourt noted, 'everyone was turning their eyes to the rising sun and seeking to approach it; the sun of Fontainebleau no longer warmed...'
## 42
# Rejection
Having signed his abdication, Napoleon lapsed into a state of listlessness punctuated by occasional bursts of anger, and a kind of bewilderment; for the first time in many years he had lost control not only of events, but also of people whom he had come to regard as elements of a well-oiled machine. For years he had triumphed by daring to dare, refusing to give up and eventually finding a way to surmount or circumvent obstacles, and by making failures disappear by writing a version of events in which they did not figure. He now faced a reality which was entirely impervious to his will.
'The well-being of France appeared to be in the destiny of the Emperor,' he wrote in his declaration to the army following the defection of Marmont. That was true for a long time. What he had lost sight of was that his destiny had been to save France from chaos and rebuild the state. Ironically, what was happening now was a testimony to the success of his endeavours; it was precisely because the state he had built was so well grounded in the institutions he had created that a change of regime was taking place without the political chaos, not to mention the bloodshed, that would have accompanied it fifteen years earlier. It was his own work that was standing up to him.
For years he had exerted control over people around him through a simple formula of fear and favour, and in the rare cases in which these did not yield the desired results he would simply banish the person from his sight, thus avoiding the unwelcome reality that there could be limits to his power over others. Those he had brushed aside had, like Alexander, Talleyrand and the members of the Senate whose views he had ignored, now been able to stand up to him, again partly as a result of the administrative structures he had put in place and the social stability these had encouraged; he had created a new hierarchy of notables whose first duty was to the state. Even the army, which worshipped him, felt its first duty was to France, and as soon as it became clear that it was not just foreign allies he was up against, pronounced itself against civil war in his cause.
The narrative he had spun in his propaganda from the beginning of his first Italian campaign had given him faith in himself as well as projecting an image which spoke to the people of France and enabled him to carry them with him on his political enterprise. But with time it had deformed his sense of reality, leading him to believe that he really did have the power to make things happen simply because he willed it. This tendency to wishful thinking, combined with his unwillingness to formulate a long-term strategy, had led to disastrous results in Spain and Russia. For a long time, his ability to manipulate facts and people had allowed him to avoid facing the consequences. He continued to write inconvenient truths out of the narrative, and even now, when they had so rudely invaded it, he instinctively fought against them.
Every morning one of the regiments of the Guard paraded before him, and their acclamations revived his fighting instinct; while even his most devoted generals had come to accept the inevitable, he kept revisiting various military options. On 7 April, the day after he sent off his act of abdication, the commander of the Old Guard, Marshal Lefèbvre, wrote his submission to the new government and left to take his seat in the Senate. He was followed by Oudinot, leaving only Berthier and Moncey at Fontainebleau. Yet on 10 April, having received a report based on gossip picked up from an Austrian officer to the effect that Francis was prepared to support the accession of his son, Napoleon sent to Caulaincourt revoking his credentials to negotiate the abdication, and began checking his troop numbers.
Caulaincourt ignored Napoleon's recall. Supported by Ney and Macdonald, he was fighting to secure the best possible terms for him. He was now having to deal not only with Alexander, but also Metternich and Castlereagh, both of whom had been appalled on reaching Paris at the promises made by the tsar, and, in the background, Talleyrand and Fouché, who had also turned up, both of them determined on the elimination of their former master. Talleyrand even engineered an intrigue aimed at provoking him to make a military move which could then be used by the allies as a justification for withdrawing from the engagements made by Alexander.
Caulaincourt wrote explaining the situation, but on receiving the letter Napoleon fumed about betrayal, and at five in the morning wrote back ordering him not to sign anything. It was too late; agreement had been reached that night, and on 11 April the Treaty of Fontainebleau was signed by Castlereagh, Metternich and Nesselrode for the allies, and by Caulaincourt, Ney and Macdonald for Napoleon. The three of them arrived at Fontainebleau the following morning with the document for him to ratify. He listened gloomily to their report and the terms of the treaty, which were that he was to be given the island of Elba to rule in all sovereignty, be provided with an annual subsidy by the French government, allowed to take a small contingent of his Guard with him, and that his family would be provided for.
He still attended the daily parades, but he had been spending his days in his own rooms, occasionally walking in the garden, sometimes taking out his frustration by swishing with his stick at the flowers. He was sickened by what he saw as the desertions of members of his staff and his _maison_ , who went off on invented errands, never to return, or simply vanished. Constant and Roustam had gone, and of those who still hovered many could barely disguise their impatience for the end to come. He complained bitterly of the ingratitude of his marshals, saying he had underestimated the baseness of men in general. Yet a handful remained faithful, most notably Maret and the marshal of the palace General Bertrand, and since the first rumours of plots against the emperor's life some of his aides slept on mattresses laid out in passages leading to his rooms to protect him. At the same time, his pistols and powder had been discreetly removed. That day he wrote to Josephine expressing his despair, and those around him could sense it.
Late that night he asked his valet Hubert to revive the fire in his bedroom and to bring writing implements and paper. Having done so, Hubert kept the door between Napoleon's bedroom and that in which he slept ajar. He heard him begin a letter several times, scrunching up the paper and throwing it into the fireplace. 'Farewell, my kind Louise,' ran the final version. 'You are what I love the most in the world. My misfortunes affect me only by the harm they do to you. You will always love the most loving of husbands. Give a kiss to my son. Farewell, dear Louise. Your devoted.' Hubert then heard him go over to the commode, on which there was always a carafe of water and a bowl of sugar, and was surprised to hear the sound of water being poured into a glass and something being mixed in with a spoon, as he had noticed that the valet in charge had failed to put any sugar in the bowl. After a moment's silence Napoleon came to the door of his room and asked Hubert to call Caulaincourt, Maret, Bertrand and Fain.
Caulaincourt was the first to arrive. He found Napoleon looking sick and haggard, having evidently taken the poison he had been wearing in a sachet around his neck since the retreat from Moscow. He began a self-justificatory ramble and asked Caulaincourt to do various things on his behalf, but Caulaincourt called for Dr Yvan. By then Napoleon was doubled up with stomach pains and complaining how difficult it was to die. When Yvan arrived he asked him to prepare a stronger poison, but the doctor instead administered a potion which made him vomit up the original dose. By morning he was out of danger.
'Since death doesn't want to take me either in my bed or on the battlefield, I shall live,' he said to Caulaincourt. 'It will take some courage to bear life after such events. I shall write the story of the brave!' He then told him to prepare everything for the signing of the treaty, which he did in the presence of Caulaincourt and Maret. At nine o'clock Macdonald, who was to take it to Paris, came into the room. He found Napoleon 'sitting in front of the fire, wearing only a simple white cotton dressing gown, his naked legs in slippers, with nothing around his neck, his head in his hands and his elbows on his knees'. He did not stir at Macdonald's entrance, and seemed lost in his thoughts. Caulaincourt roused him and he stood up, went over to Macdonald, took his hand and apologised for not having noticed him enter. 'As soon as he had lifted his face, I was struck by the change in it; his complexion was yellow and olive-coloured,' continues Macdonald. Napoleon told him he had had a bad night and sat down again, once more drifting off into a reverie, from which he had to be roused again. He then presented the marshal with the scimitar of Murad Bey, captured in Egypt, and embraced him, apologising for not having recognised before what a fine, loyal man he was.
Macdonald set off for Paris bearing Napoleon's ratification, while Napoleon set about dictating letters to some of those who had served him. He had transferred command of the army to the new minister of war, General Dupont, the 'coward of Bailén', and there were only 1,500 grenadiers of the Old Guard left in attendance. Berthier had gone to Paris to finalise the arrangements, and on his return he took up residence in his private residence in the park. Although he and Napoleon had worked closely for more than fifteen years they had never been friends, and following the Wagram campaign the marshal had begun to feel old and tired. He had disapproved of the war with Russia and continually urged Napoleon to make peace, which had soured relations between them.
The once-great _maison_ had dwindled to no more than a dozen or so, and the vast Renaissance palace resounded only to the step of sentries. When Maria Walewska turned up on 14 April to show her sympathy, she found the palace deserted and walked through several rooms before encountering Caulaincourt, who went to inform Napoleon of her presence. He seemed not to hear, and remained lost in his thoughts. She waited for several hours before going back to Paris. He wrote to her the following day apologising for not having been able to receive her, and thanked her for her feelings, saying he would love to see her when he reached Elba. The probable reason he had not received her was that he was hoping to be reunited with his wife and son, and if it were known that he was seeing his mistress it might affect Marie-Louise's and her father's views on the subject.
On 9 April he had written to Marie-Louise asking her to leave Blois and go to Orléans, whence he was hoping to bring her and his son to Fontainebleau. The reason he had not sent for her earlier was that while he believed there was a chance of his son succeeding him he felt he must keep his distance; the principal argument against allowing the King of Rome to succeed was that it would be tantamount to leaving Napoleon in power, so it was imperative he underline his detachment.
Marie-Louise and her entourage at Blois were taken aback by news of Napoleon's abdication, and her first instinct had been to join him, partly in order to get away from his brothers. Seeing in her person a form of insurance for themselves, Joseph and Jérôme planned to take her and seek refuge with Soult's Army of Spain, encamped nearby. Understanding nothing of the politics being played out, she felt disoriented and defenceless. She had seen less of Napoleon from the time he had set off for Russia two years earlier, and had been subjected to a sustained campaign by his enemies in her entourage, who fed her stories of his supposed infidelities and tried to find her a lover. Her chief lady-in-waiting, Lannes' widow the duchesse de Montebello, actually intercepted letters to her from Napoleon.
The court at Blois melted away, the chamberlains, ladies-in-waiting, maids, valets and the 1,200-strong contingent of Guards going off to Paris or elsewhere, many of them heaving sighs of relief that it was all over. Commissioners arrived from the provisional government in Paris to claim the imperial treasure which had followed them to Blois, consisting of over twenty million francs in gold, a hoard of jewellery and plate. Marie-Louise's desire to join her husband was mitigated by the prospect of accompanying him into exile, as she feared his family would congregate around him and make her life unbearable. She told Caulaincourt that she wanted to die with Napoleon, but not to live with him surrounded by them.
The matter was resolved when on 9 April a Russian officer sent by Francis arrived at Blois and took her off to Orléans, where she was robbed first by roving cossacks and then by a government official who tried to tear from her throat the diamond necklace she was wearing. Dr Corvisart, who examined her, wrote a report that she was suffering from breathing difficulties, rashes on her face and fever, and prescribed the waters of Aix. On 12 April she was taken to Rambouillet, where on 14 April she met Metternich and a couple of days later her father. 'It is impossible for me to be happy without you,' she wrote to Napoleon, but she appeared to be little concerned at his fate, according to Anatole de Montesquiou, whom he had sent to her. Whatever her feelings, she was easily persuaded to follow her father's wishes (which, unbeknown to her, were that she and her son should never see Napoleon again).
By then, arrangements were being made for his departure. He was to be accompanied by marshal of the palace Bertrand, General Drouot, his physician Dr Foureau de Beauregard, his treasurer Peyrusse, his valets Marchand, who had replaced Constant, and the Swiss Noverraz, and the Mameluke 'Ali', alias Saint-Denis. He was allowed to take a small contingent of his Guard to supplement the Corsican battalion he would find on Elba. After fierce competition between volunteers, around 600 grenadiers of the Old Guard had been selected, commanded by General Cambronne, and eighty Polish chevau-légers lancers under Colonel Jerzmanowski.
On 16 April Napoleon wrote to Josephine reassuring her that he was reconciled to his fate. 'I will in my retirement substitute the pen for the sword. The story of my reign will be interesting; I have only been seen in profile, and I shall reveal myself entirely. How many things I have to tell. How many people of whom the public has a false opinion!... I have showered with favours thousands of wretches! What have they done for me at a moment like this? They have betrayed me, yes, all of them...' He excepted Eugène, whom he believed to have remained loyal, and assured her that he would love her always and never forget her. His trust was misplaced. 'It is all over,' Josephine had written to Eugène on 8 April. 'He is abdicating. As far as you are concerned, you are no longer bound by any oath of loyalty. Anything you might do on his behalf would be pointless. Look to your family.' She and Hortense received Alexander to dinner at Malmaison, and Hortense even met Bernadotte.
That evening, the four allied commissioners who were to escort him to Elba arrived at Fontainebleau, and he received them the following morning. Colonel Sir Neil Campbell represented Britain, Count Shuvalov Russia, General Franz Köller Austria and Count von Truchsess-Waldburg Prussia. Campbell, who had an informal meeting with him that evening, found him unshaven and dishevelled, and 'in the most perturbed and distressed state of mind'. Tears poured down his face when he spoke of being separated from his wife and child, and he paced up and down the room 'like a caged beast'.
The next day, 20 April, he rose early and had a final conference with Maret, who was to stay behind and who would be his main correspondent in France. He then wrote to Caulaincourt, whom he had sent on a mission to Paris the previous day, thanking him for his loyal service. He also wrote a letter to Marie-Louise, which he handed to Bausset, who was to accompany her to Vienna, expressing his hope that once she had recovered and he was installed on Elba she would join him there.
He then received the commissioners. He was cool with the Russian, expressing anger at Alexander's fawning over Josephine at Malmaison, saying it was an insult to him, and appearing jealous of the tsar's popularity with the Parisians. He also protested at having to go to Elba without his wife and child, and stated that he would insist on being taken to captivity in England instead. He ignored the Prussian but was consistently polite with Köller, meaning to maintain the best possible relations with his father-in-law, and cordial with Campbell, as he had never quite shed his admiration for the British. He had demanded to be taken to Elba on a British ship, as he did not wish to place himself in the hands of the provisional government, with some reason.
Just before midday he came down into the grand courtyard of Fontainebleau, in which the first regiment of grenadiers of the Old Guard was drawn up. Beyond, a crowd was gathered at the railings to catch sight of him for the last time. He made a short speech, reminding his men of the glory they had shared and asking them never to forget him. Saying he could not embrace them all, he embraced their colours and kissed the eagle that topped the shaft. Everyone, including the allied commissioners, was in tears. 'Farewell, my children,' he concluded. Captain Coignet 'shed tears of blood', while Colonel Paulin admitted that he 'cried like a child who has lost his mother'.
Napoleon climbed into his carriage, followed by Bertrand. He was in tears himself. The convoy of fourteen carriages drawn by sixty horses set off for the south coast, escorted by mounted chasseurs, cuirassiers and grenadiers of the Guard. Another convoy, consisting of baggage wagons and simple carriages, bearing furniture, furnishings, china, table silver and 695 books, under the supervision of Peyrusse and a skeleton staff, had been despatched already. The 700 or so troops who had volunteered to accompany their emperor into exile took a different route.
Napoleon was cheered wherever they stopped to change horses, but after Valence, where they were received by a less than enthusiastic guard of honour, they entered traditionally royalist country. The French cavalry escort was to have been replaced by Austrians and Russians, but Napoleon had refused to be escorted by his enemies like a prisoner. On 24 April outside Valence he met Augereau, whose corps was stationed along the road. He went up to his old comrade-in-arms, removed his hat and embraced him, but the other only tipped his forage cap and did not return the embrace. They exchanged a few words, but Augereau showed no wish to prolong the encounter.
At Orange they were met with shouts of ' _Vive le Roi!_ ' and stones were thrown at his carriage. At Avignon there was no more than a sullen crowd hissing, but at Orgon he and his party were treated to the sight of a dummy representing Napoleon in a uniform covered in red paint swinging from a gibbet with a placard saying that was how the tyrant would end up. The carriage was besieged by a crowd of people 'drunk with hatred and some with wine', in the words of Shuvalov, who, along with Köller and the powerfully-built Noverraz, fought them off with fists while Napoleon cowered in the carriage. The event had been orchestrated by local royalists, probably with the support of the authorities, and Shuvalov was convinced that it was only a matter of luck that Napoleon himself had not replaced the dummy on the gibbet.
Napoleon lost his nerve. Once they had left the town he stopped to relieve himself, then put on a blue cloak and a round hat with a white Bourbon cockade, mounted a horse and rode on ahead of the conspicuous convoy. When the commissioners caught up with him at an inn at La Callade, they found him slumped at a table with tears pouring down his face; he had not been recognised, and the innkeeper had told him that Napoleon was travelling down the road and would be lynched, as he deserved to be, being responsible for the deaths of her son and her nephew. Thereafter he wore Köller's uniform, and an escort of Austrian hussars was provided.
The party stopped for the night at a château outside Le Luc, where Pauline was staying. The two siblings spent the evening together, and she promised to visit him on Elba. The journey continued without incident to Fréjus. On the evening of 28 April he boarded the British frigate HMS _Undaunted_ , Captain Ussher, greeted by a twenty-one-gun salute. The Prussian and Russian commissioners took their leave, and only Campbell and Köller went aboard with him.
The crossing took five days, and it was not until 3 May that the _Undaunted_ arrived off Portoferraio, Elba's principal port and town. The 245 square kilometres of rocky island, fifteen kilometres off the Tuscan coast, was not the most hospitable place, and its 12,000 inhabitants, who had been Napoleon's subjects since 1802, were not well disposed – there had been minor revolts against French rule recently and some of the garrison had mutinied, so both Napoleon and the British officers accompanying him were nervous. The islanders had no inkling of recent events in France, but when they discovered the war was over and they were to host the great Napoleon, they assumed a golden era had dawned for them. They greeted him with all the pomp that an island port town of 3,000 inhabitants could muster.
The day after coming ashore, Napoleon was up at four in the morning inspecting the city's defences, a presage of what was to follow; over the next few months he would apply himself to what he referred to as his 'little cabbage-patch', as he had to rebuilding France after 1799. He identified a suitable building, the Villa Mulini, for his 'palace', and had it refurbished and extended with another floor (to accommodate Marie-Louise and the King of Rome). He did the same to a smaller summer retreat in the hills, at San Martino. He designed a flag for his new kingdom, a white square with a left-to-right diagonal red band with three of his armorial bees on it. He set up a court under the marshal of the palace Bertrand, nominating chamberlains from among local notables, and a military establishment under General Drouot. Bertrand, a military engineer by profession, had been campaigning with him since the Egyptian expedition; he had succeeded Duroc in his charge and was utterly devoted. The same was true of Drouot, a talented gunner who had commanded the hundred-piece battery that had tipped the scales at Wagram.
Within a week of landing, Napoleon had scouted the whole island in detail. He set about making roads, which were almost entirely lacking, and from there went on to building aqueducts, organising drainage, sanitation, wheat cultivation, dictating letters on the subject of poultry farming, tuna fisheries and horticulture with the same concentration with which he had treated matters of state at the Tuileries. His principal collaborator was André Pons de l'Hérault, the director of the island's only major resource, its iron mines. Pons was a former Jacobin and artillery officer whom Napoleon had met at Toulon in 1793; he was then twenty, and had treated Buonaparte to his first taste of the local speciality, bouillabaisse. Originally a supporter, he had disapproved of Napoleon's assumption of the imperial title and become a declared enemy, but within a few weeks of working with him was won over and became one of his most devoted supporters. For Napoleon it was essential to get the mines working as efficiently as possible, since they were practically the only source of revenue of the barren island.
Money was a major preoccupation, and on reaching the island Napoleon had sat down with his treasurer Pierre Guillaume Peyrusse to take stock. Elba's taxes brought in 100,000 francs a year, and the iron mines yielded no more than 300,000. That would barely pay for the administration of the island. Napoleon had brought with him 489,000 francs in his _petite cassette_. Peyrusse had managed to save 2,580,000 from the imperial treasury which had followed the Regency Council to Blois, and to bring it to Fontainebleau. Marie-Louise had withdrawn another 911,000 at Orléans and despatched it to her husband. But according to their calculations, the total of just under four million francs would not last beyond 1816, given that along with his own household Napoleon had to pay for the upkeep of military personnel totalling 1,592. Under the terms of the Treaty of Fontainebleau he was to receive an annual subsidy of two and a half million francs from the French government, but nobody was under any illusion that Louis XVIII, who had assumed the throne of France, would honour them.
Napoleon would say to anyone he met that he was 'dead to the world', and he appeared content in the role of Lilliputian monarch. Although he held receptions and balls, receiving the wives of the local functionaries as though they had been those of French notables and the numerous tourists who called at the island (over sixty Britons alone dropped in as part of their Grand Tour) as though they had been visiting princes, he lived a quiet and, by his own admission, a very 'bourgeois' life. He felt the absence of female company keenly, and was anxious to have his wife and son join him. He kept writing, urging her to come, but she only received some of the letters he sent through trusted secret channels to Méneval, whom she had kept on as her secretary; those sent openly were confiscated. Letters from her only got through sporadically. At the end of June she was still declaring her intention to join him (by now it was clear that his brothers were not going to settle on Elba), but within a month she had succumbed to various pressures that changed her mind. One was that while the Treaty of Fontainebleau had awarded her the duchy of Parma, it was now clear that she would not be getting it, and the only way she could assure her future and that of her son was by staying close to her father at Vienna. Another was that an Austrian officer assigned to act as her equerry with a brief to dissuade her from going to Elba had been so successful as to become her lover (and, in time, husband). She was being urged to make a public declaration against Napoleon, and was gradually being worn down by various people telling her to be reasonable.
At the beginning of June news reached him that Josephine had died at Malmaison. He was so upset that he would not see anyone for two days. But a few days later he received a rare mark of affection and loyalty when Jérôme's wife, who was the daughter of the King of Württemberg, wrote asking him to stand godfather to the child she was carrying. 'Circumstances can have no bearing on our feelings, and we will always take pride in regarding you, Sire, as the head of our family, and I, for myself, will never forget that Your Majesty never ceased to give us proofs of his friendship and that you made my happiness by uniting me with the King,' she wrote. The arrival of Pauline at the beginning of July also cheered him; she only stayed for two days, but would be back for good in October. His mother arrived on 2 August and settled into a house close by the Villa Mulini, and they often dined together and played cards afterwards. She was the only person who dared confront him about his cheating, whereupon he would, according to Peyrusse, shuffle all the cards on the table around, scoop up the money and reply that he had played fair, but later hand it to his valet Marchand, who would give it back to its rightful owners. With the return of Pauline in October the little court grew merrier, although her hypochondria often put everyone to inconvenience. She also contrived to have the furniture from her husband's palace at Turin brought to Elba, adding some splendour to the 'palace' of Mulini.
At the beginning of September, Maria Walewska arrived with their son, accompanied by her younger sister Antonia and her brother Theodore Łączyński. Napoleon made elaborate plans to house them in an abandoned hermitage next to which he had erected a tent in which he occasionally spent the night. The party arrived at dusk on a small vessel which put into a quiet bay far away from Portoferraio, and were discreetly taken up to the hideaway, where Napoleon spent a couple of idyllic days playing with his son and visiting his mistress at night. But a small island is no place for secrets, and word soon got around that Marie-Louise and the King of Rome had arrived. The population grew excited, and Napoleon realised that if news of the visit were to leak out it would both scupper any remaining chances of Marie-Louise coming, and damage his reputation. So after two days the little party were smuggled off the island.
Napoleon could not keep anything secret for long, as he was surrounded by spies. Talleyrand had a network of informers based in Livorno, with an agent in Napoleon's household. The French government had another based on nearby Corsica, and another handled from the south of France. The British had one run by a former consul in the area, and Metternich had a formidable web of spies all over northern Italy which extended to the islands. Napoleon had his informers in Tuscany and on Corsica, and was the recipient of a great deal of information from sympathisers in France. He also gleaned much from visiting Britons.
He knew of a number of plans by French royalists and government agents to remove or assassinate him, and felt dangerously exposed; the seas around were infested by pirates operating from North Africa for whom he would have constituted a rich prize, and this greatly facilitated anyone bent on landing in order to assassinate him. At one point he became so nervous that he slept in a different room every night. His contingent of grenadiers and lancers were a defence, but as it was now almost certain that the French government was not going to pay him his due, he would soon have to let them go, and then he would be defenceless. Colonel Campbell believed Napoleon was resigned to his fate, and warned his superiors in London that the only thing that might make him restive was lack of funds.
Whether Napoleon was temperamentally capable of remaining the sovereign of a tiny island or not is academic, as the allies would not let him. Louis XVIII would not provide him with the means of support, and Francis had no intention of letting him see his daughter and grandchild again. To deprive a man of an income and the company of his wife and child is to deny him the basics of a settled life, and in this case it was also to rob him of his last remaining status symbol. The message was clear: he had been allowed to possess a princess as a conquering Attila, but now he had been defeated he was to be put in his place as the undesirable upstart he was. With a Habsburg princess at his side he had to be treated with a modicum of respect. Without, he could be treated as the allies wished.
From the moment they heard of Alexander's gesture of giving him Elba, the allied ministers determined to remove him to a more remote place. The British had presciently weaselled out of ratifying the Treaty of Fontainebleau with a bizarre formula whereby they 'took notice' of it, even though Castlereagh had signed it along with the other ministers. The prime minister Lord Liverpool had already mooted the possibility of imprisonment on some more distant island, such as St Helena in the South Atlantic. By October 1814, as the ministers and monarchs gathered at Vienna for the peace congress that had been convoked to settle the affairs of Europe, it was no secret that they intended to move him; it had even been mentioned in the press. Napoleon brought up the matter with Campbell, protesting that lack of funds and the intentions of the Great Powers were making his position untenable.
He was not the man to sit tight and wait to be assassinated or incarcerated, and he began considering his options. Short of evading the Royal Navy and making a dash for the United States, where he could settle as a private citizen, there was nowhere he could go. Only France seemed a possibility. He had never entirely accepted what had happened; when they met on his arrival at Portoferraio, he had spoken to Pons de l'Hérault of recent events as though they had nothing to do with him, and he appeared to have persuaded himself that if Marmont had not betrayed him he would still be emperor. In conversation with Campbell, he sometimes gave the impression that he was expecting to be called back to France at any moment.
In royalist parts of the country the restoration of the Bourbons was welcomed; elsewhere it was accepted with varying degrees of relief and hope. But the behaviour of Louis XVIII, and particularly of his brother Artois and the émigrés who returned with them, soon began to offend. The hierarchy that had grown up to manage France over the past decade and a half was humiliated and often penalised, there were demands for property to be returned to its former owners, the Church began a religious crusade to recapture the soul of the country, and an atmosphere of hatred and revenge entered village as well as Paris life. The army was the object of particular vindictiveness, with men and officers being humiliated and retired on half-pay. Its glorious achievements were denigrated, its regiments renumbered, its colours changed. Within six months of recovering the throne, the Bourbons had alienated a considerable proportion of the population and almost the entire army.
Active and retired officers and men began to talk of the good old days, and to conspire to bring them back. News of this reached Napoleon, and a return to France presented itself as the only way to avoid being deported to a grim island prison. It was a gamble, but daring had always worked for him in the past, and his return from Egypt must have haunted his thoughts. He began taking note of the movement of the British ships on station in the area, and of the comings and goings of Campbell, who was acting as an informal gaoler, visiting the island for days at a time and then going off to mainland Italy. By the beginning of February 1815 Napoleon had made up his mind.
He repaired the French brig _Inconstant_ , which he had inherited, and improved the seaworthiness of a number of smaller vessels, on which he surreptitiously loaded stores. He had his grenadiers lay out new gardens near the port, and invented excuses for his other troops to ready themselves. They received their order to embark on 26 February. It was a Sunday, and that morning at the _lever_ he had informed those present of his plans, after which he heard mass as usual in a provincial simulacrum of the Saint-Cloud custom. His mother, who along with Pauline had been informed on the previous day, expressed severe reservations, but Napoleon ignored them. As his men marched down to the harbour, accompanied by the townsfolk, who had no idea what was happening but warmed to a spectacle, he prepared a proclamation to the troops and to the French people. In the evening he went down to the harbour and, after a brief speech to the local authorities who had assembled and who expressed grief at his departure, he went aboard.
## 43
# The Outlaw
At nine o'clock on the evening of 26 February 1815 the _Inconstant_ slipped out of Portoferraio followed by six smaller craft. Temporarily becalmed, the flotilla spotted the sails of a British ship and in the course of its onward journey crossed the paths of three French naval vessels, but the soldiers lay down on deck to keep out of sight, and it reached the coast of France without incident, sailing into the Golfe Juan on 1 March.
A few curious locals came to gawp at the unusual number of ships in the bay, but there was little interest even when Napoleon came ashore late that afternoon and made camp on French soil once more. Twenty men sent off to nearby Antibes were arrested. Napoleon had instructed his soldiers not to use their weapons, and it is doubtful they would have even if he had wished; when questioned later they admitted that they were delighted to be back in France, but had no stomach for fighting fellow Frenchmen. In the event, they had no need to. They set off at midnight, along side roads in order to avoid confrontation, attracting little attention as they went. The soldiers had grown unused to long marches, and they had to carry all their equipment as they had brought only a few horses, so the column soon stretched into an untidy string of small groups struggling along as best they could. They bought horses along the way, but these were passed to the lancers, who had been lugging their saddles as well as their arms.
In two proclamations, from his Guard calling on former comrades to join them and from him to his people, in which he branded Marmont and Augereau as traitors, Napoleon portrayed himself as coming to the rescue of suffering France, whose laments had reached him on Elba, and announced that 'The eagle bearing the national colours will fly from belfry to belfry all the way to the towers of Notre Dame.' There was no eagle and no national colours – until in one small town someone produced a gilded wooden bedpost or curtain-rail finial in the shape of one which was attached to a pole and adorned with strips of blue, white and red cloth.
They met no resistance until they reached Laffrey on 7 March, where they found the road barred by infantry. Napoleon rode forward and addressed the soldiers. He was answered with silence, so he unbuttoned his grey coat and, baring his breast, challenged them to shoot, at which, encouraged by his grenadiers who had stepped forward and started cheering, the royal troops burst into shouts of ' _Vive l'Empereur!_ '
A larger force drawn up outside Grenoble would have presented a greater obstacle had it not been for Colonel La Bédoyère leading his regiment over to Napoleon's side. The royalist commander of Grenoble closed the gates of the city, but they were hacked open by workers, who ushered Napoleon in to a delirious welcome. At Lyon the populace tore down the barricades blocking the bridges and led him into the city in triumph. From then on the eagle did fly on to Paris with astonishing speed. Ney, who had been sent out to capture Napoleon and had solemnly promised Louis XVIII to bring him back in a cage, realised that his troops were wavering and, swayed by the prevailing mood, joined his former master.
By 20 March Napoleon was at Fontainebleau. At Essonnes later that day he was met by Caulaincourt and a multitude of officers and men who had driven out of Paris or from the surrounding area. The previous night Louis XVIII had left the Tuileries and fled for the Belgian frontier. As the news spread, supporters of the emperor came out all over the capital and the tricolour flag was hoisted on the palace and other public buildings. As Napoleon raced on to Paris his former staff and servants took over the Tuileries, so that by the time he arrived at nine o'clock that evening all was ready, and the salons were thronged with members of his erstwhile court. When he alighted, he had difficulty in making his way through the waiting crowd. As he mounted the staircase to repossess the palace, he closed his eyes and a smile lit up his face.
Within an hour of reaching the Tuileries he was working in his study with Cambacérès and Maret, putting together a new government. He had some difficulty in persuading his old ministers to take up their jobs again, as most of them were feeling their age and were tired out by what they had been through. The memory of the uncertainties of 1814 was still fresh, and when they heard of his landing, some, like Pasquier and Molé, despaired for France, foreseeing more of the same. But most let themselves be swayed by the old charm. Daru, reluctant at first, soon melted. 'I felt I was back in my world, where my memories and my affections lay,' he recalled. 'At no other moment had I felt more affection, more devotion for the emperor.' But some, like Macdonald, resisted despite repeated efforts by Napoleon.
Cambacérès agreed to serve as minister of justice, Maret took up again as secretary of state, Caulaincourt (under severe pressure) as foreign minister, Carnot took the ministry of the interior, Davout that of the army, Decrès resumed his old post at the navy, as did Gaudin and Mollien at finance and the treasury respectively. Napoleon appointed Fouché minister of police, with Savary and Réal briefed to keep an eye on him. 'It was an extraordinary sight to see things put back in their place so quickly,' reflected Savary. When he called on the evening of the next day, Lavalette felt as though he had gone back ten years in time; it was eleven o'clock at night, Napoleon had just had a hot bath and put on his usual uniform, and was talking to his ministers.
But the appearances did not hold up for long. When the legislative bodies came to present their addresses of loyalty on 26 March, Miot de Melito, now a member of the Council of State, noticed that 'the faces were sad, anxiety was etched on every feature, and there was general embarrassment'. The enthusiasm caused by the unexpected and almost miraculous return of Napoleon subsided, as, in the words of Lavalette, 'it was not so much that people wanted the emperor; it was just that they no longer wanted the Bourbons'. Napoleon realised this. 'My dear,' he replied when Mollien congratulated him on his remarkable return to power, 'don't bother with compliments; they let me come just as they let the other lot leave.' Few felt much confidence in the future.
Taking in hand the administration of the country presented a formidable challenge. Napoleon's authority did not reach far outside the _mairie_ in many areas, and not even there in the north and west, where royalist sentiment was strong. In the Midi, the king's nephew the duc d'Angoulême gathered 10,000 troops and national guards and marched on Lyon. He was forced to capitulate by Marshal Grouchy on 8 April and allowed to leave the country, but civil war simmered below the surface. In these circumstances, raising men for the army and funds to equip it would not be easy – Louis XVIII had emptied the coffers, leaving only two and a half million francs in the treasury.
Napoleon was no longer the man to galvanise the nation. He was forty-five years old and not well; his physical condition had been aggravated by haemorrhoids and perhaps other ailments. He had grown fat and had slowed down. 'Great tendency to sleep, result of his illness,' noted Lucien, who had turned up in Paris to support his brother. Napoleon himself admitted to being surprised that he had found the energy to leave Elba at all. 'I did not find the emperor I had known in the old days,' noted Miot de Melito after a long interview. 'He was anxious. That confidence which used to sound in his speech, that tone of authority, that loftiness of thought that was manifest in his words and in his gestures, had vanished; he already seemed to feel the hand of adversity which would soon weigh down on him, and he no longer appeared to believe in his destiny.' Most noticed the change, and it did not inspire confidence; all they could see was a small, fat, anxious man with an absent look and hesitant gestures.
His hesitancy was partly a consequence of his not being able to find the right persona to adopt and image to project, as he had so successfully done on his returns from Italy and Egypt, after Tilsit and even following the disaster of 1812. He now had to be all things to all men. He left the Tuileries, which required a large _maison_ and formal etiquette, both of which were expensive and inappropriate; Letizia, Fesch, Joseph, Lucien and Jérôme had all turned up to support the family business, but were given no formal status. He moved into the Élysée Palace, where he was freer to see whom he wished without the complications of a large court. His only regular company was his family, a few of the more faithful ministers, and Bertrand. He saw Hortense frequently, and soon after his return called in Dr Corvisart to enquire about Josephine's illness and last moments. These less formal surroundings made it easier for him to engage the support of people he had previously disdained. He was more affable than in the past, and, according to Hortense, more open, extending a warm welcome to anyone who wished to see him, even to the extent of receiving Sieyès. He expressed his regret at having alienated Germaine de Staël, in the hope that she might rally to him.
In the course of his march on Paris, aside from the army and former soldiers, those greeting him with the greatest enthusiasm were those most offended by Bourbon rule. From Lyon, where he paused, he had decreed the abolition of the two legislative chambers set up by the Bourbons, proscribed all émigrés who had returned with them, announced the confiscation of lands recovered by them, and voiced phrases about stringing up nobles and priests from lamp-posts. This won him support among former Jacobins and republicans. But galvanising the revolutionary masses flew in the face of his wish and need to keep on his side the nobles and former émigrés whom he had involved in his 'fusion', and it also opened up the prospect of a return to the civil war that had ravaged the country before he came to power in 1799. He felt he must enlist the support of all those moderate republicans and constitutional monarchists he had consistently bullied and pushed aside. In order to achieve that, he must bring in a new constitution.
To this end, he invited his former critic Benjamin Constant, who enjoyed a strong following and a Europe-wide reputation as a moderate liberal. Their collaboration was not an easy one; Constant noted that in conversation Napoleon displayed libertarian instincts, yet when it came to the question of power, he stuck to his old views that the only way of getting anything done was through variants of dictatorship. 'I do not hate liberty,' Napoleon told him. 'I brushed it aside when it got in my way, but I understand it, as I was nourished on it.' Constant was frustrated by his contradictory instincts and the continual swings they produced; Napoleon was still marked by the influence of Rousseau and his admiration for Robespierre.
He intended the new constitution to derive from the imperial one, in order to ensure continuity and give it what he considered to be a deeper legitimacy. It therefore took the form of an 'Additional Act' to it, passed on 23 April. This was a compromise, which had the unfortunate effect of provoking a public debate (liberty of the press had been restored) that opened up the old animosities he had sought to reconcile since 1799. The elections, held in May, satisfied no one. Turnout was little over 40 per cent, and the new hierarchy Napoleon had sought to create with his fusion did not triumph. No more than 20 per cent voted in the plebiscite to endorse the Additional Act.
Napoleon attempted to galvanise the nation through a ' _Champ de mai_ ', a version of the Federation of 1790, held on 1 June on the Champ de Mars in front of the École Militaire where he had been a cadet, watched by some 200,000 spectators. It was a ceremony in the mould of the old revolutionary festivals, with a stand for the dignitaries, graded seating for the members of the two chambers and other bodies of state, and an altar of the fatherland. But in attempting to also associate it with ceremonies of allegiance held by Charlemagne and the Capetian kings, he struck a false note. He arrived in a state coach drawn by eight horses, accompanied by his brothers, who, having no constitutional status, appeared as members of a royal family. He had designed fantastic costumes for them; they were decked out in white velvet tunics with lace frills and velvet bonnets surmounted by plumes (Lucien had protested vociferously before agreeing to wear it). Napoleon himself was encased in a similar costume, pink with gold embroidery, so tight he could hardly walk, and weighed down by an ermine-lined purple cloak.
The ceremony opened with a mass, with too many priests, after which Napoleon made a speech in which he hinted that he would recover France's 'natural frontiers', and assured his people that his honour, glory and happiness were synonymous with those of France, enjoining them to make the greatest efforts for the good of the motherland. He then swore to abide by the constitution. A _Te Deum_ was sung, after which he proceeded to distribute eagles to the regiments, and the ceremony ended with a parade, the only part the spectators enjoyed. He had failed to galvanise anyone. 'It was no longer the Bonaparte of Egypt and Italy, the Napoleon of Austerlitz or even of Moscow!' noted one observer. 'His faith in himself had died.' So had that of the crowd: for every ' _Vive l'Empereur!_ ' there were ten ' _Vive la Garde Imperiale!_ '
On his return to Paris, Napoleon had written to all the monarchs of Europe announcing that he was by the will of the people the new ruler of France, that he accepted the frontiers fixed by the Treaty of Paris of 1814, that he renounced any claims he might have previously made, and that all he wanted was to live in peace. He followed this up with personal letters to Alexander and Francis, and to Marie-Louise, asking her to join him. Hortense, who had been befriended by the tsar when he was in Paris in 1814, also wrote to Alexander supporting Napoleon. Caulaincourt wrote to Metternich assuring him of France's peaceful intentions. In an attempt to endear himself to the British, Napoleon abolished the slave trade.
The news of his escape from Elba had sown astonishment and terror among the representatives of the Great Powers gathered at the congress in Vienna. With less than a thousand soldiers, he should have been no match for Louis XVIII's army of 150,000. But within hours of hearing the news they began mustering their forces: 50,000 Austrians in Italy; 200,000 Austrians, Bavarians, Badenese and Württembergers on the upper Rhine; 150,000 Prussians further north; 100,000 Anglo-Dutch in Belgium; and, on the march from Poland, up to 200,000 Russians. The reappearance of Napoleon had re-established a solidarity which had been fraying in the course of the congress.
Talleyrand, now foreign minister of Louis XVIII representing France in Vienna, was quick to realise that if Napoleon were to reach Paris and become ruler of France, there would be no legal basis for the Powers to do anything about it, unless he were to make a hostile move. If the allies were to accept this new status quo, Talleyrand's career would be over. He therefore prepared the text of a declaration which he proposed the plenipotentiaries of the Powers should make, according to which by leaving Elba Napoleon had broken his only legal right to exist, and was therefore an outlaw and fair game for anyone to kill. Metternich and others protested at such a drastic step, but after much heated argument, an amended text was adopted. While it stopped short of sanctioning his murder, it did declare Napoleon to be outside the law, and closed the door to any negotiations.
Fouché was also a worried man. He had hedged his bets while serving Louis XVIII by setting up a conspiracy among the military to bring Napoleon back from Elba. He had hoped Napoleon would make him foreign minister but accepted the ministry of police, which he would exploit to his own ends. Using his contacts in England, he sounded out the chances of the British cabinet agreeing to leave Napoleon in power, at the same time negotiating asylum for himself were he to need it. He also persuaded his old Jacobin friend Pierre Louis Guingené, now living in Geneva and in close contact with Alexander's old tutor the philosopher César de la Harpe, to write to the tsar. Guingené had been purged from the Tribunate by Napoleon, but like many like-minded colleagues, he now saw in Napoleon the only hope for France. 'Oppressed, humiliated, debased by the Bourbons, France has greeted Napoleon as a liberator,' he wrote to Alexander. 'Only he can pull it out of the abyss. What other name could one put in place of his? May those of the allies who are most capable of it reflect on this and attempt to address this question in good faith.'
Fouché had been approached by an agent of a Viennese banking house at the behest of Metternich, who had been growing increasingly alarmed at Russian interference in European affairs and the lack of a reliable ally on the Continent to stand up to it – he had always sought one in France. He did not like war, and was not happy at the prospect of a huge Russian army marching through Central Europe while Austrian forces were engaged in Italy and France. He also knew that Alexander, who had never liked the Bourbons and had grown to despise them, might wish to take the opportunity to replace Napoleon with someone of his own choosing.
The invitation for both sides to meet at an inn in Basel was intercepted, and Napoleon substituted his own agent for Fouché's. What transpired from this and subsequent meetings was that Austria and Russia might be prepared to treat with Napoleon on condition he abdicate in favour of his son. It might not have been what Napoleon wanted, although it was an opportunity to retrieve something from a venture that was beginning to appear doomed. But Napoleon had learned nothing from his experiences; in this tiny ray of hope he saw great promise, reading into Metternich's tentative offer a sign of weakness. If the allies were split and no longer felt sure of themselves, then he would not step down and accept humiliating terms, he would play for higher stakes. He therefore cut short the negotiations and resolved to stand firm.
'I have been too fond of war, I will fight no more,' Napoleon said to Pontécoulant on his return from Elba, but the man who had helped launch him on his military career believed he had not changed, and that 'war was still his dominant passion'. Part of him undoubtedly would have preferred to be left in peace, and he made similar pacific statements to others. He admitted to Benjamin Constant that he had been lured by ambition, but said he now only wanted to lift France from her state of oppression. But war loomed, whether he liked it or not.
France faced invasion by a formidable array of enemies, which suggested two possible courses of action for Napoleon: either assuming dictatorial powers and using them to regiment the country into an efficient military machine, or harking back to 1792 and calling out the nation in arms. That was something he recoiled from. He trusted in his army, which he liked to believe was as good as ever and burning to fight. This was true of subaltern officers and the older men of the lower ranks, but not at the top. The marshals had not opposed him because they could not be bothered to fight for the Bourbons (only Marmont, Victor and Macdonald followed Louis XVIII into exile). That did not mean they could be bothered to fight for him, particularly in what looked like a lost cause. Typical was Masséna, commanding the region of Marseille, who had not lifted a finger to stop Napoleon but was living in a state of semi-retirement and just wanted to be left in peace. Most of them tried to avoid service, on either side. Much the same was true among the generals and senior officers, who were not wholly committed to Napoleon and merely went with the flow. Even where there was enthusiasm and devotion to Napoleon, there was no longer the dash of youth to support it.
He also robbed himself of a major asset in not calling on Murat, who had washed up in the south of France at the end of May. Fearing that the allies at the congress in Vienna were going to depose him, Murat had seized the opportunity offered by Napoleon's escape from Elba to march out and proclaim his intention of uniting Italy, calling on all Italian patriots to join him. Few did, and he was defeated by the Austrians at the beginning of April. He fled to France while Caroline took refuge on a British ship in the bay of Naples, from whose deck she listened to the crowds acclaiming the Bourbons returning from Sicily. Murat had betrayed Napoleon more than once, but at this stage he could do no damage, and his presence on the battlefield would have been a considerable asset.
According to Maret, Napoleon considered two possible plans. 'One consisted in remaining on the defensive, that is to say letting the enemy invade France and to manoeuvre in such a way as to take advantage of his mistakes. The other was to take the offensive [against the allied armies concentrating] in Belgium and then act as circumstances suggested.' Maret claimed that Napoleon wanted to adopt the first, but all the civilians invited to express an opinion were opposed to this, warning that the Chamber of Representatives would not support him in it.
It seems extraordinary that Napoleon should have given way to such pressures, as the first option was clearly the best: by the beginning of June he had over half a million men under arms around the country including the National Guard, and by keeping them close together in a central position he could have brought shattering force to bear on individual armies venturing into France, as he had done in his Italian campaign. There were also weighty political implications to the first option: if the allied invasion of ancient French territory could be represented in the same terms as that of 1792, it might elicit the same patriotic _élan_ , with similar results. Napoleon never tired of representing himself as the beloved of the people. 'The people, or if you wish the masses, want only me,' he boasted to Benjamin Constant. 'I am not only, as has been said, the emperor of the soldiers, I am the emperor of the peasants, the plebeians of France... That is why despite the past, you can see the people gather to me. There is a bond between us.' This was largely true, certainly of Paris and of central and north-western France.
It is also possible that, faced with an entirely pacific Napoleon and the prospect of invading a country at peace, the allies might have paused for thought. Their own troops were tired after years of war, and the desire to have a go at the French had been assuaged in the previous year. And if, as some suggested, the people had been called to arms, visions of 1792 might have haunted them too; they were only too aware of the smouldering embers of revolution in France and Europe.
But so was Napoleon, and his memories of 1792 had never left him. He bowed to reasonable counsel. 'The sensible middle course is never the right one in a crisis,' remarked General Rumigny, who believed a national call to arms would have revived a revolutionary fervour that would have saved the day. But the mood in the upper echelons of society was not one to build hopes on. After dining at Savary's house and later calling at Caulaincourt's on 15 June, Benjamin Constant noted 'discouragement and a wish for compromise' wherever he went. 'Anxiety, fear and discontent were the predominant sentiments; there was no attachment or affection for the government in evidence,' noted Miot de Melito, adding that only the poorer quarters of the city were firmly behind Napoleon.
Whether or not he was just putting on a brave face, as Hortense believed, Napoleon was merrier than usual on the day of his departure to join the army, talking of literature during dinner with Letizia, Hortense and his siblings, and saying as he took his leave of General Bertrand's wife, 'Well, Madame Bertrand, let's hope we don't live to regret the island of Elba!' Lavalette was also struck by his apparent optimism. 'I left him at midnight,' he recalled. 'He was suffering from severe chest pains, but as he climbed into his carriage he showed a gaiety that suggested he was confident of success.' But the strategy he had chosen, to take the war to the enemy, doomed him in the long run, as France would not be able to stand up to the vastly superior allied forces in a prolonged war.
The campaign opened well. Napoleon had some 120,000 men, with which he intended to defeat Blücher with his 125,000 Prussians and Wellington with an Anglo-Dutch force of 100,000 before they could join up and outnumber him. 'Our regiments are fine and animated by the best spirit,' Colonel Fantin des Odoards of the 70th Infantry of the Line, a veteran of many campaigns and a survivor of the retreat from Moscow, noted in his diary on 11 June. 'The Emperor will lead us, so let us hope that we will take a worthy revenge. Forward then, and may God protect France!'
Napoleon went for Blücher first, and dealt him a heavy blow at Ligny on 16 June. It would have been a rout if General Drouet d'Erlon had acted as Napoleon intended – not the first instance where the absence of Berthier to oversee and check orders were carried out made itself felt. Soult, who was acting as chief of staff, had neither the aptitude nor the authority required. The battle might also have eliminated the Prussians from the scene had it not been for the courtesy of some French cuirassiers who, returning from a charge which had swept over him, found Blücher himself lying helpless, pinned down by his dead horse, which his aide was unable to shift on his own. With soldierly gallantry they refrained from killing him or taking him prisoner.
Napoleon detached Marshal Grouchy with over 30,000 men to pursue Blücher and make sure he did not veer west to join Wellington. He himself marched north along the road to Brussels, on which, on the next day, Wellington took up position on a slight rise just south of the village of Waterloo, anchored to two heavily fortified farms at Hougoumont and La Haye Sainte. Heavy rain had turned the roads to mud and it took a long time for the French forces to come up. They spent a cheerless, cold night, and on the morning of 18 June the ground was so sodden that it was not possible to go into action, so Napoleon waited till noon for it to dry out.
The younger Napoleon would have tied Wellington down frontally and outflanked him, pinning him in a trap of his own making. But he had long since abandoned such manoeuvres in favour of frontal confrontation and heavy fire. With his forces reduced by detaching Grouchy to around 75,000 men and about 250 guns, he did not have much to spare, and little time, as superior Prussian forces might appear on his right flank at any moment. He meant to pin down the British forces in their strong points of Hougoumont and La Haye Sainte, and to deliver a strong blow at Wellington's centre. He was unwell and somnolent, and, as at Borodino, did not direct operations actively.
Jérôme, commanding the left wing, wasted time and lives on trying to capture Hougoumont instead of merely neutralising the British forces there. The main attack on the British centre petered out. With some urgency, since Prussian troops were approaching, Napoleon mounted a second assault on Wellington's positions, to be driven home by a massive cavalry charge. But the attack faltered and the cavalry went into action prematurely, allowing the British infantry to form squares and repel it.
Grouchy had been negligent in his pursuit of Blücher and lost touch with him when the Prussian changed course and moved westward to join Wellington. Instead of marching on the sound of the guns, as some of his generals pleaded with him to do, he carried on, moving away from the battlefield. As a result, Blücher appeared on Napoleon's right flank and rear in the late afternoon. In a last desperate attempt to break Wellington's line, Napoleon sent in the Guard, but this was poorly directed and strayed off its prescribed course. Coming under fire from front and flank, it wavered and some units fell back, shaking the morale of the rest of the army, which began a retreat that quickly turned into rout under pressure from swarming Prussian cavalry. As a moonless night fell, the chaos and fear only increased. It was not just a military defeat; it was a morale-shattering humiliation, with standards, guns, supplies and even Napoleon's famous _dormeuse_ abandoned in the flight.
The roads were so clogged with fleeing troops that he had to make his escape on horseback, riding all night and only stopping the next morning at an inn at Philippeville, where he dictated two letters to Joseph, one for public consumption, the other more honest, and two long Bulletins, one on Ligny, the other on what he called the battle of Mont-Saint-Jean, which made out that it had been hard-fought and was to all intents and purposes won when a moment of panic caused by the retreat of a single unit of the Guard caused a general retreat. It ended with the words: 'That was the result of the battle of Mont-Saint-Jean, glorious for French arms, yet so fatal.' He was utterly exhausted, and tears ran down his face, but he tried to sound optimistic. 'Everything is not lost,' he wrote to Joseph, since he had received reports that Jérôme and Soult had managed to rally some of the fleeing troops, while Grouchy was retreating in good order to join them, and he urged him to 'above all, show courage and firmness'.
He himself was in a state of shock. It had been a bloody encounter – he had lost up to 30,000 men and the allies little short of 25,000. He had also left most of his artillery and a huge number of prisoners on the field and during the flight. The losses were one thing, but the blow to his reputation as a general and to his _amour-propre_ and that of the French army was what really felled him.
He reached Paris around eight o'clock on the morning of 21 June and drove straight to the Elysée, where he was met by Caulaincourt, who was distressed that he had come back, believing he should have stayed with the army; without it, in Paris, he was politically vulnerable. Napoleon ordered a hot bath and summoned his ministers. The first to arrive, while he was still in it, were his paymaster Peyrusse, from whom he wanted to find out how much money was available, and Davout, whom he questioned about troop numbers. Davout assured him that all was not lost if he acted with determination and took the field as soon as possible with a fresh army. But Napoleon was in a state of shock. 'What a disaster!' he had exclaimed to Davout. 'Oh! My God!' he cried out with 'an epileptic laugh' as he greeted Lavalette.
At ten o'clock he sat down to a meeting with his ministers. He told them that to defend the country from invasion he needed dictatorial powers, but wished to be invested with them by the Chamber of Representatives and the Senate. He had already been informed by the president of the first and by his brothers Joseph and Lucien that news of the disaster at Waterloo had spread, and the mood in the Chamber was defeatist and strongly against him; Lafayette was calling for him to be deposed. Cambacérès, Caulaincourt and Maret urged him to confront the Chambers and make his case, but he bridled at this. Regnaud expressed the opinion that he should immediately abdicate in favour of his son. Davout, Carnot and Lucien advised him strongly to prorogue the Chambers, seize dictatorial powers and declare ' _la patrie en danger_ ', the battle cry that had galvanised France in 1792. Fouché said there was no need for that, as, he assured them, the Chambers would be only too happy to support him. Decrès stared in astonishment; he, and Savary, knew that to be nonsense, and could see that Fouché was trying to mislead Napoleon. Before giving him the job, Napoleon had told Fouché that he should have had him hanged long ago, but he seemed blind to what his minister of police was up to.
Formerly so alive to any threat and so quick to see how to snatch a winning card from an unpromising deal, Napoleon appeared curiously detached and incapable of reaction. He would not concentrate on the matter in hand, going over the available troop numbers and the possibility of calling out the _levée en masse_ one moment, asking for reports on the mood of the country the next, blaming people and events, speculating on possible manoeuvres, and confusing his own predicament with an apparently sincere conviction that he was the only person who could save France. 'It is not a question of myself,' he said to Benjamin Constant, 'it is a question of France'; if he were to retire from the scene, France would be lost.
By midday, Davout felt he had missed his chance and there was no hope left, but the emperor remained calm. 'Whatever they do, I shall always be the idol of the people and the army,' he declared on being told the Chambers were now preparing to force him to abdicate or to depose him. 'I only need to say a word, and they would all be crushed.' He was right, but he would not say the word. A crowd of workers and soldiers had gathered outside the Élysée, calling for arms, and Napoleon only had to lead them across to the Palais-Bourbon, where Fouché was working for his demise in the Chamber, and the representatives would have been scampering quicker than on 19 Brumaire.
When various family members called on him that evening, along with Caulaincourt and Maret, they advised him to abdicate. Only Lucien still begged him to act. 'Where is your firmness?' he urged him. 'Cast aside this irresolution. You know the cost of not daring.' 'I have dared only too much,' replied Napoleon, truthfully for once. 'Too much or too little,' snapped back Lucien. 'Dare one last time.' But he could not overcome his reluctance to unleash civil unrest. 'I did not come back from Elba in order to flood Paris with blood,' he said to Benjamin Constant. He continued to dither, and with every hour that passed his chances of saving anything from the debacle diminished. Savary advised him to leave and make a dash for the United States; Napoleon had already summoned the banker Ouvrard to ask him whether he could make sufficient funds available for him in America against a promissory note issued in France. He may also have tried to commit suicide that night; the evidence is patchy, but he was certainly out of sorts when he got up at nine o'clock on the morning of 22 June.
He had still not made up his mind how to proceed, but by that time a council of ministers and delegates of the two Chambers which had convened that night under the direction of Cambacérès had decided to send a deputation to allied headquarters, effectively sidelining him. Buoyed by news of the numbers of troops Jérôme and Soult had been able to rally and the good spirits of other units around the country, Napoleon started considering various military options. But at eleven o'clock a deputation from the Chamber demanded his abdication. When it had left, he erupted into a rage and declared he would not abdicate, but Regnaud observed that in doing so he might be able to obtain the succession of his son. His advice was endorsed by all the other ministers present except for Carnot and Lucien, who both strongly urged him to seize power, reminding him of Brumaire. But Napoleon no longer had it in him. He dictated to Lucien a 'Declaration to the people of France', in which he stated that he had meant to ensure the nation's independence, counting on the support of all classes, but since the allies had vowed hatred to his person and pledged that they would not harm France, he was willing to sacrifice himself for his country. 'My political life is finished, and I proclaim my son Emperor of the French, under the name of Napoleon II,' he declared, going on to delegate powers to his ministers. Carnot wept, Fouché glowed.
The declaration was delivered to the Chamber of Representatives shortly after midday, and although it was clear that nobody would accept the succession of his son, it was debated at length; Fouché and others still feared that, pushed too far, Napoleon might yet rouse himself and stage a coup. He influenced the choice of the delegates to negotiate with the allies, which alarmed those closest to him, who began to fear for his life; those chosen would not resist handing him over to the enemy as a mark of good faith. It became clear that he must get away to America as quickly as possible.
Napoleon requested Decrès to provide two frigates at Rochefort, and his librarian began preparing cases of books for him to read on the voyage and to help him in the writing of his memoirs. He went through his private papers, burning many, but, curiously, collecting together his youthful writings, including _Clisson et Eugénie_ and the description of his first sexual encounter, in a box which he entrusted to Fesch. He seemed in no hurry to get away. 'He speaks of his circumstances with surprising calm,' noted Benjamin Constant, who also came to see him on 24 June. 'Why should I not stay here?' he kept saying. 'What can the foreigners do to an unarmed man? I shall go to Malmaison, where I shall live in retirement, with a few friends who will certainly only come to see me for myself.' He nevertheless repeated his request to Decrès that a couple of frigates be made ready to take him to America.
On 25 June he left for Malmaison, going out by a side entrance to avoid the crowd that had been keeping a vigil in front of the Élysée. He would stay there four days, waiting for news that the ships were ready. Decrès replied that he required authorisation from the Commission of Ministers, effectively the provisional government. Under the influence of Fouché this sent General Becker with a contingent of troops to guard Napoleon at Malmaison, where he had been joined by Letizia, Hortense, Lucien and Joseph, Bertrand, Savary, General Lallemand, his aides Montholon and Planat de la Faye, the councillor Las Cases and Caulaincourt. He received visits from old friends, and saw his son by Éléonore de la Plaigne, whom he said he would bring over to America once he was established there. He admitted to Hortense to have been deeply moved by the child.
The allied armies had paused, checked by smaller but still battle-worthy French forces. Confused informal negotiations were going on between Fouché and Louis XVIII, who was still in Belgium, and between Talleyrand, who had joined him there, and various of his contacts in Paris. The allies were also discussing among themselves whether to reinstate Louis XVIII or install another ruler. Units in various parts of the country continued to fight. Some officers planned to kidnap Napoleon from Malmaison and rally the army to him in order to fight on – there were still 150,000 men under arms around the country, and others would have joined them.
On 29 June, when he heard that the allied armies were on the move once more, Napoleon offered his services to the provisional government, promising to retire into exile once victory had been achieved. Fouché dismissed the idea, as it had become clear that one of the preconditions of any negotiation was that Napoleon was to be handed over. Not wishing to provoke any violent moves on his part or that of his entourage, the provisional government sent Decrès to Malmaison to inform Napoleon that two frigates were waiting at Rochefort. That same day, after taking his leave of Hortense and others, and pausing for a while in the room in which Josephine had died, he left Malmaison for Rochefort, escorted by Becker and his men.
The two frigates were ready, but the port was blockaded by the Royal Navy, so there was no possibility of their sailing without a safe-conduct, which Napoleon was assured would be obtained by the government negotiators, a blatant lie; Fouché had let him reach Rochefort, where he was cut off from any support he might have found in Paris, and once he had boarded one of the frigates he was trapped. As he vainly waited for the safe-conduct, he was allowed to visit the island of Aix, next to which his vessel was anchored, and inspect the works he had commissioned; he was cheered by the troops stationed there, but that could not alter the fact that he was effectively a prisoner.
The allies had entered Paris on 7 July, and Napoleon did not relish the idea of being dragged back there as a captive, so the next day he sent Savary and his chamberlain Las Cases over to the British man-of-war blockading the port, HMS _Bellerophon_. At the same time, a number of plans were discussed for his escape. Joseph found a merchantman which would take him to America incognito, but Napoleon refused this subterfuge, judging it undignified. Captain Maitland, the commander of the _Bellerophon_ , had given Savary and Las Cases to understand that Napoleon would be offered asylum in England, which seemed a more fitting solution. Napoleon wrote the Prince Regent a letter declaring that, trusting in his magnanimity and that of his subjects, he wished, 'like Themistocles, to come and sit by the fireside of the British people'.
In the early hours of 15 July he put on his campaign uniform of colonel of the Chasseurs of the Old Guard, and at four o'clock in the morning boarded the French brig _l'Épervier_ , which took him out to within a cannon-shot of HMS _Bellerophon_ and dropped anchor. To Becker, who had suggested escorting him, he replied, 'No, General Becker, it must not ever be said that France delivered me to the English.' He drank a cup of coffee and conversed calmly about the technicalities of shipbuilding while a launch came over from the British ship. Madame Bertrand acted as interpreter during the exchange that then took place with the British naval officer, and Napoleon ordered his party to get into the launch. He got in last and sat down. As it pulled away, the crew of the _É_ _pervier_ shouted ' _Vive l'Empereur!_ ', at which Napoleon scooped up some seawater in his hand and blessed them with it.
It was 137 days since he had landed in the Golfe Juan, but supporters of the returning Louis XVIII tried to belittle the interlude by referring to the 110 that had elapsed between the king's evacuation of the Tuileries in March and his return at the beginning of July as a mere 'hundred days'. As with so much else in his extraordinary life, Napoleonic propaganda turned this into 'The Hundred Days', a tragic-glorious chapter in the emperor's march through history.
He was piped aboard the _Bellerophon_ , and declared to Captain Maitland that he had come to throw himself on the protection of the Prince Regent and the laws of England. The British naval officers had doffed their hats and addressed him as 'Sire', as did Admiral Hotham, who sailed up in HMS _Superb_ that day and invited Napoleon to dinner. He felt respected and, ironically, safe as he returned to the _Bellerophon_ , which set sail for England the same day. His Hundred Days in France were over.
As the _Bellerophon_ rounded Ushant on 23 July, Napoleon looked on the land of France for the last time, not yet knowing that Louis XVIII had resumed his place on the throne with a ministry under Fouché and Talleyrand. What he would never know was that on hearing the news Marie-Louise wrote to her father saying that it had caused her great relief, as it put paid to 'various silly rumours that had been circulating' – that her son might be made emperor of the French.
## 44
# A Crown of Thorns
On 24 July the _Bellerophon_ dropped anchor in Torbay, and as soon as news got round that Napoleon was on board it was surrounded by a multitude of small craft full of locals eager to catch a glimpse of the great man. Themistocles obliged, appearing on deck and at the poop windows, tipping his hat to the ladies, evidently enjoying the attention and taking heart from the fact that it was not hostile. The newspapers wrote of his probable exile to St Helena, but that had been in the air for over a year, and the more ordinary English people saw him the more likely it seemed that he might be allowed to retire by their fireside. On 26 July _Bellerophon_ weighed anchor and sailed for Plymouth, where it was flanked by two frigates with the aim of keeping away the tourists, but more than a thousand boats ferried people out to see the illustrious captive.
The blow fell on 31 July, when Admiral Lord Keith came aboard accompanied by the under-secretary for war Sir Henry Bunbury to inform him that he was to be taken to St Helena as a prisoner of war. Napoleon protested vehemently, saying he had been tricked into believing he would be allowed to stay in England. Captain Maitland had certainly been equivocal, allowing him to think what he wished, and some of the officers of the _Bellerophon_ felt he had been deceived. He objected that the British had no right to imprison him, as he had made war legally on the King of France, who had defaulted on a binding treaty. He retired to his cabin, from which he hardly emerged over the next three days, and on the fourth wrote out a formal protest at the manner in which he had been treated.
By then _Bellerophon_ had sailed from Plymouth to rendezvous with the flotilla under Rear Admiral Sir George Cockburn that was to escort him to St Helena. He was to travel on the flagship, HMS _Northumberland_ , and the transfer would take place at sea, as the government was keen to get him away as quickly as possible. There had already been an attempt by British sympathisers to use legal means to bring him ashore by issuing a subpoena for him to attend court. If Napoleon had been allowed on English soil it would have been very difficult to get him off, and the British penchant for making a hero out of a loser might well have turned him into Themistocles.
A limit was set to the number of people who could accompany him, and Savary and others were not allowed to go. Those permitted to share their master's captivity were Bertrand with his wife and young son, General Tristan de Montholon with his wife and five-year-old son, General Gourgaud, and the former chamberlain and member of the Council of State Émmanuel de Las Cases with his son. Napoleon's service consisted of his valet Louis Marchand, his Mameluke Louis-Étienne Saint-Denis, his second valet Noverraz, his butler Cipriani, his grooms the Archambault brothers, another valet, a cook and a pastry-cook, and a man in charge of the silver. Servants attached to the other members of the party brought the total up to twenty-seven, and since Napoleon's physician had balked at the prospect of going, the Irishman Barry O'Meara, surgeon of the _Bellerophon_ , agreed to go along in his stead.
After a cordial farewell from the officers of the _Bellerophon_ Napoleon was drummed off with the honours due to a general, but on coming aboard _Northumberland_ he and his party had their baggage searched unceremoniously. A large sum of money was confiscated without any pretext being given. Having foreseen something of the sort, Napoleon had entrusted cloth belts full of gold coins to each of his entourage, and in that manner saved a small amount.
He seemed resigned to his fate, and remained remarkably serene throughout the long passage. He bore the discomforts of shipboard life well, often remaining in his cabin to read. He chatted with the sailors, asking technical questions and trying to improve his English, and during dinner treated the ship's officers to reminiscences and accounts of his campaigns. Although they were unimpressed by his table manners, he got on well with most of them, whiling away the time in conversation or games of cards and chess. He was occasionally indisposed and sometimes irritable, which is understandable, given that from the moment he came aboard the _Bellerophon_ at Rochefort to the day he stepped off _Northumberland_ at St Helena, he would have spent three months at sea.
On 14 October they sighted their destination, a volcanic outcrop rising out of the waters of the South Atlantic, accessible only at Jamestown, a small settlement nestling in a cleft which goes down to the sea. The island has a surface area of 122 square kilometres, and lies 1,900 kilometres off the coast of Africa, the nearest land. The climate is tropical but mild, and damp for much of the year. Discovered by the Portuguese in 1502, it was currently in the possession of the East India Company, serving the vital purpose of watering ships bound for India and South-East Asia. In 1815 the population consisted of 3,395 Europeans, 218 black slaves, 489 Chinese, and 116 Indians and Malays. The island produced little, and depended heavily on the import of food from Cape Town, a three-week trip away. There was a military governor and a small British garrison manning strategic forts and batteries, which was hugely inflated by the arrival of Cockburn's fleet, with 600 men of the 53rd Regiment of Foot and four companies of artillery totalling another 360, which, along with the sailors now permanently on station, brought to about 2,500 the number who had come to guard Napoleon.
He came ashore at seven o'clock on the evening of 16 October, and was put up in provisional quarters in Jamestown. By six o'clock the next morning he was on horseback with Cockburn and off to inspect the place that was to serve as his residence, a former farmhouse situated on a remote plateau at Longwood. Described by one English observer as 'an old extremely ill-built barn', it was virtually derelict and too small, so there could be no question of his moving there for some time. The British government had ordered a prefabricated wooden house to be shipped out along with some furniture, but this would take months to arrive and erect, so Cockburn set his ship's carpenters and sailors to work on patching up the existing structure and adding further accommodation.
On their ride back, just over a mile short of Jamestown, they passed a bungalow set in flourishing gardens and known as 'The Briars' for its multitude of roses, the residence of the agent of the East India Company, William Balcombe. As there was nowhere else to put him, Napoleon was billeted in a small pavilion Balcombe had erected to serve as a ballroom, with an adjacent marquee. His campaign bed and _nécessaire_ were installed at one end, and a makeshift study was arranged at the other, with a curtain dividing the two. Las Cases and his son moved into the garret and a skeleton staff of Marchand, Saint-Denis and Cipriani accommodated themselves as best they could. The rest of his suite remained at Jamestown.
Napoleon would spend the next seven weeks there, working in the mornings with either Las Cases or Montholon, Bertrand and Gourgaud, who would take it in turns to come up from Jamestown to take dictation of his accounts of the principal episodes of his life: Las Cases the Italian campaign, Bertrand Egypt, Montholon the empire, and Gourgaud the revolutionary period, the Consulate, Elba, the Hundred Days and Waterloo. He took exercise by riding out with Captain Poppleton of the 53rd, who was detailed to keep a constant watch over him, or walking around the extensive gardens of the Briars, which were filled with fruit trees, including mangoes and figs, as well as shrubs and flowers. In the afternoons he would go for a drive with one or other of his entourage. He sometimes dined with the Balcombes and often spent his evenings with them, playing cards and other games with the children – two girls and two boys.
The second daughter, the fourteen-year-old Betsy, was pretty and vivacious, and remarkably precocious. She spoke French, and once she had got over the fear of meeting the dreaded Bonaparte and the awe of seeing 'the most majestic person [she] had ever seen', captivated by his 'fascinating smile', she began chatting away with him. He delighted in her impish ways and happily joined in whatever games his 'Mademoiselle Betsee' chose to play, displaying unexpected talents at mimicry and blind-man's-buff; one day when a young friend of hers called to catch a glimpse of the Corsican Ogre he obliged by acting a grimacing, howling monster. Betsy treated him like a companion or a brother. 'He seemed to enter into every sort of mirth or fun with the glee of a child, and though I have often tried his patience severely, I never knew him lose his temper or fall back upon his rank or age,' she later reminisced, only dimly aware of the pleasure he derived from moments spent with his ' _bambina_ ' or 'leettle monkee', as he referred to her.
He had not been on the island a week when the full implications of his position sank in. Not only was he a prisoner, he was lodged in a miserable shed without curtains or furniture, he was watched day and night, and separated from his companions, who could only visit him accompanied by a guard. The food was inadequate and revolting, with no good bread and a shortage of fresh meat and vegetables. He was soon going to be put in an uncomfortable barn in the most dismal part of the island, damp and either windswept or enveloped in cloud. He was to be treated with the barest civility by his gaolers, and, what rankled most, could expect not the slightest recognition of his former status.
On 24 October, in the presence of all four of his officers, he gave vent to his bitterness, saying that he had never treated any of his enemies with such heartless contempt. They had all been only too happy to call him their brother when he was in power, and were now assuaging their shame by humiliating him. The Emperor Francis tried to bury his grandson's origins by giving the King of Rome an Austrian title and bringing him up accordingly; the man Napoleon had made King of Württemberg was doing his utmost to get his daughter to divorce Jérôme, as was the similarly crowned King of Bavaria with regard to his daughter and Eugène.
Napoleon declared that he would make no more public protests himself, it being below his dignity, and would let others speak on his behalf. In a note he prepared for the captain of one of the accompanying ships who had come to take his leave before returning to Britain, he set out a number of points he wished him to make known there. The first was that the British government had declared him to be a prisoner of war, which was incorrect, since he had not been taken but had voluntarily placed himself under the protection of the laws of England; and if it had been true, then he should have been released as all prisoners of war are at the cessation of hostilities. The second was that by subjecting him to an unsuitable climate and harsh conditions, refusing him the consideration he deserved and preventing him from communicating with his wife and child, or even getting news of them, the British government was not only breaking international law but denying him basic human rights.
On 9 December Cockburn took him to see Longwood, which had undergone extensive work. The stone barn had been partitioned to create living quarters for Napoleon consisting of a small bedroom, a study, a bathroom and a small room for the valet on duty, a dining room and pantry, and a library. A long wooden structure had been added on to the front at right angles, containing a parlour and a sitting room. Further additions at the back provided a kitchen, servants' quarters, various utility rooms, and accommodation for the Montholon family, Gourgaud and, in a loft reached by a ladder, Las Cases and his son (the Bertrands were to be lodged separately in a cottage halfway between Longwood and Jamestown). The building work on the annexes was still in progress, and Napoleon complained that the smell of paint made him feel sick, but even though the rooms were small and there was hardly any furniture, on the whole the accommodation was an improvement on the pavilion in the Balcombes' garden. The following day he put on his uniform and, after thanking the Balcombes for their hospitality, set off on horseback with Cockburn for his new residence, where he was greeted with military honours by a detail of the 53rd.
His campaign bed had been installed in his bedroom, a portrait of Marie-Louise had been hung on the wall, with a bust of the King of Rome beneath it, and that day he was able to relax for an hour in his first hot bath since leaving Malmaison. As their quarters were not yet ready, the Montholons, Gourgaud, Dr O'Meara and others had to make do with tents in the garden. It was not long before the disadvantages of Longwood made themselves felt. The climate on the plateau was the worst on the island, and the desolate surroundings the least appealing. The buildings were entirely unsuited to the conditions. They were roofed with paper covered in pitch, which soon began letting in the rain, and damp seeped through the walls of the annexes, which were of wood covered with the same, permeating clothes, bedding, books and everything else. The house was full of flies and mosquitoes, and infested with rats. The floors were of cheap pine, and as there was no cellar or underpinning, they rotted, occasionally giving way to reveal the damp earth beneath. The smoking chimneys did not give off enough heat to dry the rooms out.
The conditions depressed Napoleon and his entourage, who were used to a dry climate, good food and a modicum of luxury. They also brought into sharp relief the reality of their situation, and aggravated tensions which had been mounting since they left Europe. Each of the four officers who had chosen to come out with Napoleon had reasons of their own for their decision, which had been made under pressure at a moment of uncertainty. Bertrand's wife Fanny, a beautiful, well-born creole of Irish descent, had threatened to drown herself when her husband declared his intention of going. Pangs of regret at what had seemed at the time the right gesture of loyalty were not long to hit all of the men, and their spouses even more so, as they contemplated limitless exile in such conditions. The spirit of emulation in these soldiers and courtiers, possibly manipulated by Napoleon, had aroused jealousies and animosities between them during the voyage, and these only grew with time. The Bertrands and Montholons, and particularly their wives, were locked in rivalry. Las Cases, a forty-nine-year-old minor nobleman of no evident talents, was generally referred to as 'the Jesuit'. Gourgaud was a product of the Napoleonic system: the son of a court violinist, he had fought his way up from the ranks at Austerlitz and Saragossa, been wounded at Smolensk and swum the Berezina, ending up with the rank of general, the tile of baron and the position of orderly officer to Napoleon. But he was excessively sensitive and histrionic, and they all took pleasure in baiting him.
They nevertheless constituted a court around Napoleon, observing imperial etiquette and routine. Unless he was receiving a formal visit, during the day he usually wore his green hunting coat or a 'colonial' costume of white linen coat and trousers. In the evenings the company assembled for dinner in full uniform, the ladies in court dresses and bejewelled, and after dinner they played cards, conversed or listened as Napoleon read from a book. He revisited his old favourites, _Paul et Virginie_ , Racine and Corneille, discussed other works and went over his life in endless monologues on what he should have done or not done, passing severe judgement on people, making unpleasant comments about the women in his life, blaming others and particularly bad luck, treachery or 'fate' for his failures. The house was furnished with whatever had come to hand, but shards of splendour were on display – imperial silver, a magnificent Sèvres coffee set depicting the salient events of his life, a few portraits and miniatures.
He took pleasure in laying out a garden at Longwood which he kept embellishing with the aid of two Chinese workers and enjoyed watering himself. He received visits from the Balcombes, particularly Betsy, who sometimes brought some local lady to see him. But they had to obtain authorisation beforehand and present a chit at the guardhouse at the outer limit of Longwood, as though they were visiting an inmate in prison.
His detention was anomalous, as he was neither strictly speaking a prisoner of war nor a convicted criminal, and while he was freer to move about than either, he was also forbidden a number of privileges guaranteed to both. Its conditions said more about the fears and insecurities of the cabinets of Europe than about any threat he might have posed. He was not allowed to walk or ride beyond certain limits without being accompanied by a British officer, and even within them he was watched by 125 sentinels during the day and seventy-two by night. In addition there were pickets of soldiers placed on every hill in the area. Twice a day an officer had to ascertain his presence face to face. A telegraph was set up to alert Jamestown instantly of his movements (with a signal for 'escaped'). Nobody could visit him without authorisation, and a curfew applied to the immediate area. The 53rd was encamped nearby, and patrolled incessantly. Two ships circumnavigated the island continuously, one clockwise, the other anti-clockwise. Dr O'Meara was enlisted by Admiral Cockburn to spy on Napoleon and report on his actions, his words and even his mood. He was not allowed any newspapers. Ships calling at Jamestown to take on water were boarded and searched, their crews and passengers screened. In June 1816, high-ranking commissioners sent by the French, Russian and Austrian governments arrived to invigilate. 'The Island of St Helena is the point on which our telescopes must be unceasingly trained,' Louis XVIII's prime minister the duc de Richelieu wrote to his ambassador in London, anxious about whether the British were taking enough precautions. It was as if some dangerous force was being contained on the remote island, a plague that needed to be quarantined.
There is no evidence that Napoleon ever contemplated or even wished to escape. On the contrary, he applied himself to making what he could of his predicament in such a way that at times he almost seemed to revel in it; the consummate actor and manipulator was gradually developing a new strategy.
Whatever his feelings about their government's actions, he had gone out of his way to be amiable to all the British officers, military and naval, during the crossing (he never cheated at cards with them). When the sailors put on their ceremony at the crossing of the Equator, he distributed money to them. He charmed the Balcombes during his stay at the Briars. He was polite and comradely towards the colonel and officers of the 53rd when they called. He received British inhabitants of the island graciously, and on the whole succeeded in engaging their sympathy, or at least in conveying the impression that he was being shabbily treated. To visiting Britons – and there were many of them, as after weeks or months at sea on their way to or from India, a glimpse of the fallen ogre was an irresistible attraction – he was charming, and appeared to bear his misfortunes with good grace. It was not long before accounts were published, and people in England began criticising the unnecessarily harsh conditions to which he was being subjected.
He applied himself to making them appear harsher than they were. While he had been on relatively cordial terms with Admiral Cockburn during the crossing, on St Helena he began to treat him as his gaoler. Rather than seek a _modus vivendi_ , he challenged him. Knowing perfectly well that all officers and officials had been instructed to accord him no more honours than those due to a general, he would nevertheless order Bertrand to inform the admiral that the emperor wished this or that, which naturally elicited the response that the admiral knew of no emperor on the island and was therefore unable to comply. When an invitation was issued to 'General Buonaparte' to attend a function, Napoleon instructed Bertrand to answer that the person in question had last been seen in Egypt in 1799. This kind of behaviour soured the admiral's view of Napoleon and encouraged him to carry out his duty with greater zeal, leading to a further deterioration in relations between them and an accumulation of grievances on either side.
In April 1816 the military governor who was to supervise his captivity reached the island and took over from Admiral Cockburn, who stayed on as commander of the naval station. Major General Sir Hudson Lowe had served mainly in the Mediterranean, taking part in the British capture of Corsica and commanding a regiment of pro-British Corsicans, and spoke French and Italian as a result. Although he was a capable soldier and a competent administrator, he was not popular, and Wellington thought him a fussy fool. Punctilious, narrow-minded and lacking in imagination, let alone human sympathy, he was the worst possible choice for his new appointment.
Napoleon was pleased at the news that his new gaoler was to be a soldier. But things got off to a bad start when, shortly after his arrival, on 15 April the new governor called at Longwood unannounced, only to be told that the emperor was unable to receive him. It was agreed that he should return the following day, when Napoleon did receive him but took an instant dislike to him. Lowe was not interested in him as a person or a historical figure, and could see no further than the limits of his instructions, which were to guard the prisoner according to guidelines laid down in London by the war secretary Lord Bathurst, who had no idea of local conditions and therefore piled on unnecessary precautions. He saw no reason to question these, and carried them out to the letter. Napoleon felt affronted, and showed his feelings with characteristic rudeness. Lowe responded with officious detachment and an extreme interpretation of his instructions, meaning to teach the French upstart a lesson. This furnished Napoleon with the perfect target for his bitterness and frustration, and, by extension, with the ideal means by which to fight his final battle against the British.
A couple of weeks after their first meeting, the ship carrying furniture and the materials for building the new house arrived at Jamestown, and Lowe came to enquire where Napoleon thought it should be erected. This carried an unwelcome suggestion of permanence regarding his captivity, and Napoleon flew into a rage about the way he was being treated, accusing his gaoler of having been sent to kill him. Lowe barely contained his anger and retired. The furniture was brought to Longwood (absurdly, since Napoleon did not play, a billiard table was installed in the parlour), and no more was said about the new residence.
In mid-June Admiral Cockburn was relieved by a new squadron under Rear Admiral Sir Pulteney Malcolm, whose wife, Clementine Elphinstone, owed Napoleon a debt of gratitude; he had saved her brother's life by getting his wounds dressed at Waterloo. They brought presents from her brother (which Lowe attempted to prevent being handed over) and French newspapers, and treated him with consideration. In the course of repeated visits this developed into cordiality, with Napoleon indulging his old fascination with Ossian by questioning her about her native Scotland. This profoundly irritated the governor, whose relations with the admiral became strained.
The new fleet also brought the commissioners designated by Russia, Austria and France to watch over Napoleon, and he briefly thought that, at least in the case of the Russian and the Austrian, they might provide a channel of communication with Alexander and Francis. When it became clear that they were only additional gaolers, he refused to receive them in their official capacity, as in doing so he would be accepting his position as a prisoner of their sovereigns. At the same time, he let it be known that he would gladly see them as private individuals. When, after having consulted their governments on the matter, they agreed, Lowe prohibited it, going so far as to forbid them to walk, ride or drive in the vicinity of Longwood, or to exchange greetings with any of its inhabitants they might meet, including servants (he issued similar injunctions on the soldiers of the 53rd, who had run out to cheer Napoleon as he passed their camp on one of his morning rides). Having intercepted a note from Bertrand to the French commissioner, the marquis de Montchenu, whom he knew to have seen his sick mother in Paris, asking for news of her, Lowe rebuked him and declared that all correspondence must pass through him. He even prevented the Russian commissioner, Count Balmain, from any contact with a passing Russian ship, presumably fearing an attempt to kidnap his prisoner.
Accompanying the Austrian commissioner, Baron Stürmer, was a young botanist employed in the gardens of Schönbrunn, Philipp Welle. He discreetly contacted Napoleon's valet Marchand and handed him a letter from Marchand's mother, who had been in service with the King of Rome and had accompanied him to Vienna. The letter contained a lock of his hair, and Welle, who had often seen the child in the gardens, was able to give news of him, which was all passed on to Napoleon; he was deeply affected and put the lock of hair away in his _nécessaire_ , next to one of Josephine's.
Another ray of sunshine in his life was the arrival of two cases of books, along with letters from Letizia and Pauline. He was so eager to get at the books that he opened the cases himself with hammer and chisel. But his mood was spoiled when Lowe confiscated two volumes sent by an English admirer stamped on the binding with the words _Imperatori Napoleoni_ , as he refused to acknowledge his prisoner's imperial title. Napoleon had a number of well-wishers in England, most notably Lord and Lady Holland, who sent him books and other creature comforts – most of which were sent back by Lowe or by pettifogging officials in London. 'Napoleon cannot need so many things,' Lord Bathurst exclaimed when Pauline attempted to send him some necessities.
Not surprisingly, Lowe met with a frosty reception when he called to discuss Napoleon's accommodation; Longwood was already showing signs of decrepitude and was fast becoming uninhabitable. Napoleon could see no point in building a new house, believing that by the time it was ready there would have been a new ministry in Britain or a change of regime in France, or he would be dead. He was reluctant to accept any favour which might give the impression that his lot had been eased. There ensued a difficult meeting lasting two hours. (Napoleon would stand throughout, forcing Lowe to do likewise, fearing that if he were to sit down Lowe would do so too, a breach of etiquette in the presence of the emperor.) Since the materials for the new house had arrived, Lowe was determined to erect it, but in the first instance remedial works to the existing one were put in hand.
The Russian commissioner reported to his superiors that as well as being 'the saddest place in the world', St Helena was impossible to attack or to escape from. Yet the British government was obsessed with the possibility of his doing so, and gave credence to every report and rumour of a plot to liberate Napoleon – including some absurd ones involving submarines. It therefore maintained the ludicrous number of troops and a naval squadron on permanent station, which, given the necessity of shipping in almost all victuals and supplies from Cape Town or even further afield, brought the cost of Napoleon's confinement up to, according to some estimates, as much as £250,000 a year.
Rather than scale down the military establishment, Lord Bathurst ordered Lowe to reduce the expense of keeping the prisoner and his household. While on Elba Napoleon had skimped and saved, here he was only too profligate with the British treasury's money (it had, after all, robbed him of a large sum when he came aboard the _Northumberland_ ). He insisted on being supplied with meat and vegetables which were unavailable on the island and often arrived spoiled, and Longwood consumed an astonishing 1,400 bottles of wine a month (assisted by Poppleton and other officers of the 53rd, who either scrounged or bought it from the servants). Lowe called at Longwood to discuss savings, but was not received, and was told to address himself to Napoleon's butler. He went to see Bertrand, who sent him to Montholon, who told him to go to the devil.
On 18 August 1816 Lowe called at Longwood once more, in the company of Admiral Malcolm, who would at least gain him access to Napoleon. As they rode up they found him walking in the garden with Las Cases and Albine de Montholon. Lowe apologised for having to bring up the matter of finances, but complained that he was obliged to communicate directly with Napoleon since Bertrand had insultingly refused to discuss it. Napoleon could not contain his antipathy towards the general; he reminded him that Bertrand had commanded armies in the field, while he was nothing but a staff clerk who had only ever commanded 'Corsican deserters', a man without honour who read other people's letters, a gaoler not a soldier, who was treating them 'like Botany Bay convicts'. He railed at the conditions he was being kept under, at the climate which was undermining his health, at his mail being read, his books being confiscated and other indignities. 'My body is in your hands, but my soul is free. It is as free as it was when I commanded Europe... And Europe will in time come to judge the treatment inflicted on me. The shame will rebound on the people of England,' he said to Lowe. If he was not prepared to feed him Napoleon would go to the camp of the 53rd, whose officers would surely not refuse to share their meagre mess with an old soldier. Red in the face, Lowe could barely contain his fury at the insulting references to his not being a real soldier and acting dishonourably when he was only following orders; he salvaged his honour by telling Napoleon that he was ridiculous and his rudeness pathetic, and left, followed by Malcolm. He would never see Napoleon alive again.
Napoleon admitted to Las Cases and Albine de Montholon that he had gone too far, but he was not one to apologise, and the hostilities continued. Faced with further demands to reduce the expense of his establishment, and a refusal to let him write to bankers who held his funds (a plot was feared), he had his servants gather up a large quantity of his table silver, hammer it out of shape and remove imperial devices, and sent it to be sold off for scrap in the square at Jamestown, in full view of the inhabitants and visiting Britons.
Lowe retaliated by reducing the limits within which Napoleon was allowed to move, and ordered the number of his servants to be reduced by four. At the end of November 1816 Las Cases was arrested, having been caught trying to smuggle out a couple of letters – apparently a ploy to get himself sent back to Europe with the four servants who were being sent away. This diminished the miniature court which was a psychological support for the fallen emperor. Observing the routine etiquette became more difficult. A combination of monotony, boredom, bad weather, worse food, the sight of the sentries at every door and window, the petty restrictions and minor vexations, along with frequent indispositions caused by all of these, sapped morale as well as their health.
As a protest against Lowe's restrictions on his movements, Napoleon isolated himself further. He stopped riding and even going for walks; the constant attendance of a British officer spoilt the pleasure. The lack of activity told on his physical condition. His dysuria had got worse, and according to Saint-Denis he would sometimes stand over his chamberpot for long periods, his head leaning against the wall, trying to urinate. By the end of 1816 he was also suffering from protracted coughing fits and fevers.
On some days he did not bother to dress at all, keeping to his rooms and reading, usually one of his old favourites. He still dictated accounts of his campaigns, to Albine de Montholon who had taken over from Las Cases, and it seems that in the spring of 1817 he began an affair with her – presumably with her husband's acquiescence, since there could have been no secrets in the confined space inhabited by so many (in January 1818 she would give birth to a daughter, Josephine, who was probably his).
After one of his visits to Longwood, Admiral Malcolm noted that Napoleon was 'not displeased' at the vexations being visited on him by Lowe, and derived some satisfaction from his accruing grievances. At a later meeting, Napoleon explained the reason to Lady Malcolm. 'I have worn the imperial crown of France, the iron crown of Italy; England has now given me a greater and more glorious than either of them – for it is that worn by the Saviour of the world – a crown of thorns. Oppression and every insult that is offered to me only adds to my glory, and it is to the persecutions of England I shall owe the brightest part of my fame.'
He composed a protest against the way he was being treated, listing all the petty indignities and legally dubious procedures, which was written out on a piece of satin from one of Albine de Montholon's dresses and sewn into the lining of the coat of one of the departing servants, the Corsican Santini, who on reaching London would contact the prominent radical General Sir Robert Wilson and get it published. It would fuel a debate initiated in the House of Lords by Lord Holland attacking the government for its shameful treatment of the captive emperor.
Napoleon was aware that his companions were making notes and recording events for posterity, and he made sure they did not lack material. He reminisced about his childhood, his family, his love for Corsica, his time as a cadet and his later military and political exploits. He expounded his views on everything from religion to music, from women to war, reflected on what he had done and why, and discoursed on what he would have done if he had not been prevented. His monologues contain a deal of self-justification and blame of those who had supposedly failed or betrayed him, of circumstances and of 'fate'. He returned time and again to subjects such as his Russian campaign, blaming treachery and bad luck. He denigrated most of his marshals, and dismissed the women he had loved with coarse comments on their attractions and desires. Unpleasant as much of it is, to anyone who does not know better the overall image that emerges from the material noted down by his four 'evangelists' is that of a man who meant well, tried to achieve the impossible, and was being horribly punished, indeed martyred, for it. Waterloo is reinvented as a kind of expiatory moral victory. And St Helena was the ideal Golgotha.
In June 1817 Malcolm and his wife sailed away, and the 53rd was also replaced. In July Dr O'Meara was expelled by Lowe, who suspected him of spying for Napoleon; the governor was increasingly suspicious of everyone, and having got wind of the meeting between Marchand and Welle, even had the Austrian commissioner expelled.
The monotony of life on the island affected everyone, and Napoleon's entourage could not hide their longing to leave. Gourgaud, who had grown neurotic and constantly feuded with Montholon, left in March 1818. Although it was something of a relief to be spared his mawkish tantrums, it further diminished Napoleon's court. The Balcombes left the same month, which upset him, as even though he had been seeing less of them recently they were a friendly presence, and Betsy always cheered him when she called. A more affecting loss was the death from appendicitis of Cipriani, whom Napoleon was fond of and who had managed to maintain a certain standard when it came to his table.
Napoleon was grateful to the Anglican chaplain who consented to give him a Christian burial and sent him the gift of a gold snuffbox. Hearing of this, Lowe forced the chaplain to return it, on the grounds that it represented an attempt by the prisoner to bribe a British official. When, as the Balcombes were about to leave, Napoleon wished to give their Malay slave Toby, whom he had befriended when staying with them, the money to buy his freedom, he was prevented from doing so on the grounds that he was fomenting a slave rebellion. Lowe did not give a political reason for not allowing the piano at Longwood to be tuned, but he did find a sinister one behind Montholon's offer to the French commissioner Montchenu of some beans, explaining in a report to Bathurst that Montchenu should only have accepted the white ones, since white was the colour of the Bourbons, and refused the green ones, since green was associated with Napoleon, the implication being that the commissioner was politically unsound.
Three months after O'Meara had been sent away, Napoleon fell ill. Bertrand requested a replacement, but the governor did not believe there was anything wrong with Napoleon, and offered to send one of the available military and naval medics. Napoleon refused, on the grounds that they would be no more than the governor's spies. He kept to his bedroom, which meant the British officer who was supposed to establish his presence twice a day could not see him, despite trying to peer through cracks in the shutters. Lowe insisted he be admitted into his bedroom. Napoleon refused. Lowe suggested sending a doctor to ascertain his presence. Napoleon would not admit him. Lowe threatened to have the door broken down, and Napoleon did eventually allow John Stokoe, surgeon of HMS _Conqueror_ , to examine him. In January 1819 Stokoe diagnosed severe hepatitis, and was ill-treated by Lowe, arrested and dismissed, the governor being convinced that his captive was shamming. In April, Napoleon sent a plea to the prime minister Lord Liverpool through a relative of his who was passing through, but he too was persuaded by Lowe that there was nothing wrong with him.
Bertrand contrived to contact Fesch in Rome, with a request for a doctor and a Catholic priest. Neither Fesch nor Letizia liked spending money (though she had sent her son some), and she appears to have been convinced by a soothsayer that Napoleon had been spirited away from St Helena and was safe in some undisclosed location; they therefore selected two decrepit Corsican priests and a young doctor with little experience who came cheap. The three of them reached the island in September 1819, and on the Sunday following their arrival, mass was celebrated in the sitting room of Longwood. Napoleon had the now largely redundant dining room turned into a chapel, and henceforth attended mass every Sunday.
Albine de Montholon had left that summer, taking her children with her, and her husband was desperate to follow. The Bertrands were also keen to get back to Europe, and Napoleon, who understood their predicament but felt he could not do without the moral support of at least one high-ranking officer, considered finding replacements among his old faithfuls such as Savary and Caulaincourt. He was deluding himself if he thought they would be allowed to come; Pauline had sought permission without success, and in the previous year Jérôme and his wife Catherine had written to Lord Liverpool and the Prince Regent begging to be allowed to visit Napoleon, only to meet with refusal. In the event, he was coming to depend more on the twenty-eight-year-old Marchand, for whom he felt great affection and whom he called ' _mon fils_ ', and who cared for him with truly filial devotion.
Although he was now gravely ill, he had moments of enthusiasm and activity; towards the end of 1819 he decided to take more exercise and, spade in hand, took up gardening, which he seemed to enjoy. In January 1820 he went out for a ride, which laid him low for several days, and he repeated the exercise in May. That summer he drove out for a picnic, but on his return had to be carried into the house, and by the autumn he was in the terminal stages of what was either cancer or gastric haemorrhage due to his stomach wall being perforated by ulcers. The Corsican doctor sent by Fesch and Letizia, Francesco Antommarchi, was out of his depth and remarkably feckless with it, but there was little he could have done.
Napoleon no longer left the house, and often not even his room, not bothering to shave on some days. He had grown very weak and unsteady, tripping over a rat in his room on one occasion, and fainted if he made an effort. He suffered from sweats and fevers, and vomited frequently, and by the end of the year it was clear to all around him that he was dying. Lowe refused to believe it, and kept insisting on his presence being verified by a British officer, again threatening forcible entry. Dr Thomas Arnott, surgeon of the regiment which had taken over to guard the ogre, was admitted at the beginning of April 1821; he confirmed that Napoleon was still there, and reported that there was nothing much wrong with his health.
In the last week of April Napoleon was vomiting blood and complaining of searing pain in his side. He asked for his bed to be moved to the drawing room, which had more light and air. He was growing weaker, and seemed to lose consciousness at times; on 29 April he muttered incomprehensibly about 'France', 'the army' and 'Josephine', and then about bequeathing his house in Ajaccio and the Salines to his son. On 3 May he was given extreme unction by one of his Corsican chaplains, Abbé Vignali, whom he instructed to follow the French royal tradition of the ' _chapelle ardente_ ', a lying-in-state with mass celebrated daily. By the next day he was delirious, and at around ten minutes before six on the evening of 5 May 1821 he died.
On hearing of Napoleon's death, the Italian poet Alessandro Manzoni felt a sense of shock and a powerful urge to write. He sat down and in the space of two days composed one of his greatest works, _Il Cinque Maggio_ , an ode in which he portrays the deceased emperor as a heroic and superhuman being whose death he likens to that of Christ on Golgotha, since it raises him to immortality. Goethe, who translated the ode into German, also made analogies between Napoleon and Christ, and his continuing fascination with the emperor's Promethean nature had a profound influence on his work, particularly on his masterpiece, _Faust_. Napoleon's talent for self-promotion had yielded its highest achievement.
'He was neither good nor bad, neither just nor unjust, neither mean nor generous, neither cruel nor compassionate; he was _wholly political_ ,' wrote Matthieu Molé, who had worked closely with him for years. That was as true of his death as of his life. When he felt death approaching, on 12 April Napoleon began dictating his last will and testament, which he would later laboriously copy out in his own hand, as his Code demands. It was to be much more than just a will. It expressed affection for his family, to whom he left no money, only personal mementos. It bequeathed his heart in an urn and a lock of his hair to Marie-Louise (who would refuse to accept them). It rewarded seventy-six of his most faithful friends and followers, high and low. It gave generous grants to the men who had followed him to Elba, to foreign soldiers who had fought for France, and to the wounded of Waterloo. As he did not possess a fraction of the sums necessary, he effectively turned tens of thousands of people into creditors of the French government, and therefore enemies of the Bourbons. The document is a political manifesto around which supporters of his son and the Bonaparte dynasty could unite.
It opens with a number of declarations, about himself, his family and his country, and states that he is dying, 'assassinated by the British government and its hired executioner'. He had been working on this theme from the moment he reached St Helena, representing himself as a martyr, and he was unfailingly assisted by Hudson Lowe to the very end – he was buried in a picturesque spot about a mile from Longwood, but his gravestone was left blank, because the governor would not permit any inscription suggesting imperial status, and neither Bertrand nor Montholon would allow 'General Buonaparte'.
Two years after his death, Las Cases published his _Mémorial de Sainte-Hélène_ , an account of the emperor's slow martyrdom after Waterloo, a best-seller which spread the gospel of Napoleon throughout the world. The spirit of the age was highly receptive, and poets across Europe and beyond embraced Napoleon's carefully crafted propaganda. 'Britannia! you own the sea,' wrote the German poet Heinrich Heine. 'But the sea has not water enough to wash away the disgrace that this great man bequeathed to you as he died.'
Napoleon had finally triumphed over his British enemy, and in the process he had achieved something else. From his earliest years he had sought role models and braced his ego by casting himself in the image of a Hannibal, Alexander, Caesar or Charlemagne, but after briefly considering Themistocles, he had lighted upon an entirely new model, one just as mythical as any of the others, which would gain far greater resonance than all of them put together – that of Napoleon the godlike genius who, misunderstood, betrayed and martyred by lesser men, would triumph over death and live on to haunt the imagination and inspire future generations; he had begun a new life as a myth.
# Notes
N.B. In some cases I have used different editions of the same title, because I have worked on this book in different places and the same edition was not always available
Preface
1. Franz Grillparzer, _Sämmtliche Werke_ , vol. I, Stuttgart 1872, 192–4
2. Beyle, _Vie de Napoléon_ , 1; see also Salvatorelli; Gueniffey, _Bonaparte_ , 257
3. Bodinier, 328–9; see also Lefèbvre, 207; Lignereux, 213
1: A Reluctant Messiah
1. Bailleu, I/163; Williams, 8–9
2. Staël, _Considérations_ , XIII/192–3; Bourrienne, 1831, II/216; see also Jomard, 17–18
3. Espitalier, 52; Bailleu, I/165; Dumont Romain, 2
4. _Recueil_ , 3
5. _Recueil_ , 4; Dumont Romain, 3; Staël, _Considérations_ , XIII/199; Bailleu, I/164; Gueniffey, _Bonaparte_ , 257
6. Williams, 8–9; Espitalier, 50
7. _Recueil_ , 4; Espitalier, 49
8. Mallet du Pan, II/356; Espitalier, 56–7; Bourrienne, 1831, II/216; Mallet du Pan, II/371–2
9. _Recueil_ , 6
10. Staël, _Considérations_ , XIII/199; Gueniffey, _Bonaparte_ , 310; Napoleon, _Mémoires_ , I/507
11. _Recueil_ , 7
12. Ibid., 9
13. Ibid _._ , 13
14. Ibid., 18
15. Ibid., 23
16. Bailleu, I/155
17. Ibid., 159; Bourrienne, 1831, II/219; Pontécoulant, II/489
18. Dumont Romain, 4; _Recueil_ , 25; Pasquier, I/134
19. Bailleu, I/162; Espitalier, 143–7
20. Espitalier, 62; Mallet du Pan, II/384; Bailleu, I/167
21. Waresquiel, 232
2: Insular Dreams
1. Branda, _Secrets_ , 25–7 (Gerard Lucotte's study)
2. Defranceschi, 46–60; see also Vergé-Franceschi, _Napoléon_ ; Paoli, _Jeunesse_ ; Carrington, _Portrait_ , 17; Gueniffey, _Bonaparte_ , 27
3. Vergé-Franceschi, _Paoli_ , 183–283
4. Vergé-Franceschi, _Paoli_ , 183–4, 188, 283, 295, 9; Vergé-Franceschi, _Napoléon_ , 73; Boswell
5. There are differences of opinion on the subject. See: Simiot, 5; Gueniffey, _Bonaparte_ , 29; Branda, _Le Prix_ , 19–20; Carrington, _Napoleon_ , 14, 19–20; Carrington, _Portrait_ , 11–14; Charles Napoléon, 66; Vergé-Franceschi, _Napoléon_ , 43–51, 55ff; Bartel, 17
6. There is no evidence for the story in Carrington, _Portrait_ , 15–17, 26–8; Vergé-Franceschi, _Napoléon_ , 54, 73; Paoli, 27, etc., of Carlo going to Rome and living it up there
7. Boswell, 96
8. On the alleged authorship of the proclamation, see: Carrington, _Portrait_ , 37; Paoli, 29; Vergé-Franceschi, _Napoléon_ , 76. See also: Carrington, _Napoleon_ , 78, 44–5; Vergé-Franceschi, _Paoli_ , 376; Gueniffey, _Bonaparte_ , 41
9. Paoli, 30–1; Carrington, _Portrait_ , 46, 42–3; Carrington, _Napoleon_ , 43
10. Versini, 21; Vergé-Franceschi, _Napoléon_ , 90, 95; Carrington, _Portrait_ , 43
11. Vergé-Franceschi, _Napoléon_ , 30; on stories surrounding his birth, see also: Charles Napoléon, 92; Carrington, _Napoleon_ ; Vergé-Franceschi, _Napoléon_ , 13
12. Versini, 26; Carrington, _Napoleon_ , 53–5; Defranceschi, 70
13. Vergé-Franceschi, _Napoléon_ , 107–11, 121; Carrington, _Portrait_ , 58; Versini, 33
14. Bartel, 38; Versini, 60–1; Carrington, _Portrait_ , 48
15. Carrington, _Portrait_ , 50–2
16. Paoli, 43
17. Carrington, _Portrait_ , 57, 55–6; Carrington, _Napoleon_ , 65, 78
18. Vergé-Franceschi, _Napoléon_ , 48; Versini, 86; Charles Napoléon, 98; Defranceschi, 72
19. Versini, 64; Bartel, 40–3; Charles Napoléon, 105; Carrington, _Portrait_ , 66, 72–3; Carrington, _Napoleon_ , 103
20. Larrey, _Madame Mère_ , 528–9; Masson, _Jeunesse_ , 36; Chuquet, I/50; Bertrand, _Cahiers, 1818–1819_ , 137
21. Larrey, _Madame Mère_ , 528, 530
22. Larrey, _Madame Mère_ , 529; see also: Vergé-Franceschi, _Napoléon_ , 294–5; Paoli, 45, 50; Chuquet, I/78; Defranceschi, 79–80
23. Vergé-Franceschi, _Napoléon_ , 319; Carrington, _Portrait_ , 48–9
24. The story that he travelled through Italy, related by Coston, I/17–18, has been disproved by Versini, 78–9; Marcaggi, 65; Carrington, Paoli and others
25. Masson, _Napoléon Inconnu_ , I/49
26. Defranceschi, 82
3: Boy Soldier
1. Bartel, 61; Masson, _Napoléon Inconnu_ , I/54
2. Paoli, 68–73; Chuquet, I/113–14
3. Bartel, 62–4
4. Vergé-Franceschi, _Napoléon_ , 335
5. _Some Account_ , 24; Bartel, 259; Bourrienne, 1829, I/25. Des Mazis seems to place this at the École Militaire; see also Thiard, 51–2
6. Belly de Bussy, 235; _Some Account_ , 27, 13
7. Bourrienne, 1829, I/30; Bartel, 255; Gourgaud, I/252–3
8. Napoleon, _Oeuvres_ , I/xx; _Some Account_ , 29–31; Chuquet, I/118, 129
9. Carrington, _Napoleon_ , 103; Vergé-Franceschi, _Napoléon_ , 49; Versini, 72–4; Defranceschi, 85–6
10. Vergé-Franceschi, _Napoléon_ , 50; Versini, 74–6
11. Garros, 25; Tulard & Garros, 20–1
12. Carrington, _Napoleon_ , 129; Versini, 174–6; Defranceschi, 72
13. Bertrand, _Cahiers, 1818–1819_ , 136–7
14. Napoleon, _Correspondance Générale_ , (henceforth CG), I/43–4
15. Ibid.; Lucien Bonaparte, I/24–5
16. Bartel. 87
17. Paoli, 84; Tulard & Garros, 24
18. Masson, _Jeunesse_ , 110; Chuquet, I/200–3; Bartel, 119
19. Chuquet, I/200ff.; Bartel, 107ff; Masson, _Jeunesse_ , 90–1; Bien, 69–98
20. Marcaggi, 62; CG, I/49; Pachoński, 243–6
21. CG, I/45. See also Las Cases, 1905, I/94
22. The supposedly prophetic story of Carlo crying out as he was dying that Napoleon would avenge him (Chuquet, I/212; Joseph, _Mémoires_ , I/29) can be safely dismissed
23. CG, I/47
24. Masson, _Jeunesse_ , 113
25. Bartel, 255–6
26. Ibid., 256, 258, 136
27. Ibid., 258, 257
28. Ibid., 257–8
29. Marcaggi, 67; see also Claire de Rémusat, _Mémoires_ , I/267
30. Bartel, 79, 256, 259, 261; Avallon, 10–17; Las Cases, 1905, I/95
31. Masson, _Jeunesse_ , 129, 139; see also Abrantès, I/112–13
32. Bartel, 260
4: Freedom
1. Paoli, 108–9; Simiot, 39–40
2. Las Cases, 1905, I/100
3. Bartel, 148–9, 261; Paoli, 113; Las Cases, 1905, I/102; Masson, _Napoléon et les Femmes_ , 8
4. Paoli, 112, 109; Beyle, _Vie de Napoléon_ , 28; Napoleon, _Oeuvres_ , I/xxi
5. Napoleon, _Oeuvres_ , I/37–8
6. Paoli, 102; Joseph, _Mémoires_ , I/33
7. Ibid., 32–3; Charles Napoléon, 137–8; Paoli, 128, 133
8. Paoli, 133, 138; Garros, 32; see also Branda, _Le Prix_ , 19–20
9. Napoleon, _Oeuvres_ , I/68–9; Joseph, _Mémoires_ , I/38
10. Branda, _Secrets_ , 35
11. Napoleon, _Oeuvres_ , I/55–6
12. Paoli, 163; CG, I/65; Chuquet, I/308; Napoleon, _Oeuvres_ , I/85ff
13. Paoli, 29–30, 247, 43–9
14. Ibid., 67, 237, 451
15. CG, I/67, 70; Simiot, 50; Bartel, 261
16. CG, I/68, 72, 74; Thiard, 37–8
17. Chuquet, I/357; CG, I/72–3
18. CG, I/74, 72
19. Ibid., 76; Napoleon, _Oeuvres_ , I/67, II/53 (according to Defranceschi, 20–1, the text was later heavily doctored by Napoleon)
20. Napoleon, _Oeuvres_ , II/69; Masson, _Jeunesse_ , 196
21. CG, I/77, 78–9; Coston, II/92–3
22. CG, I/81
23. Paoli, 178; Coston, 92–3
5: Corsica
1. Masson, _Napoléon Inconnu_ , II/107–15
2. Paoli, 193; Garros, 41
3. CG, I/83; Paoli, 198; Chuquet, II/103; Napoleon, _Oeuvres_ , II/70. See also Defranceschi, 126
4. Chuquet, II/129–34; CG, I/84
5. Gueniffey, _Bonaparte_ , 86; Chuquet, II/103, 109
6. Marcaggi, 134, 162, breaks this down into two events, placing the confrontation in the Olmo in July, which is almost certainly wrong; Masson, _Napoléon Inconnu_ , II/107–15
7. Masson, 105–6; Chuquet, II/110–24. The story of Napoleon making a sarcastic remark about Paoli's command at Ponte Novo can be dismissed
8. CG, I/89; Napoleon, _Oeuvres_ , II/133–5
9. Paoli, 198; CG, I/97; Napoleon, _Oeuvres_ , II/133–5
10. CG, I/100
11. Ibid., 97
12. Masson, _Jeunesse_ , II/349
13. Napoleon, _Oeuvres_ , II/225ff, 229, 231
14. Chuquet, II/217; Masson, _Jeunesse_ , II/262; Napoleon, _Oeuvres_ , II/254
15. Napoleon, _Oeuvres_ , II/243, 249, 260, 293–4
16. Masson, _Jeunesse_ , II/251
17. According to Branda, _Le Prix_ , there was money; Defranceschi, 154–5 believes Luciano left only debts; see also Gueniffey, _Bonaparte_ , 96. Joseph's story ( _Mémoires_ , I/47) that Luciano prophesied Napoleon's greatness on his deathbed can be dismissed
18. Schuermans, 11; Chuquet, II/246; Nasica, 175; Garros, 48
19. Nasica, 183–5; Marcaggi, 220–1; Chuquet, II/248
20. Gueniffey, _Bonaparte_ , 97–9 (Charles Napoléon (190) believes it was Saliceti); Chuquet, II/359–75; Nasica, 211ff.; Masson, _Napoléon Inconnu_ , II/357ff, 385; Marcaggi, 229–50; Napoleon, _Oeuvres_ , II/305
6: France or Corsica
1. Chuquet, III/90; Marcaggi, 253
2. Chuquet, III/16–18
3. Bourrienne, 1829, I/48
4. CG, I/110, 112
5. Bourrienne, 1829, I/49–50; CG, I/113; quoted in Garros, 50; CG, I/114
6. CG, I/116, 112
7. Masson, _Napoléon Inconnu_ , II/397, 394–5
8. Ibid., 397
9. CG, I/116
10. Las Cases, 1983, II/114
11. Ibid., 114–15; see also Claire de Rémusat, _Mémoires_ , I/269
12. Gueniffey, _Bonaparte_ , 102; Paoli, 302
13. Lucien Bonaparte, _Mémoires_ , I/74–6
14. Napoleon, _Oeuvres_ , II/333; CG, I/123; see also Garros & Tulard, 55
15. Defranceschi, 192ff
16. See Gueniffey, _Bonaparte_ , 108
17. CG, I/124–5, 126; Paoli, 343; Garros & Tulard, 56; Masson, _Napoleon Inconnu_ , II/426
18. See Chuquet, III/133–5; probably the leanest account is in Defranceschi, who (158–60, 210–11) believes most of it is nonsense
19. Paoli, 345–6
20. Ibid., 359–60
21. Chuquet, III/142–3; Charles Napoléon, 215
7: The Jacobin
1. Gueniffey, _Bonaparte_ , 109
2. Simiot, 69
3. Masson, _Jeunesse_ , claims he did, but as Garros, 59–62, points out, this is doubtful
4. The various possibilities are summed up in Garros & Tulard, 60–6; Schuermans, 15–17; Chuquet, III/159–61. According to Masson, _Napoléon et sa Famille_ , I/81, he wrote to the war ministry requesting promotion to lieutenant-colonel in the artillery of the navy; according to Chuquet, III/160, he requested a post in army of the Rhine. There is no trace of these letters in CG
5. Napoleon, _Oeuvres_ , II/388, 369–75
6. Gourgaud, II/273; seealso Abrantès, _Mémoires_ , I/38. For Saliceti's attitude, see Garros, 63
7. Quoted by Gueniffey, _Bonaparte_ , 126
8. Victor, 26, 30
9. Chuquet, III/176; Napoleon, _Mémoires_ , I/7–12
10. CG, I/129, 133, 136
11. Chuquet, III/194; Garros, 64; Napoleon, _Mémoires_ , I/16–17
12. CG, I/131–142; qutoed Garros, 64
13. Marmont, I/40–1
14. Masson, _Napoleon et sa Famille_ , I/83
15. CG, I/142–7; Chuquet, III/203–4
16. Coston, II/237
17. Chuquet, III/212, 213; Poupé, 64
18. Napoleon, _Mémoires_ , I/29
19. Las Cases, 1983, I/118–19; Victor, 70–1; Marmont, I/44–5
20. Quoted by Dwyer, _Napoleon_ , 143; Poupé, 92; Tulard, Fayard, Fierro, 152
21. Gueniffey, _Bonaparte_ , 133; Dwyer, _Napoleon_ , 145
22. CG, I/154
23. Chuquet, III/229–30; Coston, II/242–4, 245–50
24. Victor, 28
25. On his catching scabies, see: Gourgaud, I/302; Gueniffey, _Bonaparte_ , 169; Roberts, _Napoleon_ , 49 and 50 (note)
26. Masson, _Napoléon et sa Famille_ , I/834; Simiot, 76; Barras, I/288; Des Genettes, II/357–8; Metternich, _Mémoires_ , I/312
8: Adolescent Loves
1. Simiot, 79
2. Napoleon, _Oeuvres_ , II/399–404
3. Ibid. For his views on Robespierre, see: Casanova, 141–4; Englund, 68; Bertrand, _Cahiers, 1818–1819_ , 272; Joseph, _Mémoires_ , I/111–12
4. Napoleon, _Oeuvres_ , II/399–404; also, Gueniffey, _Bonaparte_ , 170
5. Coston, II/278–80
6. Masson, _Napoléon et sa Famille_ , I/97. For the story that Joseph had wanted to marry Désirée and been told to marry Julie instead by Napoleon, see Haegele, 72–3
7. CG, I/196
8. Coston, II/285–6
9. CG, I/197; Coston, II/292; Garros, 73; Dwyer, _Napoleon_ , 154–5
10. Gueniffey, _Bonaparte_ , 145
11. Masson, _Napoléon et sa Famille_ , I/97; CG, I/201–2
12. Las Cases, 1983, I/122
13. Garros, 75
14. Napoleon, _Mémoires_ , I/62–3
15. Gueniffey, _Bonaparte_ , 145
16. CG, I/221, 218–20
17. Marmont, I/60–1; Chastenay, 203
18. Chastenay, 203–4
19. Ibid., 206, 206–8
20. See Fraser, _Venus_ , 1–18
21. CG, I/243
22. Lavalette, 117; see also Frénilly, 235
23. Marmont, I/88; CG, I/246 (in Las Cases, 1983, I/598, he says he was horrified at the 'Babylon' and the perversions of Paris)
24. CG, I/224–6
25. Ibid., 226–7, 232–3
26. Ibid., 233–4, 235–6, 238–9, 241, 242; Marmont, I/64; see also Haegele, 76–82 and Branda, _Le Prix_ , 30–3
27. CG, I/230–1, 237–8, 235–6, 246, 248–9; Haegele, 85–6; CG, I/233
28. CG, I/248
29. On the Clary family, see Girod de l'Ain, 19
30. Girod de l'Ain, 51, 54, 55
31. CG, I/227–9
32. Ibid., 229
33. Ibid., 231–2, 232–3; Girod de l'Ain, 70; CG, I/246; Haegele, 86; Bruce, 119
34. Marmont, I/62; see also Abrantès, _Mémoires_ , I/275–6
35. Abrantès, _Mémoires_ , I/254, 265; Bourrienne, 1829, I/78–81
36. Barras, I/242, 285; Ouvrard, I/20–2; see also Masson, _Napoléon et les Femmes_ , 17
37. Pontécoulant, I/325; CG, I/244–5; 246, 248–9
38. Napoleon, _Oeuvres_ , II/442–51
39. Pontécoulant, I/326, 327–35; CG, I/254; Gueniffey, _Bonaparte_ , 151; see also Roederer, III/327
40. CG, I/254
41. Ibid., 256, 257, 258–62
42. Ibid., 262, 263
43. Ibid., 262, 268, 252; Pontécoulant, I/343–4
9: General Vendémiaire
1. CG, I/265
2. Barras, I/242
3. Napoleon, _Mémoires_ , I/80; Barras, I/250, 303 maliciously claims that Napoleon discussed with the insurgents the possibility of joining them if they would give him command. See also Cambacérès, _Mémoires_ , I/352, on his dislike of the existing authorities
4. Barras, I/250; Napoleon, _Mémoires_ , I/81
5. Napoleon, _Mémoires_ , I/84; Dwyer, _Napoleon_ , 174
6. Napoleon, _Mémoires_ , I/84–6, 523–6; CG, I/269
7. Barras, I/253–5, 261ff, 282; Dwyer, _Napoleon_ , 176; Coston, II/342–5; Dwyer, _Napoleon_ , 174; see also Pontécoulant, I/365–9
8. Barras, II/26; Marmont, I/95
9. Marmont, I/86; Coston, II/423–4; Las Cases, 1983, I/125; Gourgaud, I/254
10. Tulard, Fayard, Fierro, 380; Simiot, 98, 100–1; Dwyer, _Napoleon_ , 178
11. CG, I/271–2; Le Nabour, 60; CG, I/280, also 287, 291, 293–4
12. Barras, I/348–58; CG, I/270, 280, 281
13. Gourgaud, II/263–4; Beauharnais, I/31–2; also Hortense, I/42; Lavalette, 127–8; Napoleon, _Mémoires_ , I/87–8
14. Barras, II/56
15. Barras, II/52–3, 60, 60–1; Josephine, _Correspondance_ , 50
16. CG, I/277–8, 290, 283; Barras, II/27; Lavalette, 129; Barras, II/60. See also Bertrand, _Cahiers, 1818–1819_ , 262
17. Barras, II/58
18. CG, I/285
19. There was gossip about his having paid court to various young women at Auxonne and Valence, but no evidence, and the story that he had proposed to Panoria Permon (Abrantès, II/47) can be dismissed. See also Marmont, I/94–5
20. Coston, II/347–9. The letter is almost too good to be true in the way it expresses so graphically everything we know or can infer of Josephine's feelings and the nature of her relationship with Buonaparte, but it is hard to believe that anyone would have had the information in 1840 required to forge something so convincing. It also contradicts both Hortense, I/43 and Eugène, I/32, who state that they were against their mother remarrying. Eugène claims they saw it as 'a profanation, an insult to the memory of my father'. Napoleon himself later recalled (Gourgaud, II/264) that Eugène was for and Hortense against the match. But the time and circumstances in which they were recording events might well explain this discrepancy
21. Pontécoulant, I/335; Gueniffey, _Bonaparte_ , 168; Dwyer, _Napoleon_ , 181
22. Dwyer, _Napoleon_ , 183
23. Coston, I/438–40; Barras, II/66
24. Branda, _Secrets_ , 41–4
25. Ibid., 44
26. Joseph, _Mémoires_ , I/136; Louis Bonaparte, _Documents_ , I/47
27. Masson, _Napoléon et les Femmes_ , 17; Girod de l'Ain, 96
28. CG, I/298
10: Italy
1. Bouvier, 47; Pelleport, I/38
2. CG, I/305, 310
3. Napoleon, _Mémoires_ , I/130
4. Bodinier, 285; CG, I/305, 328; Bouvier, 19
5. Gourgaud, II/319; CG, I/304, 305
6. CG, I/303. See also Napoleon, _Mémoires_ , I/130
7. Vigo-Roussillon, 29; Pelleport, I/37–8
8. Bodinier, 297
9. Bouvier, 15, 39
10. CG, I/315
11. Collot, 10; CG, I/310
12. CG, I/318–19, 323, 326
13. Bouvier, 209–11
14. Arnault, 423
15. Bouvier, 244
16. Ibid., 254; Bulletins, 20–2
17. Bouvier, 281; De Jaeghere, 26; for Napoleon's expression of regret, see Costa de Beauregard, 336
18. De Jaeghere, 28; Bouvier, 431
19. Costa de Beauregard, 341
20. CG, I/357, 361–2
21. Collot, 13; Bulletins, 30–2; Collot, 11
22. Collot, 13; the story of a Gascon grenadier dubbing Bonaparte 'the little corporal' is almost certainly apocryphal. Most accounts, e.g. by Lejeune in Petiteau 36 or Collot 13, were written after the _Mémorial_ was published, and they probably took it from there – see Bouvier, 533–6
23. CG, I/343–5
24. Joseph, _Mémoires_ , I/61
25. Bouvier, 316–17; Collot, 14
26. CG, I/359, 357, 371–2
11: Lodi
1. See Chaptal, 296–7
2. Fugier, 35; CG, I/389
3. Bouvier, 527; Dwyer, _Napoleon_ , 213; Napoleon, _Mémoires_ , I/156–7, as usual exaggerates the number of prisoners taken and puts French losses at less than 200
4. Bouvier, 538; CG, I/392, 393; Fugier, 35; Dwyer, _Napoleon_ , 216
5. CG, I/396–7
6. Ibid., 377; Napoleon, _Mémoires_ , I/154–5; CG, I/357, 370–1
7. CG, I/398–400, 397–8; Dwyer, _Napoleon_ , 217; Bouvier, 556
8. Méneval, I/427; Bertrand, III/77; Marmont, I/322–3, 353; Costa de Beauregard, 354, 340
9. Beyle, _Vie de Napoléon_ , 3
10. Lavalette, 112; Marmont, I/22–3
11. Staël, _de l'Influence_ , 37, 48, 23–4
12. Fugier, 34–40; Marmont, I/180ff
13. Vigo-Roussillon, 34–5
14. Beyle, _Vie de Napoléon_ , 126–8
15. Bulletins, 43; Bouvier, 634–5
16. Fugier, 36; Bouvier, 589
17. CG, I/403; Coston, II/325; Miot de Melito, I/91
18. CG, I/416, 422, 443
19. Marmont, I/180–1
20. Bouvier, 538; Fugier, 38; see also Dwyer, _Napoleon_ , 225
21. Launay, 149
22. CG, I/428, 433–4
23. Ibid., 407–8, 414, 435
24. Ibid., 443, 441, 448, 451, 453
25. Arnault, 392
26. Bruce, 180
27. Chevallier & Pincemaille, 137
28. CG, I/505, 506, 505–7, 517
12: Victory and Legend
1. These and other figures in this chapter are taken from De Jaeghere and Béraud, and should be considered as approximate
2. Bulletins, 57
3. Marmont, I/314; Dwyer, _Napoleon_ , 246, 247
4. Pelleport, I/47
5. Reinhard, 207–8; Chaptal, 296–7
6. Marmont, I/296; Roguet, I/30
7. Napoleon, _Mémoires_ , I/206; Vigo-Roussillon, 37; Gourgaud, II/127; Napoleon, _Mémoires_ , I/208, 217; Pelleport, I/80
8. Reinhard, 108; CG, I/569
9. Napoleon, _Mémoires_ , I/225
10. CG, I/553
11. Josephine, _Correspondance_ , 47; CG, I/638
12. CG, I/610–13; Bulletins, 75–6; CG, I/621
13. CG, I/631–2, 447; Reinhard, 194–5
14. Fugier, 51; Gueniffey, _Bonaparte_ , 219; CG, I/664
15. Napoleon, _Mémoires_ , I/239
16. Reinhard, 167
17. Bulletins, 76
18. Gueniffey, _Bonaparte_ , 220. The number of Croats varies from 1,000 supported by two guns, to 2,000 with a battery: see also Pelleport, I/71 and Reinhard, 177
19. See Louis Bonaparte, I/59–61; Marmont, I/236–7; Napoleon, _Mémoires_ , I/248; Vigo-Roussillon 42–3. See also Reinhard, 177–8
20. Bulletins, 78–80. See also Napoleon, _Mémoires_ , I/256; Dwyer, _Napoleon_ , 250–1
21. Dwyer, _Napoleon_ , 4
22. See Dwyer, _Napoleon_ , 255–62 for coverage of this subject
23. CG, I/671, 672–3, 675–6
24. Ibid., 680, 681; Garros, 105
25. Garros, 106; Fugier, 63
26. Fugier, 52–4
27. Ibid., 54; CG, I/778–9
28. Defranceschi, 13–14; CG, I/638
29. CG, I/790, 791
30. Ibid., 834, 838, 841, 852
31. Ibid., 897, 902
32. Ibid., 917–18; Dwyer, _Napoleon_ , 292
13: Master of Italy
1. Gueniffey, _Bonaparte_ , 245; Miot de Melito, I/159; Napoleon, _Mémoires_ , I/425; Arnault, 421
2. Pontécoulant, II/470–2; Arnault, 421
3. Miot de Melito, I/159
4. Lavalette, 138
5. Miot de Melito, I/108, 184; Josephine, _Correspondance_ , 50
6. Arnault, 431; Claire de Rémusat, _Mémoires_ , I/204
7. Dwyer, _Napoleon_ , 296
8. Gueniffey, _Bonaparte_ , 230–1; Branda, _Le Prix_ , 35–7
9. Lareveillère-Lepaux, II/39–40; Bartel, 149
10. Dwyer, _Napoleon_ , 304
11. Gueniffey, _Bonaparte_ , 273–4; Branda, _Secrets_ , 159–69
12. CG, I/1058
13. Gueniffey, _Bonaparte_ , 273–4; Pontécoulant, II/474; see also Barras, III/99
14. CG, I/1071–3; Lareveillère-Lepaux, II/101ff
15. Niello-Sargy, I/4–5; Martin, I/130
16. Gueniffey, _Bonaparte_ , 333–4; Alexander Rodger, 31
17. CG, I/957–8
18. Lavalette, 170, 110; Gueniffey, _Bonaparte_ , 341; Marmont, I/295
19. Dwyer, _Napoleon_ , 337–8. 340–1; CG, I/1119
20. Pontécoulant, II/473
21. Fugier, 61–2; Pelleport, I/96
22. Miot de Melito, I/163–6, 182–4
23. Pontécoulant, II/474; Collot, 15–17; see also Casanova, 158–69
24. Gueniffey, _Bonaparte_ , 279; Pontécoulant, II/463; Barras, III/47–9, 62
25. CG, I/1081
26. Ibid., 1171; Napoleon, _Mémoires_ , I/474–5
27. CG, I/1209, 1213
28. Ibid., 1244
29. Gueniffey, _Bonaparte_ , 292; Gourgaud, I/115; Napoleon, _Mémoires_ , I/493
30. Dwyer, _Napoleon_ , 315; Lavalette, 172
31. CG, I/1249
32. Miot de Melito, I/195
33. Bourrienne, 1831, II/211
34. Lavalette, 174
35. Garros, 120
14: Eastern Promise
1. Talleyrand, _Mémoires_ , 40; Espitalier, 32–4
2. Pontécoulant, II/489–94
3. Garros, 122
4. Barras, III/138; Bailleu, I/166; Espitalier, 98
5. CG, I/1316–17; quoted by Gueniffey, _Bonaparte_ , 317; see also Espitalier, 59 and Launay, 181
6. Lareveillère-Lepaux, 339; Bailleu, I/163–4
7. Bailleu, I/165
8. Garros, 123; Gueniffey, _Bonaparte_ , 326; Bailleu, I/162, 176, 178, 182–3; Espitalier, 96; Jomard, 25; Cambacérès, _Mémoires_ , I/407; Miot de Melito, I, 230–1; see also Barras, II/136, 161
9. Arnault, 595; Napoleon, _Mémoires_ , I/509
10. Dwyer, _Napoleon_ , 326
11. Ibid., 328; Garros, 125, also Espitalier, 114–19; Bourrienne, 1831, II/234
12. Arnault, 607; Dwyer, _Napoleon_ , 328; Joseph, _Mémoires_ , I/70–1; Bourrienne, 1831, II/222–3; Espitalier, 99
13. Waresquiel, 244; Gueniffey, _Bonaparte_ , 344; Dwyer, _Napoleon_ , 339–40; Espitalier, 129, 136, 156–7, 163, also Jomard, 102 and Bailleu, I/182–3
14. Garros, 127; Lareveillère-Lepaux, 345–6
15. Launay, 192
16. Bourrienne, 1831, II/231–4; Launay, 192; Fleury, 278
17. Josephine, _Correspondance_ , 60
18. Napoleon, _Mémoires_ , I/517; see also Bourrienne, 1831, II/234, 231
19. Guitry, 6
20. Geoffroy Saint-Hilaire, 23–4; Pelleport, I/107–9
21. Guitry, 5; Gueniffey, _Bonaparte_ , 354
22. Niello-Sargy, I, 18; Moiret, 19–20; Bernoyer, 14; Espitalier, 238–9
23. Bernoyer, 20; Geoffroy Saint-Hilaire, 25
24. Arnault, 633, 621
25. Ibid., 629, 631; Des Genettes, _Souvenirs_ , 1–2; Arnault, 630
26. Miot, 13; Pelleport, I/111; Bernoyer, 33
27. Bernoyer, 17; Dwyer, _Napoleon_ , 354; Pelleport, I/112
28. CG, II/160–1
29. Lacorre, 23–4
15: Egypt
1. Pelleport, I/115; Beauharnais, I/140; Guitry, 97; also Bielecki, I/56 and Guitry, 101–2
2. Niello-Sargy, I, 58; Pelleport, I/112
3. Marmont, I/374; Millet, 55; _Copies of Original Letters_ , 75, 5
4. Guitry, 116
5. Miot, 39; Moiret, 25, 40; Pelleport, I/120–1, 115
6. Guitry, 97, 96; Vigo-Roussillon, 64; Moiret, 46
7. Gourgaud, I/244; Reiss, 248–50; Murat, _Lettres_ , I/26–7; Napoleon, _Mémoires_ , II/133
8. Guitry, 107, 111
9. Beauharnais, I/41; Moiret, 47; Guitry, 111–14; Moiret, 48
10. CG, II/195
11. CG, II/158; Josephine, _Correspondance_ , 63, 67, 69–71
12. Beauharnais, I/42; CG, II/199–200
13. Niello-Sargy, I/115; Marmont, I/389; Des Genettes, _Souvenirs_ , 6; see also CG, II/307
14. CG, II/298; Lavalette, 185; _Copies of Original Letters_ , 33; CG, II/297
15. Bulletins, 107; Guitry, 200
16. Bernoyer, 104, 76
17. Geoffroy Saint-Hilaire, 52; Andy Martin, 67; Bulletins, 108–9
18. Claire de Rémusat, _Mémoires_ , I/274
19. Pelleport, I/129, also Guitry, 150–2
20. Pelleport, I/130; Moiret, 65. See also Bernoyer, 79–80 and Guitry, 162
21. Moiret, 58, 53; Garros, 139; Lavalette, 188; Guitry, 117; Miot, 98–9; Bielecki, I/56
22. Guitry, 181
23. Bernoyer, 94, 100; Moiret, 33–4, 54; Niello-Sargy, I/194–5; Gueniffey, _Bonaparte_ , 389; Abrantès, III/69–70; Niello-Sargy, I/194–5; see also Gourgaud, I/106, 218
24. Masson, _Napoléon et les Femmes_ , 57–62; Niello-Sargy, 199–204; Napoleon, _Mémoires_ , II/158–9; Fourès, 165–6; Launay, 215; Beauharnais, I/45. For various versions of the event: Gourgaud, II/115; Bernoyer, 118–23; Garros, 140
25. CG, II/399–400, 513
26. Napoleon, _Correspondance_ , V/221
16: Plague
1. Moiret, 64, 78
2. CG, II/867; Lavalette, 109; Gueniffey, _Bonaparte_ , 411. See also Vigo-Roussillon, 81 and Des Genettes, _Souvenirs_ , 29
3. Bernoyer, 139–40; Guitry, 250–1
4. Bernoyer, 142–3; Pelleport, I/140
5. Millet, 83; Niello-Sargy, I/253–7; Bernoyer, 146; Guitry, 266; Lacorre, 90
6. Des Genettes, _Souvenirs_ , 15; Miot, 145–7; Vigo-Roussillon, 83–4
7. Gueniffey, _Bonaparte_ , 419–23
8. Des Genettes, _Histoire Médicale_ , 49–50; Garros, 143; Geoffroy Saint-Hilaire, 87; Dwyer, _Napoleon_ , 424
9. CG, II/872–3; Gueniffey, _Bonaparte_ , 425; Bernoyer, 153
10. Gueniffey, _Bonaparte_ , 395; CG, II/874
11. Gueniffey, _Bonaparte_ , 424; Bernoyer, 153
12. Des Genettes, _Souvenirs_ , 17
13. Bernoyer, 163–4. His later claim that he was intending to take Constantinople and come at Austria through the Balkans, or become a Muslim and lead an army to India can be dismissed as the hot air of an ageing bore
14. CG, II/910–16, 920; Napoleon, _Mémoires_ , II/560–1
15. Beauharnais, I/64; Pelleport, I/155
16. Vigo-Roussillon, 87; Bernoyer, 180–1; Niello-Sargy, I/295 says Bonaparte suggested it but doesn't confirm it was carried out at Acre, and reports what he heard about events at Jaffa, 319–23; Marmont, II/12, defends Bonaparte's action; Larrey, in Guitry 317–19, claims all the wounded were evacuated; Pelleport, I/156, claims the wounded and sick were evacuated on boats from Jaffa; Lavalette, 215, says the whole story is an atrocious calumny; see also _Documents particuliers_ , 120–2; Bernoyer, 164–5, who claims to have had the story from Desgenettes himself, thought it praiseworthy; Bourrienne, 1831, II/336–40, is typical, admitting he never saw anything but making various claims. According to Bonaparte (Las Cases, 1983, I/150–2), there were only seven men involved
17. CG, II/918–21; Lavalette, 215. See also Bourrienne, 1831, II/335 and Niello-Sargy, I/291–99
18. Millet, 128–9
19. Dwyer, _Napoleon_ , 437; Gueniffey, _Bonaparte_ , 431, estimates it was one-fifth. On opinions of those who lamented Napoleon's decision to march out of Egypt, see for instance, Lavalette, 217
20. Niello-Sargy, I/306–7; Bernoyer, 168; Vigo-Roussillon, 89 claims it fooled nobody
21. CG, II/849, 941
22. Ibid., 952–4, 972, 1032, _passim_
23. Niello-Sargy, I/324–7
24. Englund, 131
25. CG, II/1042
26. Vigo-Roussillon, 96–7, 91, 101; Guitry, 342
27. See Guitry, 354–5 for the classic version, propounded by Bonaparte himself; Niello-Sargy, I/343–57; For a full discussion of this see Gueniffey, _Bonaparte_ , 437–42
28. Launay, 222, erroneously claims she sailed with him; see also Masson, _Napoléon et les Femmes_ , 62–3 and Gueniffey, _Bonaparte_ , 442
29. Vigo-Roussillon, 102
30. Guitry, 361
31. Launay, 224
32. Denon, 340; Bourrienne, 1829, III/7–8; Lavalette, 221
33. Launay, 225
34. Carrington, _Portrait_ , 82; Le Nabour, 70–1; Denon, 340–1; Méneval, I/11
17: The Saviour
1. Gueniffey, _Bonaparte_ , 453; Marmont, II/51–2; Raza, 24
2. Boulart, 67–8
3. Coston, I/511; Marbot, I/45–8
4. Barante, I/44; Béranger, 70; Dwyer, _Napoleon_ , 462; Tulard, _Brumaire_ , 67
5. Molé, 122
6. Barante, I/40
7. Andigné, I/404; Barante, I/44; Ségur, _Histoire_ , II/1
8. McMahon, 109, 77, 97
9. Dwyer, _Napoleon_ , 458–61
10. Thibaudeau, 1
11. Chastenay, 311; Tulard, _Brumaire_ , 79
12. Gueniffey, _Bonaparte_ , 448; Vandal, _l'Avènement_ , I/244; CG, II/1089
13. Collot, 20; Vandal, _l'Avènement_ , I/244; Gueniffey, _Bonaparte_ , 459
14. Masson, _Napoléon et sa Famille_ , I/259–60; see also Le Nabour, 74–5
15. Barras, IV/31–3; Bourrienne, 1829, III/38, claims it was him; Collot, 33, gave him similar advice
16. Bourrienne, 1829, III/37, insists Bonaparte would not let her in for three days
17. Cambacérès, _Mémoires_ , I/429–31
18. Fouché, 1957, 61
19. Vandal, _l'Avènement_ , I/233
20. Ibid., 258
21. See Bourrienne, 1829, III/43–6
22. Gueniffey, _Bonaparte_ , 465; Tulard, _Brumaire_ , 88–90; Joseph, _Mémoires_ , I/77
23. Vandal, _l'Avènement_ , I/272–4
24. See Lavalette, 228–32
25. Talleyrand, _Mémoires_ , 49–50; Arnault, 748
26. Vandal, _l'Avènement_ , I/292–3; Lavalette, 227–8; Lucien Bonaparte, I/297; Gueniffey, _Bonaparte_ , 469; see also Thibaudeau, 3
27. Vandal, _l'Avènement_ , I/293–4; Tulard, _Brumaire_ , 103
18: Fog
1. Vandal, _l'Avènement_ , I/304
2. Ibid., 305; see also Barras, IV/70–2 and Bourrienne, 1831, III/68–9
3. Vandal, _l'Avènement_ , I/314
4. Ibid., 316
5. Ibid., 317
6. Ibid., 325; Gueniffey, _Bonaparte_ , 479
7. Vandal, _l'Avènement_ , I/337–9, 344
8. Ibid., 340–3
9. Tulard, _Brumaire_ , 127; Tulard, _Fouché_ , 115–16; also, Bourrienne, 1831, III/82; Savary, I/241; Fouché, 1957, 79
10. Dwyer, _Napoleon_ , 491; Tulard, _Brumaire_ , 128
11. Vandal, _l'Avènement_ , I/364
12. Joseph, _Mémoires_ , I/79
13. Vandal, _l'Avènement_ , I/367; Gueniffey, _Bonaparte_ , 483; Girardin, I/170; Napoleon, _Mémoires_ , II/561; Bourrienne, 1829, III/83–5
14. Vandal, _l'Avènement_ , I/371–2; see also Bourrienne, 1829, III/91
15. Vandal, _l'Avènement_ , I/373–5
16. Ibid., 378
17. Ibid., 381
18. Ibid., 386–7
19. Ibid., 387–9; according to Lucien Bonaparte, I/365, Bonaparte shouted, 'And if they resist, kill! kill!'
20. Dwyer, _Napoleon_ , 503; one hundred according to Tulard, _Brumaire_ , 146; eighty according to Collot, 28
21. Lentz, _Le Grand Consulat_ (henceforth GC), 83–4
22. Vandal, _l'Avènement_ , I/394–9; on Brumaire, see also Cambacérès, _Mémoires_ , I/433–47; Roederer, III/296–306; Napoleon, _Mémoires_ , II/367–401
23. Vandal, _l'Avènement_ , I/393
24. Tulard, _Brumaire_ , 153–4
25. Vandal, _l'Avènement_ , I/276
26. Bourrienne, 1829, III/105–6; Lentz, GC, 13
27. Vandal, _l'Avènement_ , I/400–1; also Bourrienne, 1831, III/105–8 and Abrantès, II/383
19: The Consul
1. Roederer, III/2–3
2. Napoleon, _Mémoires_ , II/405; Cambacérès, _Mémoires_ , I/442
3. Napoleon, _Mémoires_ , II/411–12; Garros, 157
4. Napoleon, _Mémoires_ , II/405–7; Fouché, 1957, 85; Cambacérès, _Mémoires_ , I/490; Gueniffey, _Bonaparte_ , 507; Tulard, _Brumaire_ , 157
5. Fouché, 1957, 87; Cambacérès, _Mémoires_ , I/443–4; Roederer, III/320–1; CG, II/1094
6. Lentz, GC, 196
7. Bourrienne, 1829, III/129–32
8. Napoleon, _Mémoires_ , II/433
9. Fouché, 1957, 90; Napoleon, _Mémoires_ , II/436; Tulard, _Brumaire_ , 155
10. Napoleon, _Mémoires_ , II/439
11. Garros, 159; Lentz, GC, 109; Lareveillère-Lepaux, II/423; Napoleon, _Mémoires_ , II/438
12. Tulard, _Napoléon ou le mythe_ , 120; Lentz, GC, 164; see also Gueniffey, _Bonaparte_ , 525
13. Boudon, _Histoire_ , 50; Lentz, GC, 112
14. Lentz, GC, 112
15. Ibid., 119
16. Garros, 160
17. Roederer, III/305–6
18. Chaptal quoted in Boudon, _Histoire_ , 55; Bourrienne, 1829, III/129–32
19. Ernouf, 217
20. Fouché, 1957, 48, 97; Cambacérès, _Mémoires_ , I/469
21. Bouillé, I/405–6; Lentz, GC, 166
22. Lentz, GC, 153–4, 159–61
23. Hauterive, _Napoléon et sa Police_ , 143, 197; Tulard, _Napoléon ou le mythe_ , 136
24. Healey, _The Literary Culture of Napoleon_ , Appendix B
25. Defranceschi, 14–25
26. Waresquiel, 284; Lentz, GC, 101
27. Hyde de Neuville, I/269
28. Andigné, I/414–16, 417–18, 420; Hyde de Neuville, I/270–2
29. CG, II/1118–19; Tulard, _Napoléon ou le mythe_ , 132, 134; Lentz, GC, 322
30. Mollien, I/24; Dumas, III/168; Molé, 174; Ségur, _Histoire_ , II/1–2
20: Consolidation
1. Cambacérès, _Mémoires_ , I/470
2. Garros, 163–4; Barante, I/54; Cambacérès, _Mémoires_ , I/488; Lentz, GC, 209; Thibaudeau, 2–7; Chastenay, 297
3. Hortense, I/69
4. Garros, 164; see also Bourrienne, 1829, IV/3
5. Cambacérès, _Mémoires_ , I/464; Roederer, III/335
6. Molé, 175
7. Claire de Rémusat, _Mémoires_ , I/103–4; Staël, _Considérations_ , XIII/194
8. Fain, _Mémoires_ , 291; Chaptal, 195; Chuquet, III/233–4; Saint-Denis, 170; Abell, 235
9. Choiseul-Gouffier, 100; Abrantès, III/194, 363; Staël, _Considérations_ , XIII/195, 206–7; Marmont, I/297; Claire de Rémusat, _Mémoires_ , I/101–2, 116–17, 112; Saint-Elme, 354; Bourrienne, 1829, XIII/228
10. Beugnot, I/457
11. Lentz, GC, 359; Las Cases, 1983, II/304–5; Thiard, 41; Bigarré, 152; Claire de Rémusat, _Mémoires_ , I/224
12. Molé, 137, 243
13. Roederer, III/302–3
14. Lucien Bonaparte, I/384; Masson, _Napoléon et sa Famille_ , I/319
15. Fontaine, _Journal_ , I/7; Fontaine, _Les Maisons_ , 318–19, 330
16. Chaptal, 329; Fain, _Mémoires_ , 287–9
17. CG, II/1099, 1106; Fain, _Mémoires_ , 289, 456–9; Chaptal, 225; Fleury de Chaboulon, III/176; see also Bourrienne, 1829, IV/60–1
18. Molé, 158
19. Las Cases, 1983, I/416, 652, 618–19; Las Cases, 1905, II/567; Thiard, 33–4
20. Abrantès, _Roman Inconnu_ , xv; Bourrienne, 1829, IV/36–7
21. Thibaudeau, 14–16
22. Rousseau, 25, 141
23. Gueniffey, _Bonaparte_ , 625
24. Rousseau, 106; Roederer, III/334
25. Constant, _Journal Intime_ , 224
26. Lentz, GC, 428; Lefèbvre, 84
27. Lentz, GC, 156
28. Thibaudeau, 69
29. Lentz, GC, 132
30. Garros, 158
31. Lentz, GC, 97; Andigné, I/407; Hyde de Neuville, I/252
32. Bailleu, I/357; Barante, I/50–1
21: Marengo
1. CG, II/1114–15
2. CG, III/43–4; Lentz, GC, 220; Rose, 14, 288–9
3. Guitry, 362–3, 366–8; Savary, I/183; Pelleport, I/163; Moiret, 119–22; Des Genettes, _Souvenirs_ , 37; Alexander Rodger, 131; Napoleon, _Mémoires_ , III/247; see also Las Cases, 1983, II/169–72
4. CG, III/241, 308; Tombs, 394
5. Méneval, I/88–93; see also Lucien Bonaparte, I/377
6. Lentz, GC, 227; Cambacérès, _Mémoires_ , I/474; CG, III/98, 41, 120; Gueniffey, _Bonaparte_ , 547
7. CG, III/148
8. Gueniffey, _Bonaparte_ , 550
9. CG, III/216; Gueniffey, _Bonaparte_ , 548
10. CG, III/168–70; Garros, 169–70
11. CG, III/222; Cambacérès, _Mémoires_ , I/522
12. Napoleon, _Mémoires_ , III/37
13. CG, III/235, 238
14. Napoleon, _Mémoires_ , III/38; Griois, I/120
15. Bourrienne, 1829, IV/91–2; Napoleon, _Mémoires_ , III/39, 40; Savary, I/253–4; CG, III/271
16. CG, III/278
17. Bulletins, 136; Masson, _Napoléon et les Femmes_ , 84; Gourgaud, I/217, II/92, claims it was after Marengo
18. CG, III/300
19. Lentz, GC, 234
20. Victor, 179
21. Savary, I/265–80; Marmont, II/125–36; Napoleon, _Mémoires_ , III/33–69; Victor, 160–89
22. CG, III/301
23. Ibid., 303, 312
24. Ibid., 318
25. Bulletins, 145, 147
26. Lentz, GC, 230
27. Josephine, _Correspondance_ , 101
28. Lentz, GC, 377–8
29. Cambacérès, _Mémoires_ , I/524
30. Roederer, III/330–1
31. Savary, I/313; Lentz, GC, 261; Cambacérès, _Mémoires_ , I/530
22: Caesar
1. Bertrand, _Lettres_ , 29
2. CG, III/386; Waresquiel, 320–1; see also Tulard, _Fiévée_ , 126–7; Cambacérès, _Mémoires_ , I/714; Remacle, 368; Westmorland, I/50ff; Méneval, I/226–32; Bourrienne, 1829, V/107–8; Miot de Melito, II/157–8; Desmarest, 273–4; Masson, _Napoléon et sa Famille_ , I/323
3. Girardin, I/189; see also Roederer, III/336
4. Desmarest, 33
5. Ségur, _Un aide de camp_ , 47
6. Hauterive, _Napoléon et sa Police_ , 48
7. Castanié, 231; Réal, I/359
8. Mollien, I/221–2
9. Bergeron, 29
10. Branda, _Secrets_ , 70–6; see also Saada, 25–49
11. Cambacérès, _Mémoires_ , I/567
12. Thibaudeau, 77; Lentz, GC, 370–1; Pelet de la Lozère, 8; Roederer, III/382
13. Rapp, 20; Thibaudeau, 257; Las Cases, 1983, I/207
14. Thibaudeau, 77; Molé, 411–12; Roederer, III/382; Lucien Bonaparte, I/373
15. Pelet de la Lozère, 11; Méneval, I/412–21
16. Gueniffey, _Bonaparte_ , 567; Lafayette, V/248, also 117, 138, 143–4, 146–7, 153
17. Thibaudeau, 152; Casanova, 26–8; Gourgaud, I/323; Bourrienne, 1829, IV/276–81; Las Cases, 1983, I/688–9
18. Pelet de la Lozère, 223; Roederer, III/335; CG, V/882
19. Tulard, _Fouché_ , 159
20. Lentz, GC, 264–6; see also Lucien Bonaparte, I/421–32
21. Chastenay, 310; Masson, _Napoléon et sa Famille_ , I/335; Lucien Bonaparte, I/385–6
22. Tulard, _Napoléon ou le mythe_ , 157; Espitalier, 292–3
23. Cambacérès, _Mémoires_ , I/535–7; Decaen, II/292; Claire de Rémusat, _Mémoires_ , I/192; Abrantès, II/372–3
24. Castanié, 17–18; Sparrow
25. Marquis, 211, 257–8; Castanié, 26–7
26. Barante, I/72
23: Peace
1. Gueniffey, _Bonaparte_ , 601
2. CG, III/588
3. Ibid., 664–5
4. Bertaud, Forrest & Jourdan, 40; Uglow, 282; CG, III/509, 136
5. Las Cases, 1905, II/516; Cornwallis, 406; Grainger, 60
6. CG, III/913–16; Joseph, _Mémoires_ , I/231; see also Cornwallis, 389–90
7. Josephine, _Correspondance_ , 110
8. Méneval, I/132, 145
9. Raza, 188
10. Méneval, I/142; Bigarré, 128; Gueniffey, _Bonaparte_ , 603; Ségur, _Un aide de camp_ , 70–1; see also Abrantès, IV/326–62
11. Gueniffey, _Bonaparte_ , 571; Josephine, _Correspondance_ , 121–2
12. Bonaparte, CG, III/71–2, regarded the treaty as not favourable enough; Masson, _Napoléon et sa Famille_ , II/96–7; Lucien Bonaparte, II/107, 113, 122, 219
13. Staël, _Dix Années_ , 65
14. Ibid., 18; Girardin, I/236
15. Lafayette, V/164; Lentz, GC, 317
16. Consalvi, 100–1; Lentz, GC, 311
17. Consalvi, 130–6, 147, 151–7, 342ff
18. Lentz, GC, 320
19. Fugier, 121
20. Ibid., 122
21. Ibid., 124
22. Ibid., 25
24: The Liberator of Europe
1. Grainger, 50–2; Uglow, 282; Bouillé, II/468; Tombs, 396
2. Roederer, III/430
3. Gueniffey, _Bonaparte_ , 669
4. Las Cases, 1983, I/690
5. Thibaudeau, 13; see also Bourrienne, 1829, IV/280
6. Lentz, GC, 330
7. Ibid., 332–3; Bartel, 254; Charles Napoléon, 224; CG, III/1178
8. Lentz, GC, 448
9. Napoleon, _Vues Politiques_ , 211–13, 228; Ségur, _Histoire_ , II/233–4; Lentz, GC, 450
10. Réal, I/38–9
11. Lentz, GC, 347
12. Murat, _Lettres_ , II/30; Remacle, 30–1; Gueniffey, _Bonaparte_ , 670
13. Lucien Bonaparte, II/107
14. Thibaudeau, 237
15. Lentz, GC, 339; Molé, _Souvenirs_ , 234–7
16. Lentz, GC, 340
17. Ibid.
18. Josephine, _Correspondance_ , 97; Masson, _Napoléon et sa Famille_ , II/150ff
19. Josephine, _Correspondance_ , 98–100; Chevallier & Pincemaille, 312–13
20. Lentz, GC, 341; Lentz, _Nouvelle Histoire du Premier Empire_ (henceforth NHPE), I/59; Gueniffey, _Bonaparte_ , 675
21. Lafayette, V/199
22. Cornwallis, 406
23. Lefèbvre, 144
24. Ibid., 123
25. Gueniffey, _Bonaparte_ , 680
26. Miot de Melito, I/317–18; Girardin, I/286
27. Fain, _Mémoires_ , 224–6; Méneval, III/43; Chevallier & Pincemaille, 303
28. Fontaine, I/26–8, 38, 53; Divova, 51, 72, 88, 128; Fiszerowa, 245–6; Pamiętnik Stanisława Zamoyskiego, in Biblioteka Uniwersytetu Adama Mickiewicza, etc, p. 200; Berry, 163
29. Edgeworth, 55; Greathead, 11–13, 55–6; Farington, 1906; Fiszerowa, 245–6; Burney, 271
30. Sédouy, 36
25: His Consular Majesty
1. Alger, 53; Grainger, 81–2
2. Cambacérès, _Mémoires_ , I/569
3. CG, III/1225
4. Thibaudeau, 120–1
5. Branda & Lentz, 19–22, 192
6. CG, III/600; Branda & Lentz, 120
7. Branda & Lentz, 84–5
8. Ibid., 168; Gourgaud, I/278
9. Branda & Lentz, 72–3, 86–7; CG, III/853–4
10. Roederer, III/334; CG, III/837–43, 850–1, 1227
11. CG, III/957–8; Branda & Lentz, 131
12. Branda & Lentz, 139–40
13. Ibid., 171; see also Napoleon, _Mémoires_ , III/259–76; Las Cases, 1905, II/522–3; Gourgaud, I/278
14. Alexander Rodger, 287
15. Cambacérès, _Mémoires_ , I/680; Grainger, 147, 161; for the plots against Bonaparte, see also: Desmarest, 10; Marquis and Sparrow
16. Marquis, 135, 142ff; quoted in Lentz, GC, 297
17. Grainger, 125; CG, IV/30–2
18. Grainger, 153, 160
19. Ibid., 171, 175, 185
20. CG, IV/122, 127, 131–2, _passim_ ; see also Girardin, I/291–5
21. Miot de Melito, II/73; Grainger, 188–9; Browning
22. Thibaudeau, 21; Hortense, I/326
23. Versini, 118–19
24. Thibaudeau, 391–2; see also Bourrienne, 1829, III/214; Lentz, GC, 401–2
25. Branda & Lentz, 181; Grainger, 184–5
26. Alexander Rodger, 293; Miot de Melito, II/119–20
26: Towards Empire
1. Uglow, 340–5. Many managed to avoid arrest through their connections, and while some were locked up in fortresses, most remained on parole and continued to enjoy the pleasures of Paris; Fontaine, II/63
2. Tulard & Garros, 244; CG, IV/291ff, 426–7, 448; Claire de Rémusat, _Mémoires_ , I/285
3. Lentz, GC, 517–18
4. Uglow, 335ff, 367–71; Zamoyski, _Phantom Terror_ , 58–75
5. Branda & Lentz, 164–7
6. Masson, _Napoléon et sa Famille_ , II/229–33
7. Ibid., 241; CG, IV/439
8. George, 81, 95, 116–17, 126; Claire de Rémusat, _Mémoires_ , I/206, II/88; Roederer, III/332
9. CG, IV/439; Josephine, _Correspondance_ , 137
10. Lentz, GC, 518
11. CG, IV/583–8, 594, 598, 601, 604–5, 610–12, 616, 621–7, etc.; Tulard, _Fouché_ , 203ff; Lentz, GC, 514–15
12. Lentz, GC, 532; Claire de Rémusat, _Mémoires_ , I/33–4; Thibaudeau, 322–3; Ségur, _Un aide de camp_ , 80
13. Lentz, GC, 538, 530–1; Desmarest, 102
14. Lentz, GC, 538
15. Méneval, I/264; Desmarest, 99; see also Girardin, I/322–35; Cambacérès, _Mémoires_ , I/738; Lentz, GC, 510–11, 517; Raza, 208; see also CG, IV/646–7
16. CG, IV/633–4; Pasquier, I/178, 200; Desmarest, 116–25; Waresquiel, 320–34; Talleyrand, _Mémoires_ , 62–5; Bertrand, _Cahiers, 1818–1819_ , 248; Fouché, 1957, 135; Méneval, I/305–6; Cambacérès, _Mémoires_ , I/711–12; Lentz, GC, 543
17. Garros, 215
18. Lentz, GC, 540–1
19. Joseph, I/97–9; Ségur, _Un aide de camp_ , 94–7
20. Savary, I/48–65, 337–479; Murat, _Lettres_ , III/83–103
21. Savary, I/66; Méneval, I/298–9; Cambacérès, _Mémoires_ , I/711–12; Las Cases, II/1983, 627; Beauharnais, I/91
22. CG, IV/646; Murat, _Lettres_ , III/90
23. Lentz, GC, 550
24. Ibid., 557
25. Waresquiel, 324; Pasquier, I/200; Barante, I/118, attributes the line to Boulay de la Meurthe
26. Quoted by Waresquiel, 334; Tulard, _Fouché_ , 199
27. Claire de Rémusat, _Mémoires_ , I/345–6
28. Jourdan, _Mythes_ , 25
29. Lentz, GC, 521
30. Thibaudeau, 234; Ernouf, 228; Méneval, I/99
31. Boudon, _Histoire_ , 146; Lentz, GC, 562
32. Lentz, GC, 562
33. Roederer, III/461; Cambacérès, _Mémoires_ , I/720; Thibaudeau, 462
34. Lentz, NHPE, I/25
35. Miot de Melito, II/194
36. Lentz, GC, 573
27: Napoleon I
1. NA, Jackson Papers, FO 353/18, p. 15; Bailleu, I/273; CG, IV/769; Cambacérès, _Mémoires_ , I/756
2. Boudon, _Histoire_ , 239
3. Vigo-Roussillon, 133; Rapp, 5, 12–13; Durand, 49
4. Pelleport, I/200; Davout, I/79; Murat, _Lettres_ , III/90; see also Marmont, II/226
5. On the suicide/murder issue, see: J-F Chiappe, _Georges Cadoudal et la liberté_ , 1970; E. Erlannig, _La résistance bretonne à Napoléon Bonaparte_ , 1980; B. Saugier, _Pichegru. De la gloire de la Hollande à la prison du Temple_ , Strasbourg 1995; Lentz, GC, 554
6. Quoted in Boudon, _Histoire_ , 238
7. Miot de Melito, II/166
8. Bouillé, 487–95, 531; Cambacérès, _Mémoires_ , II/10
9. Jourdan, _Napoléon_ , 27–31
10. Ségur, _Un aide de camp_ , 68, 93, 75, 103
11. Morrissey, 2, 140–1; Burney, 273
12. McMahon, 122–3; Las Cases, 1983, I/568
13. Waresquiel, 306
14. Thiard, 40
15. Boudon, _Histoire_ , 153
16. Napoleon, _Vues Politiques_ , 58; Lentz, GC, 585; Lentz, NHPE, I/57–9; see also Tulard, _Sacre_ , xix
17. See Lentz, NHPE, I/74; Tulard, _Sacre_ , xix; Jourdan, _Napoléon_ , 190
18. Lentz, GC, 416–18, 421ff
19. CG, IV/775
20. Ibid., 774, 780; Ségur, _Un aide de camp_ , 104
21. Pouget, 64–5
22. CG, IV/794
23. Ibid., CG, V/583–4; Las Cases, 1983, I/411–13; Cambacérès, _Mémoires_ , I/564–5; Bausset, I/49–50; Savary, II/10–11; Mollien, I/404; Claire de Rémusat, _Lettres_ , I/112, 139–40; Miot de Melito, II/128, 214; Bertrand, _Lettres_ , 29ff; Puget, 64; Bailleu, I/59–60; Méneval, I/411–14; Campbell, 228–30; Rose, 114ff, 129–31, 145ff
24. Marmont, II/226
25. Bailly, 589; Miot de Melito, II/241; see also Claire de Rémusat, _Mémoires_ , I/245 and Fouché, 1957, 156
26. CG, IV/828, 837
27. Ibid., 856–7, 886; Méneval, I/379
28. Masson, _Napoléon et sa Famille_ , II/344, 363; Bailleu, II/301
29. Masson, _Napoléon et sa Famille_ , II/354; Hortense, _Mémoires_ , I/229; Masson, _Napoléon et sa Famille_ , II/398
30. Masson, _Napoléon et sa Famille_ , II/397–9, 400–1, 448–9, 451–2, 454–5; Miot de Melito, II/235–7; Hortense, I/165, 397–9
31. Masson, _Napoléon et sa Famille_ , III/94–5
32. Ibid., II/451–2
33. Roederer, III/511; Hortense, II/58–9, 88–9; Chevallier & Pincemaille, 282
34. Fontaine, II/87; Charles de Rémusat, 50; see also Tulard, _Sacre_
35. Claire de Rémusat, _Mémoires_ , II/71
36. Ibid., 71–2; Boulart, 124; Bailly, 591
37. Frénilly, 296–7; Miot de Melito, II/245; see also Lentz, NHPE, I/94
38. Barrès, 14
28: Austerlitz
1. CG, V/21
2. Ibid., 20–1
3. Masson, _Napoléon et sa Famille_ , II/17
4. Claire de Rémusat, _Lettres_ , I/65–6; Fain, _Mémoires_ , 230
5. CG, V/274
6. Bigarré, 155–6; Avrillon, I/186
7. CG, V/22
8. Boudon, _Le roi_ , 109
9. Skowronek, 94; see also Cambacérès, _Mémoires_ , II/39
10. CG, V/197–208, 343, 459–62, 400, 415, 570; Pelet de la Lozère, 195
11. Miot de Melito, II/259; CG, V/530, 565–7
12. CG, V/601, 607, 618
13. Bigarré, 162; Raymond de Montesquiou, 32–4, 103
14. Bausset, I/87; Barrès, 51; CG, V/797; Raza, 227–8
15. CG, V/808
16. Comeau de Charry, 205, 207; Raymond de Montesquiou, 69
17. Comeau de Charry, 208, 219; Pouget, 85
18. CG, V/850
19. Ibid., 837
20. Joseph, _Mémoires_ , I/314, 291, 311, 317, 304; see also Cambacérès, _Lettres_ , I/287ff, 308; Cambacérès, _Mémoires_ , II/51; Claire de Rémusat, _Lettres_ , I/384, 394
21. Ségur, _Un aide de camp_ , 157
22. CG, V/866–7; Ségur, _Un aide de camp_ , 157–60; Savary, II/174–98
23. CG, V/869
24. Malye, 24; Ségur, _Un aide de camp_ , 165–7; Bulletins, 205–6; Barrès, 55; Fantin des Odoards, 71; Marbot, I/258–9
25. Barrès, 55–6; Lejeune, I/35–6
26. Lentz, NHPE, I/188
27. CG, V/876; Lentz, NHPE, I/189; Tulard, _Napoléon ou le mythe_ , 185
28. Lentz, NHPE, I/192–3
29. CG, V/873–4; Lentz, NHPE, I/193; Ségur, _Un aide de camp_ , 178
30. Méneval, I/452–7; Savary, I/320–3; CG, V/875; Hartley, 74
31. Waresquiel, 351; Dumonceau, I/145–7; Ligne, _Fragments_ , II/114
32. Archives Caulaincourt, AN, 95 AP 34, annexe no 2 (henceforth Annexe 2)
33. Cambacérès, _Lettres_ , I/319; Claire de Rémusat, _Lettres_ , I/384–94
29: The Emperor of the West
1. Branda, _Le Prix_ , 259–80; Joseph, _Mémoires_ , I/314, 219, 311
2. Quoted in Lentz, NHPE, I/199
3. Branda, _Le Prix_ , 279–80
4. Pelet de la Lozère, 236; Molé, I/59–60; Fain, _Mémoires_ , 92–3
5. Fain, _Mémoires_ , 114; Branda, _Secrets_ , 92–4, 97
6. Chaptal, 337; Lavalette, 256; Mollien, II/150
7. Pelet de la Lozère, 7; Molé, I/55
8. Lentz, NHPE, I/94; Pelet de la Lozère, 155, 162–3, 166, 170; Molé, I/55; Bergeron, 46
9. Pelet de la Lozère, 187, 213–18; Molé, I/96–7
10. Las Cases, 1983, I/408
11. Fain, _Mémoires_ , 3, 6–7
12. Ibid., 10–11
13. Ibid., 41–55
14. Ibid., 39–40
15. Ibid., 62–3, 109; Bausset, I/3
16. Fain, _Mémoires_ , 202, 180
17. Avrillon, I/121–3, 196–8, 204–5, 375–6; Hortense, I/202, 207–8, 209–11; Fain, _Mémoires_ , 307; Revel; Claire de Rémusat, _Mémoires_ , III/333; Masson, _Napoléon et les Femmes_ , 166–70
18. Méneval, I/424
19. Lentz, NHPE, I/232
20. Cambacérès, _Mémoires_ , II/89
21. Las Cases, 1983, I/583
22. Molé, I/60; see also Lucien's conversation in Masséna, V/146
23. Fouché, 1957, 155
24. Barante, I/274–5; Masson, _Napoléon et sa Famille_ , VI/36
25. Cambacérès, _Mémoires_ , II/93; Bausset, I/14, 68; Fain, _Mémoires_ , 293–4; Avrillon, I/251
26. Lentz, NHPE, III/423
30: Master of Europe
1. Bailleu, I/505, 561; CG, VI/724
2. Annexe 2; CG, VI/826–8
3. CG, VI/826–8; Annexe 2
4. Annexe 2
5. CG, VI/823–4
6. Bodinier, 347–9; Lentz, NHPE, I/247–255
7. CG, VI/1032; Boulart, 138; Coignet, 127; Savary, II/310
8. Napoleon, _Mémoires_ , III/281–2; Savary, II/292; Raza, 175–6
9. Annexe 2; Savary, II/300
10. Metternich, _Mémoires_ , I/54
11. CG, VI/190
12. Ibid., 909, 924, 1078; Byrne, II/40; Tulard & Garros, 317
13. Murat, _Lettres_ , IV/483, 488
14. Ibid., V/64–5; CG, VI/1213; Potocka, 102
15. Barrès, 79; Raymond de Montesquiou, 163; Rumigny, 35–6; Berthezène, I/118
16. Annexe 2; Raymond de Montesquiou, 168
17. Potocka, 122; Savary, III/26; Boulart, 147
18. Potocka, 120; Kicka, 98
19. CG, VII/27, 46, 52, 63–4, 97, 102
20. Ibid., 105, 111; see also Trembicka, II/38
21. CG, VII/116, 118–19, 126, 127, 129–30, 132–3, _passim_ ; Sutherland, 108
22. Rapp, 106; Waresquiel, 365; Comeau de Charry, 281
23. Coignet, 143, 136; Wołowski; see also Berthezène, I/123ff
24. CG, VII/176, 191; Bodinier, 349–50; Lentz, NHPE, I/275; Raymond de Montesquiou, 464; Rumigny, 44
25. CG, VII/472
26. Potocka, 146–9
27. Sutherland, 126–8; CG, VII/531; Constant Wairy, I/417
28. Bodinier, 349–50; Rothenberg, _Emperor's_ , 48; Lejeune, 1/81
29. Hartley, 76
30. CG, VII/916; Coignet, 148; Rumigny, 48; Masson, _Napoléon et sa Famille_ , IV/93–4
31. Lentz, NHPE, I/306; see also Raza, 151; Radziwiłł, 255, 268–86
31: The Sun Emperor
1. Claire de Rémusat, _Lettres_ , II/88, 105–6; Metternich, _Mémoires_ , I/57
2. Driault, _Tilsit_ , 241, 209; Lentz, NHPE, I/348; Bergeron, 85; Fouché, 1957, 160
3. Pontécoulant, III/165–6; Claire de Rémusat, _Mémoires_ , III/218–221
4. Crouzet, I/69
5. Fouché, 1957, 160
6. CG, VI/113–14; Consalvi, 65–7; Pelet de la Lozère, 205–8
7. Consalvi, 672–4
8. Masson, _Napoléon et sa Famille_ , IV/46, V/60–5; Haegele, 300–3
9. Fontaine, I/187; CG, VIII/120
10. Englund, 339; Dwyer, _Citizen Emperor_ , 275
11. CG, VIII/36
12. See: Talleyrand, _Mémoires_ , 97ff; Waresquiel, 378–83; Pasquier, I/329, 351; Beugnot, I/346; Cambacérès, _Mémoires_ , II/189
13. Savary, II/250–7; CG, VIII/305–6, 314, 326, 333
14. Chłapowski, 66; Avrillon, I/363
15. CG, VIII/402, 423; Metternich, _Mémoires_ , II/245; Broglie, 59; see also Bausset, I/217–19; Avrillon, II/2
16. Ernouf, 249; CG, VIII/448
17. Dwyer, _Citizen Emperor_ , 272; Fraser, _Cursed War_ , 487
18. Garros, 296; Dumas, III/316; CG, VIII/470, 487, 489
19. Brandt, 11; Vandal, _Napoléon et Alexandre_ , I/365; Fain, _Mémoires_ , 70–3; Avrillon, I/372; Josephine, _Correspondance_ , 225
20. Joseph, _Mémoires_ , IV/336; Lentz, NHPE, I/404; Masson, _Napoléon et sa Famille_ , IV/245–6; Haegele, 342
21. Haegele, 203–80; Bigarré, 201; Joseph, _Mémoires_ , III/324
22. Joseph, _Mémoires_ , IV/343, 366–7, 375
23. Ibid., 382–3, 366–98
24. CG, VIII/940–1
25. Joseph, _Mémoires_ , IV/412–13, 420–3
26. Dumas, III/321–2
32: The Emperor of the East
1. Metternich, _Mémoires_ , II/194–9, 207–14
2. Beugnot, I/388
3. Driault, _Tilsit_ , 291
4. Lentz, NHPE, I/435–6
5. Fouché, 1957, 156–7; CG, VII/1337–8; Chevallier & Pincemaille, 333–5; Josephine, _Correspondance_ , 219–20, 217; see also Metternich, _Mémoires_ , II/140ff
6. Cambacérès, _Mémoires_ , II/231
7. Talleyrand, _Mémoires_ , 152–3, 168–70
8. Alexander I, 20
9. Müffling, 23–5; Lentz, NHPE, I/416
10. Bausset, II/313, 316; Talleyrand, _Mémoires_ , 161, 170, 183; Constant Wairy's account, II/9–10, of the bad dream should be treated with scepticism
11. Müffling, 21–2; Caulaincourt, I/258, 270, 273
12. Bausset, II/319–20, 321; Talleyrand, _Mémoires_ , 178–82; CG, VIII/1126
13. Bausset, I/325
14. Branda, _Secrets_ , 153–7; Savary, V/59–67; Masson, _Napoléon et sa Famille_ , IV, 327; Beugnot, I/344–5; Chevallier & Pincemaille, 274; Boulart, 181
15. Crouzet, I/393; Caulaincourt, I/274; Napoleon's suggestion (Bertrand, _Cahiers, 1818–1819_ ) can be dismissed, so can Talleyrand's convoluted account in _Mémoires_ , 183
16. Dwyer, _Citizen Emperor_ , 284; Metternich, _Mémoires_ , II/248
17. Metternich, _Mémoires_ , II/247–9
18. CG, VIII/1130, 1131–2; Savary, IV/6
19. Chaptal, 216–17; Claire de Rémusat, _Mémoires_ , II/271; Ségur, _Histoire_ , IV/87, 79; Beugnot, I/460; Rapp, 4; Mollien, II/325; Choiseul-Gouffier, 94
20. Chaptal, 216–17; see also: Masséna, V/146; Mollien, I/40, 316–17; Ségur, _Histoire_ , IV/78
21. See Savary, IV/47
22. Garros, 304; Bigarré, 229; Miot de Melito, II/18–19
23. Ségur, _Un aide de camp_ , 257
24. Joseph, _Mémoires_ , V/265–6, 281; also Miot de Melito, II/24
25. CG, VIII/1352, 1374–6, 1306, 1314; Constant Wairy, II/22; Branda, _Le Prix_ , 57
26. CG, VIII/1359–60
27. Ibid., 1377; Bodinier, 286; see also Petiteau, 49
28. Cambacérès, _Lettres_ , II/604; _Le Moniteur_ , 15 December 1808, quoted in Lentz, NHPE, I/427
29. Pasquier, I/353–4
30. Cambacérès, _Mémoires_ , II/250; Waresquiel, 398; Tulard, _Fouché_ , 222–6; Masson, _Napoléon et sa Famille_ , IV/393
31. Dumas, III/339; Garros, 310; Malye, 65–6; Lentz, NHPE, I/422–3; CG, VIII/1438
32. Waresquiel, 400
33. Anatole de Montesquiou, 155; Pasquier, I/358; Waresquiel, 400–1, 402ff; Lentz, NHPE, I/434; Hortense, II/30
34. Langsam, 32, 64
35. Ibid., 43–4; Bodinier, 252–3
36. Wołowski; Comeau de Charry, 291; Bausset, I/88
37. Las Cases, 1983, II/142; Lentz, NHPE, I/445; Lejeune, I/302; Cambacérès, _Lettres_ , II/659
38. The figures given here, as elsewhere, are approximative. See Bodinier, 352–3; Lentz, NHPE, I/463
39. Anatole de Montesquiou, 168; Savary, IV/143; Marbot, II/201–12; Lejeune, I/357; Fouché, 1957, 168; Berthezène, I/235–6; Cadet de Gassicourt, 126–7; Chłapowski, 162
33: The Cost of Power
1. Costa de Beauregard, 336; Chłapowski, 183–4
2. CG, IX/833
3. Bodinier, 353; there is much disagreement on the number of casualties and prisoners; Bulletins, 472–4; Garros, 326; Savary, IV/185; Chłapowski, 133, 193, etc.
4. Marmont, III/243
5. CG, VII/1321
6. Boudon, _Le roi_ , 198–202
7. Ibid., 145
8. Potocka, 319; Masson, _Napoléon et sa Famille_ , IV/304–5
9. Beugnot, I/371–2, 337
10. Rapp, 143
11. Tulard, _Napoléon ou le mythe_ , 197; Grunewald, 139–41; Comeau de Charry, 318–19
12. Savary, IV/231; Joseph, _Mémoires_ , VI/259, 274, 381–9, 59–73
13. Cambacérès, _Mémoires_ , II/268–72; Cambacérès, _Lettres_ , II/685–7
14. CG, V/927; Masson, _Napoléon et sa Famille_ , VII/29
15. CG, IX/599
16. Ibid., 885; quoted by Lentz, NHPE, I/493; Fouché, 1957, 154, 169; Boigne, I/291
17. Berthezène, I/264; Macdonald, 152–9; Marbot, II/272–3; Boulart, 227
18. Pouget, 151–2
19. Abrantès, VII/93; Fantin des Odoards, 143
20. Broglie, I/73–4; Marmont, III/337; Berthezène, I/239–40
21. Dumas, III/363; Cambacérès, _Lettres_ , II/749
22. Cadet de Gassicourt, 108–9; Załuski, 176
23. CG, IX/1083, 1148, 1254, 1363, 1366; Branda, _Le Prix_ , 57
24. Rapp, 125–9; see also Dumas, III/384–5 and Savary, IV/223–4
25. Cambacérès, _Lettres_ , II/718
26. Tulard, _Fouché_ , 235–46; Cambacérès, _Mémoires_ , II/279–87
27. Claire de Rémusat, _Mémoires_ , II/265; Girardin, II/339; Branda, _Secrets_ , 82–90
28. Chevallier & Pincemaille, 338–9; Bausset, II/368ff; see also Constant Wairy, I/197–9
29. Lentz, NHPE, I/496–7
30. Constant Wairy, II/100–4; Hortense, II/42, 44–5
31. Lentz, NHPE, I/497–8; see also Claire de Rémusat, _Mémoires_ , III/279–314
32. Cambacérès, _Mémoires_ , II/315; Lentz, NHPE, I/499
33. CG, IX/1506, 1510, 1421, 1522, 1532, 1535
34. Chevallier & Pincemaille, 347, 343; Avrillon, I/166
34: Apotheosis
1. Ernouf, 272–3; Talleyrand, _Mémoires_ , 195–7; Cambacérès, _Mémoires_ , II/326–7; Lentz, NHPE, I/502, 506; Metternich, _Mémoires_ , II/312
2. Ligne, II/222; Metternich, _Mémoires_ , I/100; Beugnot, I/428
3. Savary, IV/317–18; Coignet, 187; Parquin, 176–7; Beugnot, I/423–4
4. Hortense, II/62; Garros, 341; Pontécoulant, III/123; Lejeune, II/30–1
5. Masson, _Marie-Louise_ , 82–4; Dwyer, _Citizen Emperor_ , 331–4
6. Pontécoulant, III/124; Dwyer, _Citizen Emperor_ , 334
7. Constant Wairy, II/125–6; Boudon, _Histoire_ , 314; Clary, 48
8. Lejeune, I/32; Clary, 83
9. Boigne, I/274; Pasquier, I/381; Pontécoulant, III/129–30; Masson, _Marie-Louise_ , 112–19
10. Consalvi, 211, 218, 238, 242, 246–7
11. Constant Wairy, II/132–3; Thibaudeau, 278; Coignet, 191
12. Bertrand, _Cahiers, 1818–1819_ , 18, 100, 263, 408, 411; Claire de Rémusat, _Mémoires_ , II/336
13. Jerome, _Mémoires_ , IV/402
14. Ernouf, 282, also: Fouché, 1957, 173, 181–3; Savary, IV/320–40; Pasquier, I/390–404; Cambacérès, _Mémoires_ , II/340; Boudon, _Histoire_ , 310; Lentz, NHPE, I/512; Garros, 343; Jérôme, _Mémoires_ , IV/401
15. Potocka, 200; Chastenay, 421; Masson, _Marie-Louise_ , 233
16. Potocka, 215–18
17. Ibid., 281
18. Jourdan, _Louis_ , 11–12, 18, 20, 31ff, 81ff
19. Savary, IV/346; Jourdan, _Louis_ , 150; CG, X/422
20. Savary, IV/353; Jourdan, _Louis_ , 22
21. Lejeune, II/39, 33–4; see also Metternich, _Mémoires_ , I/301–7
22. Dwyer, _Citizen Emperor_ , 336; Lejeune, I/252–3; Marmont, V/2–3
23. Metternich, _Mémoires_ , I/287, 286; Lentz, NHPE, I/522–3; Boigne, I/275
24. Chastenay, 420–1; Hortense, II/113–14, 116; Tulard, _Dictionnaire Napoléon_ , I/353
25. Fontaine, I/219, 249–50, 275; see also Branda, _Secrets_ , 105 and _Le Prix_ , 44–8
26. Thibaudeau, 278
27. Savary, IV/355; Lentz, NHPE, I/516; Fouché, 1957, 298; Tulard, _Fouché_ , 255
28. Savary, IV/311, 406; Hortense, II/117
29. Savary, IV/314, V/99; Lentz, NHPE, I/520; Pasquier, I/517; Hauterive, _Napoléon et sa Police_ , 43
30. Jérôme, _Mémoires_ , IV/410; Metternich, _Mémoires_ , I/279; Chastenay, 433; Ségur, _Un aide de camp_ , 280; Sutherland, 197–8; Josephine, _Correspondance_ , 274; Hortense, II/116; Chaptal, 340
31. Metternich, _Mémoires_ , I/283–4
32. Canova, 418; Lentz, NHPE, II/125
33. Lentz, NHPE, I/529; Marmont, III/340
35: Apogee
1. Las Cases, 1983, I/619
2. Metternich, _Mémoires_ , I/286; Masson, _Marie-Louise_ , 208–9
3. Metternich, _Mémoires_ , I/297; Ségur, _Histoire_ , III/476; Kemble, 165, 170
4. Vandal, _Napoléon et Alexandre_ , II/318
5. Méneval, II/436; Hortense, II/127; Savary, V.146–9; Raza, 202–6; Castellane, I/83; Kemble, 182–4
6. Boigne, I/291–2; Lentz, NHPE, II/13–14; Goethe, _Karlsbader Stanzen_
7. Hortense, II/125–8, 97; Constant Wairy, II/154–5; Savary, V/147–9; Méneval, II/438; Avrillon, II/275, 307–8; Josephine, _Correspondance_ , 267; Chevallier & Pincemaille, 348–51; Mollien, III/76
8. Driault, _Grand Empire_ , 323
9. Ibid., 126; Miot de Melito, III/187
10. Branda & Lentz, 187; Bodinier, 385
11. Lentz, NHPE, II/85; Branda, _Le Prix_ , 307–8, 365, 301–3, 308–11
12. Metternich, _Mémoires_ , II/328; Savary, IV/318–19
13. Bigarré, 315; Haegele, 399; for a contrary view: Marbot, II/482–3
14. Haegele, 420; Joseph, _Mémoires_ , VII/306, 488ff, VIII/42–272
15. Branda, _Secrets_ , 153–7
16. Metternich, _Mémoires_ , II/329
17. CG, VII/924
18. Comeau de Charry, 281; Rapp, 106; Broglie, I/177–9; Cambacérès, _Mémoires_ , II/400
19. Napoleon, _Correspondance_ , XX/149–54
20. Ibid., 159
21. Zamoyski, _1812_ , 111
22. Kartsov & Voenskii, 50–1
23. Fain, _Manuscrit de 1812_ , I/3; Palmer, 199
24. Zamoyski, _1812_ , 70–1; Bignon, 46ff; Metternich, _Mémoires_ , II/407
25. Metternich, _Mémoires_ , II/412–13; Ernouf, 319
26. Zamoyski, _1812_ , 72
27. Caulaincourt, I/281–316
28. Zamoyski, _1812_ , 75–6
29. Ibid., 76–7
30. Chastenay, 471; Branda, _Secrets_ , 184; Beugnot, I/480–5; Pasquier, I/430–1; Lignereux, 142; Heine, 114
31. Metternich, _Mémoires_ , II/422
36: Blinding Power
1. Napoleon, _Correspondance_ , XXIII/191
2. Villemain, I/155–67; Zamoyski, _1812_ , 106; Ségur, _Histoire_ , IV/74
3. Bodinier, 309–12; Zamoyski, _1812_ , 85, 88; Bégos, 175
4. Zamoyski, _1812_ , 88–9
5. Berthezène, I/328
6. Baudus, I/336; Fain, _Manuscrit de 1812_ , I/46; Ségur, _Histoire_ , III/65–9, 447–8, IV/125; Laugier, 9; Dumonceau, II/17, 48; Davout, III/155; Fantin des Odoards, 303
7. Jérôme, V/247; see also Zamoyski, _1812_ , 83–4
8. Napoleon, _Correspondance_ , XXIII/388
9. Fontaine, I/316
10. Pasquier, I/525
11. Fain, _Manuscrit de 1812_ , I/61
12. Castellane, I/93
13. Beauharnais, VII/340; Savary, V/226; Comeau de Charry, 439; Lejeune, II/174
14. Méneval, III/25, 109; Caulaincourt, I/315
15. Fain, _Manuscrit de 1812_ , I/68
16. Metternich, _Mémoires_ , I/122; Cambacérès, _Mémoires_ , II/395
17. Fain, _Manuscrit de 1812_ , I/75; Pradt, 56–7; Savary, V/226
18. Villemain, I/163, 165–6; Chłapowski, 235
19. Zamoyski, _1812_ , 132–3
20. Caulaincourt, I/342; Zamoyski, _1812_ , 133–4
21. Zamoyski, _1812_ , 132–7
22. Ibid., 117
23. Lejeune, I/172
24. Zamoyski, _1812_ , 142–3
25. Bulletins, 487–8
37: The Rubicon
1. Caulaincourt, I/344
2. Zamoyski, _1812_ , 147; Bulletins, 488–9
3. Lejeune, II/175
4. Planat de la Faye, _Vie_ , 71
5. Zamoyski, _1812_ , 156–7
6. Anatole de Montesquiou, 208
7. Caulaincourt, I/354
8. Dubrovin, 20–5; CG, XII/787–9
9. Zamoyski, _1812_ , 160; Bulletins, 501–3
10. Napoleon, _Correspondance_ , XXIV/61
11. Zamoyski, _1812_ , 161–4
12. Ibid., 166–8
13. Ibid., 168
14. CG, XII/879, 899
15. Ibid., 923–4
16. Zamoyski, _1812_ , 190–2
17. Méneval, III/43; Napoleon, _Correspondance_ , XXIV/128, 133; Fain, _Manuscrit de 1812_ , I/289, 306; Dumas, III/429; Castellane, I/126–7; La Flise, LXXI/465; Bourgoing, 98–100
18. Zamoyski, _1812_ , 194–5; Dedem de Gelder, 295; Caulaincourt, I/379, 407
19. Caulaincourt, I/382; Villemain, I/203–4, 208; also Zamoyski, _1812_ , 196
20. Załuski, 241; Brandt, 261, 289; Chevalier, 189; Fain, _Manuscrit de 1812_ , I/323
21. Fain, _Manuscrit de 1812_ , I/394; Caulaincourt, I/393
22. Caulaincourt, I/406
23. Rapp, 167; Denniée, 62; Lejeune, II/199; Zamoyski, _1812_ , 229
24. Bourgoing, 100; Brandt, 252–3
25. Pion des Loches, 287; Chevalier, 190
26. Caulaincourt, I/411
27. Sołtyk, 198–9; Roguet, III/474
28. Zamoyski, _1812_ , 258–9
29. Bausset, II/84; Brandt, 272; CG, XII/1080
30. Rapp, 173–5
31. Ibid., 176; Thirion, 180; Vossler, 60–1; Holzhausen, 105
32. Zamoyski, _1812_ , 271–2; Lejeune, II/217
33. Dedem de Gelder, 240; Zamoyski, _1812_ , 287–8
34. Anatole de Montesquiou, 226–7; Sanguszko, 93; Thirion, 201
38: Nemesis
1. Bourgogne, 13
2. Fain, _Manuscrit de 1812_ , I/94–7; Rapp, 184
3. Ségur, _Histoire_ , V/75
4. Caulaincourt, II/49
5. Zamoyski, _1812_ , 349–50
6. Caulaincourt, II/23
7. Zamoyski, _1812_ , 338–9
8. Ibid., 339
9. Belliard, I/112
10. Caulaincourt, II/26, 42, 56, 65
11. Fain, _Manuscit de 1812_ , I/151–2
12. Zamoyski, _1812_ , 353–4
13. Ibid., 354–5
14. Ibid., 355; Rapp, 192–3
15. See Zamoyski, _1812_ , 364–8
16. Ibid., 370–5, 377
17. Denniée, 118, 114–15; Volkonskii, 199–203; Caulaincourt, II/104–5
18. Zamoyski, _1812_ , 379–81, 383–4
19. Ibid., 409
20. Pastoret, 470–1
21. Caulaincourt, II/141; Saint-Denis, 54; Méneval, II/93–4 writes that this was at Orsha
22. Bourgogne, 116; Roguet, III/518
23. Zamoyski, _1812_ , 425
24. Ibid., 455–6, 378; Bertin, 251–2; Anatole de Montesquiou, 254–5, 267
25. Zamoyski, _1812_ , 457
26. Caulaincourt, II/168, 173; also Zamoyski, _1812_ , 459–60
27. Rapp, 213; Zamoyski, _1812_ , 461ff
28. Zamoyski, _1812_ , 491–3; Bulletins, 556
29. Ernouf, 461–2
30. Caulaincourt, II/230ff
31. Ibid., 263; Pradt, 207–18
32. Potocka, 331–4; Niemcewicz, 383; Koźmian, III/311
33. Caulaincourt, II/315
34. Zamoyski, _1812_ , 522–3
39: Hollow Victories
1. Anatole de Montesquiou, 296–7
2. CG, XII/1305
3. Driault, _Napoléon et l'Europe_ , 59
4. Masson, _Napoléon et sa Famille_ , VII/342–3; CG, XII/1305; Caulaincourt, II/389–90, 393–4
5. Napoleon, _Correspondance_ , XXIV/369; for the losses, see Zamoyski, _1812_ , 536–40 and notes
6. Molé, I/155
7. Hortense, II/152; Mollien, III/169–70; GS, HA Ministerium, 10 February 1813; see also Collot, 50–4
8. Tulard, _Fiévée_ , 154; Barante, I/371
9. Garros, 402
10. Lentz, NHPE, II/339; for Mallet Affair, see: Boudon, _Histoire_ , 366ff; Savary, VI/2–35; Pasquier, II/12–34; Cambacérès, _Lettres_ , II/914; Cambacérès, _Mémoires_ , II/434; Molé, I/118–25; Price, 29–31
11. Fain, _Manuscrit de 1813_ , I/129; see Lavalette 328 for his annoyance at not being left the chance of reprieving Mallet
12. Cambacérès, _Mémoires_ , II/429; Fain, _Manuscrit de 1813_ , I/38
13. Caulaincourt, II/315; Molé, I/129, 131; Raumer, 23–4; Mollien, III/293–5
14. Lentz, NHPE, II/399, 403
15. Masson, _Napoléon et sa Famille_ , VII/418, 448, 452, VI/74
16. Marmont, V/5; Durand, 144–5; Tulard, _Fiévée_ , 150–1; Boussingault, I/53–5; Molé, I/144; Price, 91; Napoleon, _Correspondance_ , XXIV/380–1
17. Haegele, 469–70; Lentz, NHPE, II/400
18. Hardenberg, XII/17, 13–15; Fain, _Manuscrit de 1813_ , I/210, 231–7
19. Fain, _Manuscrit de 1813_ , I/238–41, 296–9, 301–3, 306–7; Abrantès, XI/90–1; Castellane, I/222; Broglie, I/214, 218, 220
20. Shishkov, I/167; Zorin, 251, 264
21. Angeberg, I/5–7
22. Kraehe, I/43
23. Gentz, _Dépèches_ , I/8–9
24. Ibid., I/13; Oncken, I/416–20; Buckland, 459ff, 491ff; Fain, _Manuscrit de 1813_ , I/296–9
25. Napoleon, _Correspondance_ , XXIV/521; Fain, _Manuscrit de 1813_ , I/222; Lentz, NHPE, II/358–60
26. Masson, _Napoléon et sa Famille_ , VII/344
27. Napoleon, _Correspondance_ , XXIV/196–7; Driault, _Napoléon et l'Europe_ , 76
28. Fain, _Manuscrit de 1813_ , I/247–75; Driault, _Napoléon et l'Europe_ , 76; Oncken, I/439; Méneval, III/129
29. Oncken, II/624; CG, XIII/860
30. Wojciechowski, 81; Bertrand, _Lettres_ , 190; Pelleport, II/65; Chłapowski, 310; Mallardi, 404
31. Beauharnais, IX/94; Wojciechowski, 82; Dumas, III/499; Barrès, 158
32. Zamoyski, _Rites_ , 52–3; Marmont, V/25
33. Oncken, II/673–8
34. Angeberg, I/13; Metternich, _Mémoires_ , I/250; Driault, _Napoléon et l'Europe_ , 91; Ernouf, 494, 533–4, 539; Fain, _Manuscrit de 1813_ , I/390
35. Price, 66; Gross, 88
36. Fain, _Manuscrit de 1813_ , I/390; Price, 70; Chłapowski, 348
37. Chłapowski, 324–5
38. Zamoyski¸ _Rites_ , 61–2
39. Fouché, 1945, 388–9
40. Fain, _Manuscrit de 1813_ , I/426–7; Chłapowski, 341; Planat de la Faye, 43
41. Zamoyski, _Rites_ , 63
40: Last Chance
1. Cambacérès, _Lettres_ , II/922, 967, 973, 994; Fain, _Manuscrit de 1813_ , I/430; Price, 91–4; Belliard, I/125, 130
2. Cambacérès, _Mémoires_ , II/907, 938, 971–2; Fain, _Manuscrit de 1813_ , II/66–7; Fouché, 1824, II/196–7, 1945, 404; Potocka, 350
3. Metternich, _Mémoires_ , I/147–53, II/461–2; Nesselrode, V/108–15; Fain, _Manuscrit de 1813_ , II/36–44; Price, 83
4. SUA, 12, 33/9
5. Angeberg, I/18–19
6. Fain, _Manuscrit de 1813_ , II/79–80
7. Nesselrode, I/99–100; Humboldt, IV/52, 76; Hardenberg, XII/207; Price, 99–101
8. Price, 103–4
9. Fleury, 317; Boulart, 287; Skałkowski, 136; Marbot, III/257
10. SUA, 12, 33/21; Humboldt, IV/92
11. PRONI, 74, 72; Angeberg, I/74; SUA, 12, 33/22; BL Aberdeen, 161–3; Webster, 157; see also Price 103–9
12. These figures are approximate, as calculations vary wildly; on the subject of Russia's mobilisation, see Lieven
13. Beugnot, II/4–6; Beauharnais, IX/108, 117
14. See Nesselrode, I/103
15. Garros, 424
16. Hardenberg, XII/180
17. Lavalette, 278; Faucheur, 225; Dumas, III/524
18. Marmont, V/255–6; Boulart, 249; Dumas, III/524; Lentz, NHPE, II/443, 459; Szymanowski, 101–3
19. Macdonald, 224
20. Lentz, NHPE, II/467
21. Macdonald, 227; Pasquier, II/96–7; Dumonceau, II/387; Barrès, 194
22. Ginisty, 11–12; Macdonald, 232; Ségur, _Histoire_ , VI/93; Sułkowski, _Listy_ , 417–22
23. Lentz, NHPE, II/469–70; Masson, _Marie-Louise_ , 509
24. Beugnot, II/38
25. Beauharnais, IX/299ff, 384–5, 295
26. Lentz, NHPE, II/516; Masson, _Napoléon et sa Famille_ , VIII/251–6
27. Cambacérès, _Mémoires_ , II/491, 495; Cambacérès, _Lettres_ , II/1099–112; Lentz, NHPE, II/498–9, 503; Bodinier, 307, 320, 329
28. Pasquier, II/99; Bausset, V/256–7; Waresquiel, 422; also Cambacérès, _Mémoires_ , II/507; Lentz, NHPE, II/471
29. Beugnot, II/54; Pasquier, II/100; Molé, I/174–6; Cambacérès, _Mémoires_ , II/507
30. Lavalette, 279–80; Marmont, VI/7–8
31. Josephine, _Correspondance_ , 359–60; Beugnot, II/78–80
32. Pasquier, II/110
41: The Wounded Lion
1. Zamoyski, _Rites_ , 125–8; Price, 154–61
2. Angeberg, I/77–8; Price, 161–9
3. Molé, I/139–40; Lentz, NHPE, II/511–12
4. Masson, _Napoléon et sa Famille_ , IX/132, 84, 36ff, 76–7, 139, 150, 166–7, 175ff, 200, 259; Tulard, 291–2; Madelin, 295; Lentz, NHPE, II/491, 487–8; Beauharnais, IX/284–5, 295, 299ff; Josephine, _Correspondance_ , 361–2
5. Pasquier, II/143; Lavalette, 282; Pontécoulant, III/187; Hortense, II/174, 177
6. Fain, _Manuscrit de 1814_ , 72–5; Vionnet de Maringoné, 105
7. Ernouf, 623; Garros, 439; Caulaincourt, III/15–16; Montbas, 805–6; Fain, _Manuscrit de 1814_ , 75–8, 284–5; Napoleon, _Correspondance_ , XXVII/223–4
8. Benckendorff, 349; FO 92, 3; Metternich, _Mémoires_ , I/190; Méneval, III/213–15; Bertrand, _Lettres_ , 375–94; Dumonceau, III/18, 29–30; Müffling, 469–71; Bodinier, 300; Ligneureux, 306–7; where the enemy had not been seen, the attitude was very different – see Lignereux, 310; Fontaine, I/385–6; Hauterive, 354; Price, 205–11
9. Joseph, _Mémoires_ , X/63–149, 48
10. Ibid., 161; Ségur, _Histoire_ , VI/248–9
11. Molé, I/286
12. Ségur, _Histoire_ , VI/293–4
13. Grabowski, 179–83; Joseph, _Mémoires_ , X/198
14. Cambacérès, _Lettres_ , II/1131
15. Boulart, 319–20; Desmarest, 268
16. Joseph, _Mémoires_ , X/31–3; Miot de Melito, II/353; Savary, VI/363–79; VII/3
17. Combe, 275–6; Pontécoulant, III/259–61; Béranger, 141; Savary, VII/12; Marmont, VI/240–9; Lavalette, 290
18. Belliard, I/171–2; Lentz, _Vingt Jours_ , 31–2
19. Lentz, _Vingt Jours_ , 41–4
20. Caulaincourt, III/167
21. Lentz, _Vingt Jours_ , 57–69; Ségur, _Histoire_ , VII/153
22. Marmont, VI/257–70; Belliard, I/180–6; Macdonald, 279, 286; Ségur, _Histoire_ , VII/163–78; Caulaincourt, I/161–6; Lentz, _Vingt Jours_ , 70–2, 107; the most coherent account is in Price, 234–8
23. Lentz, _Vingt Jours_ , 79ff; Caulaincourt, III/233ff.; Masson, _Marie-Louise_ , 568–82
24. Lentz, _Vingt Jours_ , 220–1; Grabowski, 214–15; Szymanowski, 111–13; Boulart, 323
42: Rejection
1. Lentz, _Vingt Jours_ , 217
2. cf. Caulaincourt, I/314
3. Lentz, _Vingt Jours_ , 135–9
4. Ibid., 131–2
5. Chevallier & Laot, ed., 303
6. Caulaincourt, III/343, 357–73; Ségur, _Histoire_ , VII/196–200; Saint-Denis, 55–8; Fain, _Manuscrit de 1814_ , 255–8; Belly de Bussy, 237; Lentz, _Vingt Jours_ , 159–168
7. Caulaincourt, III/366; Macdonald, 299
8. Chevallier & Laot, 303–4; Sutherland, 255–8
9. Tulard-Garros, 549
10. Masson, _Marie-Louise_ , 541; Price, 241; Pasquier, II/237–8; Anatole de Montesquiou, 305–6
11. Masson, _Marie-Louise_ , 573–5; Price, 242–3
12. Masson, _Marie-Louise_ , 580; Anatole de Montesquiou, 334–5; Dwyer, _Citizen Emperor_ , 492; Lentz, _Vingt Jours_ , 186–9
13. Chevallier, & Laot, ed., 303–4
14. Campbell, 157
15. Ibid., 157, 160, 171–2, 182; Schouvaloff; Dwyer, _Citizen Emperor_ , 493
16. Lentz, _Vingt Jours_ , 202–3; Coignet, 331; Campbell, 185; Fain, _Manuscrit de 1814_ , 398ff
17. Lentz, _Vingt Jours_ , 170
18. Campbell, 190
19. Ibid., 198–201; Peyrusse, _Mémorial_ , 295–6; Shuvalov, 809–29; Saint-Denis, 59; Lentz, NHPE, IV/158–65; Price, 244–8; Dwyer, _Citizen Emperor_ , 493–8
20. Branda, _Le Prix_ , 62–3; Lentz, NHPE, IV/205–10
21. Méneval, III/341, 375–6, 384; Lentz, NHPE, IV/168–72; see also Anatole de Montesquiou, 350
22. Jérôme, _Mémoires_ , VI/474; Peyrusse, _Lettres_ , 232; Saint-Denis, 60ff; Pons de l'Hérault, 140, 191
23. Sutherland, 266–81; Saint-Denis, 78–80; Pons de l'Hérault, 211–14
24. Lentz, NHPE, IV/270–8; Branda, _l'Ile_ , 58–64
25. Pons de l'Hérault, 160–7; Brun de Villeret, 191–2; Campbell, 109, 156, 305; Dwyer, _Citizen Emperor_ , 352–3; Masson, _Napoléon et sa Famille_ , X/216–18
26. Campbell, 108, 318, 305, 352–3; Pons de l'Hérault, 371; Rose, 178; Lucien, III/459; Lentz, NHPE, IV/280–3; Lentz, _Vingt Jours_ , 146
27. Pons de l'Hérault, 14, 128; Campbell, 242
28. Pons de l'Hérault, 383–4
43: The Outlaw
1. Macdonald, 343, 411–12; Saint-Denis, 90
2. Lentz, NHPE, IV/291; Saint-Denis, 90
3. Lentz, NHPE, IV/294–5; Peyrusse, _Mémorial_ , 286–7
4. Miot de Melito, III/378–9; Ernouf, 645; Lavalette, 331–3
5. Pasquier, III/125; Barante, II/24; Macdonald, 287–8
6. Savary, VII/373; Lavalette, 333
7. Miot de Melito, III/381; Lavalette, 338–40; Mollien, III/419
8. Lucien, III/463; Miot de Melito, III/395
9. Hortense, III/1; Jal, 297–8; Lucien, III/263; Avrillon, II/381–4
10. Constant, _Journal_ , 351, 349, 353; Constant, _Cent-Jours_ , 211, 209, 227
11. Lentz, NHPE, IV/393–7
12. Ibid., 400–2; Jal, 287–8, 283–5; see also Lavalette, 347 and Miot de Melito, III/400–1
13. Zamoyski, _Rites_ , 460
14. Ibid., 461
15. Ibid., 447–8
16. Lucien, III/230
17. Madelin, 318–19, 330–1, 242–3; Fouché, 1945, 473, 478–9, 483–6; Fleury de Chaboulon, III/289 suggests Montrond's mission meant to bring Talleyrand over to Napoleon's side (see also Mollien, III/432; Waresquiel, 493–4; see also Savary, VIII/31ff; Méneval, III/445–6 claims Francis would have backed a regency if Napoleon had agreed to reside privately in Habsburg dominions; see also Lavalette, 342–5; Chaptal, 314–15; Tulard, _Fouché_ , 326–9; Lucien, III/296 believes Napoleon was prepared to step down; the clearest account is in Price, 251–9
18. Pontécoulant, III/328; see also Rapp, 294–5 for his unwillingness to fight; Constant, _Cent-Jours_ , 211
19. Bodinier, 302; Miot de Melito, III/398
20. Ernouf, 657
21. Constant, _Cent-Jours_ , 209; Miot de Melito, III/395
22. Rumigny, 91; Constant, _Journal Intime_ , 354; Miot de Melito, III/395
23. Hortense, III/14; Lavalette, 349
24. Bodinier, 366–9; Fantin des Odoards, 427
25. Rumigny, 102
26. Bulletins, 607–13; Lentz, NHPE, IV/507; see also Napoleon, _Mémoires_ , IV/124–5
27. Bertaud, _Abdication_ , 25, 27; Lavalette, 350
28. Bertaud, _Abdication_ , 27, 48, 28, 319 (note 19)
29. Ibid., 49, 27; Constant, _Cent-Jours_ , 284
30. Bertaud, _Abdication_ , 122
31. Lucien, III/347; Bertaud, _Abdication_ , 159, 158, 160, 170; Fouché, 1945, 493–8; Lentz, NHPE, IV/515–16
32. Bertaud, _Abdication_ , 194–5
33. Branda, _Secrets_ , 29; Lentz, NHPE, IV/526 (note); Constant, _Journal Intime_ , 355; Constant, _Cent-Jours_ , 287
34. Hortense, III/32–3
35. Planat de la Faye, 215; Rumigny, 112–13; Macdonald, 393; Savary, VIII/183
36. Savary, VIII/166–7
37. Lentz, NHPE, IV/527; Garros, 473; Bonneau, 420–3
38. Bertaud, _Abdication_ , 302
39. Ibid.
44: A Crown of Thorns
1. Tulard & Garros, 592–3
2. Ibid., 593–4; Benhamou, 18–19
3. Zamoyski, _Rites_ , 497
4. Saint-Denis, 136–8; Warden, Cockburn, etc.
5. Tulard, _Sainte-Hélène_ , 11; Montchenu, 49
6. _Letters from the Cape_ , 81
7. Abell, 20–1, 30–1, 39, 208, 72–3, 77
8. Las Cases, 1983, I/205–7
9. Ibid., 207–9
10. Planat de la Faye, 241; Martineau, 42
11. Zamoyski, _Phantom Terror_ , 133
12. Cockburn, 7
13. Ibid., 25, 45, 76–7; _Letters from the Cape_ , 12; Benhamou, 37
14. Aubry, I/199
15. Malcolm, 24–6
16. Aubry, I/203, 296, 219, II/79
17. Ibid., I/217–18
18. Fraser, _Venus_ , 232
19. Aubry, I/220–3
20. Ibid., 215–16, II/74–7; _Letters from the Cape_ , 202; see also Zamoyski, _Phantom Terror_ , 129–35; and Hazareesingh for a wonderfully exhaustive study of the subject
21. Branda, _Le Prix_ , 75–6; Benhamou, 77; Aubry, I/224
22. Martineau, 71–3; Aubry, I/225–9; Malcolm, 41, 44, 58, 62, 64
23. Branda, _Le Prix_ , 78
24. Saint-Denis, 168–9
25. Malcolm, 44, 152
26. Aubry, I/245–6
27. Roberts, _Napoleon_ , 788; Abell, 57; Aubry, II/159
28. Aubry, II/133
29. Ibid., 137–8
30. Jérôme, _Mémoires_ , VI/298–9
31. Branda, _Secrets_ , 246–51
32. Roberts, _Napoleon_ , 798
33. Aubry, II/221
34. Molé, _Souvenirs de jeunesse_ , 132
35. For an exhaustive treatment of the Testament, see Branda, _Le Prix_ , 85–94
36. Heine, 115
# Picture Section
Napoleon's mother Letizia Bonaparte in 1800, by Jean-Baptiste Greuze. She brought him up strictly, and he would later say that he owed her everything.
Two sketches of Bonaparte by Jacques-Louis David.
General Bonaparte drawn from life by Giuseppe Longhi during the Italian campaign of 1796.
Founding myth: General Bonaparte leading his troops across the Bridge of Arcole, by Antoine-Jean Gros. Napoleon never got anywhere near the bridge, and his attempt to do so ended ignominiously with his being pulled out of a muddy drainage ditch.
This portrait of Bonaparte by Francesco Cossia was commissioned in 1797 by his English admirer Maria Cosway. Cossia found his model so nervous and restless that he gave up and refused to accept any money for it – yet the unfinished work captures some of the energy and immaturity of the tortured twenty-seven-year-old general.
Josephine Bonaparte in 1797, by Andrea Appiani. Fêted and covered in looted jewels by her adoring husband, she cheated on him shamelessly throughout his epic campaign.
Auguste Marmont, by Georges Rouget, was the first of a series of exalted young men who hero-worshipped Napoleon and attached themselves to him.
Andoche Junot, sketched ten years later by Jacques-Louis David, was plucked out of the ranks by Major Buonaparte at Toulon in 1794 and became an inseparable and adoring friend.
The swashbuckling cavalryman Joachim Murat rendered vital service in the events of 13 Vendémiaire that launched Napoleon's political career, would marry his youngest sister and become a central (if untrustworthy) figure in his entourage.
Josephine's son Eugène de Beauharnais, depicted here by Antoine-Jean Gros as Napoleon's aide-de-camp, fulfilled the role of a surrogate son.
Napoleon's younger sister Pauline, by Jean Jacques Thérésa de Lusse, was his favourite, however much he might disapprove of her promiscuity, and she remained the most faithful to him.
This painting by Antoine-Jean Gros of General Bonaparte visiting victims of the plague at Jaffa during his Syrian campaign was commissioned to represent his compassionate nature, and at the same time to endow him with a Christ-like aura through the suggestion of his own immunity and of the healing nature of his touch.
According to Corsican custom Joseph was the head of the family, and Napoleon tried to give him his due, but although he felt great affection for him, he could not hide contempt for his weakness.
Jean-Baptiste Bernadotte, by Joseph Nicolas Jouy. Napoleon despised him, but since he married the sister of Joseph's wife (who had also been an early love of Napoleon's), he was part of the family.
Napoleon's mercurial younger brother Lucien saved his coup from failure and him from the scaffold, but their views soon diverged, and by the time this portrait was painted, around 1808 by François-Xavier Fabre, he would have nothing to do with the Napoleonic venture.
Bonaparte in the uniform of First Consul, 1800, by Louis-Léopold Boilly.
The house in the rue de la Victoire where Napoleon first visited Josephine and where the coup was planned.
The Tuileries, with the arch of the Carrousel, _c_.1860. The area between the palace and the arch was where the regular parades were held.
Jean-Jacques-Régis Cambacérès, Napoleon's closest political associate, by Jean-Baptiste Greuze, 1805.
The brilliant foreign minister Charles-Maurice de Talleyrand, seen here at the coronation in 1804, by Jacques-Louis David, was one of Napoleon's greatest supporters, but with time their ideas of what was best for France diverged, and he would betray him.
Joseph Fouché, the police chief who protected Napoleon, but he too eventually betrayed him.
Like her brother Eugène, Josephine's daughter Hortense de Beauharnais, portrayed by François Gérard, was adopted by Napoleon and treated as if she were his own daughter.
The Château of Malmaison, by Henri Courvoisier-Voisin, where Napoleon loved to relax and play.
Napoleon's favourite younger brother Louis (in 1809, by Charles Howard Hodges), whom he forced to marry Hortense against both their wishes.
This painting by Jacques-Louis David of Napoleon crossing the Alps in 1802 on his way to victory at Marengo is one of the icons of Napoleonic mythology: in fact, he crossed on a mule led by a guide, his hat and uniform covered in protective oilskin, and did not take the same route as Caesar or Hannibal. Nor could he be bothered to sit for the portrait, so David used his own son as a model. But he did insist that he should be depicted full of martial energy yet making a pacific gesture rather than brandishing a sword, as he was already trying to project an image of the ruler rather than the soldier.
The Emperor Napoleon I, painted in 1805 by Jacques-Louis David in the classic convention of the royal portrait established by the Sun King Louis XIV.
A fragment of Jacques-Louis David's painting of the coronation, showing, from left to right, Joseph, Louis, Napoleon's three sisters and Hortense, holding the hand of her son Napoléon-Charles.
Napoleon's youngest brother, the feckless Jérôme, 1805.
This depiction of Napoleon on the battlefield of Eylau by Antoine-Jean Gros was painted to strict instructions – that the emperor be represented casting 'a consoling eye' over the field of carnage in order 'to soften the horror of death' and exuding 'an aura of kindness and majestic splendour'. Note the fantastic 'Polish' costume of Murat, which Napoleon said made him look like a circus-master.
One of Napoleon's dearest friends, Marshal Jean Lannes, by François Gérard.
General Armand de Caulaincourt, who became a close and loyal confidant, sketched in 1805 by Jacques-Louis David.
Perhaps Napoleon's closest friend, General Géraud-Christophe Duroc, by Anne-Louis Girodet-Trioson.
Napoleon I on the Imperial Throne, painted in 1806 by Jean-Auguste-Dominique Ingres, by which time the emperor was projecting the image of himself as a latter-day Charlemagne, replicating the style and attributes recorded on Carolingian seals.
View of the proposed Palace for the King of Rome, by Pierre-François Fontaine.
This painting by Alexandre Menjaud of Napoleon _en famille_ hugging the King of Rome is part of an iconography which sought to reassure ordinary Frenchmen that an era of peace and stability had dawned, yet it was strikingly at odds with his escalating imperial programme.
Napoleon in his study at the height of his power, in early 1812, by Jacques-Louis David.
Napoleon on the bridge of HMS _Bellerophon_ after giving himself up to the British in 1815, by an evidently unimpressed witness, Charles Lock Eastlake.
The house at Longwood on the island of St Helena, where Napoleon spent his last years and died, photographed _c_.1940.
Napoleon on St Helena, drawn in June 1820 by a clearly unsympathetic British visitor.
# Bibliography
ARCHIVES
Archives Nationales, Paris (AN)
Papiers Flahaut, Archives Nationales, 565 AP, carton 18–19, dossier 4
Archives Caulaincourt, 95 AP 34
British Library, London (BL)
Dropmore Papers, Add. 58891 – Gentz to Lord Carysfort
Aberdeen Papers, XXXvII, Add. 43075
National Archives, Kew (NA)
Jackson Papers, FO 353/18, p. 15; CG, IV/769
Public Record Office of Northern Ireland, Belfast (PRONI)
Castlereagh Papers, D.3030/P
Státní Ústřední Archiv, Prague (SUA)
Rodinný Archiv Metternišský I; Acta Clementina, 1, 3, 5, 14a
Landesarchiv, Berlin (LB)
Rep. 241, acc. 3932, Nr. 1: _Erinnerungen des preußischen Kammerdieners Tamanti an den Aufenthalt von Kaiser Napoleon in Potsdam und Berlin (1806)_
Geheimes Staatsarchiv, Berlin (GS)
Hatzfeld's reports III. HA Ministerium der Auswärtigen Angelegenheiten I, Nr 4955
Gentz to Lucchesini, PK, 27 B1 10–1v
Universitäts- un Statsbibliothek Köln (USK)
VI. HA Familienarchive und Nachlasse Nl Girolamo Marchese Lucchesini, Nr, 27, Bl 10–11v
Biblioteka Uniwersytetu Adama Mickiewicza, Poznań (BUAM)
Ms. 44/II. Pamiętnik Stanisława Zamoyskiego
PRINTED SOURCES
Abell, Lucia Elizabeth, _Recollections of Napoleon at Saint Helena_ , London 1844
Abrantès, Laure Junot, duchesse d', _Mémoires de Mme la duchesse d'Abrantès, etc._ , 12 vols, Paris 1835
— _Le Roman Inconnu de la duchesse d'Abrantès_ , ed. Robert Chantemesse, Paris 1927
Alexander I, Emperor of Russia, _Correspondance de l'Empereur Alexandre Ier avec sa soeur la Grande Duchesse Catherine_ , Petersburg 1910
Andigné, Louis Marie Auguste Fortuné, comte d', _Mémoires du Général d'Andigné_ , 2 vols, Paris 1900
Angeberg, Comte d' (Leonard Chodźko), _Le Congrès de Vienne et les Traités de 1815: précédé et suivi des actes diplomatiques qui s'y rattachent_ , ed. M. Capefigue, 2 vols, Paris 1864
Antommarchi, Francesco, _Mémoires du Docteur F. Antommarchi, ou les derniers moments de Napoléon_ , 2 vols, Paris 1825
Arnault, Antoine-Vincent, _Souvenirs d'un séxagenaire_ , Paris 2003
Arnold, Theodor Ferdinand Kajetan, _Erfurt in sienem höchsten Glanze während der Monate September und Oktober 1808_ , Erfurt 1808
Arnott, A., _An Account of the last illness, decease, and post mortem appearances of Napoléon Bonaparte, etc._ , London 1822
Artaud de Montor, Alexis-François, _Histoire de la vie et des travaux politiques du comte d'Hauterive, comprenant une partie des actes de la diplomatie française_ , Paris 1839
Aubry, Joseph Thomas, _Souvenir du 12e Chasseurs_ , Paris 1899
Avallon, Cousin d', _Bonapartiana, ou recueil des Réponses ingénieuses ou sublimes, Actions heroïques et Faits mémorables de Bonaparte_ , Paris 1801
Avrillon, Mlle, _Mémoires_ , 2 vols, Paris 1896
Bailleu, Paul, ed., _Preussen und Frankreich von 1795 bis 1807: Diplomatische Corrrespondenzen_ , 2 vols, Leipzig 1881–87
Bailly, François-Joseph, _Souvenirs et anecdotes de Joseph Bailly_ , in _Revue des Etudes Historiques_ , 1904, pp.585–602
Balcombe, Lucia Elizabeth, _La Petite Fiancée de Napoléon, Souvenirs de Betsy Balcombe à Sainte-Hélène (1815–1818)_ , ed. Jacques Macé, Paris 2005
Bangofsky, Georges, _Les étapes de G. Bangofsky, officier lorrain: Fragments de son journal de campagne (1797–1815)_ , Paris 1905
Barante, Amable Guillaume Baron de, _Souvenirs du Baron de Barante_ , Vols I & II, Paris 1890–92
Barère, Bertrand, _Mémoires_ , Vol. III, Paris 1843
Barral, P.A., vicomte de, _Souvenirs de guerre et de captivité d'un Page de Napoléon (1812–1815)_ , Paris n.d.
Barras, Paul Jean-François Nicolas, vicomte de, _Mémoires de Barras, membre du Directoire_ , ed. Georges Duruy, 4 vols, Paris 1895–96
Barrès, Jean-Baptiste, _Souvenirs d'un officier de la Grande Armée_ , Paris 1923
Bartel, Paul, _La jeunesse inédite de Napoléon, d'après de nombreux documents_ , Paris 1954
Bast, L. Amédée de, _Mémoires d'un vieil avocat, écrits par lui-même_ , 3 vols, Paris 1847
Baudus, Lieutenant-Colonel K. de, _Études sur Napoléon_ , 2 vols, Paris 1841
Bausset, Louis-François-Joseph, baron de, _Mémoires_ , 4 vols, Paris 1827–29
Beauharnais, Eugène de, _Mémoires et correspondance politique et militaire du Prince Eugène, annotés et mis en ordre par A. Du Casse_ , 10 vols, Paris 1858–60
Beauvollier, Pierre-Louis, comte de, _Mémoires sur l'expédition de Russie_ , in _Mémoires secrets et inédits pour servir à l'histoire contemporaine_ , 2 vols, Paris 1825
Bégos, Louis, _Souvenirs des Campagnes du Lieutenant-colonel Louis Bégos_ , in _Soldats Suisses au Service Étranger_ , Geneva 1909
Belliard, Auguste, _Mémoires du Comte Belliard_ , 2 vols, Paris 1842
Bellot de Kergorre, Alexandre, _Un Commissaire des Guerres sous le premier Empire_ , Paris 1899
Belly de Bussy, David-Victor, _Belly de Bussy_ , in _Les Carnets de la Sabretache_ , 1914, pp.234–9
Benckendorff, Alexander, _Zapiski Benkendorfa_ , Moscow 2001
Bennigsen, Count Lev, _Mémoires du Général Bennigsen_ , 3 vols, Paris 1907–08
Béranger, P. J. de, _Ma Biographie_ , Paris 1857
Bernoyer, François, _Avec Bonaparte en Égypte et en Syrie 1798–1900, 19 lettres inédites_ , Laval 1981
Berry, Mary, _Extracts from the Journals and Correspondence of Miss Berry_ , 3 vols, London 1866
Berthezène, General Baron Pierre, _Souvenirs Militaires de la République et de l'Empire_ , 2 vols, Paris 1855
Berthier, Louis Alexandre, prince de Neuchâtel, _Relation des campagnes du général Bonaparte en Égypte et en Syrie_ , Paris 1800
— & Gainot, Bernard, Ciotti, Bruno, _Marengo: 14 juin 1800_ , Clermont-Ferrand 2010
Bertin, Georges, _La Campagne de 1812 d'après des témoins oculaires_ , Paris 1894
Bertrand, Capitaine, _Mémoires du Capitaine Bertrand_ , Angers 1909
Bertrand, Henri-Gratien, Maréchal comte, _Campagnes d'Égypte et de Syrie 1798–1799_ , 2 vols, Paris 1847
— _Cahiers de Sainte-Hélène_ , 3 vols, Paris 1949–59
— _Lettres à Fanny 1808–1815_ , Paris 1979
Besancenet, Alfred de, ed., _Le Portefeuille d'un général de la République_ , Paris 1877
Beugnot, Jacques Claude Comte, _Mémoires du Comte Beugnot, Ancien Ministre (1783–1815)_ , 2 vols, Paris 1868
Beyle, Henri (Stendhal), _Vie de Napoléon: Fragments_ , Paris 1925
— _Mémoires sur Napoléon_ , Paris 1929
— _Selected Journalism from the English Reviews_ , London 2010
Białkowski, Antoni, _Pamiętniki starego żołnierza (1806–1814)_ , Warsaw 1903
Bielecki, R. & Tyszka, A., _Dał nam przykład Bonaparte. Wspomnienia i relacje żołnierzy polskich 1796–1815_ , 2 vols, Kraków 1984
Bigarré, Auguste, _Mémoires du général Bigarré, Aide de Camp du Roi Joseph, 1775–1813_ , Paris 1893
Bignon, Édouard, baron, _Souvenirs d'un Diplomate_ , Paris 1864
Blanqui, Adolphe, _Souvenirs d'un lycéen de 1814_ , in _Revue de Paris_ , 15 April 1916, pp.847–65: 1 May 1916, pp.103–15
Blocqueville, Marie-Adélaïde Marquise de, _Le Maréchal Davout, Prince d'Eckmühl, racconté par les siens et par lui-même_ , 4 vols, Paris 1880
Boigne, Adèle comtesse de, _Récits d'une tante: Mémoires de la comtesse de Boigne, née d'Osmond_ , 4 vols, Paris 1908
Bombelles, Marc-Marie marquis de, _Journal_ , Vol. V, Geneva 2002
Bonaparte, Lucien, _Lucien Bonaparte et ses Mémoires 1775–1840_ , ed. Th. Jung, 3 vols, Paris 1882–83
Bonnau, _L'embarquement de l'Empereur à Rochefort: Relation de Bonnau, agent comptable à bord de l'Épervier_ , in _Revue retrospective_ , 1895, Tome II, pp.420–3
Boswell, James, _The Journal of a Tour to Corsica; and Memoirs of Pascal Paoli_ , London 1951
Bouillé, Louis-Joseph-Amour Marquis de, _Souvenirs et fragments pour servir aux mémoires de ma vie et de mon temps_ , 3 vols, Paris 1906–11
Boulart, Jean François, _Mémoires Militaires du Général baron Boulart sur les guerres de la République et de l'Empire_ , Paris n.d.
Bourgeois, René, _Tableau de la campagne de Moscou en 1812_ , Paris 1814
Bourgogne, Adrien, _Mémoires du Sergent Bourgogne (1812–1813)_ , Paris 1901
Bourgoing, Paul Charles Amable Baron de, _Souvenirs d'histoire contemporaine_ , Paris 1864
Bourrienne, Louis Antoine, _Mémoires de M. de Bourienne Ministre d'État sur Napoléon_ , 10 vols, Paris 1829
— _Mémoires de M. de Bourienne Ministre d'État sur Napoléon_ , 10 vols, Paris 1831
Boussingault, Jean-Baptiste, _Mémoires de J.B. Boussingault_ , 5 vols, Paris 1892–1900
Brandt, Heinrich von, _Souvenirs d'un Officier Polonais: Scènes de la vie militaire en Espagne et en Russie (1808–1812)_ , Paris 1877
Broekere, Stanisław, _Pamiętniki z wojny hiszpańskiej 1808–1814_ , Gdynia 2004
Broglie, Achille-Charles-Léonce duc de, _Souvenirs du feu duc de Broglie_ , Vol. I, Paris 1886
Browning, Oscar, ed., _England and Napoleon in 1803; being the despatches of Lord Whitworth and others, etc._ , London 1887
Brun de Villeret, Louis, Général baron, _Les Cahiers du Général Brun_ , Paris 1953
Burney, Fanny, _Fanny Burney's Diary: A Selection from the Diary and Letters_ , ed. John Wain, London 1961
Byrne, Miles, _Memoirs of Miles Byrne, Chef de bataillon in the service of France_ , 3 vols, Paris 1863
Cadet de Gassicourt, _Voyage en Autriche, en Moravie et en Bavière fait à la suite de l'armée française pendant la campagne de 1809_ , Paris 1818
Calosso, Colonel, _Mémoires d'un vieux soldat_ , Turin 1857
Cambacérès, Jean-Jacques de, _Lettres inédites à Napoléon 1802–1814_ , 2 vols, Paris 1973
— _Mémoires inédits_ , 2 vols, Paris 1999
Campbell, Major-General Sir Neil, _Napoleon at Fontainebleau and Elba, being a Journal of Occurrences in 1814–1815_ , London 1869
Canova, Antonio, _Scritti_ , Rome 2007
Carnot, Lazare Nicolas, _Mémoires historiques et militaires_ , Paris 1824
Carr, Sir John, _The Stranger in France; or, a Tour from Devonshire to Paris_ , London 1807
Carrington, Dorothy, _Portrait de Charles Bonaparte d'après ses écrits de jeunesse et ses mémoires_ , Ajaccio 2002
Castanié, François, _Les Indiscrétions d'un Préfet de Police de Napoléon_ , Paris n.d.
Castellane, Boniface de, _Journal du Maréchal de Castellane 1804–1862_ , Vol. I, Paris 1895
Caulaincourt, Armand Augustin Louis, Duc de Vicence, _Mémoires_ , 3 vols, Paris 1933
Chailly, A., _Le Boursier de l'Empereur: Document sur la vie intime de Napoléon_ , Paris 1857
Champagny, Jean-Baptiste, duc de Cadore, _Souvenirs de M de Champagny, duc de Cadore_ , Paris 1846
Chaptal, Jean-Antoine, _Mes Souvenirs sur Napoléon_ , Paris 1893
Chastenay, Victorine de, _Mémoires 1771–1815_ , Paris 1987
Chevalier, Jean-Michel, _Souvenirs des guerres napoléoniennes_ , Paris 1970
Chevallier, Bernard & Laot, Jean-Michel, ed., _Napoléon & Joséphine: Correspondance, lettres intimes_, Paris 2012
Chłapowski, Dezydery, _Mémoires sur les guerres de Napoléon 1806–1813_ , Paris 1908
Chłopicki, Jan, _Pamiętnik Jana Chłopickiego, porucz. 7 pułku Ułanów wojsk francuskich, z czasów kampanij Napoleona_ , Wilno 1849
Choderlos de Laclos, Étienne, _Le fils de Laclos: Carnets de marche du commandant Choderlos de Laclos (an XIV–1814)_ , Lausanne 1912
Choiseul-Gouffier, Comtesse de, _Reminiscences sur l'empereur Alexandre Ier et sur l'empereur Napoléon Ier_ , Paris 1862
Clary-et-Aldringen, Charles, _Souvenirs: Trois mois à Paris lors du mariage de l'Empereur Napoléon 1er et de l'archiduchesse Marie-Louise_ , Paris 1914
Cockburn, Rear-Admiral Sir George, _Extract from a Diary etc._ , London 1888
Coignet, Jean-Roch, _Les Cahiers du Capitaine Coignet_ , Paris 1968
Colbert, Auguste, _Traditions et Souvenirs, ou Mémoires touchant le temps et la vie du général Auguste Colbert_ , 5 vols, Paris 1863–73
Collot, Jean-Pierre, _Les Souvenirs du Receveur Général Collot_ , ed. Clarisse Bader, Lyon 1897
Combe, Julien, _Mémoires du Colonel Combe sur les campagnes de Russie 1812, de Saxe 1813 et de France 1814 et 1815_ , Paris 1853
Comeau de Charry, Sébastien-Joseph de, _Souvenirs des guerres d'Allemagne pendant la Révolution et l'Empire_ , Paris 1900
Consalvi, Ercole, _Mémoires du Cardinal Consalvi_ , ed. J. Crétineau-Joly, Paris 1895
Constant, Benjamin, _Journal Intime_ , Monaco 1945
— _Lettres à Bernadotte: Sources et origine de l'Ésprit de conquête et de l'usurpation_ , ed. Bengt Hasselrot, Geneva 1952
— _Mémoires sur les Cent-Jours_ , Tübingen 1993
_Copies of Original Letters from the Army of General Bonaparte in Egypt, intercepted by the Fleet_ , Dublin 1799
Cornwallis, Charles, _The Correspondence of Charles, First Marquess Cornwallis_ , Vol. III, London 1859
Costa de Beauregard, Marquis Henry de, _Un Homme d'autrefois: Souvenirs recueillis par son arrière-petit-fils_ , Paris 1891
Coston, François-Gilbert baron de, _Biographie des premières années de Napoléon Bonaparte_ , 2 vols, Paris 1840
Cuneo d'Ornano, François, _Napoléon au Golfe Juan_ , Paris 1830
Daleki, J., _Wspomnienia mojego ojca żołnierza dziewiątego pułku Księstwa Warszawskiego_ , Poznań 1864
Damas, Roger, comte de, _Mémoires du comte Roger de Damas_ , Paris 1912
Davout, Louis-Nicolas, Prince d'Eckmühl, _Correspondance du Maréchal Davout, prince d'Eckmühl_ , 4 vols, Paris 1885
Decaen, Charles-Mathieu, _Mémoires et journaux du Général Decaen_ , 2 vols, Paris 1910–11
Dedem van der Gelder, Baron Antoine-Baudouin Gisbert van, _Mémoires du Genéral Baron de Dedem de Gelder, 1774–1825_ , Paris 1900
Deifel, Joseph, _Mit Napoleon nach Russland: Tagebuch des Infanteristen Joseph Deifel_ , Regensburg 2012
Denniée, P.P., _Itinéraire de l'Empereur Napoléon pendant la campagne de 1812_ , Paris 1842
Denon, Dominique Vivant, _Voyage dans la Basse Égypte pendant les campagnes du général Bonaparte_ , Paris 1998
Des Genettes, René, _Histoire médicale de l'armée d'Orient_ , Paris 1802
— _Souvenirs de la fin du XVIIIe siècle et du commencement du XIXe_ , 2 vols, Paris 1835–36
— _Souvenirs d'un médecin de l'expédition d'Égypte_ , Paris 1893
Desmarest, Pierre-Marie, _Quinze Ans de Haute Police sous le Consulat et l'Empire_ , Paris 1900
Divova, Elizaveta Petrovna, _Journal et Souvenirs de Madame Divoff_ , Paris 1929
_Documents Particuliers en forme de lettres sur Napoléon Bonaparte, etc._ , Paris 1819
Douglas, Sylvester, _The Diaries of Sylvester Douglas (Lord Glenbervie)_ , ed. Francis Bickley, 2 vols, London 1928
Dubrovin, N., ed., _Otechestvennaya voina v pismakh sovremennikov_ , in _Zapiski Imperatorskoi Akademii Nauk_ , Vol. XLIII, St Petersburg 1882
Ducrest, Georgette, _Mémoires sur l'Impératrice Joséphine, ses contemporains, la cour de Navarre et de la Malmaison_ , Paris 2004
Dumas, comte Mathieu, _Souvenirs du lieutenant général comte Mathieu Dumas de 1770 à 1836_ , 3 vols, Paris 1839
Dumonceau, François, _Mémoires du Général Comte François Dumonceau_ , 3 vols, Brussels 1960
Dumont Romain, J.Ps., _Détail exact de tout ce qui s'est passé dans l'intérieur du Directoire et de l'évènement qui y est arrive: Singularité sur Buonaparte_ , Paris
Durand, la générale, _Mémoires sur Napoléon et Marie-Louise 1810–1814_ , Paris 1886
Durand, Jean-Baptiste Alexis, _Napoléon à Fontainebleau: choix d'épisodes_ , Fontainebleau 1850
Ebrington, H.F. Fortescue, viscount, _Memorandum of Two Conversations between the Emperor Napoleon and Viscount Ebrington, at Porto Ferrajo, on the 6th and 8th of December, 1814_ , London 1823
Edgeworth, Maria, _Maria Edgeworth in France and Switzerland_ , ed. Christina Colvin, Oxford 1979
Elbée, François-Henri d', _Mémoires du général d'Elbée_ , in _Carnets de la Sabretache_ , 1935, pp.357–81, 453–84: 1936, pp.21–30, 114–27, 179–204, 280–92, 368–86, 491–504
Ernouf, baron, _Maret, duc de Bassano_ , Paris 1884
Fain, Agathon Jean François, _Manuscrit de Mil Huit Cent Treize_ , 2 vols, Paris 1824
— _Manuscrit de Mil Huit Cent Quatorze_ , Paris 1825
— _Manuscrit de Mil Huit Cent Douze_ , 2 vols, Paris 1827
— _Mémoires du Baron Fain_ , Paris 1908
Fantin des Odoards, Général Louis Florimond, _Journal du Général Fantin des Odoards: Étapes d'un Officier de la Grande Armée_ , Paris 1895
Farington, Joseph, _The Diary of Joseph Farington_ , ed. Kenneth Garlick & Angus Macintyre, Vol. V, New Haven 1979
Faucheur, Narcisse, _Souvenirs de campagnes du Sergent Faucheur, fourrier dans la Grande Armée_ , Paris 2004
Fiszerowa, Wirydianna, _Dzieje moje własne i osób postronnych_ , London 1975
Fleury, M., _Mémoires de Fleury de la Comédie Française_ , 6 vols, Brussels 1838
Fleury de Chaboulon, P.A., _Mémoires de Fleury de Chaboulon, ex-secrétaire de l'empereur Napoléon et de son cabinet, etc., Avec annotation manuscrites de Napoléon Ier_ , 3 vols, Paris 1901
Fontaine, Pierre-François-Léonard, _Journal, 1799–1853_ , 2 vols, Paris 1987
— _Les Maisons du Premier Consul_ , Paris 1911
Fouché, Joseph, _Mémoires de Joseph Fouché, duc d'Otrante_ , 2 vols, Paris 1824
— _Mémoires_ , Paris 1945
— _Mémoires de Joseph Fouché, duc d'Otrante, Ministre de la Police Générale_ , Paris 1957
Fourès, Lieutenant, _Trois lettres du lieutenant Fourès, le mari de Bellilotte_ , in _Revue des Études napoléoniennes_ , Vol. XLI, 1935, pp.163–7
François, Charles, _Journal du Capitaine François (dit le dromadaire d'Égypte) 1792–1830_ , 2 vols, Paris 1904
Frémeaux, Paul, _With Napoleon at St Helena; being the Memoirs of Dr John Stokoe, naval surgeon_ , Lane 1902
Frénilly, François-Auguste de, _Souvenirs du Baron de Frénilly_ , Paris 1908
Gajewski, Franciszek, _Pamiętniki Franciszka z Błociszewa Gajewskiego, pułkownika wojsk polskich 1802–1831_ , 2 vols, Poznań 1913
Garnier, Jacques, ed., _Les bulletins de la Grande Armée_ , Paris 2013
Garros, Louis, _Quel roman que ma vie! Itinéraire de Napoléon Bonaparte, 1769–1821_ , Paris 1947
Gazo, Jean, _Mémoires sur l'expédition de Russie_ , in _Mémoires secrets et inédits pour servir à l'histoire contemporaine_ , 2 vols, Paris 1825
Gentz, Friedrich von, _Briefwechsel zwischen Gentz und Johannes von Müller_ , Mannheim 1840
— _Dépèches inédites aux Hospodars de Valachie_ , Vol. I, Paris 1876
Geoffroy Saint-Hilaire, Étienne, _L'Expédition d'Égypte 1798–1802_ , Paris 2012
George, Marguerite-Joséphine Wemmer, aka Mlle, _Mémoires inédits de Mademoiselle George_ , Paris 1908
Ginisty, Paul, ed., _Mémoires d'Anonymes et d'Inconnus (1814–1850)_ , Paris 1907
Girard, Étienne-François, _Les Cahiers du Colonel Girard 1766–1846_ , Paris 1951
Girardin, Stanislas-Cécile comte de, _Mémoires de S. Girardin_ , 2 vols, Paris 1834
Girod de l'Ain, Gabriel, _Désirée Clary d'après sa correspondance inédite avec Bonaparte, Bernadotte et sa famille_ , Paris 1959
Goethe, Johann Wolfgang, _Sämtliche Werke: Briefe, tagebücher un gespräche_ , Vol. XVII, Frankfurt 1994
Gohier, Louis-Jérôme, _Mémoires_ , Paris 1824
Gourgaud, Général baron Gaspard, _Journal de Sainte-Hélène 1815–1818_ , 2 vols, Paris 1944
Grabowski, Józef, _Pamiętniki Wojskowe Józefa Grabowskiego, oficera sztabu cesarza Napoleona I_ , Warsaw 1905
Greathead, Bertie, _An Englishman in Paris: 1803: The Journal of Bertie Greathead_ , London 1953
Griois, Lubin, _Mémoires du Général Griois, 1792–1822_ , 2 vols, Paris 1909
Gross, Johann Carl, _Erinnerungen aus den Kriegsjahren_ , Leipzig 1850
Grouchy, Emmanuel comte de, _Mémoires du Maréchal de Grouchy_ , 5 vols, Paris 1873–74
Grüber, Carl-Johann Ritter von, _Souvenirs du Chevalier de Grüber_ , Paris 1909
Guitard, Joseph-Esprit-Florentin, _Souvenirs militaires du Premier Empire_ , Paris 1934
Guitry, Paul Georges, _L'Armée de Bonaparte en Égypte 1798–1799_ , Paris 1898
Hardenberg, Prince, _Mémoires tirés des papiers d'un homme d'état_ , 13 vols, Paris 1828–38
Hautpoul, Armand d', _Souvenirs sur la Révolution, l'Empire et la Restauration_ , Paris 1904
Hegel, Georg Wilhelm Friedrich, _Gesammelte Werke_ , Hamburg 1968
— _Werke: Auf der Grundlage der Werke von 1832–1845 neu edierte Ausgabe_ , 20 vols, Frankfurt am Main 1986
— & Knebel, Karl Ludwig von, _Briefe von und an Hegel_ , Vol. I, Hamburg 1969
Heiberg, Peter-Andréas, _Souvenirs d'un Danois au service de la France_ , in _Revue des Études napoléoniennes_ , 1919, Tome I, pp.195–217, 283–306
Heine, Heinrich, _Ideas: The Book of Le Grand_ , in _The Harz Journey and Selected Prose_ , trans. Ritchie Robertson, London 1993
Holland, Elizabeth Lady, _The Journal of Elizabeth Lady Holland_ , 2 vols, London 1908
Hortense de Beauharnais, Queen of Holland, _Mémoires de la Reine Hortense_ , 3 vols, Paris 1927
Humboldt, Wilhelm von, _Wilhelm und Caroline von Humboldt in ihren Briefen_ , Vols IV & V, 1910–12
Hyde de Neuville, Jean-Guillaume, baron, _Mémoires et souvenirs du baron Hyde de Neuville_ , 3 vols, Paris 1888
Jackson, B., _Notes of a staff-officer_ , London 1903
Jal, Auguste, _Souvenirs d'un homme de lettres_ , Paris 1877
Jerome Bonaparte, King of Westphalia, _Mémoires et correspondance du Roi Jérôme et de la Reine Catherine_ , 7 vols, Paris 1861–66
Joachim Murat, King of Naples, _Lettres et documents pour server à l'histoire de Joachim Murat 1767–1815_ , 8 vols, Paris 1908–14
_Johannes von Müller an seinen Bruder, 25 November 1806_ , in Johannes von Müller, _sämmtliche Werke_ , Vol. VII, Tübingen 1812
Jomard, Edmé-François, _Souvenirs sur Gaspard Monge et ses rapports avec Napoléon_ , Paris 1853
Joseph Bonaparte, King of Spain, _Mémoires et Correspondance politique et militaire du Roi Joseph_ , ed. A. Du Casse, 10 vols, Paris 1854–55
— _Lettres inédites ou éparses de Joseph Bonaparte à Naples (1806–1808)_ , Paris 1911
Josephine, Empress Consort of Napoleon I, _Correspondance, 1782–1814_ , Paris 1996
Kicka, Natalia, _Pamiętniki_ , Warsaw 1972
Koch, G.G., _Histoire Abrégée des Traités de Paix, etc._ , Vol. X, Paris 1818
Köster, Albert, ed., _Briefe von Goethes Mutter_ , Leipzig 1917
Koźmian, Kajetan, _Pamiętniki_ , Vol. II, Warsaw 1972
Lacorre, Alexandre, _Journal inédit d'un commis aux vivres pendant l'expédition d'Égypte_ , Bordeaux 1852
Lafayette, Marie-Joseph Gilbert du Motier, marquis de, _Mémoires, correspondance et manuscrits du général La Fayette_ , Vol. V, Paris 1838
La Flise, N.D. de, _Pokhod Velikoi Armii v Rossiiu v 1812 g; Zapiski de la Fliza_ , in _Ruskaia Stariana_ , Vols LXXI, LXXII, LXXIII, July 1891–March 1892
Lagneau, L.V., _Journal d'un Chirurgien de la Grande Armée 1803–1815_ , Paris 1913
Lameth, Théodore de, _Mémoires_ , Paris 1913
— _Notes et souvenirs_ , Paris 1914
Lareveillère-Lepaux, Louis-Marie de, _Mémoires_ , 2 vols, Paris 1895
Larrey, baron, _Madame Mère (Napoleonis Mater)_ , 2 vols, Paris 1892
Larrey, Dominique-Jean baron, _Mémoires de Chirurgie Militaire et Campagnes du Baron D.J. Larrey_ , 4 vols, Paris 1817
— _Mémoires et campagnes du baron Larrey_ , 5 vols, Paris 1983
Las Cases, Émmanuel, comte de, _Le Mémorial de Sainte-Hélène_ , 4 vols, Paris 1905
— _Le Mémorial de Sainte-Hélène_ , ed. Marcel Dunan, 2 vols, Paris 1983
— _Le Mémorial de Sainte-Hélène, Le Manuscript Original Retrouvé_ , ed. Thierry Lentz, Peter Hicks, Françoise Houdecek, Chantal Prévot, Paris 2017
Laugier, Césare de Bellecour de, _Récits de César de Laugier, officier de la garde du Prince Eugène_ , trs. Henry Lionnet, Paris 1912
Lavalette, Antoine-Marie Chamans, comte de, _Mémoires et Souvenirs_ , Paris 1994
Lee, H., _Life of the Emperor Napoleon_ , London 1834
Lejeune, Louis François, _Souvenirs d'un officier de l'Empire_ , 2 vols, Toulouse 1831
_Letters from the Cape of Good Hope in reply to Mr Warden_ , London 1817
_Letters from the Island of St Helena, exposing the unnecessary severity exercised towards Napoleon_ , London 1818
Ligne, Charles-Joseph prince de, _Fragments de l'Histoire de ma vie_ , 2 vols, Paris 1928
Louis Bonaparte, King of Holland, _Documents Historiques et réflexions sur le gouvernement de la Hollande_ , 3 vols, London 1820
Lubowiecki, Ignacy, _Pamiętniki_ , Lublin 1997
Macdonald, Jacques-Étienne, _Souvenirs du Maréchal Macdonald, Duc de Tarente_ , Paris 1892
Malcolm, Clementina, _A Diary of St. Helena: The Journal of Lady Malcolm (1816, 1817) containing the Conversations of Napoleon with Sir Pulteney Malcolm_ , London 1929
Mallardi, Giuseppe, _Durante il Regno di Gioacchino Murat: Diario di un capitano dei lancieri_ , Polignano 2017
Mallet du Pan, Jacques, _Correspondance inédite de Mallet du Pan avec la Cour de Vienne (1794–1798)_ , 2 vols, Paris 1884
Maquin, _Le débarquement au golfe Juan: Rapport d'un douanier_ , in _Revue retrospective_ , XII, 1890, pp.135–7
Marbot, Antoine-Marcelin Baron de, _Mémoires du General Baron de Marbot_ , 3 vols, Paris 1891
Marchand, Louis, _Mémoires de Marchand, premier valet de chambre et executeur testamentaire de l'empereur_ , ed. Jean Bourguignon, Paris 1955
Marmont, Auguste, duc de Raguse, _Mémoires du Maréchal Marmont, duc de Raguse de 1792 à 1841_ , 9 vols, Paris 1857
Martin, P., _Histoire de l'expédtion française en Égypte_ , 2 vols, Paris 1815
Masséna, André, Prince d'Essling, _Mémoires de Masséna_ , 7 vols, Paris 1848–50
Masson, Frédéric, _Napoléon Inconnu: Papiers Inédits (1786–1793)_ , 2 vols, Paris 1895
Maubreuil, Marie Armand de Guerry de, Marquis d'Orvault, _Adresse au Congrès, à toutes les puissances de l'Europe_ , London 1819
Méneval, Claude-François de, _Napoléon et Marie-Louise: Souvenirs Historiques_ , Brussels 1843
— _Mémoires pour servir à l'histoire de Napoléon Ier depuis 1802 jusqu'à 1815_ , 3 vols, Paris 1893–94
Metternich, Prince Clemens Wenzel Lothar von, _Mémoires, Documents et Écrits divers laissés par le Prince de Metternich_ , ed. A. de Klinkowstroem, Vols I & II, Paris 1880
— _Clemens Metternich-Wilhelmina von Sagan: ein briefwechsel 1813–1815_ , Graz 1966
Millet, Pierre, _Le Chasseur Millet: Souvenirs de la campagne d'Égypte (1798–1801)_ , Paris 1903
Miot, J., _Mémoires pour servir à l'histoire des expéditions en Égypte et en Syrie_ , Paris 1814
Miot de Melito, André-François, _Mémoires du comte Miot de Melito, ancien ministre, ambassadeur, conseiller d'État et membre de l'Institut (1788–1815)_ , 3 vols, Paris 1858
Moiret, Joseph-Marie, _Mémoires sur l'expédition d'Égypte_ , Paris 1983
Molé, Mathieu-Louis comte, _Le Comte Molé: Sa vie, ses mémoires_ , Vol. I, Paris 1922
— _Souvenirs de Jeunesse (1793–1803)_ , Paris 1991
Mollien, François-Nicolas comte, _Mémoires d'un ministre du Trésor public 1780–1815_ , 3 vols, Paris 1898
Montalivet, Marthe-Camille Bachasson, comte de, _Fragments et souvenirs_ , 2 vols, Paris 1899
Montchenu, marquis de, _La Captivité de Sainte-Hélène d'après les rapports inédits du marquis de Montchenu_ , Paris 1894
Montesquiou, comte Anatole de, _Souvenirs sur la Révolution, l'Empire, la Restauration et le règne de Louis-Philippe_ , Paris 1961
Montesquiou, Raymond-Émery, duc de Fezensac, _Souvenirs Militaires de 1804 à 1814_ , Paris 1870
— _Journal de la campagne de Russie en 1812_ , Paris 2012
Montet, Alexandrine, baronne du, _Souvenirs de la Baronne du Montet, 1785–1866_ , Paris 1914
Montholon, Albine, comtesse de, _Souvenirs de Sainte-Hélène_ , Paris 1901
Montholon, Charles, comte de, _Histoire de la Captivité de Ste-Hélène_ , 2 vols, Brussels 1846
Mounier, Claude-Philibert-Édouard, _Souvenirs intimes et notes du baron Mounier, secrétaire de Napoléon 1er, pair de France_ , Paris 1896
Müffling, Baron Carl von, _The Memoirs of Baron von Müffling, a Prussian Officer in the Napoleonic Wars_ , London 1997
Müller, Friedrich von, _Erinnerungen aus den Kriegszeiten 1806–1813_ , Hamburg 1906
Muralt, Konrad von, _Hans von Reichard Bürgemeister des eidgenössischen Stades Zürich und Landamann der Schweiz_ , Zürich 1839
Napoleon I, Emperor of the French, _Correspondance de Napoléon Ier_ , 32 vols, Paris 1858–70
— _Mémoires pour servir à l'histoire de France sous le Règne de Napoléon écrits à Sainte-Hélène, etc._ , ed. Désiré Lacroix, 5 vols, Paris n.d.
— _Vues politiques_ , ed. Adrien Dansette, Paris 1939
— _Oeuvres littéraires et écrits militaires_ , ed. Jean Tulard, 3 vols, Paris 1967–69
— _Napoléon à Sainte-Hélène: Textes préfacés, commentés et choisis par Jean Tulard_ , Paris 1981
— _Correspondance Générale_ , 13 vols, Paris 2004–17
— _Mémoires de Napoléon: La campagne d'Égypte (1798–1801)_ , ed. Thierry Lentz, Paris 2011
— _Les Bulletins de la Grande Armée_ , ed. Jacques Garnier, Paris 2013
_Napoléon à Waterloo, ou Précis de la Campagne de 1815, Avec des Documents nouveaux et des Pièces inédites, par un Ancien Officier de la Garde Imperiale_ , Paris 1866
_Napoleon i Polacy, epizod z nieogłoszonych pamiętników_ , in _Czas_ , 1874 pp.161ff
Nasica, Toussaint, _Mémoires sur l'enfance et la jeunesse de Napoléon_ , Paris 1852
Nesselrode, A. de, ed., _Lettres et Papiers du Chancelier Comte de Nesselrode 1760–1850_ , Vol. I, Paris n.d.
Niello-Sargy, Jean-Gabriel, _Mémoires sur l'expédition d'Égypte_ , in _Mémoires secrets et inédits pour servir à l'histoire contemporaine_ , 2 vols, Paris 1825
Niemcewicz, Julian Ursyn, _Pamiętniki Czasów Moich_ , Paris 1848
Noel, J.N.A., _Souvenirs Militaires d'un Officier du Premier Empire_ , Paris 1895
_Notice sur le Dix-Huit Brumaire, par un témoin qui peut dire Quod vidi testor_ , Paris 1814
Oncken, Wilhelm, _Österreich und Preussen im Befreiungskriege_ , 2 vols, Berlin 1876–79
Ouvrard, G.-J., _Mémoires de G.-J. Ouvrard_ , 3 vols, Paris 1827
Pacca, Cardinal Bartolomeo, _Memorie Storiche del Ministero, de Due Viaggi in Francia, et della prigionia nel Forte de S. Carlo in Fenestrelle_ , 2 vols, Orvieto 1843
Parquin, Denis-Charles, _Souvenirs du commandant Parquin_ , Paris 1979
Pasquier, Étienne Denis, _Mémoires du Chancelier Pasquier_ , 3 vols, Paris 1893
Pastoret, Amédée de, _De Vitebsk à la Bérézina_ , in _La Revue de Paris_ , 9e année, Tome II, 1902
Pelet de la Lozère, Privat-Joseph, _Opinions de Napoléon sur divers sujets de politique et d'administration, receuillis par un membre de son conseil d'État et récit de quelques événements de l'époque_ , Paris 1833
Pelleport, Pierre Vicomte de, _Souvenirs Militaires et Intimes du Général Vte de Pelleport_ , 2 vols, Paris 1857
Pelletreau, Gédéon-Henri, _L'embarquement de l'Empereur à Rochefort_ , in _La Nouvelle Revue Rétrospective_ , 1895, Tome II
Peyrusse, Guillaume Baron, _Mémorial et archives 1809–1815_ , Paris 1869
— _Lettres Inédites du Baron Guillaume Peyrusse écrites à son frère André pendant les campagnes de l'Empire_ , Paris 1894
Pion des Loches, Antoine, _Mes campagnes (1792–1815)_ , Paris 1889
Planat de la Faye, Nicolas Louis, _Rome et Sainte-Hélène de 1815 à 1821_ , Paris 1862
— _Vie de Planat de la Faye_ , Paris 1895
Plumptre, Anne, _A Narrative of Three Years' Residence in France, etc._ , 3 vols, London 1810
Pons de l'Hérault, André, _Souvenirs et anecdotes de l'Île d'Elbe_ , Paris 1897
Pontécoulant, Louis Gustave comte de, _Souvenirs historiques et parlementaires du comte de Pontécoulant_ , 4 vols, Paris 1861–65
Potocka, Anna, _Mémoires de la Ctesse Potocka (1794–1820)_ , Paris 1897
Pouget, Général Baron, _Souvenirs de Guerre_ , Paris 1895
Poupé, Edmond, ed., _Lettres de Barras & de Fréron en mission dans le Midi_, Draguignan 1910
Pradt, Dominique Dufour de, _Histoire de l'ambassade dans le Grand Duché de Varsovie en 1812_ , Paris 1816
Radozhitskii, I.T., _Pokhodnia Zapiski artillerista s 1812 goda_ , Vol. I, Moscow 1835
Radziwiłł, Louise de Prusse, princesse Antoine, _Quarante-cinq années de ma vie (1770 à 1815)_ , Paris 1911
Rapp, Jean, _Mémoires du Général Rapp, Aide de Camp de Napoléon_ , London 1823
Raumer, Georg Wilhelm von, _Preußens Lage, vor dem Ausbruch des Kriegs gegen Napoleon im Jahre 1813, in Berliner Taschenbuch_ , Berlin 1849
Raza, Roustam, _Souvenirs de Roustam Mamelouck de Napoléon Ier_ , Paris 1911
Réal, Pierre-François, _Indiscrétions. 1798–1830: Souvenirs anecdotiques et politiques tirés du portefeuille d'un fonctionnaire de l'Empire_ , 2 vols, Paris 1835
_Recueil complet des discours prononcés par le citoyen Barras, président du Directoire, par le général Bonaparte, par les ministres des Relations extérieures et de la Guerre, et par le général Joubert et le chef de brigade Andréossy, à l'audience solennelle donnée par le Directoire, le 20 frimaire an VI, pour la ratification du traité de paix conclu à Campo-Formio par le général Bonaparte, et la présentation du drapeau de l'armée d'Italie ; accompagné de la description fidèle de cette fête et des hymnes qui y ont été chantés_ , Paris [1797]
Reichardt, Johann Friedrich, _Vertraute Briefe aus Paris Geschrieben in den jahren 1802 un 1803_ , Hamburg 1804
Reinhard, Marcel, _Avec Bonaparte en Italie: D'après les lettres inédites de son aide de camp Joseph Sulkowski_ , Paris 1946
Remacle, comte L., _Bonaparte et les Bourbons: Relations secrètes des agents de Louis XVIII à Paris sous le Consulat_ , Paris 1899
Rémusat, Charles de, _Mémoires de ma vie_ , Vol. I, Paris 1958
Rémusat, Claire Elisabeth comtesse de, _Mémoires de Madame de Rémusat 1802–1808_ , 3 vols, Paris 1880
— _Lettres_ , 2 vols, Paris 1881
Revel, Jean-François, _Souvenirs_ , in _Nouvelle Revue Rétrospective, 1er janvier & 1er février_ 1903, pp.1–24, 73–91
Ricard, Joseph de, _Autour des Bonaparte: Fragments de mémoires_ , Paris 1891
Rochechouart, Léon Comte de, _Souvenirs sur la Révolution, l'Empire et la Réstauration_ , Paris 1889
Roederer, Pierre-Louis, _Oeuvres du comte P.L. Roederer_ , 8 vols, Paris 1853–59
Roguet, Christophe Michel, _Mémoires Militaires_ , 4 vols, Paris 1862–65
Rousseau, Jean-Jacques, _Du Contrat Social_ , in _Oeuvres complètes_ , Vol. V, Paris 1832
Routier, L.M., _Récits d'un soldat de la République et de l'Empire_ , Paris 1899
Rumigny, général comte Théodore de, _Souvenirs du général comte de Rumigny, aide de camp du roi Louis-Philippe (1789–1860)_ , Paris 1921
Saint-Denis, Louis-Étienne, _Souvenirs du Mameluck Ali sur l'Emepereur Napoléon_ , Paris 1926
Saint-Elme, Ida, _Souvenirs d'une courtisane de la Grande Armée_ , Paris 2004
Sanguszko, Eustachy, _Pamiętnik 1786–1815_ , Kraków 1876
Savary, Anne-Jean-Marie, duc de Rovigo, _Mémoires du duc de Rovigo, pour servir à l'histoire de l'Empereur Napoléon_ , 8 vols, Paris 1828
Schouvaloff, Paul, _De Fontainebleau à Fréjus – Avril 1814_ , in _Revue de Paris_ , 15 avril 1897
Scott, Walter, _Scott on Waterloo_ , London 2015
Ségur, Philippe-Paul, comte de, _Histoire et Mémoires_ , 7 vols, Paris 1873
— _Un aide de camp de Napoléon (1800–1815): Mémoires_ , Simon, Paris n.d.
Senfft von Pilsach, Count, _Mémoires du comte de Senfft, ancien ministre de Saxe_ , Leipzig 1863
Shishkov, A.S., _Zapiski, Mnenia i Perepiska Admirala A.S. Shishkova_ , 2 vols, Berlin 1870
Shorter, Clement, ed., _Napoleon and His Fellow Travellers_. _Being a Reprint of Certain Narratives of the Voyages of the Dethroned Emperor on the Bellerophon and the Northumberland, etc._ , London 1908
Skałkowski, A.M., ed., _Fragmenty_ , Poznań 1928
Sołtyk, Count Roman, _Napoléon en 1812, Mémoires Historiques et Militaires sur la Campagne de Russie_ , Paris 1836
_Some account of the early years of Buonaparte at the military school of Brienne and his conduct at the commencement of the French Revolution, by Mr. C.H. one of his school fellows_ , London 1797
Soult, Jean de Dieu, duc de Dalmatie, _Mémoires: Espagne et Portugal_ , Paris 2013
Staël-Holstein, Anne-Louise-Germaine baronne de, _Considérations sur la Révolution française_ , in _Oeuvres complètes_ , Vol. XIII, Paris 1820
— _De l'influence des passions sur le bonheur des individus et des nations_ , Paris 1845
— _De la littérature considérée dans ses rapports avec les institutions sociales_ , Paris 1845
— _Dix Années d'Exil_ , La Renaissance du Livre, Paris n.d.
Sturmer, Baron Bartholomeus von, _Napoleon à Sainte-Hélène_ , ed. Jacques St Cere & H. Schlitter, Paris n.d.
Sułkowski, Antoni, _Listy do żony z wojen napoleońskich_ , Warsaw 1987
Sułkowski, Józef, see Reinhard
Suphan, Bernhard, _Napoleons Unterhaltungen mit Goethe und Wieland und Fr. v. Müllers Memoire darüber für Talleyrand_ , in Goethe-Jahrbuch, Bd. 15 (1894)
Szymanowski, Józef, _Pamiętniki jenerała Józefa Szymanowskiego_ , Lwów 1898
Talleyrand, Charles Maurice Prince de, _Lettres Inédites de Talleyrand à Napoléon_ , Paris 1889
— _Lettres de M. de Talleyrand à Madame de Staël_ , in _Revue d'Histoire Diplomatique_ , 1890, I/78
— _Mémoires: L'époque napoléonienne_ , ed. Jean Tulard, Paris 1996
Tarnowska, Urszula, _Król Hieronim w Warszawie w roku 1812_ , in _Ruch literacki_ , 1876, Tome II, pp.54–5
Thiard, Marie-Théodose de, _Souvenirs diplomatiques et militaires du Général Thiard_ , extrait de la Nouvelle Revue, Tome III, vingt-et-unième année, 1900
Thibaudeau, Antoine-Claire, _Mémoires de A.-C. Thibaudeau 1799–1815_ , Paris 1913
Thirion, Auguste, _Souvenirs Militaires_ , Paris 1892
Trembicka, Françoise, _Mémoires d'une Polonaise pour servir à l'histoire de la Pologne, depuis 1764 jusqu'à 1830_ , 2 vols, Paris 1841
Truchsess-Waldburg, baron, _Nouvelle relation de l'itinéraire de Napoléon de Fontainebleau à l'ile d'Elbe..._ , Paris 1815
Tulard, Jean, ed., _Napoléon à Sainte-Hélène_ , Paris 1881
— _Procès-verbal de la cérémonie du Sacre et du couronnement de Napoléon_ , Paris 1993
— & Garros, Louis, _Itinéraire de Napoléon au jour de jour 1769–1821_ , Paris 1992
Versini, Xavier, _M. de Buonaparte, ou le livre inachevé_ , Paris 1977
Victor, Claude Perrin, duc de Bellune, _Extraits des Mémoires Inédits de feu Claude-Victor Perrin, duc de Bellune_ , Paris 1846
Vigo-Roussillon, François, _Journal de Campagne (1793–1837)_ , Chaintraux 2013
Villemain, Abel François, _Souvenirs contemporains d'histoire et de littérature_ , Vol. I, Paris 1854
Villiers du Terrage, Édouard de, _Journal et Souvenirs sur l'Expédition d'Égypte (1798–1801)_ , Paris 1899
Vionnet de Maringoné, Louis Joseph, _Campagne de Russie et de Saxe_ , Paris 1899
Volkonskii, S.G., _Zapiski_ , St Petersburg 1902
Voss, Sophie Marie Gräfin von, _Neunundsechzig Jahre am Preussischen Hofe_ , Leipzig 1887
Vossler, H.A., _With Napoleon in Russia 1812: The Diary of Lt. H.A. Vossler, a soldier of the Grand Army_ , trans. Walter Wallich, London 1969
Wairy, Louis Constant, _Mémoires de Constant, premier valet de chambre de l'empereur sur la vie privée de Napoléon, sa famille et sa cour_ , 2 vols, Paris 1967
Warden, William, _Letters written on board His Majesty's Ship the Northumberland and at Saint Helena, etc._ , London n.d.
Wellington, Arthur Wellesley, Duke of, _Supplementary Despatches, Correspondence, and Memoranda_ , Vol. IX, London 1864
Westmorland, John Fane, Earl of, _Memoirs of the Great European Congresses of Vienna-Paris, 1814–1815 – Aix-la-Chapelle, 1818 – Troppau, 1820 – and Laybach, 1820–1821_ , London 1860
Williams, Helen Maria, _A Narrative of the Events which have taken place in France, from the Landing of Napoleon Bonaparte on the 1st of March, 1815_ , London 1815
Wojciechowski, Kajetan, _Pamiętniki Moje w Hiszpanii_ , Warsaw 1978
Wołowski, Aleksy, _Główna kwatera Napoleona_ , in _Rozmaitości lwowskie_ , 1835, 29 & 30
Wybicki, Józef, _Pamiętniki_ , Warsaw 1927
Załuski, Józef, _Wspomnienia_ , Krakow 1976
STUDIES
Adams, Michael, _Napoleon and Russia_ , London 2006
Alger, John Goldworth, _Napoleon's British Visitors and Captives 1801–1815_ , London 1904
Amini, Iradj, _Napoleon and Persia: Franco-Persian Relations Under the First Empire_ , London 1999
Aubry, Octave, _Sainte-Hélène_ , 2 vols, Paris 1935
Bahr, E. & Saine, T., eds, _The Internalized Revolution: German Reactions to the French Revolution, 1789–1989_ , New York 1992
Barbero, Alessandro, _Waterloo_ , Paris 2005
Benhamou, Albert, _L'Autre Sainte-Hélène: La captivité, la maladie, la mort et les médecins autour de Napoléon_ , Hemel Hempstead 2010
Béraud, Stéphane, _Bonaparte en Italie: naissance d'un stratège (1796–1797)_ , Paris 2008
— _La révolution militaire napoléonienne_ , 2 vols, Paris 2007–13
Bergeron, Louis, _L'Épisode napoléonien: I. Aspects intérieurs 1799–1815_ , Paris 1972
Bertaud, Jean-Paul, _Le duc d'Enghien_ , Paris 2001
— _L'Abdication: 21–23 juin 1815_ , Paris 2011
— & Forrest, Alain, Jourdan, Annie, _Napoléon, le monde et les Anglais: Guerre des mots et des images_ , Paris 2004
Bien, David, _The Army in the French Enlightenment: Reform, Reaction and Revolution_ , in _Past & Present_, No. 85 (Nov. 1979), pp.68–98
Blaufarb, Rafe, _The French Army 1750–1820: Careers, Talent, Merit_ , Manchester 2002
Blin, Arnaud, _Iéna_ , Paris 2003
— _Wagram_ , Paris 2010
Bodinier, Gilbert, _La Révolution et l'armée; Les campagnes de la Révolution; Du soldat républicain à l'officier impérial: Convergences et divergences entre l'armée et la société; L'armée impériale; Les guerres de l'Empire_ , in Jean Delmas, ed., _Histoire Militaire de la France: 2 – De 1715 à 1871_ , Paris 1992
Bonnet, J.C., _L'Empire des Muses_ , Paris 2004
Boudon, Jacques-Olivier, _Histoire du Consulat et de l'Empire_ , 2003
— _Le roi Jérôme, frère prodigue de Napoléon_ , Paris 2008
— _Napoléon et la campagne de France_ , Paris 2014
Bourdon, Jean, _Napoléon au Conseil d'État_ , Nancy 1963
Bouvier, Félix, _Bonaparte en Italie 1796_ , Paris 1899
Branda, Pierre, _Les secrets de Napoléon_ , Paris 2014
— & Lentz, Thierry, _Napoléon, l'esclavage et les colonies_ , Paris 2006
— _Le Prix de la Gloire: Napoléon et l'Argent_ , Paris 2007
— _Napoléon et ses hommes: La Maison de l'Empereur (1804–1815)_ , Paris 2011
— _L'Île d'Elbe et le retour de Napoléon 1814–1815_ , Paris 2014
Brauer, Kinley & Wright, William E., _Austria in the Age of the French Revolution 1789–1815_ , Minneapolis 1990
Brégeon, Jean-Joël, _L'Égypte de Bonaparte_ , Paris 2006
— _Napoléon et la guerre d'Espagne_ , Paris 2006
Broers, Michael, _The Napoleonic Empire in Italy, 1796–1814: Cultural Imperialism in a European Context_ , London 2005
— _Napoleon's Other War: Bandits, Rebels and their Pursuers in the Age of Revolutions_ , Oxford 2010
— _Napoleon: Soldier of Destiny_ , London 2014
— _Europe Under Napoleon_ , London 2015
Brown, Howard G. & Miller, Judith A., _Taking Liberties_ , Manchester 2002
Bruce, Evangeline, _Napoleon and Josephine: An Improbable Marriage_ , London 1995
Buckland, C.S.B., _Metternich and the British Government from 1809–1813_ , London 1932
— _Friedrich von Gentz' relations with the British Government_ , London 1933
Carrington, Dorothy, _Napoleon and His Parents_ , New York 1990
— _Portrait de Charles Bonaparte: D'après ses écrits de jeunesse et ses mémoires_ , Ajaccio 2012
Casanova, Antoine, _Napoléon et la pensée de son temps_ , Paris 2008
Castle, Ian, _Austerlitz: Napoleon and the Eagles of Europe_ , Barnsley 2005
Chaline, Nadine-Josette, _La paix d'Amiens_ , Amiens 2005
Chandler, David, _Austerlitz 1805_ , London 1990
Chanteranne, David, _Le Sacre de Napoléon_ , Paris 2004
Chappey, Jean-Luc & Gainot, Bernard, _Atlas de l'Empire Napoléonien 1799–1815: Ambitions et limites d'une nouvelle civilisation européenne_ , Paris 2008
Chardigny, Louis, _L'Homme Napoléon_ , Paris 2010
Charles-Roux, Charles, _Les Origines de l'expédition d'Égypte_ , Paris 1910
Chatel de Brancion, Laurence, _Le Sacre de Napoléon: Le rêve de changer le monde_ , Paris 2004
Chevallier, Bernard & Pincemaille, Christophe, _L'impératrice Joséphine_ , Paris 1988
Chuquet, Artur, _La Jeunesse de Napoléon_ , 3 vols, Paris 1897
Clayton, Tim, _Waterloo: Four Days That Changed Europe's Destiny_ , London 2014
Colson, Bruno, _Leipzig: la bataille des Nations (16–19 octobre 1813)_ , Paris 2013
Coston, baron de, _Premières années de Napoléon_ , Paris 1840
Crouzet, François, _L'Économie britannique et le blocus continental (1806–1813)_ , 2 vols, Paris 1958
Cyr, Pascal, _Waterloo: origines et enjeux_ , Paris 2011
Dard, Émile, _Napoléon et Talleyrand_ , Paris 1935
Defranceschi, Jean, _La Jeunesse de Napoléon: Les dessous de l'histoire_ , Paris 2001
De Jaeghere, Michel & Grasselli, Jérôme, _Atlas Napoléon_ , Paris 2001
Derrécagaix, Général, _Le Lieutenant-général comte Belliard_ , Paris 1908
Driault, Édouard, _La politique extérieure du Premier Consul (1800–1803)_ , Paris 1910
— _Tilsit: France et Russie sous le Premier Empire_ , Paris 1917
— _Le Grand Empire_ , Paris 1924
— _Napoléon et l'Europe: La chute de l'Empire. La Légende de Napoléon_ , Paris 1927
Dufraisse, Roger & Kerautret, Michel, _La France napoléonienne: Aspects extérieurs 1799–1815_ , Paris 1999
Durey, Michael, _William Wickham, Master Spy_ , London 2009
Dwyer, Philip, _Napoleon: The Path to Power 1769–1799_ , London 2007
— _Citizen Emperor: Napoleon in Power 1799–1815_ , London 2013
Englund, Steven, _Napoleon: A Political Life_ , New York 2004
Ernouf, Alfred Auguste, _Maret duc de Bassano_ , Paris 1878
Esdaile, Charles J., _The Wars of Napoleon_ , London 1995
Espitalier, Albert, _Vers Brumaire: Bonaparte à Paris, 5 Décembre 1797–4 Mai 1798_ , Paris 1913
Forrest, Alan, _Conscripts and Deserters: The Army and French Society During the Revolution and Empire_ , Oxford 1989
— _Napoleon's Men: The Soldiers of the Revolution and Empire_ , London 2002
— _Napoleon: Life, Legacy, and Image. A Biography_ , London 2011
Fraser, Flora, _Venus of Empire: The Life of Pauline Bonaparte_ , London 2009
Fraser, Ronald, _Napoleon's Cursed War: Popular Resistance in the Spanish Peninsular War_ , London 2008
Fugier, André, _Napoléon et l'Italie_ , Paris 1947
Garnier, Jacques, _Austerlitz: 2 décembre 1805_ , Paris 2005
— _Friedland, 14 juin 1807: Une victoire pour la paix_ , Paris 2010
Godechot, Jacques, _Les institutions de la France sous la Révolution et l'Empire_ , Paris 1998
Goetz, Robert, _1805: Austerlitz_ , London 2005
Grainger, John D., _The Amiens Truce: Britain and Bonaparte, 1801–1803_ , Woodbridge 2004
Graziani, Antoine-Marie, _La Corse Génoise: Economie, société, culture_ , Ajaccio 1997
Gries, Thomas E., ed., _Atlas for the Wars of Napoleon_ , West Point Military History Series, Wayne, NJ 1986
Grot, Zdzisław, _Dezydery Chłapowski 1788–1879_ , Warsaw 1983
Grunewald, Constantin de, _Baron Stein, Enemy of Napoleon_ , London 1936
Gruyer, Paul, _Napoléon roi de l'Île d'Elbe_ , Paris 1906
Gueniffey, Patrice, _Le dix-huit brumaire: l'épilogue de la Révolution française, 9–10 novembre 1799_ , Paris 2008
— _Bonaparte_ , Paris 2013
Guèry, Alain, _Les comptes de la mort_ , in _Histoire et Mesure_ , Vol. VI, 3–4, pp.289–312, Paris 1991
Haegele, Vincent, _Napoléon et Joseph Bonaparte: Le Pouvoir et l'Ambition_ , Paris 2010
Hampson, Norman, _A Social History of the French Revolution_ , London 1966
Hanley, Wayne, _The Genesis of Napoleonic Propaganda 1796–1799_ , New York 2005
Hartley, Janet M., _Alexander I_ , London 1994
Hauterive, Ernest d', _Mouchards et Policiers_ , Paris 1936
— _Napoléon et sa Police_ , Paris 1943
Hazareesingh, Sudir, _The Legend of Napoleon_ , London 2004
Healey, F.G., _Rousseau et Napoléon_ , Geneva 1957
— _The Literary Culture of Napoleon_ , Geneva 1959
Helfert, Joseph Alexander freiherr von, _Napoleon I: Fahrt von Fontainebleau nach Elba. April-Mai 1814. Mit Benutzung der amtlichen Reiseberichte des kaiserlichen österreichischen Commissars General Koller, hrsg. von Joseph Alexander Freiherr von Helfert_ , Vienna 1874
Hippler, Thomas, _Citizens, Soldiers and National Armies: Military Service in France and Germany, 1789–1830_ , London 2008
Hofschröer, Peter, _Wellington's Smallest Victory: The Duke, the Model-Maker and the Secret of Waterloo_ , London 2004
Holzhausen, Paul, _Les Allemands en Russie avec la Grande Armée en 1812_ , trans. Commandant Minard, Paris 1914
Jomard, Edmé-François, _Souvenirs sur Gaspard Monge et ses rapports avec Napoléon_ , Paris 1853
Jomini, A.H. de, _Vie politique et militaire de Napoléon, racontée par lui-même, au tribunal de César, d'Alexandre et de Frédéric_ , 2 vols, Brussels 1842
Jourdan, Annie, _Napoléon: Héros, Imperator, Mécène_ , Paris 1998
— _Mythes et légendes de Napoléon: Un destin d'exception entre rêve et réalité..._ , Toulouse 2004
— ed., _Louis Bonaparte: Roi de Hollande_ , Paris 2010
Kartsov, Yu. & Voenskii, K., _Prichiny Voiny 1812 goda_. St Petersburg 1911
Keegan, John, _The Face of Battle_ , New York 1976
Kemble, J., _Napoleon Immortal: The Medical History and Private Life of Napoleon Bonaparte_ , London 1959
Knight, Roger, _Britain Against Napoleon: The Organization of Victory 1793–1815_ , London 2013
Kraehe, Enno, _Metternich's German Policy_ , 2 vols, Princeton 1963–83
Langsam, W.S., _The Napoleonic Wars & German Nationalism in Austria_, Columbia 1930
Latreille, C., _Le Catéchisme Imperial de 1806_ , Lyon 1935
Launay, Louis de, _Un Grand Français: Monge, Fondateur de l'École Polytechnique_ , Paris n.d.
Laurens, Henry, _L'expédition d'Égypte 1798–1801_ , Paris 1997
Lefèbvre, Georges, _Napoléon_ , Paris 1953
Leggiere, Michael V., _The Fall of Napoleon: The Allied Invasion of France_ , Cambridge 2007
— _Napoleon and the Struggle for Germany: The Franco-Prussian War of 1813_ , 2 vols, Cambridge 2015
Le Nabour, Eric, _Napoléon et sa famille: Une destinée collective_ , Paris 2012
Lentz, Thierry, _Le Grand Consulat 1799–1804_ , Paris 1999
— _Le 18 brumaire: Les coups d'état de Napoléon Bonaparte (novembre-décembre 1799)_ , Paris 2010
— _Nouvelle Histoire du Premier Empire_ , 4 vols, Paris 2010
— _Les vingt jours de Fontainebleau: La première abdication de Napoléon 31 mars–20 avril 1814_ , Paris 2014
Lescure, A. de, _Le château de la Malmaison_ , Paris 1867
Lieven, Dominic, _Russia Against Napoleon: The Battle for Europe 1807 to 1814_ , London 2009
Lignereux, Aurélien, _L'Empire des Français 1799–1815_ , Paris 2012
McMahon, Darrin M., _Divine Fury: A History of Genius_ , New York 2013
Madelin, Louis, _Fouché 1759–1820_ , Paris 1979
Malye, François, _Napoléon et la folie espagnole_ , Paris 2007
Manceron, Claude, _Austerlitz: The Story of a Battle_ , trans. George Unwin, London 1966
Mansel, Philip, _The Eagle in Splendour: Inside the Court of Napoleon_ , London 2015
Marcaggi, J.B., _Une Genèse_ , Ajaccio 1895
Marquis, Hugues, _Agents de l'ennemi: les espions à la solde de l'Angleterre dans une France en révolution_ , Paris 2014
Martin, Andy, _Napoleon the Novelist_ , Cambridge 2000
Martineau, Gilbert, _La Vie Quotidienne à Sainte-Hélène au temps de Napoléon_ , Paris 1966
Masson, Frédéric, _Napoléon et les Femmes_ , Paris 1894
— _L'impératrice Marie-Louise_ , Paris 1902
— _Napoléon et sa Famille_ , 12 vols, Paris 1897–1919
— _Joséphine impératrice et reine_ , Paris 1910
— _Napoléon dans sa jeunesse, 1769–1793_ , Paris 1911
Masson, Philippe, _La marine sous la Révolution et l'Empire_ , in Jean Delmas, ed., _Histoire Militaire de la France: 2 – De 1715 à 1871_ , Paris 1992
Mathew, Nicholas, _Political Beethoven_ , Cambridge 2013
Montbas, vicomte de, _Caulaincourt à Châtillon_ , in _La Revue de Paris_ , June & July 1928
Morrissey, Robert, _The Economy of Glory: From Ancien Régime to the Fall of Napoleon_ , Chicago 2014
Muir, Rory, _Britain and the Defeat of Napoleon 1807–1815_ , London 1996
— _Tactics and the Experience of Battle in the Age of Napoleon_ , Yale 1998
— _Wellington: Waterloo and the Fortunes of Peace, 1814–1852_ , London 2015
Napoléon, Charles, _Bonaparte et Paoli, aux origines de la question corse_ , Paris 2008
Naulet, Frédéric, _Eylau, 8 février 1807_ , Paris 2007
Pachoński, J., _Wladysław Jabłonowski_ , in _Polski Słownik Biograficzny_ , Vol. X, Warsaw 1964
Palmer, Alan, _Alexander I: The Tsar of War and Peace_ , London 1974
Paoli, François, _La Jeunesse de Napoléon_ , Paris 2005
Parsons, Timothy, _The Rule of Empires; Those Who Built Them, Those Who Endured Them, and Why They Always Fail_ , Oxford 2010
Petiteau, Natalie, _Guerriers du Premier Empire: Expériences et mémoires_ , Paris 2011
Pigeard, Alain, _Arcole: un pont vers la légende (15–17 novembre 1796)_ , Paris 2009
Price, Munro, _Napoleon: The End of Glory_ , Oxford 2014
Ramm, Agatha, _Germany 1789–1919: A Political History_ , London 1967
Reiss, Tom, _The Black Count: Napoleon's Rival and the Real Count of Monte Cristo – General Alexandre Dumas_ , London 2013
Rey, Marie-Pierre, _Alexandre Ier_ , Paris 2009
Richardson, Frank, M.D., _Napoleon: Bisexual Emperor_ , London 1972
Roberts, Andrew, _Waterloo_ , London 2005
— _Napoleon the Great_ , London 2014
Rodger, Alexander, _The War of the Second Coalition 1798–1801_ , Oxford 1964
Rodger, N.A.M., _The Command of the Ocean_ , London 2004
Rolin, Vincent, _Rivoli, 14–15 janvier 1797: La conquête de l'Italie_ , Paris 2001
Rose, J. Holland, _Pitt and Napoleon: Essays and Letters_ , London 1912
Rothenberg, Gunther E., _The Art of Warfare in the Age of Napoleon_ , London 1977
— _Atlas des guerres Napoléoniennes_ , Paris 2000
— _The Emperor's Last Victory: Napoleon and the Battle of Wagram_ , London 2004
Saada, Leila, _Les interventions de Napoléon au Conseil d'État sur les questions familiales_ , in _Naopoleonica_ , No.14, 2012
Sale, Nigel, _The Lie at the Heart of Waterloo_ , Stroud 2014
Salvatorelli, Luigi, _Leggenda e realta di Napoleone_ , Rome 1960
Schroeder, Paul W., _The Transformation of European Politics, 1763–1848_ , Oxford 1994
Schuermans, Albert, _Itinéraire Général de Napoléon Ier_ , Paris n.d.
Schwarzfuchs, Simon, _Napoleon, the Jews and the Grand Sanhedrin_ , London 1979
Sédouy, Jacques-Alain, _Chateaubriand: Un diplomate insolite_ , Paris 1992
Simiot, Bernard, _De quoi vivait Bonaparte?_ , Paris 1992
Skowronek, Jerzy, _Antynapoleońskie koncepcje Czartoryskiego_ , Warsaw 1969
Sokolov, Oleg, _Austerlitz: Napoléon, l'Europe et la Russie_ , Saint-Germain-en-Laye 2006
Sparrow, Elizabeth, _The Alien Office_ , in _Historical Journal_ , 33, 1990
Strathern, Paul, _Napoleon in Egypt_ , London 2007
Sutherland, Christine, _Marie Walewska: Le Grand Amour de Napoléon_ , Paris 1979
Tombs, Robert, _The English and Their History_ , London 2014
Tulard, Jean, _Joseph Fiévée, conseiller secret de Napoléon_ , Paris 1985
— _Joseph Fouché_ , Paris 1998
— & Fayard, Jean-François, Fierro, Alfred, _Histoire et Dictionnaire de la Révolution Française 1789–1799_ , Paris 1998
— _Le 18 brumaire: comment terminer une révolution_ , Paris 1999
— _Dictionnaire Napoléon_ , 2 vols, Paris 1999
— _Napoléon et la noblesse d'Empire_ , Paris 2003
— _Napoléon ou le mythe du sauveur_ , Paris 2011
— _Napoléon, chef de guerre_ , Paris 2012
Uffindell, Andrew, _The Eagle's Last Triumph: Napoleon's Victory at Ligny, June 1815_ , London 2006
Uglow, Jenny, _In These Times: Living in Britain through Napoleon's Wars, 1793–1815_ , London 2014
Vandal, Albert, _L'Avènement de Bonaparte_ , 2 vols, Paris 1903
— _Napoléon et Alexandre 1er: L'Alliance Russe sous le Premier Empire_ , 3 vols, Paris 1891
Vergé-Franceschi, Michel, _Paoli: Un Corse des Lumières_ , Paris 2005
— _Napoléon: Une enfance corse_ , Paris 2014
Waresquiel, Émmanuel de, _Talleyrand: Le prince immobile_ , Paris 2003
Webster, C.K., _The Foreign Policy of Castlereagh 1812–1815_ , London 1931
Welschinger, _Le divorce de Napoléon_ , Paris 1889
Woolf, Stuart, _Napoleon's Integration of Europe_ , London 1991
Zamoyski, Adam, _1812: Napoleon's Fatal March on Moscow_ , London 2004
— _Rites of Peace: The Fall of Napoleon and the Congress of Vienna_ , London 2007
— _Phantom Terror: The Threat of Revolution and the Repression of Liberty 1789–1848_ , London 2015
Zorin, Andrei, _Kormia Dvuglavovo Orla_ , Moscow 2004
# Index
The page numbers in this index relate to the printed version of this book; they do not match the pages of your ebook. You can use your ebook reader's search tool to find a specific word or passage.
NOTE: Ranks and titles are generally the highest mentioned in the text
Aberdeen, George Hamilton Gordon, 4th Earl of, 576
Aboukir: N defeats Turks at, 204–5, 213
Aboukir Bay: naval battle (1898), 169, 188, 195
Abrial, André-Joseph, 245
Acre, 196, 199–202
Addington, Henry, 302, 338
Additional Act (1615), 611
Ajaccio, Corsica, 14–15, 36, 51
Alexander I, Tsar of Russia: makes peace with Britain (1800), 301; attends Recess of Ratisbon, 333–4; mediates between France and Britain, 338; N's relations with, 342; protests at execution of Enghien, 347; attitude to N, 374; persuades Frederick William to join coalition against N, 380; leaves field at Austerlitz, 383–4; sends Oubril to negotiate treaty, 396; rejects peace negotiations with France (1806), 401–2; agrees Treaty of Tilsit, 414–16; hopes of occupying Constantinople, 428; meets N at Erfurt, 437–41; N seeks dynastic alliance with, 442; denies N marriage prospects with sister, 472–3, 493; Polish policy, 494; prepares for war with N, 495–8, 507; demands N withdraw troops beyond Rhine, 509; N hopes to reach agreement with, 511–12, 518, 563, 565; rejects N's peace envoy, 511; interferes with commanders, 518; and N's advance into Russia, 523; N attempts to contact after fall of Moscow, 531–2; celebrates action at Berezina river, 543; advances westwards, 552–3; alliance with Prussia, 556; invades Saxony, 556; and Lützen defeat, 556–7; war effort, 566; snubs Frederick Augustus, 571; wishes to invade France, 576; favours Bernadotte as successor to N, 583; threatens Paris, 585; and N's abdication, 587; meets N's delegates presenting abdication terms, 588; stands up to N, 591–2; Caulaincourt negotiates with, 592; dines with Josephine at Malmaison, 597–8; prevents N from seeing Marie-Louise and son, 603; letter from N on return from Elba, 612; Fouché writes to, 613
Alexandria, Egypt, 181–2
Ali Effendi, 173
Allies (Prussia-Russia-Austria-Britain): military strength and plans, 566; reject N's offer to negotiate, 570; pause at Rhine, 576; continue advance, 578
Alvinczy, Field Marshal Baron Jozef, 139, 140–1, 143, 146–7
Amiens, Treaty of (1801), 302, 312–13, 327–8, 334–5
Ancona, 148–9, 426
Andigné, Louis, comte d', 211, 248–9
Andréossy, General Antoine, 332, 335
Angoulême, Louis Antoine, duc d', 609
Anhalt Coethen, Augustus Christian Frederick, Prince of, 510
Anna, Grand Duchess of Russia, 472, 493
Antommarchi, Dr Francesco, 641
Antraigues, Louis-Alexandre, comte d', 158, 343
Archambault, Achille and Joseph (N's grooms), 626
Arcis-sur-Aube, battle of (1814), 583
Arcole, 141, 142–4
Aréna, Barthélemy, 284
Aréna, Joseph, 284, 292
Arish, El, 197; Convention of (1800), 269
Armed Neutrality, 301
army (French): view of N, 289–90, 317; reaction to N's new status as emperor, 353–4; marshals in, 375–6
Army of Batavia, 317
Army of England: N commands, 7, 167, 170, 172; N reconstitutes (1803–5), 339–40, 361, 375–6; _see also_ Grande Armée, La
Army of Italy: N's regiment stationed with, 65; contingent at Toulon, 68; N given command of artillery, 76; N drafts plans for attack on Vienna (1795–6), 103; N given overall command, 103–4, 107; condition and low morale, 108–10; N reforms and disciplines, 109–10, 116–17; strength, 110–11; inadequate and makeshift dress, 125, 135; victories over Austrians, 134–8; sense of comradeship, 136; casualties and replacements, 139–40
Army of the Orient, 174
Army of Spain, 586
Arnault, Antoine-Vincent, 154, 178
Arnott, Dr Thomas, 642
Artois, Charles, comte d' ( _later_ King Charles X), 49, 283, 315, 604
Aspern, 452
Aspern-Essling, battle of (1809), 452, 456
Aubry, François, 82–3
Auerstadt, battle of (1806), 404
Augereau, Marshal Charles-Pierre: in Army of Italy, 107, 110; in action against Austrians in northern Italy, 112–14, 135, 142–3, 148; leadership at Castiglione, 136; attacks Würmser, 138; as rival to N, 162, 317; commands troops in Paris region, 163; given command of Army of Germany, 164–5; snubs N, 168; as potential dictator, 211; and Brumaire coup, 230, 232; in Netherlands, 283; made marshal, 357, 375; commands troops for invasion of England, 361; and proposed invasion of Ireland, 364; opposes Austrians, 377; N criticises, 379; in Poland, 408; and Catalonian separatism, 461; on war against Russians and Prussians, 560; criticises N at Leipzig, 570; reserve stationed at Lyon, 573, 582; message from N encouraging action, 581; surrenders Lyon, 584; and fall of Paris, 586; meets N on way to Elba, 598–9; N proclaims a traitor, 606
Augusta, princess of Bavaria: marriage to Eugène, 385
Austerlitz, battle of (1805), 383–4
Austria: war with France (1792–5), 54, 103; supports Sardinia, 80; in Italy, 111; N first engages in Piedmont, 112–14; aims to recover Lombardy, 133, 146; military practices, 135; N agrees to French negotiations with, 144–5, 158; renews campaign in Italy, 148; N negotiates peace with (1797), 151, 164–7; rearms, 161; rejects N's peace offer, 270; offensive against Masséna, 271; Marengo defeat, 274–7; signs subsidy treaty with Britain, 277–8; conflict with Papal States, 291; peace treaty with France (1801), 297; territorial expansion, 299; cedes territory at Recess of Ratisbon, 333; population, 337; negotiates alliance with Russia and Britain, 362; arms for war, 364; N's offensive against, 377–81; Austerlitz defeat, 383–4; cedes territories under Treaty of Pressburg, 385; N's lack of regard for, 385; pays indemnity to France, 385, 388; in new coalition against France, 402; resents post-Austerlitz terms, 436; prepares for war against N (1809), 444, 448; Wagram defeat, 454–6; concessions in Treaty of Vienna, 468; cost of campaign against, 491; hopes to strengthen position in Balkans, 497; and N's war with Russia, 507; proposes mediating in French peace negotiations with Russia, 550; in alliance against N, 564–5; proposes treating with N on condition of abdicating, 613
Autun: Joseph attends seminary at, 19, 23
Auxonne, 38–9, 42, 47
Babeuf, François Noël ('Gracchus'), 93, 170
Bacciochi, Élisa _see_ Bonaparte, Élisa
Bacciochi, Félix, 155, 207
Bachasson de Montalivet, Jean-Pierre, 48
Bacler d'Albe, Louis Abert, 393
Badajoz, Peace of (1801), 302
Baden, Karl I, Grand Duke of, 510
Bagration, General Piotr Ivanovich, 514, 520–1, 523
Bailén, battle of (1808), 434–5, 446, 456
Bailly, Dr Joseph, 369
Balashov, General Alexander, 518
Balcombe, Betsy, 628, 631, 640
Balcombe, William, 628, 633, 640
Balmain, Count Alexandre Antonovich, 635
Balzac, Honoré de, 14
Banque de France, 267, 387–8
Baraillon, Jean-François, 223
Barante, Amable de, 210, 267
Barbé-Marbois, François, 387–8
Barclay de Tolly, General Mikhail Bogdanovich: plans strike against Poland, 497; opposes N's Russian campaign, 513–14, 518, 520–1, 523, 526; N writes to, 526; commands Russians in alliance, 566
Bard, 273
Baring Brothers (bankers), 477
Barlow, Joel, 533
Barras, Paul François: praises N, 5–6; and N's replacement of Carteaux, 70; and siege of Toulon, 72; purge in Toulon, 73–4; career, 83; protects and promotes N, 83, 88, 95–8; keeps Josephine as mistress, 99–101; and N's infatuation with Josephine, 103–5, 118; and N's campaign in Italy, 122; persuades Josephine to join N in Italy, 131; letters to Josephine, 132; and Josephine's improving relations with N, 155; suppresses right-wing deputies, 157–8; and N's silence over Directors' coup, 164; N demands to be discharged from army, 165; N meets in Paris, 169–70; Josephine enquires about N in Egypt, 187; and N's wish to divorce Josephine, 216; N's relations with, 218–20; removed from power in Brumaire coup, 226–7; associates, 262; in plot against N, 549
Bartenstein, Convention of (1807), 413
Bassano, 138
Batavian Republic (Netherlands), 297, 334; _see also_ Holland
Bathurst, Henry, 3rd Earl, 634, 636
Bausset, Louis, 399, 450, 469, 527, 574, 597
Bautzen, battle of (1813), 558–60
Bavaria: Austria invades, 376, 449; in coalition against France, 402
Bayonne, 430–2, 444
Beauharnais, Alexandre de, 99
Beauharnais, Eugène de: N's relations with, 102, 187, 305; visits N in Milan, 155; leaves Milan with N, 167; travels to Toulon with N, 177; in Egypt, 183; black mistress in Cairo, 192; in Jaffa, 198; acting, 320; N appoints viceroy in Italy, 372; opposes Austrians in Italy, 379, 413; marriage to Augusta, 385; ordered to despatch Polish staff officers to Polish legion, 407; in Russian campaign, 414, 520, 531, 536; victories against Austrians (1809), 452–3; at battle of Wagram, 454; discusses N's divorce from Josephine, 470; proposes to Marie-Louise on N's behalf, 473; announces Louis' giving up Dutch throne, 478; in retreat from Moscow, 538–40; replaces Murat and withdraws troops to Elbe, 554; forms Army of Italy against allies, 567, 582; falls back on Milan, 573; Austrian offensive against in Italy, 578; Josephine frees from loyalty on N's abdication, 597
Beauharnais, Hortense de: N's relations with, 102, 105, 169, 177, 305, 336; accompanies Josephine to meet N on return from Egypt, 214; marriage and child with Louis, 305, 308, 365; acting, 320; at Malmaison, 320; denied coffee, 389; and N's decision to divorce Josephine, 468–9, 471; teaches N to dance, 474; on prudishness of N's court, 481; on N's charm, 483; on N after Russian campaign, 548; meets Bernadotte, 597; N sees in Paris on return from Elba, 609–10
Beauharnais, Rose de _see_ Josephine, Empress
Beaulieu, Field Marshal Jean-Pierre de, 111–14, 119, 121, 128, 134
Beauregard, Colonel Costa de, 115–16, 123, 454
Becker, General Nicolas Léonard, 622–3
Bekri, Sheikh El-, 207
Belgium: France invades (1792), 299; in Metternich's peace proposals, 576
_Bellerophon_ , HMS, 623–6
Belliard, General Augustin Daniel, 302, 354, 561, 586
Bellisle, Marguerite-Pauline ('Bellilotte'), 192–3, 206
Belly de Bussy, General David-Victor, 33, 583
Bennigsen, General Levin August von, 408, 411–13
Béranger, Pierre-Jean de, 210
Berezina, river, 541–3
Berg, Grand Duchy of, 460, 491
Berlin: N enters (1806), 404
Berlin Decrees, 406, 427
Bernadotte, Désirée, 216, 219, 305
Bernadotte, Marshal Jean-Baptiste ( _later_ King Charles XIV of Sweden): in Italian campaign, 149; as ambassador in Austria, 176; as potential dictator, 211; marriage to Désirée, 216, 219, 305; differences with N, 219, 222; and Brumaire coup, 225, 227; commands Army of the West, 271; suggested as successor to N, 279, 583; Joseph's friendship with, 305; in plot against N, 318; made marshal, 357, 375; opposes Austrians, 377; N criticises, 379, 404, 455; as prince of Pontecorvo, 398; at Wagram, 454–5; sent to counter British landing at Walcheren, 467; Sweden invites to take throne, 495–6; arranges Swedish treaty wih Russia, 506; leads Swedish-Prussian corps against N, 568, 581; plots for power in France, 575, 581; N attempts to win over to French side, 582
Bernadotte, Oscar, 258
Bernier, Étienne-Alexandre, abbé, 292, 307
Bernoyer, François, 189
Berry, Mary, 326
Berthezène, General Pierre, 506, 514
Berthier, Marshal Alexandre: as N's chief of staff in Italy, 108–9, 113; at Lodi, 120; in Milan, 125; and N's actions against Italian civilians, 127; with N in Paris (December 1797), 169; in Egypt, 185; informs N of Josephine's infidelities, 187; pleads for clemency at Jaffa, 198; leaves Egypt with N, 206; and Brumaire coup, 225; made minister for war, 237; N presses to purge and improve army, 246, 260, 317; commands Reserve Army, 271, 272; profits from rumours, 279; and anti-N feeling in army, 317; made grand huntsman, 357; N writes to on invasion of Ireland, 364; travels in N's coach, 372; made marshal, 375; as prince of Neuchâtel, 398; with N at Bayonne, 444; in Spain with N, 444–5; at Wagram, 454; made Prince of Wagram, 473; stands as proxy for N's marriage with Marie-Louise, 473; organises hunts, 486; as nominal commander in Spain, 492; in Russian campaign, 516, 522, 524, 525; N insults and rebukes, 525, 569; at Borodino, 529; in retreat from Moscow, 538; on Murat, 547; urges concentrating forces on Rhine, 561; decline, 568; N dictates orders to, 582; advises N to abdicate, 587; remains with N after abdication, 592
Berthollet, Claude, 128, 171, 206
Bertrand, Fanny, 616, 623, 626, 630–1, 641
Bertrand, General Henri, comte: and N's entry into Vienna, 379; on excellence of army, 556; with N at Fontainebleau, 593; accompanies N to exile on Elba, 596, 598, 600; and N's return to Paris, 609; with N on St Helena, 626, 628, 630, 635, 637; and N's illness and death, 640–1, 643
Bessières, Marshal Jean-Baptiste, 434, 455
Beugnot, Jacques-Claude, 441, 460, 502, 566, 572
Bigot de Préameneu, Félix-Julien, 286
Binasco, Italy, 127
Blois, 589, 595–6
Blücher, Prince Gebhard von: reports on French threat to Hanover, 402; in offensive against France (1813), 556; commands army in Silesia, 566; N's plans against, 567; avoids N, 568; describes Bernadotte as traitor, 568; surprises N at Leipzig, 570; crosses Rhine, 578; counters N's attack near Brienne, 579–80; N defeats at Vauchamps and Craonne, 580–1, 583; opposes N in final campign, 616; defeated at Ligny, 617; at Waterloo, 618
Bocagnano (Corsica), 52
Boisgelin, Monsignor de, Archbishop of Tours, 313
Bologna, 148
Bonaparte (Buonaparte) family: ennobled, 16; condemned in Corsica, 63; N's commitment to, 85–6; N advances, 258; hostility to Josephine, 319, 366; in imperial structure, 364; _see also_ Buonaparte
Bonaparte, Caroline ( _later_ Murat; _formerly_ Maria Nunziata; N's sister): N first meets as child, 36; flees home with mother, 62; visits N in Milan, 155; marriage to Murat, 259; N suggests Moreau marry, 294; made princess, 365; and Éléonore de la Plaigne, 394; affair with Junot, 424; affair with Metternich, 436; and Talleyrand-Fouché plan to have Murat succeed N, 447; welcomes N's divorce from Josephine, 469; and N's marriage to Marie-Louise, 474; and treaty of alliance with Austria, 578; takes refuge on British ship in Naples, 614
Bonaparte, Charlotte ('Lolotte'; Lucien's daughter), 427
Bonaparte, Christine ( _née_ Boyer; Lucien's wife), 77, 105
Bonaparte, Élisa ( _formerly_ Maria-Anna; _later_ Bacciocchi; N's sister): birth and christening, 18; schooling, 25, 43, 55, 57; appearance, 55; Truguet attracted to, 59; flees home with mother, 62; moves to Paris, 259; as Duchess of Lucca and Piombino, 398; N awards Grand Duchy of Tuscany to, 426; breaks off relations with France, 578
Bonaparte, Geronimo _see_ Bonaparte, Jérôme
Bonaparte, Jérôme (N's brother): 36, 62, 85; birth, 28; excluded from Paris court life, 74; marriage to Elizabeth Patterson, 366, 427; naval career, 366, 373, 458; returns to France, 372–3; institutes Order of the Union, 399; as King of Westphalia, 416, 458–9; flouts N's anti-British blockade, 441; in Austrian campaign (1809), 457; marriage to Princess Catherine of Württemberg, 458; on N's unwillingness to go to war with Russia, 504; N proposes as King of Poland, 513; in Russian campaign, 520; statue in Kassel, 551; flees Kassel, 572; actions after N's abdication, 589; plans to take Marie-Louise to refuge with Soult's army, 596; joins N in Paris on return from Elba, 609; at Waterloo, 617–18; raises troops, 621; Catherine's father attempts to engineer divorce, 629; refused permission to visit St Helena, 641
Bonaparte, Jérôme Napoléon (Jerome/Elizabeth's son), 372
Bonaparte, Joseph (N's brother): birth, 13, 17; Church career planned, 18–19; attends Autun seminary, 19, 23; changes career to military, 25; N disparages as potential soldier, 25–6; impracticality, 35; N re-encounters during visit to Corsica, 36–7; letters from N, 40, 42; political offices in Ajaccio, 44–5, 50; meets Paoli, 46; and uncle Luciano's death, 51; on Paoli's rejection of Buonaparte, 53; N advises on political direction, 55; and N's remaining in France, 57; Paoli dismisses, 58; in Paris to petition for Corsican exiles, 64–5; appointed commissary to army, 65; in Nice, 76; marriage, 79, 86; N visits in Marseille, 80; sends consumer goods to N in Paris, 85; N attempts to find consulate in Italy for, 91, 98; N sends money to, 98; and N's marriage to Josephine, 105; takes captured standards to Paris, 117; secures family estate in Corsica, 146; visits N in Milan, 155; as French ambassador to Holy See, 156; informs N of Josephine's affair with Charles, 176; buys land around Ajaccio, 207; wishes N to divorce Josephine, 216; plots to bring Bernadotte and N together, 219; in Brumaire coup, 229; political role under N's consulship, 259; as potential successor to N, 271, 280, 284–5, 357, 371; reports on consuls to N during absence, 272; intercedes over Lucien's dismissal, 293; brokers peace with USA, 299; negotiates Treaty of Amiens, 302; intellectual pretensions, 305; wealth, 305; brings Treaty of Amiens to N, 312; exhumes and reinters father, 337; urges supreme authority for N, 350; made grand elector, 357; N offers throne of Italy to, 364–5, 371; takes charge in N's absence on campaign, 376, 380; and financial crisis (1805), 380, 386; in Council of State, 390; as King of Naples, 395–6, 398, 426, 432; institutes new orders of chivalry, 399; N presses to invade Sicily, 425, 428; confers with N in Venice, 427; as King of Spain (José I), 430–4, 461; and N's visit to Spain, 444–5; renounces rights to Spanish throne, 445; re-enters Madrid (1810), 461; and French defeats in Spain, 462; and military situation in Spain, 492; differences with Soult in Spain, 551; Wellington defeats at Vitoria, 563; N urges to abdicate in Spain, 573; instructions from N during allied threat to Paris, 581–2; surrenders Paris, 586; actions after N's abdication, 589; and allied advance on Paris, 594–5; joins N in Paris on return from Elba, 609; letters from N on Waterloo defeat, 618; and N's attempted flight to America, 623
Bonaparte, Julie _see_ Bonaparte, Marie-Julie
Bonaparte, Letizia ( _née_ Ramolino; N's mother): marriage, 12; Marbeuf's infatuation with, 16–17; children, 17; qualities and character, 17; visits N at Brienne, 24; letters from N, 40; flees Corsica for France with children, 62–3; hardships in France, 75; accepts N's marriage to Josephine, 105; disapproves of Josephine, 155, 214; visits N in Milan, 155; refurbishes home in Ajaccio, 207; N's generosity to, 258–9; intercedes over Lucien's dismissal, 293; accompanies Josephine to spa at Plombières, 304; given own court and title ('Madame Mère'), 365; welcomes N's divorce from Josephine, 469; settles in Elba with N, 602; opposed to N's plot to return to France from Elba, 605; joins N in Paris, 609; writes to N in St Helena, 635; disbelieves N's condition in St Helena, 641
Bonaparte, Louis (N's brother): N first meets as child, 36; in Ajaccio, 43; accompanies N on return to France, 47; flees home with mother, 62; as ADC to N on campaign against Sardinia, 78–9; accompanies N to Paris, 82; N installs in officers' school at Châlons, 85; as aide to N in Paris, 97; on poor quality of French replacement troops in Italy, 139; returns from Egypt, 216; N esteems and favours, 259, 305, 365; courtship and marriage to Hortense de Beauharnais, 305, 308; N sees as successor, 308; neuroses, 320, 365; takes title of _Connétable_ , 357; refuses throne of Italy, 371; as King of Holland, 396–8, 477; institutes new orders of chivalry, 399; flouts N's anti-British blockade in Holland, 441; entertains N and Marie-Louise, 477; abdicates Dutch throne and flees to Gratz, 478–9; offers to return to Holland, 551; _Louis, ou les peines de l'amour_ , 551
Bonaparte, Lucien ( _formerly_ Luciano; N's brother): birth, 17; admitted to Autun seminary, 25; trains at Brienne military academy, 26; N helps find place at seminary, 37; judicial post in Ajaccio, 43; unemployed in Ajaccio, 43; and N's attitude to Paris mob, 55; revolutionary ideas, 56; Paoli rejects as secretary, 58; Sémonville engages as secretary, 59; speech denouncing Paoli, 60–1; in Toulon, 64; changes name to Brutus and marries Christine, 76–7, 105; in Saint-Maximin ('Marathon'), 76; N appoints as commissary to Army of the North, 98; Josephine dislikes, 155; discussion with N on return from Egypt, 215–16; wishes N to divorce Josephine, 216; Sièyes colludes with, 218; and Brumaire coup, 222, 226, 229, 231–5; as minister of interior, 245; sister Élisa acts as hostess, 259; speech on greatness of France, 281; and assassination plot against N, 283; impressed by N in Council of State, 288; dismissed from post as interior minister, 293; negotiates peace treaties, 300; art collection, 305; denounces N as tyrant, 305–6; returns from ambassadorship in Spain, 305; returns to Tribunate, 311; proposes changes to Tribunate, 313; and succession to N, 319, 357; urges supreme authority for N, 350; secret marriage and children, 365, 427; refuses N's demands to divorce, 427; captured by Royal Navy and imprisoned in England, 479; meets N in Mantua, 527; offers Castlereagh peace negotiations, 551; on N's physical deterioration, 609; objects to costume for _Champ de mai_ , 611; advises and supports N after Waterloo defeat, 619–21; _Parallèle entre César, Cromwell, Monck et Bonaparte_ , 292
Bonaparte, Marie-Julie ( _née_ Clary; Joseph's wife), 79, 86, 98, 259
Bonaparte, Napoléon-Charles (Hortense-Louis' son), 343, 365; death, 437
Bonaparte, Pauline (Maria Paolina; _later_ Leclerc; then Princess Borghese; N's sister), 36, 62; steals figs in France, 75; Fréron falls for, 83, 98, 105; marriage to Leclerc, 155; visits N in Milan, 155; education, 216; anxiety over N's fate in Brumaire coup, 235; accompanies husband to Saint-Domingue, 331; nurses dying husband, 341; remarries (Borghese), 341; made princess, 366; and N's dalliance with Christine Ghilini, 468; welcomes N's divorce from Josephine, 469; and N's marriage to Marie-Louise, 474; meets N on way to Elba, 599; visits N on Elba, 602; denied visit to St Helena, 641
Borghese, Prince Camillo, 341
Borghese, Princess Pauline _see_ Bonaparte, Pauline
Borisov, 541–2
Borodino: battle of (1812), 526–9; wounded evacuated, 536
Boswell, James, 12–13, 16; _An Account of Corsica_ , 13, 28
Bottot, Carlo, 164, 225
Bou, Claudine-Marie, 33
Bougainville, Admiral Louis-Antoine de, 26, 30, 169
Bouillé, Louis-Amour, marquis de, 355
Boulart, General Jean-François, 209–10, 368, 410, 441, 584
Boulogne, 360–2, 371, 374, 376
Bourbon family: prospective restoration, 164, 583, 586; restoration and unpopularity after N's downfall, 604–5, 608, 610; _see also_ Louis XVIII, King of France
Bourbonne-les-Bains, 24
Bourgeois, Dr René, 540
Bourgogne, Sergeant Adrien, 530, 540
Bourgoing, Lieutenant Armand Charles Joseph de, 525
Bourrienne, Louis Antoine de Fauvelet de: friendship with N, 23, 54; in diplomatic service, 54; and N's finances, 98; and N's negotiations with Cobenzl, 166; and N's expedition to Egypt, 175, 177; leaves Egypt with N, 206; with N in Brumaire coup, 227, 230, 235; as N's secretary, 239, 304; on N's singing, 245; organises staff at Tuileries, 252; walks Paris streets with N, 262; accompanies N to war against Austria, 272; acting, 320; dismissed, 321; as commissioner in Hamburg, 441
Boyer, Christine _see_ Bonaparte, Christine
Boyer, Claude (pharmacist), 201–2
Brandt, Heinrich, 525
Brienne: N studies at military academy, 21–3; N revisits, 372
Britain: France declares war on (1793), 60, 103; occupies Corsica, 81; gains colonies from French, 160; peace talks with France (1797), 164; prospective French invasion of, 172–5; finances coalition, 268, 278, 299, 405; rejects N's peace offer (December 1799), 268–70; Napoleon blames for preventing peace terms, 277; loses Austria as ally in Treaty of Lunéville, 297; extends overseas dominions, 298; N isolates, 300–2; hostility to France, 301; opposes French in Egypt, 301–2; union with Ireland, 301; peace treaty with France (1802), 312–13, 327; tourists in Paris and on continent, 325–6; commercial rivalry with France, 327; caricatures and slanders N, 332, 340, 369; N mistrusts, 332; alarm at French expansionism, 334–5; population, 337; declares war on France (1803), 338; N plans invasion, 339, 360–2, 364, 371, 374–5; Austria negotiates alliance with, 362; imposes blockade on European countries, 396, 401; new ministry under Grenville, 396; peace negotiations with France (1806), 401; and N's blockade (Continental System), 405–6, 416, 441–2, 493, 496–8, 506; bombards French ports, 419; N's economic war against, 421; supports Portugal, 425; orders seizure of neutral ships, 427; N plans action against eastern empire, 428; clandestine trade with Europe during blockade, 441; raids on French coastal forts, 467; sends troops to Cuxhaven and Walcheren, 467; economic effect of war on, 493, 496; trade with France, 493; poor harvest (1810), 496; N makes peace offer (1812), 509; Metternich makes approaches to, 553; joins alliance against France (1813), 566; declines to ratify Treaty of Fontainebleau, 604
Brittany: British land émigré force in, 93
Broglie, Achille de, 465
Brueys, Admiral François Paul de, 176, 178, 188
Bruix, Admiral Eustache, 217, 225–6, 232, 360
Brumaire coup (1799): planned, 221–4; execution and success, 227–35
Brune, General Guillaume, 94, 96, 213, 279, 283, 317, 335, 361
Brunswick, Karl Wilhelm Friedrich, Duke of, 404, 456
Brunswick-Oels, Friedrich Wilhelm, Duke of, 58, 456
Brussels, 616–17
Bubna, General Ferdinand, 549–50, 557–8
Bunbury, Sir Henry, 625
Buonaparte, Carlo Maria (N's father): in Corsica, 10–14; legal career, 14–18; and N's birth and christening, 14, 16; claim to nobility, 18–19; lifestyle, 18; presented to Louis XVI, 20; sits in Corsican Estates, 23; landownership and enterprises, 24–5, 35, 51; health decline and death, 28–9; holds office in Corsica, 46; social ambitions, 224–5
Buonaparte, Filippo, 19, 129
Buonaparte, Gabriele (16th century), 10
Buonaparte, Geronimo (Gabriele's son), 10
Buonaparte, Giuseppe Maria (N's grandfather), 11
Buonaparte, Luciano (N's great uncle), 11–12, 17–18, 23, 35–6, 41, 51
Buonaparte, Napoleone (N's great uncle), 11, 13–14
Buonaparte, Paola Maria (N's great aunt), 11
Buonaparte, Sebastiano (N's ancestor), 11
Buonaparte, Sebastiano (N's great uncle), 11
Buonarroti, Filippo, 45, 111
Burke, Edmund, 301
Burney, Fanny, 326
Buttafocco, Matteo, 43, 46
'Ça Ira' (revolutionary song), 235
Cabanis, Pierre, 243
Cabarrus, Thérèse de ( _Notre Dame de Thermidor_ ), 88
Cádiz, 434
Cadoudal, Georges, 250, 283, 295, 340, 342–5, 349, 354
Cagliari, Sardinia, 59
Cairo: French occupy, 187, 191–2; Institute, 189, 203; revolt in, 193–4; Napoleon returns to from Syrian campaign, 201–3
calendar: Gregorian reintroduced, 376
Calmelet, Étienne, 104
Cambacérès, Jean-Jacques: N consults, 217; N retains as justice minister, 237; moderates anti-Jacobin proposals, 238, 295; as consul, 242; background and character, 243–4; Abrial succeeds as justice minister, 245; warns N of Talleyrand, 247; and move to Tuileries, 251–2; financial management, 267; and N's peace negotiations, 270; on Italian campaign, 272; and intrigues against N, 279; and Mollien's suggestions for economic reforms, 285; opposes N's religious reforms, 291; issues _senatus-consulte_ , 295; and Civil Code, 308; urges upgrade in N's status, 318; and succession to N, 319; on Treaty of Amiens, 327; and N's belief in popularity in Britain, 333; and royalist plotters, 344–5; and execution of Enghien, 346; on N's status as consul, 351; addresses N as emperor, 352; and N's confusion over status as emperor, 356, 370; named arch-chancellor, 357; proposes bee as dynastic symbol, 358; and N's plans for invasion of England, 361–2; takes charge in N's absence on campaign, 376, 419; and financial crisis (1805–6), 386; in Council of State, 390; and N's return from Tilsit, 418; warns against alliance with Spain, 429; and N's Erfurt meeting with Tsar, 438; orders customs-free ham from Berg, 441; and N's victory at Ratisbon, 450–1; drafts constitution for Westphalia, 458; on declining public support for N, 462; ineffectiveness in countering British landing at Walcheren, 467–8; on N's birthday celebrations in Paris, 467; arranges N's divorce from Josephine, 469–70; and N's remarriage, 473; homosexuality, 481; unease at N's obsession with grandeur, 482; and N's plans against Russia, 512; messages from N on Russian campaign, 520; and N's return from Russia, 546; and proposed peace negotiations with Russia, 550; ordered to advance conscription in France, 573; on pessimism in Paris, 574; and N's fury at Assembly, 578; on grave national situation under threat from allies, 583; advises N to return to Paris, 584; leaves Paris with Marie-Louise, 585; in Blois, 589; and N's return to Paris from Elba, 608; advises N after Waterloo defeat, 619; sends delegation to allied headquarters, 621
Cambronne, General Pierre, 597
Campan, Henriette, 105, 169, 216, 262
Campbell, Colonel Sir Neil, 597–9, 603–5
Campo Formio, Treaty of (1797), 167–8, 170
Canada: France loses to British, 160
Canova, Antonio, 484
Carnot, Lazare: orders _levée en masse_ , 67; Toulon plan, 72; calls off Sardinia operation, 80; disparages N and Italian operation, 103; N reports to from Italy, 109, 117, 119, 121–2; hostility to N, 169–70; N reappoints to War Ministry, 271; suggested as successor to N, 279; opposes declaring France an empire, 351; appointed minister of interior on N's return from Elba, 608; advises N after Waterloo defeat, 619, 621
Carteaux, General Jean-François, 67–70, 94, 256
Castaños, General Francisco, 434, 445
Castellane, Boniface de, 510
Castiglione, 134, 136
Castlereagh, Robert Stewart, Viscount, 551, 578, 592–3, 604
Catalonia, 461
Catherine, Grand Duchess of Russia, 415, 439
Catherine, Queen of Westphalia _see_ Württemberg, Catherine, Princess of
Catholic Church: status recognised, 292, 306–8, 313–15; acknowledges N's elevation to emperor, 355; _see also_ Pius VII, Pope
Caulaincourt, Louis de, duc de Vicence: accompanies N to crowning in Italy, 372; on Josephine at Eugène's marriage, 386; and N's dismissal of Prussia, 402–3; on muddy conditions on march to Warsaw, 409; on unpopularity of Tilsit treaty in Russia, 437; and N's wish to marry Russian royal, 472; and impending war with Russia, 495, 511; N instructs to order Russia to raise tariffs, 496; consults with N in Paris, 498; in Russian campaign, 515, 522–6, 531, 533, 534; in retreat from Moscow, 538–9, 541, 545; accompanies N back to Paris from Russia, 543–4, 546; and peace negotiations with Russia, 550, 558; at peace congress with Russia and Austria, 564–5; replaces Maret as foreign minister, 577; allies impose peace conditions on, 580; negotiates with allies, 580–2, 592–3; mission to Alexander in Paris, 586–9; advises N to abdicate, 587; and acceptance of new government, 589; reports to N, 589; and N's reconsidering abdication, 592; signs Treaty of Fontainebleau, 593; N calls after taking poison, 594; meets Maria Walewska at Fontainebleau, 595; N thanks for loyal service, 597; and N's return to Paris from Elba, 607–8; writes Metternich with assurances of French peaceful intentions, 612; advises N after Waterloo defeat, 619–20; and N's entourage in St Helena, 641
Cavaignac, Jean-Baptiste, 335
Ceracchi, Joseph, 284, 292
Cesari, Colonel Pietro Paulo Colonna, 43–4, 60
Champagny, Jean-Baptiste, 361–2, 421, 468, 494–5
Champaubert, battle of (1814), 580
Champion de Nansouty, Étienne-Marie, 22
Championnet, General Jean-Étienne, 169
Chaptal, Jean-Antoine: relations with N, 257–8; on N's daily routines, 260; devises new administrative structure, 265; replaces Lucien as interior minister, 293; at election of N as president of Cisalpine Republic, 310; supports protectionism, 328; on N's consciousness of low birth, 443; and N's charitable acts, 483
Charles IV, King of Spain, 298, 421, 424, 429–31
Charles, Archduke of Austria, 149, 150, 376, 379–80, 449, 451–3, 454–5
Charles, Father (Brienne chaplain), 272
Charles, Lieutenant Hippolyte: affair with Josephine, 118, 131–3, 144, 173, 176
Charles XIII, King of Sweden, 495
Chastenay, Victorine de, 82, 481, 502
Château-Sallé, Antibes, 76
Chateaubriand, René de, 259, 326; _Génie du Christianisme_ , 315, 326
Châtillon: negotiations (1814), 580–2
Chaumont, Treaty of (1814), 583
Chauvet, Félix, 71, 105, 112
Chénier, Marie-Joseph, 6, 170
Cherasco, armistice of (1796), 118
Chernyshev, General Alexander, 498
Chłapowski, Dezydery, 512, 558
Christianity: rejected in Europe, 123
Cipriani (N's butler), 626, 628, 640
Cisalpine ( _later_ Italian) Republic, 159, 297, 309, 334; N elected president, 310–11
Cispadane Republic, 146, 151, 159
Civil Code ( _Code Civil des Français_ ; _Code Napoléon_ ), 285–7, 308, 426, 458, 469
Clarke, General Henri-Jacques, 144–6, 151, 549
Clary family: move to Genoa, 85
Clary, Bernardine Eugénie Désirée: N courts, 80, 81, 86, 91; moves to Genoa, 86–7; N withdraws from, 98; and N's marriage to Josephine, 105; marriage to Bernadotte, 216, 219, 305, 404
Clausewitz, Karl Marie von, 545
Club des Amis de la Constitution, 49
Cobenzl, Count Ludvig, 164–6, 297
Cockburn, Rear Admiral Sir George, 626–7, 629–30, 632–4
Code Napoléon _see_ Civil Code
Coignet, Captain Jean-Roch, 598
Coigny, Aimée de, 88
coinage: bears N's effigy, 325, 336
Colli, Field Marshal Michael, baron de, 111, 115
Collot, Jean-Pierre, 105, 112, 117, 156, 216
Colombier, Caroline du, 34
Colombier, Madame du, 34, 48
Comeau de Charry, Sébastien, 378
Commercial Code, 418
Committee of Public Safety, 78
Concordat: agreed with Catholic Church, 307–8, 313; weakened, 463; revised, 554, 574
Condé, Louis-Joseph, prince de, 283
Confederation of the Rhine: N forms, 397; French rule, 436, 460; rulers at Erfurt, 438, 440; questionable loyalty to France, 499; rulers join allies, 552; Alexander aims to overthrow, 553; _see also_ Germany
Consalvi, Cardinal Ercole, 307
Constant, Benjamin, 240, 264, 305, 306, 610, 614–15, 620–1
Constant, Louis, 412, 466, 543, 593
Constantine, Grand Duke of Russia, 415
Constitution of Year VIII, 242–3
Consular Guard, 251
consulate and consuls: powers, 241–4, 246–50; move to Tuileries, 251; hold reception for diplomatic corps, 253
Continental System, 405–6, 416, 441–2, 493, 496–8, 506
Convention: replaces National Assembly, 60; opposition to, 65; on new constitution (1795), 94
Copenhagen: bombarded by Royal Navy (1800), 301; Britain attacks (1807) and seizes fleet, 421
Corday, Charlotte, 76
Cordier, Louis, 193
Corneille, Pierre, 306, 382; _Cinna_ , 428, 438
Cornet, Mathieu-Agustin, 223, 224
Cornwallis, Charles, 1st Marquis, 302, 321, 350
Corsica: history and social conditions, 9–13; Assembly of Estates, 16, 23; as semi-autonomous province of France, 16; N revisits, 36–8; N writes history of, 41, 45, 48; N returns to on outbreak of French Revolution, 42; riots and disorder, 43, 52–3, 59; sends deputies to Estates General at Versailles, 43; separatists in, 43–4; integrated into French nation, 44; Joseph stands for municipal council, 45; N renounces, 66; British occupy, 81
Coruña, La, 446
Corvisart, Dr Jean-Nicolas, 257, 303, 304, 367, 466–7, 596, 609
Cosway, Maria, 325
Council of French bishops, 502
Council of State ( _Conseil d'État_ ): formulates new laws, 241; composition, 243–4; installed in Tuileries, 251; considers Civil Code, 286; N supervises, 287; reservations over Concordat with Catholic Church, 307; debates extension to N's consulship, 319; under N's extended consulate, 323; conduct of business, 390
_Courrier de l'armée d'Italie_ , 157
_Courrier de l'Égypte, Le_ , 193
Craonne, battle of (1814), 583
Crétet, Émmanuel, 467
Croisier, Captain (N's aide-de-camp), 198
Cromwell, Oliver, 292
Czartoyski, Prince Adam Jerzy, 374
Dąbrowski, General Jan Henryk, 146
Damanhur, 184
Danubian Principalities, 497
Danzig, 413
Daru, Pierre, 388–9, 513, 541, 608
Daubenton, Louis, 239
Daunou, Pierre-Claude, 240, 265
David, Jacques-Louis, 2–3, 123, 128, 171, 175, 261, 278–9, 427
Davidovitch, General Paul, 137–8, 140, 142–3, 149
Davout, Marshal Louis-Nicolas: in Egypt, 185; on N's elevation to emperor, 354; made marshal, 376; opposes Austrians, 377, 382; at Austerlitz, 384; at Auerstadt, 404; opposes Russians in Poland, 408; at Wagram, 454–5; ordered to prepare for war with Russia, 497; N considers as King of Poland, 513; in Russian campaign, 520, 523; at Borodino, 527, 529; in retreat from Moscow, 539–40; attempts to restrain Murat, 554; stranded in Hamburg, 566; rejoins N on return from Elba, 608; and N after Waterloo defeat, 619–20
Decaen, General Charles Mathieu Isidore, 334–5
Decrès, Admiral Denis, 330, 363, 374, 465, 608, 619, 621–2
Dego, 114
Delmas, General Antoine Guillaume, 149
Dembiński, Lieutenant Henryk, 532
Denmark: in League of Neutrals, 300; and Treaty of Tilsit, 416; Britain captures fleet, 421; _see also_ Copenhagen
Denon, Vivant, 206–7
d'Erlon, General Jean Baptiste Drouet, 616
Desaix, General Louis, 161, 190, 196, 197, 275–8, 280, 376, 399
Descartes, René, 212
Desgenettes, Dr René, 189, 201, 204
Desmarest, Pierre, 344
Destaing, General Jacques-Zacharie, 204
Diavolo, Fra (Michele Pezza), 432
Directors, Directory (Paris): in Luxembourg Palace, 2–3; and Talleyrand's presentation of N, 4, 7; N's reports to, 117, 139, 141, 143, 148, 152, 203; orders N to march on Rome with reduced forces, 121; and N's independent acts, 126; commissioners, 145–6; supports N in Italian campaign, 149–50; right-wing plot against, 158; interest in settlements in Egypt and Africa, 162; suppresses opposition and recovers majority, 163; and N's concluding Treaty of Campo Formio, 167; summons N to Paris, 168, 169–72; and proposed invasion of England, 172; and N's bid for shared power, 176; and N's expedition to Egypt, 177; and N's return from Egypt, 214–15; dissolved in Brumaire coup, 221, 226, 229–30, 236; administrative reforms, 322
Divova, Elizaveta Petrovna, 326
Djezzar Pasha (Ahmad Pasha al-Jazzar), 196, 199–201
Dnieper, river, 523
Dolgoruky, Prince, 381
Dolomieu, Déodat, 179
Dominica, 329
Dommartin, Lieut. Colonel Elzéar Auguste Cousin de, 68
Doppet, General François, 70–1
_Doris_ , HMS, 338
Drake, Francis, 343
Dresden, 546, 557, 562, 564–5, 578; battle of (1813), 567
Drouot, General Antoine, 596, 600
Dubois, Dr Antoine, 487–8
Duchâtel, Adèle, 304
Ducis, Jean-François, 175
Ducos, Roger: and Brumaire coup, 219–20, 222, 226–7; nominated consul, 234, 236–7
Dugommier, General Jacques, 71–3, 256
Dugua, General Charles, 204
Dumas, General Alexandre, 139, 185
Dumas, General Mathieu, 250, 431, 435, 465, 569
Dumerbion, General Pierre, 77, 80, 81
Dumouriez, General Charles François, 61, 159, 344
Dupont, General Pierre-Antoine, 429, 434–5, 509, 595
Duroc, General Christophe: familiarity with N, 257, 394; accompanies N to Italy, 274; on N's appointment as emperor, 352; made grand marshal of the palace, 262, 357–8; and Maria Walewska, 410–11, 466; receives grand chamberlain's key from Talleyrand, 448; and N's grief at Lannes' death, 452; in Russian campaign, 522; in retreat from Moscow, 541; accompanies N back to Paris, 543; killed at Bautzen, 560, 568
du Teil, General Jean-Pierre, 38, 47, 65, 71, 256
Eckmühl, battle of (1809), 450
École Militaire, Paris, 26–31
Edgeworth, Maria, 326
education: reformed, 316, 390–1
Egypt: Ottoman oppression in, 159; French aim to colonise, 160, 164; Talleyrand proposes invasion, 173–4; French expedition to, 174–5; scientists and scholars accompany expedition, 175–6; French arrive in, 181–2; conditions, 183–5; N's administration and researches in, 188–95, 203; N leaves, 206–8, 269; impending French collapse in, 269; French continue occupation, 300; British land forces in and French occupation ends, 301–2
Elba (island): ceded to France, 298, 334; N exiled to, 588, 593, 599–600; N's life and administration in, 600–1
Elders, Council of: and Brumaire coup, 225–6, 228–30, 232–4; members draft new constitution, 239
Elliott, Sir Gilbert, 81
Elphinstone, Clementine _see_ Malcolm, Lady
émigrés: N grants amnesty to, 315–16
Enghien, Louis Antoine Henri Condé, duc d': suggested as successor to N, 279; arrested and shot, 344–7, 374
_Épervier, l'_ (French brig), 623
Erfurt: N's meeting with Tsar (1808), 437–43
Ermenonville, 283
Essling, 452
Estates General (France): Louis XVI calls, 40; Corsican deputies attend, 43; transforms into National Assembly, 44
Etruria, 297, 426
Europe: and balance of power, 298; N reorganises, 387–8, 422–3
Eylau, battle of (1807), 311–12
Fabvier, Colonel Charles, 527, 588
Fain, Agathon, 321, 391, 393–4, 399, 497, 510–11, 543, 563, 594
Faipoult, Guillaume, 121
Fantin des Odoards, Colonel Louis Florimond, 616
Farington, Joseph, 326
Faucheur, Sergeant Narcisse, 569
Fauvelet de Bourrienne, Louis Antoine de _see_ Bourrienne, Louis Antoine de Fauvelet de
_fédérés_ , 65, 67–8
Ferdinand, Archduke of Austria: commands Austrian army, 376–7, 449, 457; N favours as successor to Francis I, 468
Ferdinand IV, King of Naples, 373, 395–6, 401
Ferdinand VII, King of Spain ( _earlier_ Prince of the Asturias), 424–5, 427, 429–33, 435, 573
Fère Champenoise, La, 584
Fère, La (regiment), 31–3; retitled as First, 48
Ferrières, General, 534
Fesch, Cardinal Joseph (Giuseppe): accompanies Letizia out of Ajaccio, 19; letters from N, 25, 39, 47, 55; cares for dying Carlo, 29; falsifies Joseph's age, 45; flees Corsica for France, 62–3; as quartermaster in Chauvet, 64; sets up business in Basel, 85; N finds jobs for, 91, 98; meets Josephine in Parma, 133; visits N in Milan, 155; buys land around Ajaccio, 207; made Archbishop of Lyon and primate of France, 315; as grand almoner, 357; conducts secret religious marriage for N and Josephine, 368; celebrates mass in Lyon, 372; and N's marriage to Marie-Louise, 474–6; and N's religious scepticism, 485; baptises N's son, 489; exiled, 502; swears allegiance to Pope, 502; joins N in Paris after return from Elba, 609; and N's preparations for flight to America, 621; Bertrand appeals to from St Helena, 641
Fiévée, Joseph, 548
Finckenstein, Treaty of (1807), 413
Fiszerowa, Wiridianna, 326
Five Hundred, Council of the: resists Brumaire coup, 226–9, 231–4; members draft new constitution, 239
Flaxman, John, 325
Florence, 130
Fontaine, Pierre, 128, 260, 303, 326, 427, 481, 574
Fontainebleau, 336, 359, 367, 372, 437, 464, 468, 473, 485, 502, 554, 582, 586, 590, 592–3, 595, 597–8, 607
Fontainebleau, Treaty of (1807), 424
Fontainebleau, Treaty of (1814), 593, 601, 604
Fontanes, Louis-Marcelin de, 259
Fouché, Joseph: relations with N, 217, 221; urges N to ally with Barras, 219; police reports, 220; and Brumaire coup, 228, 234; on N's reaction to Sièyes' draft constitution, 240; independence, 245; and censorship of press and theatre, 246–7; network of informers, 246, 321; profits from rumours, 279; and scheming over successor to N, 279; and plots to kill N, 283–4, 295; opposes restoring status of Church, 291; N gives seat in Senate, 318; uncovers military plots against N, 318; and proposed extension of N's consulship, 319; supports Josephine, 319; and royalist conspiracy, 345; claims to oppose execution of Enghien, 348; reinstated as minister of police, 348; on government after succession to N, 350; urges granting supreme authority to N, 350; on granting of hereditary titles, 398; made Duke of Otranto, 398; administration during N's absence, 419; on N's reaction to British seizure of Danish fleet, 421; persuades Josephine to request divorce, 437; letter from N in Spain, 445; conspires with Talleyrand, 447; N leaves unpenalised, 448; on Lannes' closeness to N, 452; counters British landing at Walcheren, 467; N rebukes, 468; and N's remarriage, 473; favours peace with Britain, 477; sacked by N, 477, 482; policing style, 482; N appoints governor of Illyria, 562; sent to Naples, 578; plans elimination of N, 593; reappointed minister of police on N's return from Elba, 608, 612; self-protective plot, 612–13; plots against N after Waterloo defeat, 619–21; frustrates N's flight to America, 622–3; and Louis XVIII's return to throne, 624
Foureau de Beauregard, Dr Louis, 596
Fourès, Lieutenant, 192–3
Fourth Regiment: N posted to, 48
Fox, Charles James, 325, 396
France (and French Empire): declares war on Britain and the Netherlands (1793), 60; revolts and risings against Convention, 65; under threat from coalition of nations, 67, 103, 205, 211, 268, 299; peace with Spain (1795), 93; royalist resurgence, 93–5; constitutions, 94, 239–42, 322, 323, 357; interests in Middle East and Mediterranean, 160–1; loses colonies to British, 160; navy damaged by revolutionaries, 172; N arrives in from Egypt, 207–8, 209; critical condition (1799), 211; under consulate, 236–8; monarchists in, 239, 293–4; royalist forces capitulate, 249; administrative structure and local government, 264–6; economic and financial reforms, 266–7, 285; royalist opposition declines, 283; legal code, 285–7, 418; sinking fund established, 285; peace treaty with Austria (1801), 297–8; and balance of power, 298; extends borders, 299; makes peace treaties, 300; hostility towards Britain, 301; peace with Britain and Turkey (1802), 312–13; commercial rivalry with Britain, 327; N rebuilds economic and political power in peace period, 327–8; colonial empire, 328–31; expansion and population, 337; Britain declares war on (1803), 338; royalists arrested and condemned to death, 342–7; fear of royalist return, 349; declared an empire, 351–2; popular reaction to N as emperor, 353; offices, titles, ceremonies and symbols, 358; plebiscite on change to imperial regime, 358–9; revolutionary ceremonies and symbols phased out, 358; and hereditary nature of monarchy, 359; financial crisis (1805–6), 380, 386–8; imperial status, 397; peace negotiations with Britain and Russia (1806), 401; retains established military equipment, 464; penal and policing system under Savary, 482–3; condition of navy, 490–1; Empire expands on Continent and declines overseas, 490; industry and agriculture, 490; roads and communications developed, 490; economic problems, 491–3; trade with Britain, 493; vulnerability, 499; Prussia declares war on (1813), 552; discontent under Bourbon restoration, 604; _see also_ French Revolution
Francis I, Emperor of Austria (Francis II, Holy Roman Emperor), 130, 277; title, 353; letter from N on Joseph's accession to throne of Italy, 371; N warns, 374; declines N's peace offer, 379; abandons coalition after Austerlitz, 384; loses territory under Treaty of Pressburg, 385; delays recognising Joseph as King of Spain, 436; prepares for war against N, 444; and Treaty of Vienna, 468; and impending war between Russia and France, 497; N hopes for support from, 552; N suggests making separate peace, 579, 581; readiness to support accession of N's son, 592; letter from N on return from Elba, 612; cares for grandson Napoleon II, 629
François, Captain Charles, 540
Frankfurt proposals and Declaration (1813), 576–7
Franklin, Benjamin: as 'man of genius', 212
Frederick Augustus, King of Saxony, 416, 439, 510, 513, 546, 557, 569, 571
Frederick I, King ( _earlier_ Elector) of Württemberg, 377, 384–6, 403, 458, 468–9, 489, 510, 629
Frederick William II, King of Prussia: supports Louis XVI, 298; congratulates N on becoming emperor, 353; undecided allegiance, 380; and peace negotiations (1806), 401–3, 405; at Auerstadt, 404; signs Convention of Bartenstein (1807), 413; Alexander supports, 414; at Tilsit, 415–16; N disdains, 416; letter to N unanswered, 419; meets N at Dresden, 516; joins allies in war against France, 551–2; invades Saxony with Russians, 556; sense of honour, 556; wary of invading France, 576
Frederik VI, King of Denmark, 547
Freemasonry, 322
French Revolution (1789): conduct of, 1–2, 263; outbreak, 41–2; changed values and rejection of Christianity, 123; and _mission civilatrice_ , 159; ideals, 264; and overthrow of feudalism in ancien régime, 293; symbols and commemorations end, 358; anti-clericalism, 433
Frénilly, François Auguste de, baron, 369
Fréron, Stanislas, 70, 72–3, 83, 96, 98, 105
Friedland, battle of (1807), 413–14
Frochot, Nicolas, 549
Frotté, Louis de, 249
Fructidor coup (1797), 163–4
Fuseli, Henry, 325
Gallo, Marzio Mastrilli, Marchese de, 158, 164–6
Ganteaume, Rear-Admiral Honoré, 206–7
Gardanne, General Gaspard Amédée, 235, 437
Garrau, Pierre-Anselme, 145, 149
Gasparin, Thomas, 67, 70, 72
Gassendi, Jean-Jacques, 70, 79
Gaudin, Martin, 237, 245, 267, 285, 460, 608
Gaza, 198
Gendarmerie, 321
Geneva: N visits, 167, 272–3
Genoa, 274–5, 373
Gentz, Friedrich von, 353
George III, King of Great Britain, 81, 268, 312, 340, 350, 371, 442
George, Marguerite Josephine, 341, 563
Gérard, François, 527, 532
Germany: boundary changes, 426; and Austria's war with N, 449, 456; emancipation hopes, 457; N's policy in, 457, 459; hostility to N, 552; _see also_ Confederation of the Rhine
Ghilini, Christine, 468
Girardin, Stanislas, 283
Girodet, Anne-Louis, 128
Girondins, 64–5
Giubega, Lorenzo, 16, 41
Globbo Patriotico (Patriotic Club of Ajaccio), 46
Godoy, Manuel, 413, 424, 429–30
Goethe, Johann Wolfgang von, 124, 440, 488, 642
Gohier, Louis-Jérôme, 214–15, 218, 220, 225–6
Golfe Juan, 606
Gossec, François-Joseph, 3
Gourgaud, General Gaspard, baron, 626, 628, 630–1, 639
Gouvion Saint-Cyr, General Laurent, 317, 514, 567, 569
Grande Armée, La: formed from Army of England, 375–6; marches against Austria, 377; behaviour, 378–9; foreign contingents, 465, 505; in war against Russia, 505, 508; strength in Russian campaign, 514; and difficult conditions during advance into Russia, 517, 519–22; in retreat from Moscow, 535–43; casualties and losses in Russian campaign, 547–8
Grassini, Giuseppina, 125, 274, 278, 279, 304, 475
Great Powers (Britain, Russia, Prussia, Austria), 583
Greathead, Bertie, 326
Grégoire, Henri, abbé, 307, 319, 350
Grenoble, 607
Grenville, William Wyndham, Baron, 268–9, 396
Gribeauval, General Jean-Baptiste Vaquette de, 33
Gros, Antoine, 154, 356, 444
Grossbeeren, battle of (1813), 567–8
Grouchy, Marshal Emmanuel, marquis de: in Russian campaign, 520; overcomes Angoulême at Lyon, 609; at Waterloo, 616–18
Guadeloupe, 328, 330–1
Gudin, Charles-Étienne de, 22
Guibert, General Jacques Antoine Hippolyte, comte de, 33
Guides, 162
Guingené, Pierre Louis, 613
Hanover: N orders invasion of, 339; annexed by Prussia, 385, 401
Hanseatic ports: N annexes, 497
Hardenberg, Karl August, Baron ( _later_ Prince) von, 401, 552, 560, 568
Hatzfeld, Prince Franz Ludwig von, 404, 548, 552
Haugwitz, Count Christian von, 381
Hawkesbury, Robert Banks Jenkinson, Baron _see_ Liverpool, 2nd Earl of
Heilsberg, battle of (1807), 464
Heine, Heinrich, 502, 643
Heliopolis, 269
Helvetic Republic and Confederation, 297, 334, 573; _see also_ Switzerland
Hesse-Darmstadt, Ludwig I, Grand Duke of, 510
Hobart, Robert, Baron, 334
Hoche, General Lazare, 83, 93, 99–101, 143, 150, 157, 159; death, 164, 167
Hofer, Andreas, 449
Hohenlinden, battle of (1800), 294
Hohenlohe, Prince Louis Aloysius, 404
Holland: France invades, 211; kingdom created with Louis as king, 396–8, 477; economy, 477, 478; Louis gives up throne, 478; N closes frontiers with France and imposes demands, 478; N incorporates into France, 479
Holland, Elizabeth, Lady, 636
Holland, Henry Richard Vassall Fox, 3rd Baron, 636, 639
Holy Roman Empire: reorganised, 297, 333, 342, 353
Homer: _Odyssey_ , 178
Hompesch, Ferdinand von, 179–80
Hood, Admiral Samuel, 1st Viscount, 65, 67, 72
Hope (London banking house), 388
Hoppner, John, 325
Hostages, Law of: N repeals, 239
Hubert (N's valet), 593–4
Hulot, Madame (Moreau's mother), 294
Humboldt, Wilhelm von, 3
'Hundred Days, the', 624
Hyde de Neuville, Jean-Guillaume, baron, 248, 267, 283, 295
Iberian Peninsula: cost of war, 491
Ibrahim Pasha, 188
Ideologues, 218, 239, 306
Ilari, Camilla Carbon, 17, 364
Illyria, 572
_Inconstant_ (French brig), 605–6
India: French interests in, 160, 330, 334–5; N proposes joint offensive with Russia against, 437
Institute of Arts and Sciences, 171, 239, 248, 360
Ionian Islands, 416
Ireland: Act of Union with Britain (1801), 301; N plans invasion of, 364
Isabey, Jean-Baptiste, 304
Italy: campaign in, 103–4, 111, 121–2, 128–9, 134–5; effect of N's administration in, 126–8; plundered by French, 128; N's plans for northern republic, 159; N offers throne to brothers, 364–5, 371–2; N crowned King, 372–3; N extends Civil Code to, 426; and N's strategic policy, 462
Jabłonowski, Władysław, 27
Jackson, Francis James, 353
Jacob, Georges, 214
Jacobin Club: N closes down, 97
Jacobins: hostility to N, 8, 219; and Corsican Globbo Patriotico, 46; terrorise Toulon, 64; reaction against, 65; and Paris riots, 83; hopes for N's restoring Republic, 218; and Brumaire coup, 227, 229, 235; consuls' policy on, 238–9; N regards as threat, 283, 295
Jaffa, 198, 202
Jefferson, Thomas, 427
Jena, battle of (1806), 404
Jerusalem, 199
Jerzmanowski, Colonel Jan Paweł, 597
_jeunesse dorée_ (anti-Jacobin faction), 83
Jews: N's attitude to, 391, 418
João, Dom, regent of Portugal, 424
John, Archduke of Austria, 376, 379–80, 449, 453
Josephine, Empress of the French ( _earlier_ Marie-Josèphe-Rose de Beauharnais): as socialite, 88, 100, 154; background, 99–100; appearance and manner, 100; early relations with N, 101–3; marriage with N, 104–5; letters from N, 112, 118, 130–1, 138, 144, 148, 187, 274–5, 320, 341, 363, 383, 404, 408, 410, 412, 415, 442, 445, 593, 597; affair with Hippolyte Charles, 118, 131–3, 144, 173, 176; N begs to come to Italy, 118; claims pregnancy as reason for not travelling to N, 121; Junot presents for acclaim in Paris, 126; in Milan with N, 131–2, 146, 155; accompanies N to Mantua, 149; dislikes N's family, 155; improving relations with N, 155, 187; and N's negotiations with Austrians, 165; joins N in Paris (December 1797), 172; not on expedition to Egypt, 176; travels to Toulon with N, 177; infidelities, 187, 286; injured in balcony collapse, 187; and N's return to France from Egypt, 214; effects reconciliation with N, 216–17; N considers divorcing, 216; and N in Brumaire coup, 230, 235; anxiety over N's fate in Brumaire coup, 235; in Petit Luxembourg, 239; in Tuileries, 251, 262–3; receives diplomatic corps, 253; qualities, 259–60; at La Malmaison, 260; and N's absence in Italian campaign, 273; Madame Hulot hates, 294; and N's improving health, 303; jealousy of N's affairs, 304; prevents N from shooting swans, 304; N's happiness in marriage, 305; favours Hortense's marriage to Louis Bonaparte, 308; in Lyons, 309–10; opposes extension of N's consulate, 318; inability to produce heir, 319–20; and N's philandering, 320, 341; accompanies N on progress through Normandy, 324–5; impresses foreign visitors, 326; weeps on hearing of Moreau's arrest, 343; pleads for Enghien, 345; pleads for Rivière and Polignac, 354; official court of twenty-seven, 357; and N's rescue operations in Boulogne, 361; Bonaparte family conspire to force divorce from N, 366; wardrobe, 366–7; coronation, 368; secret religious marriage to N, 368; arranges Ney's marriage, 376; and N's absence on Austrian campaign, 377; attends Eugène's marriage to Augusta, 385; extravagance, 388; changing relations with N, 391–2, 394; accompanies N on campaign against Prussia, 403; and N in Poland, 410; in Biarritz with N, 432; campaign to force divorce, 437–8; buys smuggled silks and brocades, 441; reassures N over achievements, 443; wrongly addresses delegation of the Legislative, 446; N decides to divorce, 468–70; divorce settlement, 471; informed of birth of N's son, 489; encourages N after Leipzig, 575; writes to Eugène urging loyalty to N, 578; entertains Alexander at Malmaison, 597–8; and N's abdication and exile in Elba, 597; death, 602, 609
Joubert, General Barthélemy, 147, 218, 283
Jourdan, General Jean-Baptiste: as potential dictator, 211; proposes supporting N, 220; and Brumaire coup, 222, 227, 230, 232; in Spain, 461
_Journal de Paris_ , 217
_Journal des hommes libres_ , 8
Jullien, Thomas: informs N of Josephine's infidelities, 187
Junot, Jean-Andoche: bravery at Toulon, 71; as ADC to N on campaign against Sardinia, 78–9; and N's arrest, 79–80; accompanies N to Paris, 82, 87–8; N selects for post on staff in Constantinople, 92; praises N in Italy, 108; takes captured standards to Paris, 117; presents Josephine for acclaim in Paris, 126; accompanies Josephine to N in Italy, 131; affair with Josephine's maid, 173; on voyage to Egypt, 178; informs N of Josephine's infidelities, 187; fathers black son in Egypt, 192; opposes Ottomans at Acre, 200; treatment of women, 262; joins N on Austrian campaign, 382; leads occupation of Portugal, 424–5, 429; mental problems, 425; defeated by Wellington, 435; at Borodino, 527; broken by Russian campaign, 548; suicide, 568
Kant, Immanuel, 212
Keith, Admiral George Keith Elphinstone, Viscount, 275, 625
Kellermann, General François, 103, 121, 277
Kléber, General Jean-Baptiste: on march to Syria, 197, 200; congratulates N on victory at Aboukir, 205; on N's departure from Egypt, 269; assassinated in Cairo, 280
Kleist, General Friedrich, Graf, 566
Köller, Colonel Franz, 597–9
Kościuszko, Tadeusz, 407
Krasny, 539
Kray, Field Marshal Paul, 270
Kulm, battle of (1813), 567–8
Kurakin, Prince Alexander, 495, 499, 509
Kutuzov, General Mikhail Ilarionovich, 377, 526–9, 532, 535–6, 540, 543, 545, 547, 552
La Bédoyère, Colonel Charles de, 607
La Billardière, Jacques, 128
Labouchère, Pierre-César, 477
Laclos, Choderlos de: _Les Liaisons dangereuses_ , 35
Łączyński, Theodore, 602
Lafayette, Marie Joseph Gilbert du Motier, marquis de, 279, 289, 299, 306, 320, 619
Laforêt, Antoine de, 462
La Harpe, César de, 613
Langeron, Louis, comte de, 384
Lannes, General Jean: at Lodi, 120; in Egypt, 185, 204; leaves Egypt with N, 206; familiarity with N, 257; on expedition against Austrians in Italy, 273; at Marengo, 276; regrets N's elevation to emperor, 354; N reviews troops at Marengo, 372; opposes Austrians, 377, 379; defeats Prussians at Saalfeld, 403; defeats Russians at Pułtusk, 408; disparages Pułtusk, 411; in Spain, 445; killed at Aspern-Essling, 452, 568; on Russian improvement in fighting, 464
La Pérouse, Jean François de, 30
Laplace, Pierre-Simon, marquis de, 170, 237, 245
La Poype, General Jean, 68, 256
Lareveillère-Lepaux, Louis-Marie, 169, 171
Lariboisière, Jean-Ambroise de, 33, 535
Larrey, Dr Dominique-Jean, 198, 452, 536
Las Cases, Emmanuel, comte de, 623, 626, 628, 630–1, 637–8; _Mémorial de Sainte-Hélène_ , 643
Latouche Tréville, Admiral Louis-René Levasson de, 374
Lauberie de Saint-Germain, Mlle ( _later_ Bachasson de Montalivet), 34, 48
Lauderdale, James Maitland, 8th Earl of, 396
Laugier de Bellecour, Pierre François, 23, 30–1
Laurenti, Joseph, 80
Lauriston, General Jacques, 313, 320, 499, 511, 531
Lavalette, Antoine, comte de: on dissoluteness in Paris, 84; on youthful generals, 123; on Desaix, 161; reports to N on situation in Paris, 163; N orders to marry Josephine's niece Émilie, 176; leaves Egypt with N, 206; on silence at reception for N and Moreau, 221; and discussion of the Five Hundred, 229; as head of postal service, 342, 447; N confides in, 575; on N's departure to confront allies, 579; advises Joseph against surrendering Paris, 585; and N's return to Paris from Elba, 608; and N's defeat at Waterloo, 619
la Valette, Jean Parisot de, 300
Lavater, Johann Caspar, 212
Lays, François, 175
League of Neutrals, 300
Lebrun, Charles-François: as consul, 242, 244, 251–3, 272; and scheming over successor to N, 279; opposes relations with Catholic Church, 291; urges upgrade in N's status, 318; and royalist plotters, 345; speech on proclaiming N as emperor, 352; as arch-treasurer, 357; and new imperial insignia, 358; in Council of State, 390
Leclerc, Dermide, 258
Leclerc, Paulette _see_ Bonaparte, Pauline
Leclerc, General Victor Emmanuel: Lieut. Charles joins at Verona, 132; marries Paulette, 155; and Brumaire coup, 231–2; commands expedition to Saint-Domingue, 330; death from yellow fever, 332, 337
Lecourbe, General Claude Jacques, 272, 317
Ledoux, Claude Nicolas, 102
Lefèbvre, Marshal François (duc de Danzig), 231, 413, 457, 587, 592
Legendre, General François-Marie Guillaume, 447
Legion of Honour, 316, 358, 460–1
Legislative Body ( _Corps législatif_ ), 241
Leipzig: N withdraws to, 569; battle of (1813), 570–1
Lejeune, Colonel Louis, 480, 529
Le Lieur de Ville sur Arce, Jean-Baptiste, 23, 30, 71
Le Marche (papal province), 426
Le Marois, Jean, 104, 143
Lemercier, Louis, 222, 224–5
Leoben, 150–1, 158–9, 162
Leopold II, Holy Roman Emperor, 298
Le Paute d'Agelet, Joseph, 30
Le Picard de Phélippeaux, Louis-Edmond Antoine, 30, 201
Letourneur, Charles-Louis, 164, 169
Levant: French interest in, 160
Levie, Jean Jérôme, 45, 62
Ligne, Charles-Joseph, prince de, 385, 473
Lithuania, 519
Liverpool, Robert Banks Jenkinson, 2nd Earl of ( _earlier_ Baron Hawkesbury), 301, 335, 338, 604, 641
Livorno, 129
Lodi, 119–22
Lombardy, 126, 139
Loménie de Brienne family, 21, 372
Loménie de Brienne, Étienne-Charles de, 37
Lonato, battle of (1796), 134, 136
Longwood (house), St Helena, 627, 629–32, 634, 636, 638
Louis XIV, King of France, 398
Louis XV, King of France, 13
Louis XVI, King of France: calls Estates General, 40; arrested on attempted escape, 49; executed, 60, 83, 171; supported by Austria and Prussia, 299; fatal firework display, 480
Louis XVIII, King of France: assumes succession, 93; ambitions, 158, 349; letter from N, 282; and unwanted return of monarchy, 293; and N's revival of religion, 315; British plan to place on French throne, 340; attempts to intercede for Enghien, 347; and N's marriage to Marie-Louise, 473; denies N means of support, 603; flees on N's return from Elba, 607, 624; in Belgium, 622; negotiates with Fouché, 622; resumes throne, 624
Louis Charles, Dauphin, 93
Louise (Josephine's maid), 173
Louisiana (North America), 330–1; sold to USA, 337
Lowe, Major General Sir Hudson: as governor of St Helena, 633–9, 643; and N's illness, 640–2
Ludvig, Prince of Prussia, 403
Luise, Queen of Prussia, 380, 401, 416
Lunéville, Treaty of (1801), 297, 309, 333–4
Lützen, battle of (1813), 560
Lyon: N elected president of Cisalpine Republic at, 309–11; Augereau surrenders, 584
Macdonald, Marshal Étienne-Jacques-Joseph-Alexandre, 452–3, 514, 547, 567–8, 570–1, 587–9, 593–5, 608, 614
Mack, General Karl, 376–8
Maddalena (island), 60
Madrid: riot against French, 431; Wellington captures, 533, 563
Magallon, Charles, 159–60
Maida, battle of (1806), 401
Maillard, Colonel Louis, 52–3, 54
Maillebois, Marshal Jean-Baptiste Desmarets, marquis de, 111
Mainz, 564
Maison Royale de Saint-Cyr, 25
Maitland, Captain Frederick, RN, 623, 625
Malcolm, Clementine, Lady, 634, 638
Malcolm, Rear Admiral Sir Pulteney, 634, 637–8, 639
Malet, General Claude-François de, 446, 549–50, 555
Maleville, Jacques de, 286
Malmaison, La: Josephine acquires and improves, 260, 303; N visits, 284, 303–4, 320, 323; Hortense at, 320
Malmesbury, James Harris, Baron ( _later_ 1st Earl), 164
Maloyaroslavets, 536
Malta, 161, 175, 179, 269, 302, 335, 338
Mamelukes: battles with French, 185–6, 188
Mantua, 128, 132–4, 138–40, 142, 146–8
Manzoni, Alessandro: _Il Cinque Maggio_ , 642
Marat, Jean-Paul, 76
Marbeuf, Charles Louis, comte de, 16–18, 22, 24–5, 34, 45; son, 256
Marchand, Louis, 597, 602, 626, 628, 635, 639, 641
Marengo: battle of (1800), 275–8, 280; N revisits, 372
Maret, Hugues-Bernard, duc de Bassano: N appoints secretary to Consuls, 237; as secretary of state, 245, 394; on assassination threat to N, 350; controls Polish council, 411; as foreign minister, 499; advocates creating Polish state as buffer, 512; in Vilna, 519, 522; in Russian campaign, 521; letter from N on evacuation of Moscow, 535; and retreat from Moscow, 543; attempts to revive Prague congress, 566; and N's view of fortunes of war, 567; and N's reaction to Metternich's peace terms, 577; advises N to abdicate, 587; remains loyal to N, 593–4; and N's departure for Elba, 597; and N's return to Paris from Elba, 608; on N's options in facing allied invasion, 614–15; advises N after Waterloo defeat, 619–20
Maria Augusta, Princess of Saxony, 472
Maria-Carolina, Queen of Naples, 373, 395
Maria Ludovica, Empress of Francis I of Austria, 449, 510
Maria-Luisa of Parma, Queen of Philip IV of Spain, 424, 430
Marie-Antoinette, Queen of Louis XVI, 251, 480
Marie-Louise, Empress of Napoleon I ( _formerly_ Archduchess of Austria): marriage to N, 472–5; awkward manner, 478, 481; pregnancy and birth of son, 482, 487–9; Canova's bust of, 484; N blames for downfall, 486; accompanies N on departure for Russian campaign, 510; N bids farewell on leaving for Russia, 513; letters from N on Russian campaign, 520–1, 533; sends portrait of son to N in Russia, 527; and N's return to Paris from Russia, 546; N's devotion to, 552; N nominates as regent, 555, 579, 587; and N's departure to oppose Russia and Prussia, 555; N visits in Mainz, 564; N reassures during campaign against allies, 572; proposes public prayers for success, 582; note from N intercepted, 584; leaves Paris with son, 585; Louis attempts to rape, 589; moves to Blois with son, 589; final letter from N, 594, 597; at N's abdication, 595–6; sent to Orléans and robbed, 596; N furnishes rooms for in Elba, 600; sends money to N in Elba, 601; supposed visit to Elba, 603; letter from N on return from Elba, 612; expresses relief at N's exile, 624
Marmont, Auguste: joins N at Toulon, 71; in campaign against Sardinia, 78–9; accompanies N to Paris, 82, 87; N selects for staff on post in Constantinople, 92; as aide to N in Paris, 97; on N's relations with Josephine, 101; praises N in Italy, 108; on N's victories in Italy, 123; values and ambitions, 124; meets Josephine on journey to Italy, 131; exhausting practices, 135; on spirit of French soldiers, 136; takes captured flags to Paris from Italy, 138; in Egypt, 196; leaves Egypt with N, 206; assesses army morale, 246; and anti-N feeling in army, 317; commands troops for invasion of England, 361; on N's ambitions, 363; and proposed invasion of Ireland, 364; opposes Austrians, 377; on indecisiveness of Wagram, 456; Salamanca defeat, 526–7; at La Fère Champenoise, 584; and defence of Paris, 585–6; defects to allies, 588–9, 591; negotiates with allies, 588; N proclaims a traitor, 606; follows Louis XVIII into exile, 614
marshals of the empire, 357, 375–6
Martinique, 328, 330–1
Masséna, Marshal André: in campaign against Sardinia, 77, 80; in Army of Italy, 107–8, 110, 278; in advance from Savona, 112–13, 115; at Lodi, 120; demands protection money in Italy, 127; on ill-equipped army, 135; courage, 137; opposes Alvinczy, 141–2; moves against Arcole, 142; in battle for Mantua, 147–8; in advance on Vienna, 149; defeats Russians in Switzerland, 213; on army's reaction to Brumaire coup, 246; Austrian offensive against, 271–2, 274; capitulates at Genoa, 275; attends Concordat celebration, 314; rivalry with N, 317; Whitworth reports on, 336; made marshal, 357; campaign in Italy, 379; N criticises, 379; in Austrian campaign (1809), 452; at Wagram, 454–5; ambitions, 465; success against Wellington in Spain, 492; semi-retirement in Marseille, 614
Masseria, Filippo, 45
Maupeou, René de, 244
Maury, Cardinal Jean-Sifrein, 3
Maximilian, King of Bavaria, 573–4
Mazis, Alexandre des, 30–2, 33–4, 47–8, 315
Mediterranean: French strategic interests in, 160–1, 425; British dominance in, 269
Méhul, Étienne, 6, 175, 314
Melas, Field Marshal Michael von, 271, 274–7
Melzi d'Eril, Francesco, 162, 309–11, 341
'men of genius', 212
Méneval, Claude-François: on N's behaviour, 304; takes over as N's secretary, 321; and Enghien's supposed conspiracy against N, 340, 346; looks after Camilla Carbon Ilari, 364; accompanies N to Milan for coronation, 372; and N's meeting with Francis, 384; on N's variable routine, 394; sees Maria Walewska, 413; on N's reluctance to go to war against Alexander, 511; incapacitated by overwork, 548; N sends letters through, 601
Menou, General Jacques (Abdullah), 95, 301–2
_Mercure, Le_ (journal), 247
Meszaros, General Johann, 134
Metternich, Count ( _later_ Prince) Clement von: on N not making peace with Prussia, 405; and N's proposed Franco-Prussian campaign against Turkey, 428; affair with Caroline, 436; Talleyrand contacts, 442, 448; negotiates Treaty of Vienna, 468; and N's marriage to Marie-Louise, 473; on N's social awkwardness, 480; on N's conversational charm, 483–4; attempts to resolve N's conflict with Pope, 484; on N as family man, 486; toasts N as 'King of Rome', 487; declares Russia acting out of fear, 493; on inevitability of war between Russia and France, 497, 503; and N's advance against Russia, 511–12; on France as counterbalance to Russia, 552; and Russian threat to western Europe, 553; declines to fully support France, 555; proposes negotiating terms, 557–8; negotiates with N at Dresden, 562–5; opts for war with France, 566; leaves Murat in Naples, 571; sends peace proposal to N, 576–7; wary of invading France, 576; suggests further talks, 578; Caulaincourt negotiates with, 592; signs Treaty of Fontainebleau, 593; spy network, 603; and Talleyrand's declaration against N, 612; contacts Fouché, 613
Mignard, Pierre, 228
Milan: N enters, 124, 129; Josephine joins N in, 131–2, 138, 146; N returns to, 153, 274, 278; N leaves, 167; N crowned in (1805), 373
Milleli, Les (property), 24–5, 35
Minsk, 534–5, 541
Miollis, General Sextius Alexandre François de, 463
Miot de Melito, André-François, 154, 162, 167, 355, 363, 489, 608–9, 616
Mirabeau, Honoré Gabriel Riqueti, comte de, 44
_mission civilatrice_ , 159
Moiret, Captain Joseph-Marie, 186, 197
Molé, Mathieu, 210, 250, 288, 548, 577, 582, 608, 643
Mollien, Adèle, 304, 548
Mollien, François-Nicolas: on N's destiny to command men, 250; appointed director of sinking fund, 285; explains economics to N, 285; takes over treasury, 388, 608; on N's grasp of detail, 389; on N's need to be at centre, 443; and Josephine's request for more attendants, 489; and N's belief in financial rewards of war, 504; N enquires after wife's health, 548; and N's need personally to sign peace agreements, 550
Mombello, near Milan, 153–4
monarchy: restoration question in France, 293–4
Moncey, General Bon-Adrien Jannot de, 429, 584, 587, 592
Monck, General George (1st Duke of Albemarle), 238, 292
Monge, Gaspard, 128, 171, 175, 177, 206
_Moniteur, Le_ (journal), 246, 256, 339, 446, 463
Monroe, James, 337
Montagnards ( _La Montagne_ ), 64–5
Montansier, Mlle de (Marguerite Brunet), 98
Montbarrey, Alexandre-Marie, prince de, 20
Montchenu, Claude, marquis de, 636, 640
Montebello, battle of (1800), 275
Montebello, Louise Antoinette Lannes, duchesse de, 596
Montereau, battle of (1814), 581
Montesquiou, Anatole de, 540, 596
Montesquiou, comtesse de (Louis XVI's children's governess), 488
Montholon, Albine de, 637–9, 641
Montholon, General Tristan, comte de, 626, 628, 630–1, 639–40, 641, 643
Monts, Raymond de, 26
Moore, General Sir John, 445–6
Morand, Colonel Charles Antoine, 177
Moreau, General Jean-Victor: commands Army of the Rhine, 103, 271; in campaign against Austria in Italy, 128; depicted in engraving, 143; and N's advance on Vienna, 150; in plot to restore Bourbons, 158, 342; as potential alternative to N as dictator, 211; N first meets, 218; honoured at banquet, 221; in Brumaire coup, 226; victory at Stockach, 272; suggested as successor to N, 279; as potential threat to N, 284; Hohenlinden victory, 294; avoids Concordat celebration, 314; rivalry with N, 317; N orders arrest, 343; tried, acquitted but sentenced on retrial, 354; death on return from America, 568
Moreau le Jeune (Jean Michel Moreau), 128
Moreau, Madame, 314
Mortefontaine: treaty (1800), 299, 305
Mortier, Marshal Adolphe-Edouard-Casimir-Joseph, 339, 406, 530, 536, 584
Moscow: N advances on, 525; abandoned by Russians and burned, 529, 531; N occupies, 530–5; maintains communications with Paris, 533; N evacuates, 535–6
Moulin, General Jean, 220, 226
Muiron, Jean-Baptiste, 71, 73, 78, 92, 142
Munich, 379
Murad Bey, 185, 188, 190, 196, 595
Murat, Achille, 258
Murat, Caroline _see_ Bonaparte, Caroline
Murat, Marshal Joachim: in Vendémiaire crisis, 95, 97; N sends armistice of Cherasco document and captured standards to, 118; on Josephine's pregnancy, 121; informs N of Josephine's illness, 131; in Italian campaign, 147; wounded in Egypt, 185; opposes Ottomans at Acre and Aboukir, 200, 204; leaves Egypt with N, 206; and Brumaire coup, 222, 224, 231–3; rescues N from angry Five Hundred, 231; marriage to Caroline, 259; at Lyon meeting, 309; reports disaffection in Italy, 317; and royalist conspiracy, 345; and N's elevation to emperor, 354; titled grand admiral, 357; made marshal, 375; sent to southern Germany, 375; commands cavalry against Austrians, 377, 379; N criticises, 379; as Grand Duke of Berg, 398; institutes new orders of chivalry, 399; dress, 407–8; opposes Russians in Poland, 407–8; as prospective king of Poland, 407, 497; relations with Grand Duke Constantine, 415; rivalry with Junot, 424; protects Charles IV of Spain, 429; repression in Spain, 431; as king of Naples, 434; Fouché and Talleyrand conspire to put on throne in event of N's death, 447; moves from Berg to Naples, 460; and N's marriage to Marie-Louise, 473–4; in offensive against Russia, 514; in Russian campaign, 520–1, 523, 532; reports on dire state of cavalry in Russia, 533; takes charge of army in retreat from Russia, 543; at Vilna, 547; returns to Naples, 554, 571; commands cavalry against allies, 567; N accuses of treason, 569; signs treaty of alliance with Austria, 578, 582; failed Italian coup and flight to France, 614
Naples, kingdom of: N signs armistice with, 129, 133; Austria seeks alliance with, 148; declares war on France (1798), 195; France invades, 211; conflict with Papal States, 291; British in, 373; Anglo-Russian forces in, 395; Joseph rules as king, 396, 426, 432–3; Murat made king, 434
NAPOLEON I (BONAPARTE), Emperor of the French: acclaimed in Paris (1797), 1, 3–8; appearance, 3, 22, 51–2, 74, 88, 98, 110, 153, 248, 253, 326; idealises classical figures, 5, 28, 124, 273, 278, 432, 643; commands Army of England, 7, 167, 170, 172–3; birth and background, 9–11, 14, 16; christening, 16; childhood and upbringing, 17–18; education, 17; military career planned, 18, 20; enters college at Autun, 19; imperfect French, 19, 22, 30, 88, 249; attends Brienne military academy, 21–3; reading, 23, 28, 30, 34, 39, 82, 89; selected for artillery and attends École Militaire (Paris), 26–7, 30–1; rejoins regiment, 28; and father's death, 29; posted to La Fère regiment in Valence, 31–3; religious views and practices, 31, 39, 290–1, 306, 314–15, 372, 484–5; serious-mindedness, 31; early writings, 35, 39; petitions in Paris, 36–7; revisits Corsica, 36; theatre-going, 37, 87, 94, 97, 167, 170, 173, 176, 213, 261, 353, 373, 394, 427, 438–9, 551; encounter with prostitute, 38; contracts fever, 39–40; embraces Republicanism, 39, 49; financial prudence and control, 40, 98, 388–90; on outbreak of Revolution, 41–2; writes on Corsica, 41, 45, 48; returns to Corsica on Revolution, 42; accepts integration into French nation, 44–5; political activism in Corsica, 44–7; meets Paoli, 46; returns to France from Corsica, 47; welcomes Revolution, 47–8; as first lieutenant in Fourth Regiment, 48; on love, 48–9; enters Lyon essay competition on human happiness, 49–50; elected lieutenant colonel in Corsica, 51–2; given command in National Guard of Ajaccio, 51; and Ajaccio riot, 52–3; denounced by Corsican deputies in Legislative Assembly, 54; rejoins artillery as captain, 55; witnesses mob attacks on Tuileries, 55, 57, 66; changes political allegiance and remains in France, 56–7; takes sister Maria-Anna (Élisa) back to Corsica, 57–8; considers service with British in India, 59; on expedition against Sardinia, 60; assassination threats in Corsica, 61; defends Paoli against outlawing decree, 61; arrested and freed, 62; issues political manifesto and declares for France, 65–7; posted to Nice, 65; commands artillery at Toulon, 68–74; promoted to brigadier general, 74; appointed inspector of coastal defences in south, 75, 76; commands artillery in Army of Italy, 76; plans campaign against Sardinia, 77, 80; affair with Marguerite Ricord, 78; declines accompanying Augustin Robespierre to Paris, 78; memorandum giving strategic overview of French military position, 78; arrested on orders of Saliceti, 79; love affair and engagement to Eugénie Désirée Clary, 80–1, 86–7, 91, 93; philandering and affairs, 80, 89, 304, 320, 341, 394, 468–9; love of music, 81, 90, 221; and recovery of Corsica from British, 81; removed from list of artillery officers and transferred to Army of the West, 81–3, 90; stays in Paris after transfer, 84–8; seeks property to purchase, 85, 90, 98; as patron to family and friends, 86, 98; social awkwardness, 88–9, 256, 258, 480; depressions, 89, 156; appointed to Cabinet Historique et Topographique, 90; submits plan for conquest of northern Italy, 90; appointed to post in Constantinople, 91–2; welcomes new constitution (1795), 94; role in Vendémiaire crisis, 95–7; adopts new manner, 97; promoted and made commander of Army of Interior, 97; early relations with Josephine, 99, 101–3; growing independence and ambition, 101, 122–3; given command of Army of Italy, 103–4, 107; plans attack on Vienna (1795), 103; marriage with Josephine, 104–6; first signs as 'Bonaparte', 106; strategy in Italy, 111; belief in superior numbers in battle, 112; on death of Chauvet, 112; first engagement against Austrians in Italy, 112–15; letters to Josephine, 112, 118, 130–1, 138, 144, 148, 187, 274–5, 320, 341, 363, 383, 404, 408, 410, 412, 415, 442, 445; inflates reports of battles against Austrians, 114, 143; wins over troops in Army of Italy, 116–17; fame and reputation after victories in Italy, 117–18; on French aptitude for forced marches, 119; Lodi victory, 119–21; depicted in icons, 121, 143–4, 278; Directory orders Italy command split, 121–2; plan to subdue Italy, 121–2; enters Milan, 124–5; encourages army in Italy, 125–6; decrees army be paid half in specie, 126; movements in Italy, 128–30; narrow escape at Valeggio, 128; ordered to march on Rome, 129; pursues Beaulieu in northern Italy, 128; attends opera, 130, 241, 261, 272, 294, 312, 320, 349, 373, 377, 386, 426–7, 448, 466; Josephine joins in Milan, 131–2; victories over Austrians in Italy, 134–9, 147, 153; leadership qualities, 136; on qualities of French soldier, 136; jealous rivals, 140; agrees to negotiations with Austrians, 144, 158; Clarke praises to Directory, 145; relations with Directory's commissioners, 145; agrees to formation of independent Italian republic, 146; conflict with Pope, 148, 462–4; moves against Vienna (1797), 149–51; negotiates peace with Austria (1797), 151, 164–7; war on and plunder of Venice, 151; manner and social style, 153–4, 304; authority in northern Italy, 154; portraits, 154, 171, 427; devotion to Josephine, 155; appropriates wealth and plunder from Italian conquests, 156; celebrity and public image, 156–7, 212–14, 278; sensitivity to criticism, 157; negotiations with Pope, 159; plans Cisalpine Republic in northern Italy, 159; interest in expedition to Egypt, 161; warns against Austria rearming, 161; forms bodyguard (Guides), 162; reinforces personal status in Army, 162–3; political ideals, 163, 263–4, 293, 306; summoned to Paris by Directory, 168; meets Talleyrand and Directors in Paris, 169; in Paris (December 1797), 169–72; care on eating, 170; elected to Institute of Arts and Sciences, 171; admiration for British, 172, 598; opinion of women, 173, 179, 257, 286; declares invasion of England impractical, 174; plans expedition to Egypt, 174–5; on voyage to Egypt, 177–9; plans to improve Paris, 179, 260, 360, 399–400, 481–2; and conditions in Egypt, 183–5; enters Cairo, 187; told of Josephine's infidelities, 187; learns of loss of French fleet at Aboukir Bay, 188; administration and researches in Egypt, 189–95, 203; marches to Syria, 197; atrocities in Middle East, 198–9; fails to take Acre, 199–201; returns to Cairo from Syrian expedition, 201–2; supposedly orders poisoning of wounded men in Middle East, 201–2; view of French navy, 203; defeats Turks at Aboukir, 204; leaves Egypt by sea, 206–8, 269; considers divorcing Josephine, 214–17; political manoeuvring in Paris, 217–21; thrown from horse, 220; honoured at banquet, 221; and Brumaire coup, 222, 224–31, 235; poor oratory, 230; assaulted and denounced by the Five Hundred, 231–2; nominated consul, 234, 236–7; assumes dictatorial powers, 237–8; and Sièyes' draft constitution, 240; powers under new constitution, 243; takes office as first consul, 243; administration and government as first consul, 244–6, 249–50, 264–7, 288–9, 306, 322; tuneless singing, 245, 395; on Fouché, 246; view of theatre and drama, 247; rejects appeal for restoration of monarchy, 248; conversational manner, 249, 256; proclaims amnesty and freedom of religious practice, 249; qualities assessed by contemporaries, 250; moves to Tuileries, 251–3; eating and drinking, 252; dress as consul, 253, 263; appropriates crown jewels, 256; behaviour and treatment of others, 256–8, 261; manner with women, 257; disapproves of Murat's marriage to Caroline, 259; daily routines and activities, 260–2, 391–4; impatience to fulfil plans, 260; malapropisms, 261; prudishness, 262; ceremonial routines, 263; peace overtures, 268–70, 299–300; builds up army against Austria, 270–2; leaves Paris to command against Austria, 272; crosses Alps, 273; Marengo victory, 276–8, 280; moodiness, 279; profits from rumours, 279; scheming over succession to, 279–80; commemorative ceremonies, 280–1; assassination plots against, 283–4, 294–6, 318, 342, 467; at Malmaison, 284, 303–4; interest in money, 284–5; supervises Civil Code, 286–7; supervises Council of State, 287–8; industriousness, 288–9; relations with army, 289–90, 317–18; and restoration of Catholic Church's status, 292, 306–7; uses _senatus-consulte_ against criminal activities, 295; policy of isolating Britain, 300; satirised and caricatured in Britain, 301, 332–3, 340, 369; and Treaty of Amiens with Britain, 302–3; health concerns, 303; happy marriage relations with Josephine, 305; political hostility to, 308; elected president of Cisalpine Republic in Lyon meeting, 309–10; celebrates Concordat, 313–14; educational reforms, 316, 390–1; denies ambitiousness, 317; proposed extension of powers, 318–19; succession question, 319–20, 357, 365; made consul for life (1802), 320, 322–3; dismisses Bourrienne and appoints Méneval as secretary, 321; intelligence network, 321, 343; reintroduces court ceremonial, 322; revises constitution (1802), 323; thirty-third birthday celebrated, 323; moves to Saint-Cloud, 324; progress through Normandy, 324–5; grants amnesty to émigrés, 325; prepares Paris for foreign visitors, 326; develops economic and political power of France in peace period, 327–8; and trade rivalry with Britain, 327; colonial policy, 329–30; accuses Britain of harbouring hostile émigrés, 332; and Recess of Ratisbon, 333; expansionist policy, 334–5; horseriding and driving, 336; hunting, 336, 364, 367, 386, 392, 394, 428, 440, 468, 474, 476, 486, 511, 574; self-regard, 336–7; plans invasion of England, 339–41, 360–2, 364, 374–5; reaction to British declaration of war (1803), 339; British plan to capture and send into exile, 340; clumsy foreign relations, 342; and royalist conspiracy, 343–5, 349; orders arrest and trial of Enghien, 345–8; distrust of Talleyrand, 348; seen as indispensable single ruler, 349–50; proposed and nominated as emperor, 350–2; reactions to status as emperor, 353–6; and trial and fate of conspirators, 354; titles and ranks under, 357; coronation, 359, 367–70; sense of destiny, 363; optimism in preparations for war, 364; suffers fit, 364; secret religious marriage to Josephine, 368; proposes new peace settlement to George III (1805), 371; crowned King of Italy, 372–3; travelling coach, 372; reintroduces Gregorian calendar, 376; campaign against Austria (1805), 377–81; Austerlitz victory, 383–4; Francis I recognises as King of Italy, 385; and French financial crisis (1806), 387–8; private treasury ( _Domaine extraordinaire_ ), 388; presence at meetings, 390; social/legal reforms, 390–1; changing relations with Josephine, 392; dress as emperor, 392; entertainments, 394; disdain for other rulers and administration, 395; pan-European organisation, 397–8; creates imperial nobility and grants titles, 398; son by Éléonore de la Plaigne, 398, 622; court ceremonial, 399, 480–1; maintains simplicity and modesty, 399; in peace negotiations (1806), 401; dismisses Prussia as unimportant and undeveloped, 402–3, 405; campaign against Prussia and Russia, 403–4; blockade of Britain (Continental System), 405–6, 496–7; proposes founding Polish state, 407; in Poland, 409–10; affair with Maria Walewska, 410–13, 428, 466, 602; agrees Treaty of Tilsit with Tsar Alexander, 415–16; snubs Queen Luise of Prussia, 416; returns to Paris after Tilsit, 418; popular indifference to victories, 419; aloofness and exercise of power, 420; distributes titles and honours, 420; directs foreign policy, 421; tours Italian dominions, 425; browbeats Pope, 426–7; orders seizure of ships complying with British decrees, 427; sends troops and travels to Spain, 429–31; makes Joseph King of Spain, 430–4; orders travelling library, 432; and military actions in Spain, 435; withholds troops from Spain, 436; meets Tsar Alexander at Erfurt, 437–43; proposes joint offensive with Russia against British India, 437; urged to divorce Josephine, 437; sense of insecurity, 443–4; revisits Spain, 444–6; learns of conspiracies in France, 446–7; returns to Paris from Spain, 447–8; dismisses and insults Talleyrand, 448; campaign against Austria (1809), 449–53; travelling comforts, 449–50; wounded at Ratisbon, 450; at battle of Wagram, 454–6; seen as oppressor in Europe, 457, 460; contradictory imperial principles and practice, 459–60; declining popular support for, 462, 464, 561; Pope excommunicates and anathematises, 463; unchanging military practices, 464–5; criticised by senior military officers, 465; at Schönbrunn, 466; decides to divorce Josephine, 468–70; remarriage question, 472; marriage to Marie-Louise, 473–5; dismisses Fouché, 477; honeymoon tour and festivities, 477–9; acts against Holland, 478–9; adopts new walk, 480; wealth, 481; generosity and human behaviour, 483–4; marriage relations with Marie-Louise, 486, 492; puts on weight, 486–7; and birth of son by Marie-Louise, 487–9; economic concerns, 491–2; divides Spain into military provinces, 492; Polish policy, 494–5, 498; and Russian demands over Poland, 494–5; reluctance to go to war against Russia, 497–9, 503–4, 507, 511; closes down Council of French bishops, 502; assembles army for Russian campaign, 505; prepares for Russian war, 505, 507–15; bad omen at Niemen, 516; behaviour on Russian campaign, 516–24; and difficult conditions in advance to Russia, 517; resolves to advance on Moscow, 523, 525; awards and honours on battlefield, 524; at Borodino, 527–9; suffers dysuria, 527, 638; occupies Moscow, 530–5; attempts to contact Alexander after fall of Moscow, 531–2; withdrawal from Moscow, 535; in retreat from Russia, 536–43; leaves Grande Armée at Vilna and returns to Paris, 543–7; condition after Russian experience, 548; disturbed by reaction to news of supposed death, 549; raises troops after Russian expedition, 549–51; speech to Legislative Assembly, 554; leaves Paris to oppose Russians and Prussians, 555; plans advance into Poland, 555; fantasises about Marie-Louise and son being murdered by mob, 558; rejects Metternich's negotiating terms, 558; in war against Russia and Prussia, 558–60; agrees armistice (1813), 560–1; meets and mistrusts Metternich, 562–3; campaign against allies (1813), 566–72; conscription advanced, 573–4; manpower shortage, 573–4; behaviour in Paris after Leipzig, 574–5; and Metternich's Frankfurt peace terms, 576–7; unable to take long view, 577; decrees _levée en masse_ to mobilise forces, 578; sees wife and son for last time, 579; war with allies (1813–14), 580–1; 'in bond to glory', 582; personal leadership in battles, 584; plans to attack allies from rear, 584; learns of surrender of Paris, 586; advised to abdicate, 587; abdicates and banished to Elba, 588–91, 593; and successor government in France, 591; belief in power to control, 592; ratifies Treaty of Fontainebleau, 594–5; supposed suicide attempts, 594, 620; travels to Elba, 598–9; life on Elba, 600–3; receives intelligence from informers, 603; vulnerability to assassination and kidnap, 603; plots return to France from Elba and embarks, 605; lands on French soil and marches to Paris, 606; physical deterioration, 609; political aims on return, 610–14; organises _Champ de mai_ , 611; abolishes slave trade, 612; faces invasion by allies, 612, 614; boasts of popularity, 615; final campaign against allies, 616; Waterloo defeat, 617–20; prepares for flight to America, 621–3; refuses to abdicate, 621; protests at banishment to St Helena, 625; on voyage to St Helena, 626–7; life on St Helena, 627–39; sends complaints to British government, 629; dislikes Hudson Lowe, 634, 637; receives books at St Helena, 635–6; affair with Albine de Montholon, 638; reminisces on St Helena, 639; illness and death on St Helena, 640–2; burial on St Helena, 643; dictates will, 643; reputation, 643–4; _Clisson et Eugénie_ (novella), 89–90, 621; _Le Comte d'Essex_ (novella), 39; _Dialogue sur l'amour_ , 48; _Lettre à Buttafocco_ , 47–8; _Lettres sur la Corse_ , 41, 55; _Le Masque Prophète_ (story), 39; _Nouvelle Corse_ , 41; _Le Souper de Beaucaire_ , 65, 68
Napoleon II, titular Emperor of the French and King of Rome (N's son): birth, 487–9; christening, 489; portrait, 527, 532; (burnt), 540; N arranges regency for, 555; N presents to Paris National Guard, 579; security during allied advance, 585; N nominates as successor on abdication, 587, 595; N proclaims Emperor of the French, 621; given Austrian title by Francis, 629; lock of hair passed to N on St Helena, 635
Napoléon-Vendée, 435
Narbonne, Louis de, 511–12, 523, 555, 557–8, 564–5
National Guard: N reforms, 97
Necker, Jacques, 272
Nelson, Admiral Horatio, Viscount: sails to Mediterranean, 180–1; Aboukir Bay victory, 188; on severe treatment of French, 301; Trafalgar victory, 379
neo-classical movement, 123
Nesselrode, Karl von, 442, 564, 576, 593
Netherlands: and Metternich's peace proposals, 576; _see also_ Holland
Neuhoff, Theodor von, Baron, 11–12
Newton, Sir Isaac, 212
Ney, Marshal Michel: made marshal, 376; opposes Austrians, 377–8; in Poland, 408; Bennigsen attacks, 413; commands in Spain, 435; animosity towards Soult, 461; in advance on Moscow, 523; at Borodino, 527; in retreat from Russia, 539–42; delay at Bautzen, 558; defeated at Dennewitz, 568; advises N to abdicate, 587; meets Alexander in Paris, 588–9; reports to N, 589; pledges submission to new government, 590; signs Treaty of Fontainebleau, 593; joins N on return from Elba, 607
Nice: incorporated into French Republic, 76
Normandy: N's progress through, 324–5
_Northumberland_ , HMS, 626–7, 636
Noverraz, Jean Abram, 597, 626
Novosiltsev, Count Nikolai, 373–4
Ocaña, battle of (1809), 462
Odoards, Colonel Fantin des _see_ Fantin des Odoards, Colonel Louis Florimond
Odone family: Buonaparte lawsuit against, 24–5, 35
O'Hara, General Charles, 72
Olmütz, 380–1
O'Meara, Barry, 626, 630, 632, 639–40
Oneglia, Republic of Genoa, 76–7, 80
_Ordre de la Réunion_ , 459
_Orient, l'_ (French warship), 178, 188
Orléans, Louis-Philippe, duc d' ( _later_ King Louis-Philippe): suggested as successor to N, 279
Orthez, battle of (1814), 582
Ossian (James Macpherson): N admires, 82, 106, 118, 124, 178, 221, 634
Ott von Bátorkéz, General Peter Karl, 274–5
Otto, Louis-Guillaume, 268, 301
Ottoman Empire: French relations with, 159–61; and French expedition to Egypt, 174; declares war on France, 195–6, 200; defeated at Aboukir, 204; N encourages to move against Russia, 413; makes peace with Russia, 507, 522
Oubril, Peter von, 342, 364, 396, 401–2
Oudinot, General Nicolas-Charles: in anti-N plot, 318; at Wagram, 454; despatched to Holland, 479; in war against Russia, 514; in retreat from Moscow, 542; threatens Berlin, 560; defeated at Grossbeeren, 567; advises N to abdicate, 587; leaves N, 592
Ouvrard, Gabriel, 387, 477, 620
Pacca, Cardinal Bartolomeo, 463
Palais-Royal, Paris, 37–8
Palm, Johann Philipp, 402
Panattieri (Corsican), 146
Paoli, Pasquale: proclaims and rules Corsican republic, 12–13; Carlo serves, 13–14; resists French takeover of Corsica, 13, 29; N admires, 28, 41, 50; returns to Corsica, 44–6; powers in Corsica, 46; N sends writings to, 48; mistrusts French, 50–1; rejects N, 53; administration fails, 58; Lucien denounces, 60–1; N sends report of Sardinia expedition to, 60; outlawed, 61; N denounces, 66; second exile in London, 81; and Panattieri, 146; N's relations with, 247; N considers return of, 316
papacy: French hostility to, 148
Papal States: conflict with Austria and Naples, 291; N occupies strategic ports, 426–7; N orders military occupation, 428; N incorporates into French Empire, 462–3, 484
Paravicini, Geltruda, 13
Paravicini, Saveria ('Minanna'), 17
Paris: terror in, 70; coup topples Robespierre, 79; hedonism after end of Terror, 83–4; financial crisis, 84–5; N stays in after transfer to Army of the West, 84–8; women socialites, 88–9; susceptibility to riots, 97; prisons, 99–100; N's plans for improvement, 179, 260, 360, 399–400, 481–2; Invalides (Temple of Mars), 212; Pantheon, 212; N reaches on return from Egypt, 214; Temple of Victory ( _formerly_ church of Saint-Sulpice), 221; administrative structure, 265; attracts foreign visitors, 325–6; civic improvements for N's coronation, 359–60; N returns to after Tilsit, 418; Madeleine, 480; Louvre, 481; improved and beautified, 489–90; communication with Moscow after occupation, 533; allies advance on, 584–5; surrenders to allies, 586–7; N returns to from Elba, 607–10; allies enter, 623
Paris, Treaty of (1814), 611
Parma, duchy of, 121, 1333
Parma, Ferdinand, Duke of, 297
Pasquier, Étienne, 509, 574–5, 608
Patterson, Elizabeth: marriage and child with Jérôme, 366, 372–3; N demands Pope annul marriage to Jérôme, 427
Paul I, Tsar of Russia, 282, 300, 313, 332, 345, 348
Paulin, Colonel Jules Antoine, 598
Pavia, 127
Pelet de la Lozère, Jean, 390
Pelleport, Colonel Pierre de, 191, 556
Penal Code, 483
Peraldi, Giovanni, 51–2
Peraldi, Marius, 51, 54, 62
Percier, Charles, 128
Peretti, abbé, 43, 46
Permon, Charles Martin (tax official), 29, 32
Permon, Laure, 88
Permon, Panoria, 55, 89
Persia: signs Treaty of Finckenstein, 413
Petit Luxembourg: N moves to, 239
Petrovskoe, 531
Peyrusse, Pierre Guillaume, 596, 601–2, 619
_Philadelphes_ (secret organisation), 340
Piacenza, 121
Pichegru, General Charles, 145, 158, 170, 283, 340, 342–4, 349, 354
Picot, Louis, 340, 343
Piedmont: N promises to liberate, 111, 125; regiments disbanded, 139; incorporated into France, 297, 334–5
Pietrasanta, Giuseppe Maria, 14
Pillnitz, Saxony, 299
Pitt, William the Younger, 268–9, 301, 374; death, 396
Pius VI, Pope, 148–9, 291
Pius VII, Pope: elected pope, 291; refuses to release Talleyrand from clerical vows, 292; Louis XVIII protests to, 315; and N's coronation, 359, 367–9; and N's seizure of Papal ports, 426; abducted and detained, 463, 470, 502, 554, 574; excommunicates N, 463; N's inflexible attitude to, 484; French bishops swear allegiance to, 502; abrogates new concordat, 554, 574
plague: in Middle East, 198–9, 203
Plaigne, Éléonore de la: as N's mistress and mother of son, 398, 409, 622
Plesswitz: armistice (1813), 560
Plutarch, 124
Poland: partitioned, 298–9; N incorporates soldiers into army, 406–8, 494; pleads for independence, 406; welcomes N, 407; conditions, 408–9; N cedes half to Russia, 457, 494–5; N borrows on income, 491; N's policy on, 494–5, 498; and Russian war with N, 497, 513, 519; proposed creation as buffer state, 512; N nominates Jérôme as king, 513; N threatens to destroy, 558
Polignac, Prince Jules de, 342, 344, 354
Pomerania, 506
Poniatowski, Prince Joseph, 457, 520, 522, 527, 553, 555, 561; death at Leipzig, 571
Pons de l'Hérault, André, 600, 604
Pont-de-Briques, near Boulogne, 361
Pontécoulant, Louis Gustave Le Doulcet de, 90, 153, 163, 420, 579, 613
Poppleton, Captain William Thomas, 628, 637
Portalis, Jean-Étienne, 286
Portugal: and Peace of Badjoz, 302; and Treaty of Tilsit, 416; N plans to take over with Charles IV, 424; Britain supports, 425; Wellington's successes in, 435
Posen, 406–7
Potocka, Countess Anna, 410
Pouget, Colonel François-René, 379
Pozzo di Borgo, Carlo Andrea di, 44, 46, 54, 81, 507
Pozzo di Borgo, Maria Giustina, 24–5
Pozzo di Borgo, Matteo, 51–2
Pradt, Dominique Dufour de, Archbishop of Malines, 512, 544
Prague: congress (1813), 564–5
press: N's view of freedom, 246–7
Pressburg, Treaty of (1805), 385
Primolano, 138
Provera, General Giovanni, marquese de, 114, 147–8
Prussia: territorial expansion, 299; in League of Neutrals, 300; population, 337; Russia seeks alliance with, 352; threatens to join coalition (1805), 380–1; acquires Hanover, 385, 401; N signs treaty of alliance with (1805), 385; opposition to N, 401–2; invades Saxony, 402; N belittles, 402–3, 406; war with N (1806–7), 403–4; N receives indemnities from, 419–20, 460; effect of French domination, 460; anti-French sentiments, 461; and N's war with Russia, 507; declares war on France (1813), 552, 555
Pułtusk, battle of (1806), 408
Pyramids, battle of the (1898), 186
Quasdanovitch, General Peter, 134, 138
Quenza, Giovanni Battista, 52, 59–60
Raab, battle of (1809), 453
Racine, Jean: _Phèdre_ , 585
Radet, General Étienne, 463
Ragny, 84–5
Raguidot (notary), 104
Rapp, General Count Jean: serves N as aide, 277; dislikes formality and ceremony, 354; at Austerlitz, 383; in Russian campaign, 525, 528, 535; besieged in Danzig, 566
Rastatt, congress of (1797), 167–8, 170, 173
Ratisbon (Regensburg): Recess of (1803), 333; battle of (1809), 450
Raynal, Guillaume Thomas, abbé, 34
Razumovsky, Count Andrey, 536
Réal, Pierre-François, 214–15, 218, 295, 321, 342–5, 608
Récamier, Juliette, 88
Recco, abbé, 17
Regnaud de Saint-Jean-d'Angély, Michel, 157, 217, 220, 349, 458, 470, 619, 621
Regnier, Claude-Ambroise, 345
Reims, battle of (1814), 583
religion: N's views on, 31, 39, 290–1, 306; N revives, 314–15; in N's coronation, 359; in Spain, 432
Rémusat, Auguste de, 368
Rémusat, Claire de, 258, 420
Reserve Army, 271–2
Reubell, Jean-François, 169, 174
Revel-Honoré, Captain Jean-François, 394
Ricard, General Étienne Pierre Sylvestre, 582
Richelieu, Armand Emmanuel de Vignerot du Plessis, duc de, 632
Ricord, Jean-François, 70, 73, 77–9
Ricord, Marguerite, 78
Rigo, Michel, 204
Rivière, Charles François Riffardeau, marquis de, 342, 344, 354
Rivoli, 147
Robert, Hubert, 128
Robespierre, Augustin, 72–3, 77–9
Robespierre, Maximilien, 78–9, 83, 88, 93, 100, 163, 610
Rochambeau, General Jean-Baptiste-Donatien de Vimeur, comte de, 340
Roederer, Pierre-Louis: supports N's bid for office, 217–19; on return from Egypt, 228, 234; on N's inarticulacy, 236; opposes anti-Jacobin measures, 238; N disclaims ambitions to, 253; N offers gift to, 258; and N's administrative aims, 264–5; and N at Marengo, 280; and N's view of religion in state, 290; urges upgrade in N's status, 318; and expedition to Saint-Domingue, 331; and N's reaction to being emperor, 351; on popular anger at government over conspiracy trials, 354; N defends Josephine to, 366
Roguet, General François, 526, 540
Rome: N ordered to march on, 129
Rosetta, 184
Rostopchin, Fyodor Vasilyevich, Count, 530, 536
Rouget de l'Isle, Claude, 271
Rousseau, Jean-Jacques: visits Corsica, 12, 16; influence on N, 35, 37, 39, 49–50, 124, 194, 610; on noble savage, 184; reputation, 212; N regrets having been born, 283; _Du Contrat Social_ , 263–4
Roustam Raza, 207, 209, 251, 304, 405, 445, 450, 543, 593
Roustan, Antoine Jacques, 35
Roveredo, 137
Rowlandson, Thomas, 332
Royal Navy (British): in Mediterranean, 269; supremacy, 374; captures Spanish ships, 387
Royer-Collard, Antoine, 318
Rumbold, George, 343
Rumiantsev, Count Nikolai, 437
Rumigny, General Théodore de, 409, 615
Russia: signs anti-French alliance with Naples and Britain (1798), 196; Masséna defeats in Switzerland, 213; territorial expansion, 298–9; resents British power, 300; negotiates alliance with Austria and Britain, 362; prepares for war, 364, 497–9; supports Austria (1805), 380–1; at Austerlitz, 383; peace negotiations with France (1806), 401; and Treaty of Tilsit, 415–16, 437; contravenes Continental System against Britain, 441–2, 496–8; N cedes half of Poland to, 457; fear of France, 493–4; anger at Bernadotte's election to Swedish throne, 496; economic hardships, 496; Metternich blames for war, 503; N raises army against, 505–6; treaty with Turkey, 507, 522; organisation of army against N, 513; adopts scorched-earth policy, 525; casualties at Borodino, 529; N retreats from, 536–7; N considers Austria mediating in peace negotiations with, 550; advance into Europe, 552–3; proposes treating with N on condition of abdicating, 613; _see also_ Alexander I, Tsar
Sade, Donatien Alphonse François, comte de (marquis de Sade): _Zoloé et ses deux acolytes_ , 101
Saint-Denis, Louis-Étienne ('Ali'), 597, 626, 628
Saint-Domingue (Haiti), 328–32, 337, 340
Saint-Elme, Ida, 257
Saint-Germain, Charles-Louis de, 27
St Helena (island): as potential prison for N, 604, 625; N arrives at, 627; N's life on, 627–39; allied commissioners arrive, 635–6; cost of N's confinement, 636–7
Saint-Hilaire, Geoffroy de, 189
Saint-Pierre, Bernardin de: _Paul et Virginie_ , 82, 89
Saint-Simon, Claude-Henri de, 356
Salamanca, battle of (1812), 526–7
Salayeh, battle of (1898), 188
Saliceti, Cristoforo: as Corsican deputy to States General, 43–4; appointed commissioner to investigate Paoli, 60–3; flees Corsica for France, 64, 67; and N at Toulon, 68, 70, 72–3; publishes N's _Le Souper de Beaucaire_ , 68; supervises Army of Italy, 77; sends N to Genoa, 78; accuses N of sabotaging army operations in Italy, 79; supports N in Italy, 108, 116, 121, 145; exploitation in Italy, 127; transferred to Corsica, 145; and Brumaire coup, 227; rules in Genoa, 373
Salines, Les (Corsica), 24–5, 35–6
Sandoz-Rollin, Daniel von, 1, 7–8
Santini, Jean-Noël (Corsican servant on St Helena), 639
Saragossa, 461
Sardinia: invasion from Corsica, 58–60; forces invade southern France, 76; Austria supports against French, 80, 103; armistice with France, 103; army strength, 111; war with N's Army of Italy, 112–15
Savary, General Anne-Jean-Marie: joins N's staff after Marengo, 277; acting, 320; intelligence service, 321; and trial and execution of Enghien, 346; and N's negotiations with Tsar, 381; and N's peace negotiations with Britain (1806), 396; in Warsaw, 410; in Spain with N, 445; investigates Fouché plot, 477; policing methods and style, 482–3; and Malet plot, 549; negotiates with Talleyrand, 589; and N's return from Elba, 608; and N's position after Waterloo defeat, 619; and N's attempted flight to America, 620, 623; prevented from accompanying N to St Helena, 626; and N's entourage in St Helena, 641
Savona, 112
Savoy: incorporated into French Republic, 76; in Metternich's peace proposals, 576
Savoy, house of: rule in Sardinia, 59
Saxony: Prussia invades, 402; Russia invades with Prussia, 556
Scherer, General Barthélémy, 6, 103
Schill, Major Ferdinand von, 449
Schlegel, Friedrich, 449
Schwarzenberg, Prince Karl von: as Austrian ambassador in Paris, 473; and N's marriage to Marie-Louise, 473, 479; commands Austrians in Russian campaign, 514, 539, 545, 547; disparages Kutuzov, 545; withdraws through Poland, 553, 557; on N's wish to avoid war, 555; in allied army against N, 566–9, 578, 580–1; repels N at Arcis-sur-Aube, 583–4
Sébastiani, Captain Horace, 222, 224, 232, 335; _see also_ Louis XVIII, King of France
Ségur, Louis-Philippe de, 368, 448
Ségur, Philippe-Paul de, 250, 355, 445, 504, 506, 572
Selim III, Ottoman Sultan, 414
Sémonville, Charles Huguet de, 59
Senate: at Luxembourg, 251; and proposed extension of N's consulship, 319; expanded, 323, 357
_senatus-consulte_ (edict), 295, 319, 323, 398, 470, 555
Sérurier, General Jean-Mathieu: in Army of Italy, 107, 110; at Savona, 112; pursues Beaulieu, 119–20; invests Mantua, 128
Seurre, 40
Seven Years' War (1756–63), 13, 22
Shakespeare, William, 212
Shuvalov, Pavel Andreyevich, Count, 497, 597, 599
Sicily, 425–6, 428
Sièyes, Emmanuel-Joseph, abbé: N discusses metaphysics with, 170; prepares coup and change to constitution, 211, 218, 220–3; N's relations with, 219; and Brumaire coup, 226–7, 229, 235; nominated consul, 234, 236; accepts N's supremacy, 237; drafts new constitution, 239–40, 242, 322; nominates N as first consul, 242; helps launch Revolution, 243; resigns as provisional consul, 243; devises French administrative structure, 265; schemes against N, 279; N berates in Senate, 308; and proposed extension of N's consulship, 319; opposes granting N supreme status, 350; N receives in Paris after return from Elba, 610
slaves and slavery: abolished in French colonies, 328–9, 331; rebellions, 330–1; N abolishes trade, 612
Smith, Spencer, 344
Smith, Commodore Sydney, 200–1, 205–6, 269
Smolensk, 523–4, 534, 536, 538–9
Songis, Nicolas-Marie, 78–9, 92
Sorbier, Jean-Joseph, 33
Soult, Marshal Nicolas: questions possibility of embarking army for invasion of England, 361; made marshal, 375; opposes Austrians, 377; skirmish with Bennigsen, 411; in Spain, 445, 461–2, 492, 563; animosity towards Ney, 461; differences with Joseph, 551; Wellington defeats at Orthez, 582; arrives in France from Spain, 586; at Ligny and Waterloo, 616, 618; raises troops after Waterloo, 621
Spain: peace treaty with France (1795), 93; treasure and bullion, 387–8; prospective alliance with coalition, 413; and French advance on Portugal, 425; social/political backwardness, 428–9; French forces in, 429; N travels to, 429–30; Joseph as king (José I), 431–4; N devises new constitution for, 432; hostility to French, 433; French military actions in, 434–5; N visits and seeks to pacify, 444–6; anti-French Europeans look to for liberation, 461; _guerrilla_ warfare in, 461; progress of war in, 492; N proposes bilateral withdrawal of troops, 509; N withdraws troops from, 550; Wellington's offensive in, 563
Spina, Monsignor Giuseppe, Archbishop of Corinth, 292
Stadion, Count Johann Philipp, 449
Staël, Germaine de, 88, 169, 173, 256, 279, 289, 305, 306, 507; _De l'influence des passions sur le bonheur des individus et des nations_ , 124
Staps, Friedrich, 467
Stein, Baron Karl vom, 507
Stendhal (Marie-Henri Beyle), 123
Stengel, General Henri, 110
Stockach, battle of (1800), 272
Stokoe, John, 640
Stürmer, Bartholomäus, Baron, 636
Suchet, General Louis-Gabriel, 72, 108, 272, 461
Suez Canal, 39, 160, 175, 193, 217, 300
Sułkowski, Prince Antoni, 406
Sułkowski, Józef, 136, 140, 185, 194
Sweden: in League of Neutrals, 300; as potential enemy of France, 402; and Treaty of Tilsit, 416; invites Bernadotte to take throne, 495–6; rejects N's demands for alliance against Russia, 506; joins coalition (1813), 568
Switzerland: France invades, 211; Britain defends, 334
Syria: N's campaign against, 197–203
Talavera, battle of (1809), 462
Talleyrand, Charles-Maurice de: praises N as peacemaker, 4–5; perceives N's power and ambition, 8; proposes colonies in Egypt and Africa, 162, 173–4, 195; N meets in Paris (1797), 169, 173; advocates invasion of Egypt, 173; and scheming over successor to N, 179; proposed visit to Constantinople, 181; discussions with N, 217, 221; favours N allying with Barras, 218–19; and Brumaire coup, 228, 230; N names as foreign minister, 237; qualities, 247–8; relations with N, 247–8; presents diplomatic corps to Josephine, 253; letter from Grenville replying to N's peace offer, 268; profits financially from rumours, 279; contacts with royalists, 282; attitude to Church, 291–2; negotiations with Spina, 292, 307; and N's action against Jacobins, 295; disparages British, 301; and N's treatment of opponents, 306; meets Cisalpine delegates at Lyon, 309–11; urges upgrade in N's status, 318; at Ratisbon, 333; denies French intention to oust British from Egypt, 335; Whitworth demands French evacuate Netherlands, 336; recommends alliance with Austria, 342; and royalist conspiracy, 344–6; demands expulsion of active émigrés from foreign courts, 347; claims to oppose execution of Enghien, 348; distrustful relations with N, 348; on N's qualities as ruler, 349; advocates granting supreme authority to N, 350; as grand chamberlain, 357; released from holy orders and marries mistress, 357; messages to Francis I, 374, 374–5; and N's intention to invade England, 374–5; Austrian and Prussian delegates confer with, 381; urges clemency towards Austria, 385; message from Fox on royalist plot against N, 396; N withdraws from negotiations over Ferdinand of Naples, 396; as prince of Benevento, 398; and N's dismissal of Prussian threat, 402; favours founding of Polish state, 407; controls Polish council, 411; N removes from Ministry of Foreign Relations, 420; believes in alliance with Spain, 429; and N's negotiations in Spain, 430, 430–1; with N at Erfurt, 438–9, 442; on N's lack of confidence in achievements, 443; conspires with Fouché, 447; N dismisses and insults, 448; favours Marie-Louise as N's second wife, 473; restraining influence on N, 482; advocates using Polish state as buffer, 512; and proposed peace negotiations with Russia, 550; Ferdinand of Spain stays with, 573; N threatens, 574; settlement with Alexander after fall of Paris, 586–7; and N's delegates' meeting with Alexander, 588; Ney submits to, 590; plans elimination of N, 592–3; stands up to N, 592; gathers intelligence on N at Elba, 603; at Congress of Vienna, 612; drafts declaration outlawing N, 612; joins Louis XVIII in Belgium, 622; and Louis XVIII's return to throne, 624
Tallien, Jean-Lambert, 88, 104
Tallien, Thérèse, 89, 100, 132, 138, 262
Talma, Julie, 88
Tardivon, Monseigneur de, abbot of Saint-Ruf, 34
Terror: ends, 83
Theophilanthropy, 169, 172
Théviotte, Lieut. Colonel, 192
Thibaudeau, Antoine-Claire, 213, 265, 288, 290, 314, 318, 328, 349
Thouin, André, 128, 156
Thugut, Johann Amadeus von, 158, 164
Thurn und Taxis, Princess Theresa of, 442
Tilsit, treaty of (1807), 414–16, 437, 494
Tipu Sahib, Sultan of Mysore, 160
Toby (Malay slave), 640
Tolentino, Treaty of (1797), 149
Tolstoy, Count Pyotr Alexandrovich, 437
Tone, Wolfe, 172
Töplitz, Treaty of (1813), 570
Tormasov, General Alexander, 514, 522
Toulon: Jacobin terror in, 64; N commands artillery at, 68–73; British evacuate, 73; French purge, 73–4; N protects returning French noble families, 81; N embarks at for Egypt, 177–8
Toussaint Louverture, Pierre-Dominique, 329–32
Trafalgar, battle of (1805), 379–80
Transpadane Republic, 159
Trento, 137
Tréville, Admiral Latouche _see_ Latouche Tréville, Admiral Louis René Levassor
Tribunal de Cassation, 265
Tribunate: composition, 241; appointments to, 311; and proposed elevation of N's powers, 318–19; reduced (1802), 323; declares France an empire, 351
Trieste, 138
Tronchet, François-Denis, 286
Truchsess-Waldburg, Count von, 597
Truguet, Rear-Admiral Laurent, 59
_Tugendbund_ , 461
Tuileries: attacked by Paris mob, 55, 57; consuls move to, 251–3; life and court at, 261–3
Turenne, Marshal Henri de la Tour d'Auvergne, vicomte de, 280
Turner, J.M.W., 325
Turreau, Louis, 80
Tuscany, Ferdinand III, Grand Duke of _see_ Würzburg, Ferdinand III, Grand Duke of
Tuscany, Grand Duchy of, 426
Tussaud, Marie, 325
Tyrol: rising, 449, 457
Ulm, battle of (1805), 377–9
_Undaunted_ , HMS, 599
United States: N signs treaty with, 299; and N's colonial policy, 330; purchases Louisiana from France, 337; N prepares for flight to, 621–2
University of France: founded, 390
Valence, 33, 47, 48, 210
Valette, General Antoine: demoted, 136
Valfort, chevalier de, 27
Vandamme, General Dominique-René, 465, 504, 567
Vanlerberghe, Joseph, 387–8
Varese, abbé, 19
Vauban, Sébastien le Prestre de, 33
Vaubois, General Claude-Henri Belgrand de, 140, 142, 180
Vauchamps, battle of (1814), 581
Vendée, the, 65, 82–3, 299
Vendémiaire event (1795), 93, 95–7
Venice: N declares war on and plunders, 151, 260; N occupies, 159; N meets Joseph in, 427
Verdier, General Jean-Antoine, 96, 192
Verninac, Raymond, 159
Verona, 128, 134, 140, 151
Versailles, Treaty of (1768), 13
Victor Amadeus, King of Sardinia, 115, 126, 139
Victor, Marshal Claude: on N's appearance, 74; at Marengo, 276; in Spain, 461–2; in retreat from Moscow, 542; follows Louis XVIII into exile, 614
Vienna: N marches on (1797), 149–50; N occupies (1805), 379; N reaches (1809), 451
Vienna, Congress of (1814–15), 604
Vienna, Treaty of (1809), 468
Vigée-Lebrun, Elisabeth, 325
Vignali, Ane Paul, abbé, 642
Vigo-Roussillon, Sergeant François, 110, 125, 184, 206
Villeneuve, Admiral Pierre de, 379
Villeret, Louis Brun de, 409
Vilna (Vilnius), 53, 511, 513, 517–19, 534, 545, 547
Vincent, General Charles, baron de, 444
Vitebsk, 521–2, 538
Volkonsky, Prince Sergei, 496
Volney, Constantin de, 51, 306, 350
Voltaire, François Marie Arouet, 12, 212; _Mahomet_ , 438; _Oedipe_ , 439
Wagram, battle of (1809), 454–6, 464, 467
Walcheren, 467, 479
Walewska, Maria, Countess: affair with N, 410–13, 428, 466; pregnancy, 466; installed in Paris, 483; and N's return to Paris after Russian campaign, 545; visits N at Fontainebleau, 595; visits N on Elba, 602
Warsaw, 407–10, 544; Grand Duchy of, 416, 420, 457, 491, 494, 498, 553, 564
Washington, George, 299
Waterloo, battle of (1815), 617–19
Welle, Philipp, 635, 639
Wellesley, General Arthur _see_ Wellington, 1st Duke of
Wellesley, Richard Colley, Marquis, 477
Wellington, Arthur Wellesley, 1st Duke of: defeats Junot in Portugal, 435; advances into Spain, 461–2; pushed back into Portugal, 492; Salamanca victory, 526–7; captures Madrid, 533, 563; defeats Joseph at Vitoria, 563; Orthez victory, 582; opposes N, 616; Waterloo victory, 617–18
West, Benjamin, 325
Westphalia, kingdom of: created, 416; under Jérôme's rule, 457–8
Whitworth, Charles, Earl, 300, 332, 335–6
Wickham, William, 282
Wieland, Christoph Martin, 440
Wilson, General Sir Robert, 541, 639
Wintzingerode, General Ferdinand von, 536
Wittgenstein, General Ludwig von, Prince, 556
women: social leaders in Paris, 88–9; N's view of, 173, 179, 257, 286; in Egypt, 192
Würmser, Field Marshal Dagobert von, 134, 137–8, 139, 148
Württemberg, Catherine, Princess of ( _later_ Queen of Westphalia; Jérôme's wife): marriage to Jérôme, 427, 458; meets N in Dresden, 510; asks N to stand godfather to child, 602; father attempts to engineer divorce, 629; refused permission to visit St Helena, 641; _see also_ Frederick I, King of Württemberg
Würzburg, Ferdinand III, Grand Duke of ( _earlier_ Grand Duke of Tuscany), 510
Yarmouth, Francis Charles Seymour Conway, Earl of ( _later_ 3rd Marquess of Hertford), 396
Yorck von Wartemburg, General Ludwig, 551–2
Young, Edward: _Night Thoughts_ , 56
Yvan, Dr Alexandre Urbain, 539, 594
Zajączek, General Józef, 406–7
_Zealous_ , HMS, 188
Znaïm, 456
# Also by Adam Zamoyski
CHOPIN: A BIOGRAPHY
THE BATTLE FOR THE MARCHLANDS
PADEREWSKI
THE POLISH WAY
THE LAST KING OF POLAND
THE FORGOTTEN FEW: THE POLISH AIR FORCE IN THE SECOND WORLD WAR
HOLY MADNESS: ROMANTICS, PATRIOTS AND REVOLUTIONARIES, 1776–1871
1812: NAPOLEON'S FATAL MARCH ON MOSCOW
RITES OF PEACE: THE FALL OF NAPOLEON AND THE CONGRESS OF VIENNA
WARSAW 1920: LENIN'S FAILED CONQUEST OF EUROPE
POLAND: A HISTORY
CHOPIN: PRINCE OF THE ROMANTICS
PHANTOM TERROR: THE THREAT OF REVOLUTION AND THE REPRESSION OF LIBERTY 1789–1848
# About the Author
ADAM ZAMOYSKI is the author of over a dozen books on key figures and aspects of European history, among them _1812: Napoleon's Fatal March on Moscow_ and its sequel _Rites of Peace: The Fall of Napoleon and the Congress of Vienna_ , both _Sunday Times_ bestsellers. His books have been translated into Russian, Chinese, Japanese and Persian as well as most of the European languages. He lives in London and Poland, and is married to the painter Emma Sergeant.
# About the Publisher
Australia
HarperCollins Publishers (Australia) Pty. Ltd.
Level 13, 201 Elizabeth Street
Sydney, NSW 2000, Australia
www.harpercollins.com.au
Canada
HarperCollins Canada
Bay Adelaide Centre, East Tower
22 Adelaide Street West, 41st Floor
Toronto, ON, M5H 4E3, Canada
<http://www.harpercollins.ca>
India
HarperCollins India
A 75, Sector 57
Noida, Uttar Pradesh 201 301, India
<http://www.harpercollins.co.in>
New Zealand
HarperCollins Publishers (New Zealand) Limited
P.O. Box 1
Auckland, New Zealand
www.harpercollins.co.nz
United Kingdom
HarperCollins Publishers Ltd.
1 London Bridge Street
London SE1 9GF
www.harpercollins.co.uk
United States
HarperCollins Publishers Inc.
195 Broadway
New York, NY 10007
www.harpercollins.com
|
{
"redpajama_set_name": "RedPajamaBook"
}
| 9,853
|
Employer supported childcare The tax and NIC exemption for employer-contracted childcare and employer-provided childcare vouchers has been very popular with both employers and employees alike. This factsheet outlines the exemptions available.
Childcare and employer provided childcare vouchers are very popular with both employers and employees alike. If your business is in the North Yorkshire area or you are employed in the area we, at Chipchase, can advise you on the exemptions available for employer supported childcare.
If your business is located in the North Yorkshire area and you would like to discuss childcare in further detail, please do not hesitate to contact us at Chipchase.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 6,369
|
\section{Introduction}
The idea that gravity may be an emergent phenomenon
\footnote{By emergence we understand
that in the systems in question \cite{sil} ''short-distance physics is radically different from long-distance physics''.}
described by an effective low-energy theory which a is consequence of averaging over (yet unknown) microphysical
degrees of freedom dates back at least to the proposal of Sakharov \cite{sakha} in 1968. Since then, it has been shown
that
is not difficult to get a low-energy effective metric (although it is considerably harder to get dynamical equations controlling it, see for instance \cite{matt0}). In fact,
the effective metric arises in systems of very different types (see \cite{mattlr} for a review). The basic idea behind this
generality has been exposed in \cite{matt0},
where it was shown that given
a classical single-field theory described by a Lagrangian that is an arbitrary function of the field and its derivatives, the fluctuations of the linearized theory
around a non-trivial background propagate in a curved spacetime. The geometry of this
spacetime is encoded by
the effective metric, which is unique in the case of a single field, and depends on the background field configuration.
This feature of nonlinear theories led to the construction of
analog models of gravity, which imitate the kinematical properties of
gravitational fields (see \cite{mattlr} for a complete list).
In this article we shall show that the relation between the effective metric
in
nonlinear electromagnetic theories and the corresponding energy-momentum tensor
can be used
to classify the possible metrics in terms of the Segr\`e types of $T_{\mu\nu}$ (see Sects.
\ref{rel}, \ref{algeb} and \ref{eig}).
We will see that for a given type of metric, the form of the light cone is
univocally described by a scalar function, that depends on the Lagrangian of the theory and the background field
configuration (Sect.\ref{seco}).
Following the variation of the light cone along a given path, we can see how the particle is diverted
from the background geodesic motion due to the nonlinearities of the interaction.
Some examples of this application are given in Sect.\ref{simple}.
Finally we will discuss our results and consider future work in Sect.\ref{conc}.
\section{The effective geometry for nonlinear electromagnetism}
\label{rel}
Nonlinear electrodynamics is relevant in several areas of physics.
In quantum field theory, the polarization
of the vacuum leads naturally to a nonlinear corrections to Maxwell's electrodynamics,
which are described by Euler-Heisenberg's Lagrangian \cite{dunne}.
In material media, such as some
dielectrics and crystals, the complex interaction between the molecules and external electromagnetic fields can be described by an effective nonlinear theory, which is typically observed at very high light intensities such as those provided by pulsed lasers \cite{shen}.
The result that
the high-energy
perturbations of a nonlinear electromagnetic theory propagate along
geodesics that are not null in the background geometry
but in an effective spacetime has been obtained several times in the literature \cite{nlemef}.
In the case of
${\cal L}={\cal L}(F)$, where $F\equiv F_{\mu\nu}F^{\mu\nu}$ ,
the equation of motion is given by
\begin{equation}
({\cal L}_F F^{\mu\nu})_{,\nu}=0.
\end{equation}
By perturbing this equation around a fixed background solution and taking the eikonal limit
(see for instance \cite{matt1}),
we obtain for the effective metric
\begin{equation}
g^{\mu\nu} = {\cal L}_{F0} \eta^{\mu\nu}-4{\cal L}_{FF0}F^\mu_{\;\alpha 0} F^{\alpha\nu}_0,
\end{equation}
where the subindex 0 means that the quantity is evaluated using the background solution.
Both this and the inverse metric can be expressed in terms of the energy-momentum tensor, given by
\begin{equation}
T^{\mu}_{\phantom a\nu}=-4{\cal L}_FF^{\mu}_{\phantom a\alpha}F^\alpha_{\phantom a\nu}-{\cal L} \delta^{\mu}_{\phantom a\nu}.
\end{equation}
in particular, the inverse effective metric takes the form
\begin{equation}
g_{\mu\nu}=a_0\eta_{\mu\nu}+b_0T_{\mu\nu 0},
\label{emem}
\end{equation}
where $a_0$ and $b_0$ are given by
\begin{equation}
a_0=-b_0\left[ \frac{{\cal L}_F^{2}}{{\cal L}_{FF}}+{\cal L}+\frac{1}{2}T\right]_0,
\label{azero}
\end{equation}
\begin{equation}
b_0=\frac{16{\cal L}_{FF0}}{{\cal L}_{F0}}\left[ \kappa^{2}{\cal L}_{FF}^{2}-16({\cal L}_F+F{\cal L}_{FF})^{2}\right]^{-1}_0.
\label{bzero}
\end{equation}
with $\kappa = \sqrt{F^2+G^2}$, and
$G\equiv
F_{\mu \nu}^{*}F^{\mu\nu}$.
We shall discuss next how to use the dependence of the effective metric with $T_{\mu\nu}$ to classify the different possibilities
for $g_{\mu\nu}$.
\section{Algebraic properties of $T_{\mu\nu}$}
\label{algeb}
Due to the relation between the effective geometry and the energy-momentum tensor, the algebraic properties of
$T_{\mu\nu}$ determine the propagation of the high-energy perturbations of a given nonlinear theory. These properties
can be exhibited as a typical eigenvalue problem. Hence
it is useful to review some basic results concerning this problem in the context of relativity.
At a given point $p$ of a manifold $\mathcal{M}$, the object $T^{\alpha}_{\phantom a\beta}$ can be thought as a linear map of the tangent space $T_p$ onto itself. The principal directions of this map and its correspondent
eigenvalues are determined by
\footnote{To be precise, the eigenvalue problem for the energy momentum tensor
can be viewed as an immediate consequence of the
extremization of a scalar function
$\chi={T_{\mu\nu}\xi^\mu\xi^\nu}/{g_{\alpha\beta}\xi^\alpha\xi^\beta}$
with respect to $\xi^\alpha$ (in the same way as Petrov's classification of the
Weyl tensor is based on the extremization of the sectional curvature function).
In fact, deriving $\chi$ with respect to $\xi^\alpha$ and imposing the condition of
extremum implies, the eigenvalue equation (5) results.}
\begin{equation}
T^{\alpha}_{\phantom a\beta}\xi^{\beta}=\lambda \xi^{\alpha},
\end{equation}
where $\lambda$ is a scalar and $\xi^{\beta}$ is an eigenvector. A fourth order characteristic polynomial for $\lambda$ is obtained by the condition $p(\lambda)={\rm det}(\lambda \textbf{1}-\textbf{T})=0$ \footnote{We sometimes use the symbols
$\textbf{T}$ and $\textbf{1}$
as matricial versions of the mixed tensors
$T^{\alpha}_{\:\beta}$ and
$\delta^{\alpha}_{\:\beta}$. Successive contractions of $T^{\alpha}_{\:\beta}$ will be denoted as
powers of $\textbf{T}$, i.e: $\textbf{T}^{2}\doteq T^{\mu}_{\:\alpha}T^{\alpha}_{\:\nu}$,
$\textbf{T}^{3}\doteq T^{\mu}_{\:\alpha}T^{\alpha}_{\:\beta}T^{\beta}_{\:\nu}$
and so on.}.
Although the algebraic properties of this equation are well known, it
is important to note that in a positive definite metric,
a real symmetric matrix can always be diagonalized by a real orthogonal transformation.
However, the hyperbolic character of a Lorentzian metric leads to a more complicated
algebraic situation. In particular,
the eigenvectors $\xi^{\beta}$ do not necessarily constitute a
linearly independent set, implying that $\textbf{T}$ may not have a
diagonal representation.
Notwithstanding this undesirable property, it is always possible to
reduce the matrix $\textbf{T}$ to a typical canonical form,
as will be briefly discussed in Sec.\ref{revis}.
\subsection{The Segr\`e classification revisited}
\label{revis}
The Segr\`e classification is a local, invariant and algebraic classification of
arbitrary second rank symmetric tensors (see for instance \cite{Hall2}).
Tensors of this type play a very
important role several areas of physics, and
the coordinate-independent method provided by Segr\`e has been
discussed by many authors in different contexts
\cite{Bona}.
It is possible to show that, depending on the properties of the characteristic polynomial $p(\lambda)$
given by
\begin{equation}
p(\lambda) = \lambda^{4} -a_3\lambda^{3} +a_2\lambda^{2}-a_1\lambda+a_0=0,
\label{char}
\end{equation}
where the coefficients $a_n (n=0..3)$
are simple functions
of the scalar invariants built with powers of $\textbf{T}$,
and the nature of the eigenvectors, there exist at most four different classes (known as Segr\`e types) of symmetric tensors \cite{Hall2}. Those belonging to Segr\`e types I, II and III have only real eigenvalues and admit respectively, four, three or two linearly independent eigenvectors. Type IV describes tensors associated to complex and conjugated eigenvalues
\cite{Bona}. Each type is associated to a canonical form for the corresponding tensors.
By construction, type I is the only Segr\`e type in which the given linear map
admits a diagonal representation, and it can be shown that this is the only class that admits a timelike eigenvector
\cite{Bona, JSantos1}.
We list next two important properties that will be useful below \cite{Hall1}:\\[0.3cm]
\noindent (i) There always exists a two-dimensional subspace $S_p$ of $T_p$ which is invariant under the action of $\textbf{T}$\\
\noindent (ii) If $S_p$ is an invariant 2-space under the action of $\textbf{T}$, then so is the 2-space orthogonal to $S_p$.\\
The subspace \noindent$S_p$ will be called timelike, null or spacelike if it contains exactly two, one or no null vectors.
We shall see next how the Segr\`e classification can be useful in the determination of
possible types of effective metrics, in the particular example of nonlinear electromagnetism.
\section{Nonlinear electrodynamics and the eigenvalue problem of the energy-momentum tensor}
\label{eig}
\subsection{Linear case}
In order to study the properties of the energy-momentum tensor in nonlinear electromagnetism, we shall review first those of the linear theory, which furnishes a
simple realization of the Segr\`e classification \cite{Synge}. In this case, the energy-momentum tensor is given by
\begin{equation}
\tau^{\mu}_{\phantom a\nu}=F^{\mu}_{\phantom a\alpha}F^{\alpha}_{\phantom a\nu}+\frac{1}{4}F \delta^{\mu}_{\phantom a\nu}
\end{equation}
Beyond its obvious symmetric nature, $\mbox{\boldmath$\tau$}$ satisfies
additional algebraic properties, such as
tr$(\mbox{\boldmath$\tau$})=0$, and ${\rm tr}({\mbox{\boldmath$\tau$}}^{2}) = \tau^{\mu}_{\phantom a\nu}\tau^{\nu}_{\phantom a\mu}=\frac{1}{4}\kappa^{2}$,
where $\kappa\equiv (F^{2}+G^{2})^{1/2}$.
It is easily shown that the characteristic equation (\ref{char}) for Maxwell's energy-momentum tensor becomes
\begin{equation}
\left(\lambda^{2}-\frac{\kappa^{2}}{16}\right)^{2}=0
\end{equation}
From this relation, two important results follow:\\
(i) Since the characteristic equation factors in two identical second order polynomials, the four eigenvalues of the electromagnetic energy-momentum tensor in linear electromagnetism are real and equal in pairs.\\
(ii) The eigenvalues at each point of spacetime are entirely described by a given function of the field invariants $F$ and $G$ at that point:
\begin{equation}
\lambda_\pm=\pm\frac{1}{4}\kappa
\end{equation}
We shall consider next the eigenvector structure,
which can be determined by the analysis of the only two possible cases for $\kappa$ ($\kappa\neq 0$ and $\kappa =0$) \cite{Synge, Kramer}.
Note that because there exist at most two eigenvalues, the structure of a given %
eigenspace is degenerate, and there is an infinite number of $\xi^{\alpha}$ associated to a given $\lambda$.
\subsubsection{Non-null field ($\kappa\neq0)$: two different eigenvalues.}
In this case, there exist two orthogonal invariant eigenspaces $S_p$, each of them in correspondence with a given eigenvalue $\lambda_{\pm}$. It also follows that the timelike two-flat (which admits exactly two null eigenvectors) is associated to the positive eigenvalue $\lambda_{+}$ \cite{Synge}. Because the other two-flat admits two orthogonal spacelike vectors, it is possible to diagonalize $\mbox{\boldmath$\tau$}$ and it follows that non-null Maxwell fields are of Segr\`e type I.
\subsubsection{Null field ($\kappa =0$): one single null eigenvalue.}
It is possible to show that in this case the eigenvectors of $\mbox{\boldmath$\tau$}$ do not constitute a linearly independent set. Nevertheless, there exist a three-flat in $T_p$ that admits a null direction and two independent spacelike vectors. This three-flat is tangent to the light cone at $p$. According to the Segr\`e classification, this case belongs to type II. Hence $\mbox{\boldmath$\tau$}$ does not admit a diagonal representation but can be reduced to a
canonical form (which will be given in Sec.\ref{st2}) \cite{corm}.
\subsection{Nonlinear electromagnetism}
We now turn to the algebraic analysis of the energy-momentum tensor constructed with nonlinear and real Lagrangians for the electromagnetic field. As will be shown below, such analysis will be very useful in the description of the light cone structure
of an arbitrary nonlinear electromagnetic theory.
First we will consider
Lagrangians that are
arbitrary functions of the electromagnetic invariants $F$ and $G$.
Following the standard defnition of the energy-momentum tensor \cite{Landau}, we get
\begin{equation}
T^{\mu}_{\phantom a\nu}=-4{\cal L}_FF^{\mu}_{\phantom a\alpha}F^\alpha_{\phantom a\nu}-({\cal L}-{G\cal L}_G)\delta^{\mu}_{\phantom a\nu},
\end{equation}
where ${\cal L}_A\equiv \partial {\cal L}/\partial A$, $A=F,G$.
The roots of the characteristic
polynomial $p(\lambda)$ (Eqn.(\ref{char}))
would give the spectrum
of
eigenvalues for a given configuration of fields in the context of a given nonlinear
theory.
However, a simple inspection of the symmetries of $\textbf{T}$
reveals a much more complicated structure than that of Maxwell's.
First of all, the trace of $T^{\mu}_{\phantom a\nu}$ does not vanish
and is given by tr$(\textbf{T})=-4({\cal L}-F{\cal L}_F-G{\cal L}_G)$
Furthermore,
a calculation of the powers of \textbf{T} reveals that, for a given integer $n$
\begin{equation}
\textbf{T}^n=\alpha\textbf{F}^{2}+\beta\textbf{1},
\end{equation}
with $\alpha$ and $\beta$ are functions of the
invariant $F$ and $G$, and of ${\cal L}$ and its derivatives. Thus, the nonlinearity of the theory deforms the Rainich algebra \cite{Rainich} $\textbf{\mbox{\boldmath$\tau$}}^{2}\sim\textbf{1}$ valid in the linear theory, making the calculation of the coefficients of the characteristic polynomial
hard.
Nevertheless, it is possible to bypass this difficulty by
decomposing $\textbf{T}$ in terms of its traceless part $\textbf{N}$ and its trace, that is
$$
N^{\alpha}_{\;\;\beta}=T^{\alpha}_{\;\; \beta}-\frac{1}{4}T\delta^{\alpha}_{\;\; \beta}.
$$
Then, if $\mathbf{\xi}$ is an eigenvector of $\textbf T$ with eigenvalue $\lambda$ it will be also an eigenvector of $\textbf N$ with eigenvalue $\lambda-T/4$. Hence we are led to the study the properties of $N^{\alpha}_{\phantom a\beta}$ which for an
arbitrary Lagrangian is given by
\begin{equation}
N^{\alpha}_{\phantom a\beta}=-4{\cal L}_F\left(
F^{\alpha}_{\phantom a\lambda}F^{\lambda}_{\phantom a\beta}+\frac{1}{4}
F\delta^{\alpha}_{\phantom a\beta}\right).
\end{equation}
In other words, the traceless part of the nonlinear energy-momentum tensor is just a conformal transformation of Maxwell's $\mbox{\boldmath$\tau$}$, and the eigenvalues of $\textbf{N}$ are just that of $\mbox{\boldmath$\tau$}$
multiplied by $-4{\cal L}_F$
This interesting fact permits to obtain the eigenvalues of \textbf{T} with the expression
\begin{equation}
\lambda_{\pm}=F{\cal L}_F+G{\cal L}_G-{\cal L}\mp {\cal L}_F \kappa.
\end{equation}
Thus, the eigenvalues are given in terms of the field invariants and specific functions of them.
Notice that
the first three terms are just the trace of the energy-momentum tensor divided by four. Furthermore, the invariant subspaces of Maxwell's theory determine entirely the invariant subspaces of a nonlinear theory. We conclude that even in a nonlinear theory with ${\cal L} = {\cal L} (F,G)$, the algebraic properties of the energy-momentum tensor are such that the only possible Segr\`e types are I and II. Furthermore, type II is only possible if $\kappa =0$. In the next section we show how the Segr\`e types determine the light cone structure in
the particular example of nonlinear electromagnetism.
\section{Second order surfaces and a classification of nonlinear regimes}
\label{seco}
The light cone structure of a nonlinear theory is governed by the effective metric
$g_{\mu\nu}$ through the condition
\begin{equation}
g_{\mu\nu}k^\mu k^\nu=0,
\label{lc}
\end{equation}
where the $k^\mu$ are null vectors in the effective geometry but are not null, in general, in the background geometry (which maybe flat or curved). We shall study next the the relation between the newly-defined light cones and the background light cones (which for definiteness
we assume to be those of Minkowski spacetime). It will be shown that there exist many possibilities that are associated with the algebraic nature of the energy-momentum tensor at a given spacetime point, and to the properties of the Lagrangian. Notice that although $g_{\mu\nu}$
can be taken as a new Riemannian metric, it is also licit to think of it
as a tensor field defined in Minkowski spacetime. Because of the expression
$$
g_{\mu\nu}=a_0\gamma_{\mu\nu}+b_0T_{\mu\nu 0},
$$
with $a_0$ and $b_0$ given by Eqns.(\ref{azero}) and (\ref{bzero}),
the principal directions (eigenvectors) of $g_{\mu\nu}$ and its invariant subspaces are entirely determined by the eigenvectors of $T^{\mu}_{\phantom a\nu}$. The analysis will be divided in two different classes, following the two different algebraic types of the energy-momentum tensor discussed above.
\subsubsection*{Class 1: Segr\`e type I background}
If, at a given point $p$, the energy-momentum is of Segr\`e type I, the following lemma ensues:\\[0.3cm]
\noindent \textit{Lemma:} There exist a non-null intersection between Maxwell's light cone and the nonlinear light cone, which is given by the null eigenvectors of $T^{\mu}_{\phantom a\nu}$.
\noindent Proof: As stated before, in Segr\`e type I there are two eigenvectors of $\mathbf T$ (those with eigenvalue $\lambda_+$) that are null in the background metric. Denoting them by $\xi^\mu_{(i)}$, $i=1,2$, we have
$$
g_{\mu\nu}\xi^\mu_{(i)}\xi^\nu_{(i)}=a_0\gamma_{\mu\nu} \xi^\mu_{(i)}\xi^\nu_{(i)}+
b_0\xi^\mu_{(i)}T_{\mu\nu}\xi^\nu_{(i)}= (a_0+\lambda_+b_0)\gamma_{\mu\nu} \xi^\mu_{(i)}\xi^\nu_{(i)} =0.$$
Since we have $g_{\mu\nu}\xi_{(i)}^{\mu}\xi_{(i)}^{\nu}=0$ and $\eta_{\mu\nu}\xi_{(i)}^{\mu}\xi_{(i)}^{\nu}=0$, the
$\xi_{(i)}^{\mu}$ are
contained in both light cones, proving that they are tangent along these vectors.
By choosing a specific orthogonal basis at $p$, the energy-momentum tensor admits a diagonal representation. which allows the light cone condition
to be written as
\begin{equation}
f_{+}[(k^0)^{2}-(k^1)^{2}]-f_{-}[(k^2)^{2}+(k^3)^{2}]=0
\label{cono1}
\end{equation}
where $f_\pm=a_0+b_0\lambda_\pm$ are the eigenvalues of the effective metric tensor given in Eqn.(\ref{emem}).
At a given point $p$, this is the equation of a three dimensional surface representing locally the light cone of a nonlinear theory in the tangent space $T_p$. The coefficients $f_{+}$ and $f_{-}$ depend explicitly on the Lagrangian and its derivatives, and on the background field,
but in a sense, for a given theory, the three-surface
will depend only on the invariant $F$. In the context of Maxwell's linear theory this equation reduces to that of the light cones of Minkowski spacetime.
To develop a geometrical understanding of the causal structure, we will set $k^0=1$ in Eqn.(\ref{cono1}). From a physical point of view, we can interpret the resulting bidimensional surface as the position of the wavefront
after a given infinitesimal lapse of time. In the case of linear electromagnetism, this surface is a sphere (called
Maxwell's sphere from now on). Because there exist two common null vectors to both surfaces, the two-dimensional surface that follows from Eqn.(\ref{cono1})(which we will call
the photon surface)
intersects Maxwell's sphere precisely at two points ($k_{1}=\pm1$ in this frame).
Defining the function $\Upsilon\equiv f_{-}/f_{+}$ we have
\begin{equation}
(k^1)^{2}+\Upsilon [(k^2)^{2}+(k^3)^{2}]=1.
\end{equation}
From the theory of quadrics we have the following possibilities for the resulting photon surface. If $\Upsilon>0$,
the surface is an ellipsoid of revolution around the $k^1$ axis. The ellipsoid touches Maxwell's sphere from inside
if $\Upsilon>1$ (with the major axis along $k^1$) and from outside
if $0<\Upsilon<1$ (with minor axis along $k^1$, see Fig.\ref{s1}). The difference between the two light cones shows that
because of the interaction with the
background field, the nonlinear photons (NLP)
propagate with different velocities in different directions. In the first case,
all the NLP (except those along $k^{1}$) propagate with velocities that are less than $c$, while in the second
case all the NLP (leaving aside those along $k^{1}$) propagate with velocity greater that $c$. The limiting case $\Upsilon=1$ coincides with Maxwell's sphere, in such a way that any theory with a background such that $\Upsilon =1$ at a
given point will locally reproduce every property of Maxwell's theory from the point of view of photon propagation.
Notice that there exist two more exotic allowed situations. When the condition $\Upsilon=0$ is satisfied,
the photon surface is determined by planes satisfying the condition $k^1=\pm1$.
These planes intersect Maxwell's sphere in two points, in which case the velocity of the NLP coincides with $c$.
This in this case the nonlinear theory and the background are such that light propagation is
forbidden in spacelike directions which in the chosen frame, are orthogonal to the $k^{1}$ axis.
A second exotic possibility is
$\Upsilon<0$, since the three-surface will be a two-sheet hyperboloid touching the sphere from outside.
In this interesting case the spacelike directions in which the NLP cannot propagate are many more than in
the $\Upsilon=0$ case.
The following table displays the catalogue of possible light cone
structures for a Segr\`e I type background energy-momentum
tensor, along with a notation based on
the algebraic type and resulting photon surface.
\begin{table}[ht!]
\centering
\begin{tabular}{ccc} \hline\hline
$\Upsilon$ & $\mathrm{photon}\: \mathrm{surface}$ & ${\rm symbol}$ \\
\hline
$\Upsilon>1$ & ${\rm internal}\: {\rm ellipsoid}$ &$ Ie_{-}$ \\
$\Upsilon=1$ & ${\rm sphere}$ & $× Is$\\
$0<\Upsilon<1$ & ${\rm external}\:{\rm ellipsoid}$ & $Ie_{+}$ \\
$\Upsilon=0$ & ${\rm planes}$ & $×Ip$ \\
$\Upsilon<0$ & ${\rm two-sheet}\:{\rm hyperboloid}$ & $Ih_{2}$\\
\hline
\end{tabular}
\caption{The table shows the different photon surfaces for a Segr\`e type I energy-momentum tensor.}
\label{t1}
\end{table}
A straightforward calculation shows that for ${\cal L} = {\cal L} (F)$,
\begin{equation}
\Upsilon=\frac{{\cal L}_F+{\cal L}_{FF}(F-\kappa)}{{\cal L}_F+{\cal L}_{FF}(F+\kappa)}.
\label{upsi}
\end{equation}
Thus, the local causal structure in any nonlinear theory of electrodynamics is determined by computing a single function of the field invariant.
The figures \ref{s1},\ref{s1h2}, and \ref{s1p} show some properties of the resulting surfaces and their relation with the Minkowski light cone.
\begin{figure}[h]
\begin{center}
\includegraphics[width=0.6\textwidth]{s1}
\caption{Minkowski and nonlinear light cones for Segr\`e type I and $\Upsilon >0$.}
\label{s1}
\end{center}
\end{figure}
\begin{figure}[h]
\begin{center}
\includegraphics[width=0.5\textwidth]{s1h2}
\caption{Minkowski and nonlinear light cones for Segr\`e type I and $\Upsilon < 0$.}
\label{s1h2}
\end{center}
\end{figure}
\begin{figure}[h]
\begin{center}
\includegraphics[width=0.5\textwidth]{s1p}
\caption{Minkowski and nonlinear light cones for Segr\`e type I and $\Upsilon \geq 0$.}
\label{s1p}
\end{center}
\end{figure}
\subsubsection*{Class 2: Segr\`e type II background}
\label{st2}
In this case the energy-momentum tensor cannot be diagonalized and, because $F=0$, there exists only one eigenvalue $\lambda=-{\cal L}$. Nevertheless, it is always possible to reduce $\textbf{T}$
to the following matrix representation by choosing a specific orthogonal frame:
\begin{equation}
T^{\mu}_{\phantom a\nu}=\left(
\begin{array}{llll}
\lambda-\mu & -\mu & 0 & 0 \\
\mu & \lambda+\mu & 0 & 0 \\
0 & 0 & \lambda & 0 \\
0 & 0 & 0 & \lambda
\end{array}\right)
\end{equation}
where $\mu\equiv 2{\cal L}_F(E^2+H^2)$. Following the procedure sketched in the last subsection, \textit{i.e.} imposing the condition
$k^0=1$ and introducing $f_0\equiv a_0+b_0\lambda$, Eqn.(\ref{lc}) becomes
\begin{equation}
(\Phi+1)(k^1)^2+(k^2)^2+(k^3)^2+2\Phi k^1+(\Phi-1)=0
\end{equation}
where $\Phi\equiv b_0\mu_0/f_0$. Since there exists only one null eigenvector for a Segr\`e type
II energy-momentum tensor, it is immediate to show that the corresponding photon surface intersects
Maxwell's sphere only at one point ($k^1=-1$ in the chosen frame). Also, the non-diagonal terms in $\textbf{T}$
imply that the resulting surface is not centered at the origin. As in Segr\`e type I, we have several possibilities.
If $-1<\Phi<\infty$, the three-surface will be an ellipsoid of revolution along $k^{1}$.
When $0<\Phi<1$, the surface is entirely contained inside Maxwell's sphere, while in the case $-1<\Phi<0$
Maxwell's sphere is inside, in such a way that the limiting case $\Phi=0$ is the sphere itself (see Fig.\ref{s2}).
There are also some exotic situations. If $\Phi=-1$, the NLP define a paraboloid of revolution around $k^{1}$, which prohibits propagation in some directions. Finally, the condition $\Phi<-1$ determines a strange situation in which a one-sheet hyperboloid
is tangent to the sphere. The different possibilities are given in the following table, where
for ${\cal L} = {\cal L} (F)$, $\Phi$ is given by
\begin{equation}
\Phi=-\mu \left.\frac{{\cal L}_{FF}}{{\cal L}_{F}}\right|_0.
\end{equation}
\begin{table}[ht!]
\centering
\begin{tabular}{ccc} \hline\hline
$\Phi$ & $\mathrm{photon}\:\mathrm{surface}$ & $\mathrm{symbol} $\\
\hline
$0<\Phi<\infty$ & $\mathrm{internal}\;\mathrm{ellipsoid}$ & $IIe_{-} $\\
$\Phi=0$ & $\mathrm{sphere}$ & $IIs$ \\
$-1<\Phi<0$ &$ \mathrm{external}\:\mathrm{ellipsoid}$ &$ IIe_{+} $\\
$\Phi=-1$ & $\mathrm{paraboloid}$ & $IIp$ \\
$\Phi<-1 $& $\mathrm{one-sheet}\:\mathrm{hyperboloid}$ & $IIh_{1}$\\
\hline
\end{tabular}
\caption{The table shows the different photon surfaces for a Segr\`e type I energy-momentum tensor.}
\end{table}
\begin{figure}[h]
\begin{center}
\includegraphics[width=0.65\textwidth]{s2}
\caption{Minkowski and nonlinear light cones for a Segr\'e type II energy-momentum tensor.}
\label{s2}
\end{center}
\end{figure}
\section{Simple realizations of the classification}
\label{simple}
In this section we will discuss the relation between the orientation of the
light cones in a nonlinear ${\cal L} (F)$ theory
and a given electromagnetic field. For simplicity, we will concentrate only in Segr\'e I type energy-momentum tensors.
In terms of the electromagnetic vectors $E^{\:\mu}$, $H^\mu$ and a given timelike congruence
$V^{\mu}$,
the electromagnetic field tensor admits the following
decomposition:
$$
F^{\mu \nu}\equiv E^{\left[\mu\right.}V^{\left.\nu\right]}+\frac{1}{2}\eta^{\mu \nu}_{\phantom a \phantom a \alpha \beta}H^{\alpha}V^{\beta}
$$
where the electric and magnetic vectors $E^\mu(x)$ and $H^\mu(x)$
are defined respectively as $E^\mu = F^{\mu}_{\phantom a \nu}V^{\nu}$ and $H^{\mu}\equiv \eta^{\mu}_{\phantom a \varepsilon \alpha \beta}V^{\varepsilon}F^{\alpha \beta}$, and $F=2(H^{2}-E^{2})$, $G=-4E\cdot H$. The energy-momentum tensor for a theory described by ${\cal L} = {\cal L} (F)$ can be similarly decomposed as
\begin{eqnarray}
T_{\mu\nu} & = & -4{\cal L}_F(E^{2}V_{\mu}V_{\nu}-E_{\mu}E_{\nu}+2q_{(\mu}V_{\nu)}))\\
& &-4{\cal L}_F(H^{2}V_{\mu}V_{\nu}-H_{\mu}H_{\nu}-H^{2}g_{\mu\nu})-{\cal L}g_{\mu\nu},
\end{eqnarray}
where $E^{2}=-E_{\mu}E^{\mu}$, $H^{2}=-H_{\mu}H^{\mu}$ and $q_{\lambda}=\frac{1}{2}\eta_{\lambda}^{\phantom a\mu\rho\sigma}E_{\mu}V_{\rho}H_{\sigma}$ is
the Poynting vector.
In Segr\'e type I tensors, it is always possible to find an observer such that the electric and
magnetic fields are parallel, \textit{i.e.} $H_{\mu}=\xi E_{\mu}$ and, consequently, the Poynting vector
vanishes \cite{Landau}. It is also possible to show that $V^{\mu}$ and $E^{\mu}$ are eigenvectors of
$T^{\alpha}_{\phantom a\beta}$ with eigenvalue $\lambda_{+}$. Thus, the timelike invariant subspace $S_p$
is spanned by a linear combination of $V^{\mu}$ and $E^{\mu}$. The spacelike subspace is determined by means of
two spacelike orthonormal vectors $n^{\mu}$ and $m^{\mu}$ satisfying $n^{\mu}E_{\mu}=m^{\mu}E_{\mu}=0$.
It is immediate to see that these vectors are eigenvectors of the energy-momentum tensor with eigenvalue $\lambda_{-}$. In the frame where $H_{\mu}=\xi E_{\mu}$,
the eigenvalues have the form:
\begin{eqnarray}
&&\lambda_{+}=-4{\cal L}_{F}E^{2}-{\cal L}\\
&&\lambda_{-}=4 {\cal L}_{F}\xi^{2}E^{2}-{\cal L},
\end{eqnarray}
In particular, if the observer is such that the magnetic part $H^{\mu}$
vanishes ($\xi =0$), the electric field direction determines completely the orientation of the timelike subspace which, as proved by the
lemma in Sec.\ref{seco},
determines the only directions in space in which light propagation is not affected by the nonlinear interaction. We will analyze next the problem of a static electrically charged particle in the context of two different nonlinear theories of electrodynamics, which illustrates what has been exposed here.
\subsection{Example 1}
Following the developments of the
previous section, we shall examine here
the light cone structure generated by the field of an electric charge placed at the origin in
Born-Infeld theory, with Lagrangian given by
$$
{\cal L}=b^2\left(1-\sqrt{1+\frac{F}{2b^2}}\right).
$$
The equations for the EM field,
$$
(\sqrt{-g}{\cal L}_FF^{\mu\nu})_{;\nu}=0
$$
in the spherically symmetric case have been solved for instance in \cite{wh}.
The only nonzero component of $F^{\mu\nu}$ is $F^{tr}$ in such a way that
$$
\frac{F}{2b^2}=-\frac{16\alpha^2}{r^4b^2+16\alpha^2},
$$
where $\alpha$ is proportional to the electric charge.
Defining the new variable
$$
y=\left(\frac{b^2r^4}{16\alpha^2}\right)^{1/4},
$$
the function $\Upsilon$ introduced in Eqn.(\ref{upsi}) is in this case given by
$$
\Upsilon = 1 - \frac{1}{1+y^4}.
$$
$\Upsilon$ tends to 1 for large $r$ (meaning that the linear theory is recovered far from the charge),
and it is actually restricted to the interval $[0,1]$.
From the classification in Table \ref{t1}, we see that the light cones
go from a sphere (for very large values of $r$) to an external ellipsoid, deforming
finally to two parallel planes (for $r=0$).
Note that these considerations are valid in the reference frame in which $H_\mu $ is zero.
This case has been discussed before in \cite{wh}, from the point of view of the effective potential for the NLP
arising from the effective metric, given by
$$
V(r) = \frac{L^2r^2}{r^4+\frac{8\alpha^2}{b^2}}.
$$
We see that for NLP travelling in the radial direction, $V=0$. Hence, these photons move
with velocity $c$, as was shown in Sec.\ref{seco}. The motion for $L\neq 0$ can be
described
in the formalism presented here by the analysis of the variation of the local light cone,
exactly as is done for instance in the case of the Schwarzschild's black hole.
Notice that all the necessary information about the light cones
is encoded in $\Upsilon$.
\subsection{Euler-Heisenberg}
The second example that will be examined here is that of an Euler-Heisenberg-like Lagrangian (in the weak-field
limit), given by
$$
{\cal L} (F) = -\frac 1 4 F+\beta F^2,
$$
where for the time being we leave $\beta$ unspecified.
Taking into account that $\kappa=+\sqrt{F^2+G^2}$,
we can distinguish two cases:
1) $F>0\rightarrow \kappa = F$. In this case,
$$
\Upsilon = \frac{8\beta F-1}{24\beta F-1}.
$$
2) $F<0$, then $\kappa = - F$, and
$$
\Upsilon = \frac{24\beta F-1}{8\beta F-1}.
$$
On the other hand, the equations of motion
$$
({\cal L}_FF^{\mu\nu})_{;\nu}=0,
$$
in the case of the EH-like Lagrangian for an electric charge
lead to
$$
\frac{E(r)}{4}+4\beta E(r)^3 = \frac{Q}{r^2},
$$
where $Q$ is proportional to the electric charge.
This expression can be inverted to give
$$
r^2=\frac{Q}{\sqrt{\frac E 4 + 4 \beta E^3}}.
$$
We see that for $\beta >0$, the electric field must
satisfy $0<E^2<\infty$.
It follows that in this case
$-\infty < F < 0$. From the plot of $\Upsilon$ in terms of $F$
it follows that $\Upsilon$ goes from the value 1 (at $r\rightarrow\infty$)
to the value 3 (at $r\rightarrow 0$). Hence the photon spheres
in this case vary qualitatively shown in Fig.\ref{erico11}.
\begin{figure}[h]
\begin{center}
\includegraphics[width=0.6\textwidth]{erico11}
\caption{Variation of Minkowski and photon spheres for $\beta >0$.}
\label{erico11}
\end{center}
\end{figure}
In the same way,
for $\beta <0$, we have that $\Upsilon \rightarrow 1$ for $r\rightarrow\infty$, and
$\Upsilon \rightarrow -\infty$ for $\rightarrow 0$. The qualitative variation
of the photon spheres in this case is shown in Fig.\ref{erico22}
\begin{figure}[h]
\begin{center}
\includegraphics[width=0.6\textwidth]{erico22}
\caption{Variation of Minkowski and photon spheres for $\beta >0$.}
\label{erico22}
\end{center}
\end{figure}
\section{Conclusion}
\label{conc}
We have shown that the presence of $\mathbf{T}$ in the effective metric along with the help of the Segr\`e classification of second rank symmetric tensors
furnishes a classification of the possible forms of the effective metric for nonlinear electromagnetic theories.
We developed this classification in the case of
Lagrangians given by
${\cal L} = {\cal L} (F)$ \footnote{The generalization to ${\cal L} (F,G)$ Lagrangians should be straightforward, taking into
account that the effective metric can still be expressed as in Eqn.(\ref{effmet}), see \cite{klo}},
showing that there are only two possible general forms for the effective metric (associated to Segr\`e
types I and II, which are the only types that appear in this case). The explicit form of the effective metric
can be used to compare the effective light cone with the Minkowskian light cone.
We have presented the different possibilities, each of them associated to
a single scalar function of the Lagrangian,
its derivatives, and the background field. Finally, we have analyzed two examples,
which illustrate the power of the method, in the sense that
the variation of the light cones is encoded in $\Upsilon$.
To close, let us remark that although we have focused in the case of the nonlinear electromagnetic field, the classification of the effective metric in terms of the Segr\`e types
is possible for other fields. This follows from the fact that,
as shown in \cite{mariofierz} and \cite{mm}, the effective geometries
associated to nonlinear scalar field and the nonlinear spin two field theories
can also be written in the form
\begin{equation}
g_{\mu\nu}=\Omega^{(1)}_0\gamma_{\mu\nu} +\Omega^{(2)} _0 T_{\mu\nu 0}.
\label{effmet}
\end{equation}
In this expression, $\gamma_{\mu\nu}$ is the background metric, and
$\Omega^{(1)}_0$ and $\Omega^{(2)}_0$ are functions of the background field, the detailed form of which depends on
the given theory, and $\Omega^{(2)}_0$ is such that it goes to zero when the theory
is linear. We also leave for future work half-integer spin fields, and the case of multi-fields.
\section{Acknowledgements}
SEPB would like to acknowledge support from ICRANet (where part of this
work was done), and FAPERJ.
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 381
|
Andreas Bienz (born 16 June 1960) is a Swiss sailor. He competed in the Star event at the 1992 Summer Olympics.
References
External links
1960 births
Living people
Swiss male sailors (sport)
Olympic sailors of Switzerland
Sailors at the 1992 Summer Olympics – Star
Place of birth missing (living people)
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 7,626
|
Professional Certificate Programme in Nursing Leadership and Management - The Nethersole School of Nursing, Faculty of Medicine, The Chinese University of Hong Kong.
This programme leads to the award of a Professional Certificate in Nursing Leadership and Management from The Chinese University of Hong Kong (CUHK).
This is a 4-month intensive programme specially designed to prepare senior registered nurses with a bachelor's degree to become nurse leaders or managers, capable of dealing with the challenges of population ageing and the increasingly complex healthcare environment. The programme emphasises advancing students' knowledge and skills in nursing leadership and management, and enriching their exposure to international healthcare management. Students are also expected to further develop their competence in management decision-making and evidence-based evaluation in their relevant healthcare management areas.
preferably have at least 5 years' post-registration clinical experience.
Students are assessed in every course through a combination of written assignment, project management, oral presentation and discussion, etc.
The Professional Certificate in Nursing Leadership and Management is recognised by the Education Bureau of HKSAR Government as Level 6 under the Qualifications Framework (QR Registration No.: 18/000889/L6; Registration Validity Period: 05/12/2018 to On-going).
Teaching and learning strategies include lecture, case discussion, project management, professional visit, web-based teaching and learning and self-directed study, as appropriate.
Classes are usually held on Fridays and Saturdays in the CUHK Shenzhen Research Institute (Shenzhen) or CUHK campus (Hong Kong). Please click here for the tentative class schedule for 2018-19.
Opportunities to attend lectures or forums delivered by experienced healthcare leaders or managers.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 6,834
|
{"url":"https:\/\/socratic.org\/questions\/what-is-the-molecular-equation-for-the-following-reaction-hydrochloric-acid-reac","text":"What is the molecular equation for the following reaction: Hydrochloric acid reacts with sodium hydroxide to produce a salt, water and heat?\n\nNov 5, 2016\n\n$\\text{HCl + NaOH}$$\\rightarrow$$\\text{NaCl + H\"_2\"O + heat}$","date":"2019-10-19 08:19:53","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 3, \"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\": 0.9242460131645203, \"perplexity\": 5362.110813909821}, \"config\": {\"markdown_headings\": false, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2019-43\/segments\/1570986692126.27\/warc\/CC-MAIN-20191019063516-20191019091016-00201.warc.gz\"}"}
| null | null |
\section{\label{SecPreliminaries}Preliminaries}
\begin{figure}
\begin{center}
\includegraphics[width=6cm]{discriminant.png}
\end{center}
\caption{\label{FigDiscriminant}The ``swallowtail''}
\end{figure}
Figure \ref{FigDiscriminant} shows the \textit{swallowtail}: a two-dimensional slice of the degree four discriminant $\Delta_4$ in the neighbourhood of the form $x^4$. The ``true'' discriminant near $x^4$ is the product of the surface shown in Figure \ref{FigDiscriminant} and an affine line. We see that $\Delta_4$ has a singular locus with two components, each in codimension one. The \textit{caustic}, denoted $\Gamma$, where the surface folds, is the locus of forms with a root of multiplicity three. The \textit{self-intersection locus}, where the surface crosses itself, is the locus of forms with more than one distinct pair of double roots. Both loci will be important in the sequel. These observations are true more generally, as the following theorem shows.
\begin{theorem}
\label{ThmSingSigma}
The singular locus of $\Delta$ is the locus of polynomials with either a root of multiplicity strictly greater than $2$ or more than one distinct pair of roots of multiplicity $2$. The former has codimension one and the latter has codimension one when $n\geq 4$ and is empty otherwise.
Furthermore, the singular locus of $\Gamma$ is contained in its intersection with the self-intersection locus of $\Delta$.
\end{theorem}
\begin{proof}
This is just a special case of \cite[Theorem 5.4]{Chi00}. The codimensions can be calculated by parametrizing the relevant loci to compute the dimensions thereof.
\end{proof}
In our study, the dictionary, introduced by Eisenbud in \cite{Eis80}, between maximal Cohen-Macaulay modules and matrix factorizations is crucial. Namely, given a determinantal formula $D_n=\det A$ for $D_n$, the pair $(A,\adj A)$, where $\adj A$ is the classical adjoint of $A$, is a matrix factorization of $D_n$ in the sense that $A(\adj A)=D_n\cdot I=(\adj A)A$, where $I$ is the identity matrix of appropriate size. The cokernel of $A$ is then a maximal Cohen-Macaulay module over $\KK[a_0,\dots,a_n]/(D_n)$. Furthermore, since $D_n$ is irreducible, given an MCM module $M$ over $\KK[a_0,\dots,a_n]/(D_n)$, a presentation of $M$ over $\KK[a_0,\dots,a_n]$ is a square matrix of determinant $D_n^r$, where $r$ is the rank of $M$. In particular, determinantal formulae correspond under this dictionary to \textit{maximal Cohen-Macaulay modules over $\KK[a_0,\dots,a_n]/(D_n)$ of rank one}. Under this dictionary, the classical determinantal formulae for $D_n$ correspond to the push-forward of the normalization $\bar{\Delta}$ of $\Delta$, which we now describe.
Denote by $W$ the $\KK$-vector space with basis $\{x,y\}$. Let $\Pbf:=\PProj(V)\times\PProj(W)$ and let
\[F:=a_0x^n+a_1x^{n-1}y+\cdots+a_{n-1}xy^{n-1}+a_ny^n\in H^0(\Pbf,\Ocal(1,n))\]
be the universal homogeneous polynomial of degree $n$ in $x$ and $y$. Its partial derivatives\footnote{In general, for a polynomial $g(x,y)$, we denote $g_x:=\frac{\partial g}{\partial x}$ and $g_y:=\frac{\partial g}{\partial y}$.} $F_x:=\frac{\partial F}{\partial x}$ and $F_y:=\frac{\partial F}{\partial y}$ are sections of $\Ocal_{\Pbf}(1,n-1)$. Consider the \textit{incidence variety} $\bar{\Delta}$ defined by the sections $F_x$ and $F_y$. It is a smooth codimension two subvariety of $\Pbf$, as can be seen easily from the Jacobian criterion. The Euler identity \[ nF = xF_x+yF_y \] shows that on the affine pieces $U_y:=\{y\neq 0\}$ and $U_x:=\{x\neq 0\}$, respectively, $\bar{\Delta}$ coincides with the varieties defined by the sections $\{\frac{n}{y}F,F_x\}\subseteq\Gamma(U_y,\Ocal_{\Pbf}(1,n-1))$ and $\{\frac{n}{x}F,F_y\}\subseteq\Gamma(U_x,\Ocal_{\Pbf}(1,n-1))$. Thus points on $\bar{\Delta}$ are pairs $(f,t)\in\Pbf$ such that $t$ is a repeated root of $f$, the latter viewed as a homogeneous polynomial. In particular, the projection map $p_V:\Pbf\to\PProj(V)$, restricted to $\bar{\Delta}$, defines a map $\pi:\bar{\Delta}\to\Delta$.
\begin{proposition}
\label{PropPHNormalization}
The map $\pi:\bar{\Delta}\to\Delta$ described above is the normalization of $\Delta$.
\end{proposition}
\begin{proof}
The map $\pi$ is finite since the number of preimages of a point on $\Delta$ is the number of distinct roots of multiplicity at least $2$ of the associated degree $n$ form, which is clearly a finite number. In addition, a generic polynomial of degree $n$ with a root of multiplicity $2$ has exactly one root of multiplicity exactly $2$, so $\pi$ is generically one-to-one. Finally, $\bar{\Delta}$ is smooth, hence normal. Thus the map $\pi$ is the normalization of $\Delta$, as claimed.
\end{proof}
We may make an analogous construction for the normalization of $\Gamma$. Namely, we define the incidence variety $\bar{\Gamma}$ to be the variety defined by the second-order partial derivatives $F_{xx}$, $F_{xy}$, and $F_{yy}$ of $F$, which are sections of $\Ocal_\Pbf(1,n-2)$. It is again easily seen that $\bar{\Gamma}$ is smooth. The same arguments as above show that the projection $p_V:\Pbf\to\PProj(V)$ maps $\bar{\Gamma}$ onto $\Gamma$ and that the restriction of $p_V$ to $\bar{\Gamma}$ is the normalization of $\Gamma$. The Euler identities $(n-1)F_x=xF_{xx}+yF_{xy}$ and $(n-1)F_y=xF_{xy}+yF_{yy}$ imply that $\bar{\Gamma}$ is a subvariety of $\bar{\Delta}$ of codimension one. We therefore have:
\begin{proposition}
\label{PropGammaBarCM}
The variety $\bar{\Gamma}$ embeds in $\bar{\Delta}$ as a smooth subvariety of codimension one. In particular, $\Ocal_{\bar{\Gamma}}$ is a Cohen-Macaulay module over $\Ocal_{\Delta}$ of codepth one.
\end{proposition}
\section{\label{SecAlgebraicDefinition}An algebraic definition}
In this section we develop an algebraic construction of the \textit{open swallowtail}, showing that it is a maximal Cohen-Macaulay module of rank one and therefore defines a determinantal formula for $D_n$.
The following theorem is key. It characterizes the sheaf of relative differentials $\Omega^1_{\bar{\Delta}/\Delta}$ of the normalization map $\bar{\Delta}\to\Delta$ described above and provides the main motivation for the algebraic definition of the open swallowtail, as well as the means to construct its presentation explicitly. Denote by $p$ the restriction of the projection $\Pbf\to\PProj(W)$ to $\bar{\Delta}$ and denote by $j$ the inclusion $\bar{\Gamma}\hookrightarrow\bar{\Delta}$.
\begin{theorem}
\label{ThmCharOmega1}
We have $\Omega^1_{\bar{\Delta}/\Delta}\cong j_*j^*p^*\Omega^1_{\PProj(W)/\KK}$ as $\Ocal_{\bar{\Delta}}$-modules.
\end{theorem}
\begin{proof}
Let $\pi:\bar{\Delta}\to\Delta$ be the normalization map as given above. Let $i:\Delta\hookrightarrow\PProj(V)$ and $\bar{i}:\bar{\Delta}\hookrightarrow\Pbf$ be the natural embeddings. This gives rise to the diagram
\begin{equation}
\label{EqEmbeddingsDiagram}
\begin{diagram}
& & \bar{\Delta} & \rTo_\pi & \Delta \\
& \ldTo_p & \dInto_{\bar{i}} & & \dInto_i \\
\PProj(W) & \lTo_{p_W} & \Pbf & \rTo_{p_V} & \PProj(V).
\end{diagram}
\end{equation}
We have $\Omega^1_{\Pbf/\KK}\cong p_V^*\Omega^1_{\PProj(V)/\KK}\oplus p_W^*\Omega^1_{\PProj(W)/\KK}$, where $p_W:\Pbf\to\PProj(W)$ and $p_V:\Pbf\to\PProj(V)$ are the natural projections. The Zariski-Jacobi sequence for the maps $\Pbf\to\PProj(V)\to\KK$ is just the split sequence associated to this direct sum decomposition:
\begin{equation}
\label{EqZJProduct}
\begin{diagram}
0 & \rTo & p_V^*\Omega^1_{\PProj(V)/\KK} & \rTo & \Omega^1_{\Pbf/\KK} & \rTo & \Omega^1_{\Pbf/\PProj(V)}\cong p_W^*\Omega^1_{\PProj(W)/\KK} & \rTo & 0.
\end{diagram}
\end{equation}
The relations in \eqref{EqEmbeddingsDiagram}, along with the definition of $p$, imply that $\bar{i}^*p_V^*\Omega^1_{\PProj(V)/\KK}\cong\pi^*i^*\Omega^1_{\PProj(V)/\KK}$ and that $\bar{i}^*p_W^*\Omega^1_{\PProj(W)/\KK}\cong p^*\Omega^1_{\PProj(W)/\KK}$. Furthermore, because \eqref{EqZJProduct} is split, it remains exact after the application of $\bar{i}^*$. In view of the commutativity of \eqref{EqEmbeddingsDiagram}, we obtain the following commutative diagram:
\[ \begin{diagram}
& & \pi^*\Omega^1_{\Delta/\KK} & \rTo & \Omega^1_{\bar{\Delta}/\KK} & \rTo & \Omega^1_{\bar{\Delta}/\Delta} & \rTo & 0 \\
& & \uTo & & \uTo \\
0 & \rTo & \pi^*i^*\Omega^1_{\PProj(V)/\KK} & \rTo & \bar{i}^*\Omega^1_{\Pbf/\KK} & \rTo & p^*\Omega^1_{\PProj(W)/\KK} & \rTo & 0.
\end{diagram} \]
The top row is the Zariski-Jacobi sequence associated to the maps $\bar{\Delta}\to\Delta\to\KK$ and the bottom row is \eqref{EqZJProduct}. The vertical maps are the surjections $\pi^*i^*\Omega^1_{\PProj(V)/\KK}\to\pi^*\Omega^1_{\Delta/\KK}$ and $\bar{i}^*\Omega^1_{\Pbf/\KK}\to\Omega^1_{\bar{\Delta}/\KK}$ induced by the embeddings $i$ and $\bar{i}$. There is therefore an induced surjection $\rho:p^*\Omega^1_{\PProj(W)/\KK}\to\Omega^1_{\bar{\Delta}/\Delta}$, as in the following diagram:
\begin{equation}
\label{EqZJDiagram}
\begin{diagram}[height=.5cm]
& & 0 & & 0 & & 0 & & \\
& & \uTo & & \uTo & & \uTo & & \\
& & \pi^*\Omega^1_{\Delta/\KK} & \rTo & \Omega^1_{\bar{\Delta}/\KK} & \rTo & \Omega^1_{\bar{\Delta}/\Delta} & \rTo & 0 \\ \\
& & \uTo & & \uTo & & \uDashto_{\exists\rho} & & \\ \\
0 & \rTo & \pi^*i^*\Omega^1_{\PProj(V)/\KK} & \rTo & \bar{i}^*\Omega^1_{\Pbf/\KK} & \rTo & p^*\Omega^1_{\PProj(W)/\KK} & \rTo & 0.
\end{diagram}
\end{equation}
It now suffices to prove that $\ker\rho=\Jcal\otimes p^*\Omega^1_{\PProj(W)/\KK}$, where $\Jcal$ is the ideal sheaf defining $\bar{\Gamma}$ in $\bar{\Delta}$. We have an injection $\Jcal\otimes p^*\Omega^1_{\PProj(W)/\KK}\hookrightarrow p^*\Omega^1_{\PProj(W)/\KK}$. Let $\Ical$ be the ideal sheaf defining $\bar{\Delta}$ in $\Pbf$. The cotangent sequence
\[ \begin{diagram} \Ical/\Ical^2 & \rTo^d & \bar{i}^*\Omega^1_{\Pbf/\KK} & \rTo & \Omega^1_{\bar{\Delta}/\KK} & \rTo & 0 \end{diagram} \]
then gives rise to the diagram
\begin{equation}
\label{EqCotDiagram}
\begin{diagram}
0 & & 0 \\
\uTo & & \uTo \\
\Omega^1_{\bar{\Delta}/\KK} & \rTo & \Omega^1_{\bar{\Delta}/\Delta} \\
\uTo & & \uTo_\rho \\
\bar{i}^*\Omega^1_{\Pbf/\KK} & \rTo & p^*\Omega^1_{\PProj(W)/\KK} \\
\uTo & & \uTo \\
\Ical/\Ical^2 & \rDashto & \ker\rho
\end{diagram}
\end{equation}
whose middle rows come from \eqref{EqZJDiagram}. Thus there is an induced map $\Ical/\Ical^2\to\ker\rho$ making \eqref{EqCotDiagram} commute.
For $i,j\geq 0$, let $F_{i,j}:=\frac{\partial^{i+j}}{\partial^i x\partial^j y}F$. Then $\Ical$ is defined by the sections $\{F_{1,0},F_{0,1}\}$ of $\Ocal(1,n-1)$. We claim that the composition $\Ical/\Ical^2\to\bar{i}^*\Omega^1_{\Pbf/\KK}\to p^*\Omega^1_{\PProj(W)/\KK}$ factors through a map $\chi:\Ical/\Ical^2\to\Jcal\otimes p^*\Omega^1_{\PProj(W)/\KK}$ given via
\begin{align*}
\chi(F_{0,1}) &:= F_{2,0}\ dx+F_{1,1}\ dy \\
\chi(F_{1,0}) &:= F_{1,1}\ dx+F_{0,2}\ dy.
\end{align*}
The kernel of the surjection $\bar{i}^*\Omega^1_{\Pbf/\KK}\to\Omega^1_{\bar{\Delta}/\KK}$ is the subsheaf of $\bar{i}^*\Omega^1_{\Pbf/\KK}$ generated by the sections
\begin{align*}
\label{EqdF}
dF_{1,0} &= \alpha_0\ da_0+\cdots+\alpha_n\ da_n + F_{2,0}\ dx+F_{1,1}\ dy \\
dF_{0,1} &= \beta_0\ da_0+\cdots+\beta_n\ da_n + F_{1,1}\ dx+F_{0,2}\ dy,
\end{align*}
where $\alpha_0,\dots,\alpha_n,\beta_0,\dots,\beta_n$ are sections of $\Ocal(0,n-1)$. The summands $\alpha_0\ da_0+\cdots+\alpha_n\ da_n$ and $\beta_0\ da_0+\cdots+\beta_n\ da_n$ are in the component $\pi^*i^*\Omega^1_{\PProj(V)/\KK}$, while the summands $F_{2,0}\ dx+F_{1,1}\ dy$ and $F_{1,1}\ dx+F_{0,2}\ dy$ are in the component $p^*\Omega^1_{\PProj(W)/\KK}$. Since $\Jcal$ is generated by $F_{i,2-i}$ for $0\leq i\leq 2$, the image of the composition $\Ical/\Ical^2\to\bar{i}^*\Omega^1_{\Pbf/\KK}\to p^*\Omega^1_{\PProj(W)/\KK}$ lies in the image of the injection $\Jcal\otimes p^*\Omega^1_{\PProj(W)/\KK}\hookrightarrow p^*\Omega^1_{\PProj(W)/\KK}$, proving the claim.
We now show that $\chi$ is surjective by a local calculation. Recall that, on $\bar{\Delta}$, for $i\in\{0,1\}$,
\[ 0 = (n-1)F_{i,1-i} = xF_{i+1,1-i}+yF_{i,2-i}. \]
On the affine piece $\{y\neq 0\}$, we therefore have
\begin{align*}
F_{i,2-i} &= -\frac{x}{y}F_{i+1,1-i} \\
&= (-1)^{2-i}\left(\frac{x}{y}\right)^{2-i}F_{2,0}.
\end{align*}
In particular, since $\Omega^1_{\PProj(W)/\KK}$ is generated by $\frac{1}{y^2}(y\ dx-x\ dy)$ on the affine piece $\{y\neq 0\}$, $\Jcal\otimes p^*\Omega^1_{\PProj(W)/\KK}$ is generated by
\[ F_{2,0}\frac{1}{y^2}(y\ dx-x\ dy) \]
on this affine piece. On the other hand,
\begin{eqnarray*}
F_{i+1,1-i}\ dx+F_{i,2-i}\ dy
&=& (-1)^{1-i}\left(\frac{x}{y}\right)^{1-i}F_{2,0}\ dx+(-1)^{2-i}\left(\frac{x}{y}\right)^{2-i}F_{2,0}\ dy \\
&=& (-1)^{1-i}y\left(\frac{x}{y}\right)^{1-i}F_{2,0}\frac{1}{y^2}(y\ dx-x\ dy)
\end{eqnarray*}
Thus, taking $i=1$, the image of $\chi$ is also seen to be generated by $F_{2,0}\frac{1}{y^2}(y\ dx-x\ dy)$ on this affine piece, and $\chi$ is therefore surjective thereupon. The argument that $\chi$ is surjective on the other affine piece $\{x\neq 0\}$ is entirely symmetric.
The arguments just given imply that the injection $\Jcal\otimes p^*\Omega^1_{\PProj(W)/\KK}\to p^*\Omega^1_{\PProj(W)/\KK}$ maps $\Jcal\otimes p^*\Omega^1_{\PProj(W)/\KK}$ into $\ker\rho:p^*\Omega^1_{\PProj(W)/\KK}\to\Omega^1_{\bar{\Delta}/\Delta}$. To prove the result, it remains to show that the image of $\Jcal\otimes p^*\Omega^1_{\PProj(W)/\KK}$ is in fact all of $\ker\rho$. To do this, we restrict to an affine open subset $U$ of $\bar{\Delta}$ on which $\Omega^1_{\bar{\Delta}/\Delta}$ is trivial. Being a quotient of the invertible module $p^*\Omega^1_{\PProj(W)}$, $\Omega^1_{\bar{\Delta}/\Delta}$ is a cyclic module on that affine piece and, applying the local trivialization identifies $\Gamma(U,\ker\rho)$ with an ideal $I\subseteq\Gamma(U,\Ocal_{\bar{\Delta}})$. The above arguments show that $I$ contains $\Gamma(U,\Jcal)$, which, since $\bar{\Gamma}$ is smooth and connected, is prime of codimension one. Hence any ideal properly containing $\Gamma(U,\Jcal)$ has codimension at least two.
It follows from \cite[Proposition 5.1]{Chi00} that $\Omega^1_{\bar{\Delta}/\Delta}$ is at least supported at all points of $\Gamma$ outside of the self-intersection locus. Thus, as the set of such points is dense in $\Gamma$, it is supported at least on $\Gamma$, a codimension one set.
\end{proof}
Once we have characterized $\Omega^1_{\bar{\Delta}/\Delta}$, the following theorem, which motivates the definition of the open swallowtail, is immediate.
\begin{theorem}
The universal derivation $d:\Ocal_{\bar{\Delta}}\to\Omega^1_{\bar{\Delta}/\Delta}$ is surjective.
\end{theorem}
\begin{proof}
Locally, say, on the affine piece $\{a_0\neq 0, y\neq 0\}$, $\Omega^1_{\bar{\Delta}/\Delta}$ is cyclic and $d$ takes a local section $g\left(t,\frac{a_1}{a_0},\dots,\frac{a_n}{a_0}\right)\in\Ocal_{\bar{\Delta}}$ to $\frac{\partial g}{\partial t}\ dt$, where $t:=x/y$.
\end{proof}
\begin{definition}
\label{DefOpenSwallowtail}
The $n$-th \textit{(algebraic) open swallowtail} $\Scal_n$ is the kernel of $d:\Ocal_{\bar{\Delta}}\to\Omega^1_{\bar{\Delta}/\Delta}$. It is an $\Ocal_\Delta$-subalgebra of $\Ocal_{\bar{\Delta}}$. We refer $\Scal_n$ via $\Scal$ when the $n$ is understood.
\end{definition}
The following proposition shows that $\Scal$ indeed defines a determinantal formula for $D_n$.
\begin{proposition}
\label{PropOSProps}
The open swallowtail is a maximal Cohen-Macaulay module of rank one over $\Ocal_\Delta$.
\end{proposition}
\begin{proof}
We have that $\Ocal_{\bar{\Delta}}$ is maximal Cohen-Macaulay over $\Ocal_\Delta$ and, by Proposition \ref{PropGammaBarCM} and Theorem \ref{ThmCharOmega1}, $\Omega^1_{\bar{\Delta}/\Delta}$ has codepth one. The exact sequence
\[ \begin{diagram} 0 & \rTo & \Scal & \rTo & \pi_*\Ocal_{\bar{\Delta}} & \rTo & \pi_*\Omega^1_{\bar{\Delta}/\Delta} & \rTo & 0 \end{diagram} \]
of $\Ocal_\Delta$ modules implies that the depth of $\Scal$ is at least the minimum of $\depth\Ocal_{\bar{\Delta}}$ and $\depth\Omega^1_{\bar{\Delta}/\Delta}+1$. Thus $\Scal$ is maximal Cohen-Macaulay. That $\Scal$ has rank one follows from its being embedded in $\Ocal_{\bar{\Delta}}$.
\end{proof}
We shall see that the formula defined by $\Scal$ is nontrivial and not equivalent to the classical formulae in Section \ref{SecConstPresMatrix}.
\section{\label{SecConstPresMatrix}Construction of the presentation matrix}
In this section we show how to construct a presentation matrix for $\Scal$ using the mapping cone construction applied to the short exact sequence
\[ \begin{diagram} 0 & \rTo & \Scal & \rTo & \pi_*\Ocal_{\bar{\Delta}} & \rTo^d & \pi_*\Omega^1_{\bar{\Delta}/\Delta} & \rTo & 0. \end{diagram} \]
We shall see in Section \ref{SecCayleyMethod} that $p_{V*}\Ocal_{\bar{\Delta}}$ and $p_{V*}\Omega^1_{\bar{\Delta}/\Delta}$, over $\PProj(V)$, have resolutions of the form
\[ \begin{diagram} 0 & \rTo & F_1 & \rTo^A & F_0 & \rTo & p_{V*}\Ocal_{\bar{\Delta}} & \rTo & 0 \end{diagram} \]
and, respectively,
\[ \begin{diagram} 0 & \rTo & G_2 & \rTo^{\partial_2} & G_1 & \rTo^{\partial_1} & F_0 & \rTo & p_{V*}\Omega^1_{\bar{\Delta}/\Delta} & \rTo & 0. \end{diagram} \]
We obtain the mapping cone diagram
\begin{equation} \label{EqMappingCone} \begin{diagram}
0 & & 0 & & G_2 \\
\dTo & & \dTo & & \dTo_{\partial_2} \\
G_2 \oplus F_1 & \rTo & F_1 & \rTo_{D_1} & G_1 \\
\dTo_B & & \dTo_A & & \dTo_{\partial_1} \\
G_1 \oplus F_0 & \rTo & F_0 & \rTo_{D_0} & G_0 \\
\dTo_E & & \dTo & & \dTo \\
G_0 & & 0 & & 0.
\end{diagram} \end{equation}
The maps $D_0$ and $D_1$ are liftings of the universal derivation $d$ to the resolutions of $\Ocal_{\bar{\Delta}}$ and $\Omega^1_{\bar{\Delta}/\Delta}$. The map $B$ is given by the matrix
\[ \begin{gmatrix} \partial_2 & D_1 \\ 0 & A \end{gmatrix}, \]
while the map $E$ is given by the matrix
\[ \begin{gmatrix} \partial_1 & D_0 \end{gmatrix}. \]
Since $D_0$ is surjective, $E$ is surjective as well, so the complex
\[ \begin{diagram} 0 & \rTo & G_2\oplus F_1 & \rTo^B & G_1\oplus F_0 & \rTo^E & G_0 & \rTo & 0 \end{diagram} \]
is exact except at $G_1\oplus F_0$, where the homology is precisely $\Scal$. Therefore, we desire a presentation of the form
\[ \begin{diagram} G_2\oplus F_1 & \rTo^{\bar{B}} & G_1\oplus\ker D_0 & \rTo & \Scal & \rTo & 0, \end{diagram} \]
where $\bar{B}$ is given by the matrix
\[ \begin{gmatrix} \partial_2 & D_1 \\ 0 & \bar{A} \end{gmatrix}, \]
$\bar{A}$ being the restriction of $A$ to $A^{-1}(\ker D_0)$.
To construct the presentation matrix $\bar{B}$, we need three data:
\begin{itemize}
\item the matrix $\bar{A}$,
\item the matrix $\partial_2$, and
\item the lifting $D_1$.
\end{itemize}
In Subsection \ref{SecCayleyMethod} we address the construction of $A$ and $\partial_2$, while in Subsection \ref{SecLiftingD} we address the construction of $D_1$. The restriction from $A$ to $\bar{A}$ is then quite easy and we address that at the end of this section.
\subsection{\label{SecCayleyMethod}Resolving $\Ocal_\Delta$ and $\Ocal_\Gamma$}
In this subsection, we construct resolutions of $\Ocal_{\bar{\Delta}}$ and $\Omega^1_{\bar{\Delta}/\Delta}$ --- or, rather, modules which are locally isomorphic to those. In view of Theorem \ref{ThmCharOmega1}, we replace the latter module with $\Ocal_{\bar{\Gamma}}$. Originally due to Cayley, the method we use was developed to construct determinantal formulae for the equation of the \textit{dual variety} $X^\vee$ of a given projective variety $X$. In our case, the variety $X$ is $\PProj(W)$, embedded via the $n$th Veronese embedding in $\PProj^n$, and $X^\vee$ is $\Delta_n$. Our treatment omits many of the technical points required for the general case. See \cite[Chapter 2]{GKZ94} for a thorough, modern treatment of this method.
\begin{figure}
\[ \begin{diagram}[width=6cm]
0 & 0 \\
\uTo & \uTo \\
\Ocal_{\bar{\Delta}} & \Ocal_{\bar{\Gamma}} \\
\uTo & \uTo \\
\Ocal & \Ocal \\
\uTo_{\mbox{\tiny $\begin{gmatrix} F_x & F_y \end{gmatrix}$}} & \uTo_{\mbox{\tiny $\begin{gmatrix} F_{xx} & F_{xy} & F_{yy} \end{gmatrix}$}} \\
\Ocal(-1,1-n)^{\oplus 2} & \Ocal(-1,2-n)^{\oplus 3} \\
\uTo_{\mbox{\tiny $\begin{gmatrix} F_y \\ -F_x \end{gmatrix}$}} & \uTo_{\mbox{\tiny $\begin{gmatrix} 0 & F_{yy} & -F_{xy} \\ -F_{yy} & 0 & F_{xx} \\ F_{xy} & -F_{xx} & 0 \end{gmatrix}$}} \\
\Ocal(-2,2-2n) & \Ocal(-2,4-2n)^{\oplus 3} \\
\uTo & \uTo_{\mbox{\tiny $\begin{gmatrix} F_{xx} \\ F_{xy} \\ F_{yy} \end{gmatrix}$}} \\
0 & \Ocal(-3,6-3n) \\
& \uTo \\
& 0
\end{diagram}. \]
\caption{\label{FigKoszulComplexes} Koszul complexes resolving $\Ocal_{\bar{\Delta}}$ and $\Ocal_{\bar{\Gamma}}$}
\end{figure}
The normalizations $\bar{\Delta}$ and $\bar{\Gamma}$ of the discriminant $\Delta$ and respectively the caustic $\Gamma$ are global complete intersections in $\Pbf$, so their structure sheaves are resolved over $\Pbf$ via Koszul complexes, as shown in Figure \ref{FigKoszulComplexes}. To construct the required maps, we first twist the Koszul complex for $\bar{\Delta}$ by $\Ocal_\Pbf(0,n-2)$ and the Koszul complex for $\bar{\Gamma}$ by $\Ocal_\Pbf(0,n-3)$. We then construct the spectral sequence associated to the derived push-forward functor $Rp_{V*}$ and recover the required maps therefrom.
It follows from the projection formula that, for $l,p,q\in\ZZ$,
\[R^lp_{\PProj(V)*}\Ocal_{\Pbf}(p,q)\cong\Ocal_{\PProj(V)}(p)\otimes_\KK H^l(\PProj(W),\Ocal_{\PProj(W)}(q)).\]
In particular, $R^0p_{\PProj(V)*}\Ocal_{\Pbf}(p,q)=0$ when $q<0$ and $R^1p_{\PProj(V)*}\Ocal_{\Pbf}(i,j)$ when $q>-2$. The first page of the spectral sequence for $\Ocal_{\bar{\Delta}}$ is
\begin{align*}
\Ocal_{\PProj(V)}\otimes_\KK H^0(\PProj(W),\Ocal_{\PProj(W)}&(n-2)) \\ \\
& \Ocal_{\PProj(V)}(-2)\otimes_\KK H^1\left(\PProj(W),\Ocal_{\PProj(W)}(-n)\right),
\end{align*}
while the first page for $\Ocal_{\bar{\Gamma}}$ is
\begin{align*}
\Ocal_{\PProj(V)}\otimes_\KK H^0(\PProj(W),\Ocal_{\PProj(W)}&(n-3)) \\ \\
& \begin{diagram}
\Ocal_{\PProj(V)}(-2)\otimes_\KK H^1\left(\PProj(W),\Ocal_{\PProj(W)}(1-n)^3\right) \\
\uTo_{d_1^{-3,1}} \\
\Ocal_{\PProj(V)}(-3)\otimes_\KK H^1\left(\PProj(W),\Ocal_{\PProj(W)}(3-2n)\right).
\end{diagram}
\end{align*}
In both cases, the second page of the spectral sequence is
\[ \begin{diagram}
\Ocal_{\PProj(V)}\otimes_\KK H^0\left(\PProj(W),\Ocal_{\PProj(W)}(n-k)\right) & & \\
& \luTo_{d_2^{-2,1}} & \\
& & \coker d_1^{-3,1},
\end{diagram} \]
where $k=2$ for $\bar{\Delta}$ and $k=3$ for $\bar{\Gamma}$. The cokernel of $d_2^{-2,1}$ is $\pi_*\Ocal_{\bar{\Delta}}(n-2)$, respectively $\pi_*\Ocal_{\bar{\Gamma}}(n-3)$, and the spectral sequence degenerates after this step. The map $A$ is then just a lifting of $d_2^{-2,1}$ to $\Ocal_{\PProj(V)}(-2)\otimes_\KK H^1\left(\PProj(W),\Ocal_{\PProj(W)}(-n)\right)$, while the map $\partial_2$ is just $d_1^{-3,1}$ in the diagram above.
We seek explicit formulae for $d_2^{-2,1}$ and $d_1^{-3,1}$. It is convenient to compute in the fibre over a fixed point $[a_0:\dots:a_n]\in\PProj(V)$. The restriction of the Koszul complex to this fibre is a map of vector spaces whose differentials vary polynomially in the coordinates $a_0,\dots,a_n$. In doing so, we replace the sheaves of the Koszul complex with \v{C}ech complexes which compute the cohomology of each term. We show the resulting double complex for both cases in Figure \ref{FigHCSpectralSequence}. Therein, $k=2$ for $\Ocal_{\bar{\Delta}}$ and $k=3$ for $\Ocal_{\bar{\Gamma}}$, and we use the convention that $\binom{k}{3}=0$ if $k=2$.
\begin{figure}
\[ \begin{diagram}[height=1.4cm,loose]
\begin{array}{c} \Gamma\left(U_x,\Ocal(n-k)\right) \\ \bigoplus \\ \Gamma\left(U_y,\Ocal(n-k)\right) \end{array} & \rTo_{d_H^{0,0}} & \Gamma\left(U_{xy},\Ocal(n-k)\right) \\
\uTo_{d_V^{-1,0}} & & \uTo_{d_V^{-1,1}} \\
\begin{array}{c} \Gamma\left(U_x,\Ocal(-1)^k\right) \\ \bigoplus \\ \Gamma\left(U_y,\Ocal(-1)^k\right) \end{array} & \rTo_{d_H^{-1,0}} & \Gamma\left(U_{xy},\Ocal(-1)^k\right) \\
\uTo_{d_V^{-2,0}} & & \uTo_{d_V^{-2,1}} \\
\begin{array}{c} \Gamma\left(U_x,\Ocal(k-n-2)^{\oplus\binom{k}{2}}\right) \\ \bigoplus \\ \Gamma\left(U_y,\Ocal(k-n-2)^{\oplus\binom{k}{2}}\right) \end{array} & \rTo_{d_H^{-2,0}} & \Gamma\left(U_{xy},\Ocal(k-n-2)^{\oplus\binom{k}{2}}\right) \\
\uTo_{d_V^{-3,0}} & & \uTo_{d_V^{-3,1}} \\
\begin{array}{c} \Gamma(U_x,\Ocal(2(k-n)-3)^{\oplus\binom{k}{3}}) \\ \bigoplus \\ \Gamma(U_y,\Ocal(2(k-n)-3)^{\oplus\binom{k}{3}}) \end{array} & \rTo_{d_H^{-k,0}} & \Gamma(U_{xy},\Ocal(2(k-n)-3)^{\oplus\binom{k}{3}}) \\
\end{diagram} \]
\caption{\label{FigHCSpectralSequence}Double complex for $\Kcal^k_\bullet$ over $[a_0:\cdots:a_n]$.}
\end{figure}
The differentials $d_1^{-i,0}$ and $d_1^{-i,1}$ are just the maps of the associated Koszul complex restricted to the given fibre. In particular, in the case of $\Ocal_{\bar{\Gamma}}$, the matrix of the last map $d_1^{-3,1}$ is a \textit{generalized Sylvester matrix} whose structure we now describe.
The map $d_1^{-3,1}$ is
\[ g\mapsto\left(\frac{\partial^2F}{\partial x^2}g,\frac{\partial^2F}{\partial x\partial y}g,\frac{\partial^2F}{\partial y^2}g\right), \]
where $g$ is a homogeneous element of $\KK[x^{-1},y^{-1}]$ of degree $3-2n<0$. The associated matrix is therefore divided horizontally into $3$ blocks of $n-2$ rows each. Each block is associated with a given second-order partial derivative of $F$. Each block is of the form
\[ \begin{gmatrix}
\alpha_0 & \alpha_1 & \cdots & \alpha_{n-2} \\
& \alpha_0 & \alpha_1 & \cdots & \alpha_{n-2} \\
& & \ddots & \ddots & & \ddots \\
& & & \alpha_0 & \alpha_1 & \cdots & \alpha_{n-2}
\end{gmatrix}, \]
where $\alpha_0,\dots,\alpha_{n-2}$ are the coefficients of the associated partial derivative of $F$. In particular, the entries are linear in the coefficients $a_0,\dots,a_n$.
We now characterize the map
\[A:H^1\left(\PProj(W),\Ocal(-n)\right)\to H^0\left(\PProj(W),\Ocal(n-2)\right).\]
It will be convenient to treat at the same time the corresponding map in the spectral sequence for $\bar{\Gamma}$, so we shall do so with the same notational conventions as above. Since $H^i(\PProj(W),\Ocal(-1))=0$ for all $i$, the map
\[d_H^{-1,0}:\Gamma\left(U_x,\Ocal(-1)^k\right)\oplus\Gamma\left(U_y,\Ocal(-1)^k\right)\to\Gamma\left(U_{xy},\Ocal(-1)^k\right)\]
is an isomorphism. Thus the map
\[\left(d_H^{-1,0}\right)^{-1}:\Gamma\left(U_{xy},\Ocal(-1)^k\right)\to\Gamma\left(U_x,\Ocal(-1)^k\right)\oplus\Gamma\left(U_y,\Ocal(-1)^k\right)\]
is well-defined and $A$ is the composition
\begin{eqnarray*}
\Gamma\left(U_{xy},\Ocal(k-n-2)^{\oplus\binom{k}{2}}\right) & \overset{d_V^{-2,1}}{\longrightarrow} & \Gamma\left(U_{xy},\Ocal(-1)^k\right) \\
& \overset{\left(d_H^{-1,0}\right)^{-1}}{\longrightarrow} & \Gamma\left(U_x,\Ocal(-1)^k\right)\oplus\Gamma\left(U_y,\Ocal(-1)^k\right) \\
& \overset{d_V^{-1,0}}{\longrightarrow} & \Gamma\left(U_x,\Ocal(n-k)\right)\oplus\Gamma\left(U_y,\Ocal(n-k)\right)
\end{eqnarray*}
restricted to $H^1\left(\PProj(W),\Ocal(k-n-2)^{\oplus\binom{k}{2}}\right)$.
In the case of $\Ocal_{\bar{\Delta}}$, we obtain the classical \textit{B\'ezout formula} for $D_n$, which we recall here. For a homogeneous binary form $f(x,y)$ of degree $n$, set
\[ \Bcal_P(x_0,y_0,x_1,y_1):=\frac{f_x(x_0,y_0)f_y(x_1,y_1)-f_y(x_0,y_0)f_x(x_1,y_1)}{x_0y_1-x_1y_0}. \]
Then $\Bcal_P(x_0,y_0,x_1,y_1)$ is a bihomogeneous polynomial which we write
\[ \Bcal_P(x_0,y_0,x_1,y_1)=\sum_{i,j=0}^{n-2}b_{ij}x_0^iy_0^{n-i-2}x_1^jy_1^{n-j-2}. \]
The \textit{B\'ezout matrix} is the matrix $B_P$ with entries $b_{ij}$. It gives a determinantal formula for $D_n$. The following proposition is proved in \cite{GKZ94}.
\begin{proposition}[\cite{GKZ94}, Chapter 2, Proposition 5.4]
The matrix $B_P$ presents precisely the map $A$ as defined above.
\end{proposition}
\subsection{\label{SecLiftingD}Lifting the universal derivation}
We now describe how to construct the liftings $D_0$ and $D_1$ of the universal derivation $d$ to the resolutions of $\Ocal_{\bar{\Delta}}$ and $\Ocal_{\bar{\Gamma}}$. As in the previous, we fix a point $f\in\PProj(V)$ and work in the fibre of $p_V:\Pbf\to\PProj(V)$ over $f$.
There is one difficulty: while the universal derivation
\[ d:p_{V*}\Ocal_{\bar{\Delta}}\to p_{V*}\Omega^1_{\bar{\Delta}/\Delta} \]
is a well-defined map of $\Ocal_{\PProj(V)}$-modules, it cannot be twisted to form a map
\[ p_{V*}\left(\Ocal_{\bar{\Delta}}(n-2)\right)\to p_{V*}\left(\Omega^1_{\bar{\Delta}/\Delta}(n-3)\right). \]
We shall therefore construct maps $D_0$ and $D_1$ as in \eqref{EqMappingCone} and such that $D_0$ is a lifting of $d$ on the affine subset $U_y=\{y\neq 0\}$ of $\Pbf$. The mapping cone construction will then yield a module $\Scal'$ which is isomorphic to $\Scal$ on $U_y$, but may not agree with $\Scal$ globally. The affine piece $U_y$ corresponds to univariate polynomials of degree $n$, so this restriction suffices for our purposes.
As in the previous subsection, we shall fix a point $f\in\PProj(V)$ and compute in the fibre of $p_V$ over $f$. On $U_y$, $\Omega^1_{\PProj(W)/\KK}$ is trivial, being generated freely by $d(x/y)=\frac{1}{y^2}(y\ dx-x\ dy)$. In addition $\Ocal_{\PProj(W)}(i)$ is trivial for every $i$; the map $g\mapsto y^i g$ is an isomorphism $\Gamma\left(U_y,\Ocal_{\PProj(W)}\right)\to\Gamma\left(U_y,\Ocal_{\PProj(W)}(i)\right)$. We define
\[\tilde{D}_0:\Gamma\left(U_y,\Ocal_{\PProj(W)}(n-2)\right)\to\Gamma\left(U_y,\Omega^1_{\PProj(W)/\KK}(n-3)\right)\]
by composing with the local trivializations: for $h\in\Gamma(U_y,\Ocal_{\PProj(W)}(n-2))$, $\tilde{D}_0(h)=y^{n-3}d\left(y^{2-n}h\right)=h_x\ d(x/y)$. We then define
\[D_0:H^0\left(\PProj(W),\Ocal_{\PProj(W)}(n-2)\right)\to H^0\left(\PProj(W),\Omega^1_{\PProj(W)/\KK}(n-3)\right)\]
as the restriction of $\tilde{D}_0$ to $H^0\left(\PProj(W),\Ocal_{\PProj(W)}(n-2)\right)$.
Now we construct $D_1$. To do so, we lift $\tilde{D}_0$ through each map in the spectral sequence through which the homomorphisms
\[H^1\left(\PProj(W),\Ocal_{\PProj(W)}(1-n)^{\oplus 3}\right)\to H^0(\PProj(W),\Ocal_{\PProj(W)}(n-3))\]
and
\[H^1(\PProj(W),\Ocal_{\PProj(W)}(-n))\to H^0(\PProj(W),\Ocal_{\PProj(W)}(n-2))\]
are found.
We begin with the lifting
\[\begin{diagram}
\Gamma\left(U_y,\Omega^1_{\PProj(W)/\KK}(-1)^{\oplus 3}\right) & \rTo & \Gamma\left(U_y,\Omega^1_{\PProj(W)/\KK}(n-3)\right) \\
\uTo_{\tilde{D}_1^{(1)}} & & \uTo_{\tilde{D}_0} \\
\Gamma\left(U_y,\Ocal_{\PProj(W)}(-1)^{\oplus 2}\right) & \rTo & \Gamma(U_y,\Ocal_{\PProj(W)}(n-2))
\end{diagram}.\]
Finding $\tilde{D}_1^{(1)}$ amounts to finding, for given $g_1,g_2\in\Gamma\left(U_y,\Ocal(-1)^{\oplus 2}\right)$, some sections $\tilde{g}_1,\tilde{g}_2,\tilde{g}_3\in\Gamma\left(U_y,\Ocal(-1)^{\oplus 3}\right)$ such that
\[(\tilde{g}_1f_{xx}+\tilde{g}_2f_{xy}+\tilde{g}_3f_{yy})\ d\left(\frac{x}{y}\right)=D_0(g_1f_x+g_2f_y).\]
Using the identities
\begin{align*}
(n-1)f_x &= xf_{xx}+yf_{xy} \\
(n-1)f_y &= xf_{xy}+yf_{yy},
\end{align*}
we compute directly
\begin{align*}
(n-1)&\tilde{D}_0(g_1f_x+g_2f_y) \\
=\ & (\left((n-1)g_1+xg_{1x}\right)f_{xx} + \left((n-1)g_2+yg_{1x}+xg_{2x}\right)f_{xy} \\
& + yg_{2x}f_{yy})\ d\left(\frac{x}{y}\right).
\end{align*}
Thus
\begin{align*}
(n-1)\tilde{g}_1 &= (n-1)g_1+xg_{1x}\\
(n-1)\tilde{g}_2 &= (n-1)g_2+yg_{1x}+xg_{2x}\\
(n-1)\tilde{g}_3 &= yg_{2x}.
\end{align*}
This provides the lifting $\tilde{D}_1^{(1)}$.
The next lifting
\[\begin{diagram}
\Gamma\left(U_{xy},\Omega^1_{\PProj(W)/\KK}(-1)^{\oplus 3}\right) & \rTo & \Gamma\left(U_y,\Omega^1_{\PProj(W)/\KK}(-1)^{\oplus 3}\right) \\
\uTo_{\tilde{D}_1^{(2)}} & & \uTo_{\tilde{D}_1^{(1)}} \\
\Gamma\left(U_{xy},\Ocal_{\PProj(W)}(-1)^{\oplus 2}\right) & \rTo & \Gamma\left(U_y,\Ocal_{\PProj(W)}(-1)^{\oplus 2}\right)
\end{diagram}\]
is easy --- we just use the same definition as for $\tilde{D}_1^{(1)}$. We proceed to the final lifting
\[\begin{diagram}
\Gamma\left(U_{xy},\Omega^1_{\PProj(W)/\KK}(1-n)^{\oplus 3}\right) & \rTo & \Gamma\left(U_{xy},\Omega^1_{\PProj(W)/\KK}(-1)^{\oplus 3}\right) \\
\uTo_{\tilde{D}_1} & & \uTo_{\tilde{D}_1^{(2)}} \\
\Gamma(U_{xy},\Ocal_{\PProj(W)}(-n)) & \rTo & \Gamma\left(U_{xy},\Ocal_{\PProj(W)}(-1)^{\oplus 2}\right)
\end{diagram}.\]
This is tantamount to finding, for a given section $g\in\Gamma(U_{xy},\Ocal_{\PProj(W)}(-n))$, sections \[h_1,h_2,h_3\in\Gamma\left(U_{xy},\Omega^1_{\PProj(W)/\KK}(1-n)^{\oplus 3}\right)\]
such that
\begin{align*}
(n-1)(h_2f_{yy}-h_3f_{xy}) &= (n-1)g_1+xg_{1x} \\
(n-1)(-h_1f_{yy}+h_3f_{xx}) &= (n-1)g_2+yg_{1x}+xg_{2x} \\
(n-1)(h_1f_{xy}-h_2f_{xx}) &= yg_{2x},
\end{align*}
where $g_1:=f_yg$ and $g_2:=-f_xg$. We compute each in turn:
\begin{align*}
(n-1)^2(h_2f_{yy}-h_3f_{xy})
&= y\left((n-1)g+xg_x\right)f_{yy}+x\left(2(n-1)g+xg_x\right)f_{xy}, \\
(n-1)^2(-h_1f_{yy}+h_3f_{xx})
&= y^2g_xf_{yy}-x\left(2(n-1)g+xg_x\right)f_{xx}, \\
(n-1)^2(h_1f_{xy}-h_2f_{xx})
&= -y^2g_xf_{xy}-y\left((n-1)g+xg_x\right)f_{xx}.
\end{align*}
Thus we conclude
\begin{eqnarray}
h_1 &=& -\frac{1}{(n-1)^2}y^2g_x \nonumber\\
h_2 &=& \frac{1}{n-1}y\left(g+\frac{1}{n-1}xg_x\right) \label{EqLiftingD} \\
h_3 &=& -\frac{1}{n-1}x\left(2g+\frac{1}{n-1}xg_x\right). \nonumber
\end{eqnarray}
Thus, for a section $g\in\Gamma(U_{xy},\Ocal_{\PProj(W)}(-n))$, we set
\[ \tilde{D}_1(g):=\left(-\frac{1}{(n-1)^2}y^2g_x,\frac{1}{n-1}y\left(g+\frac{1}{n-1}xg_x\right),-\frac{1}{n-1}x\left(2g+\frac{1}{n-1}xg_x\right)\right). \]
We then define $D_1$ as the restriction of $\tilde{D}_1$ to $H^1\left(\PProj(W),\Ocal_{\PProj(W)}(-n)\right)$.
The map $D_0$ is essentially differentiation with respect to $x$. The kernel of $D_0$ is therefore the sub-vector space of $F_0$ generated by $y^{n-2}$.
\begin{theorem}
The matrix
\begin{equation}
\label{EqPresentOS}
\begin{gmatrix} \partial_2 & D_1 \\ 0 & A_{(y^{n-2})} \end{gmatrix},
\end{equation}
where $\partial_2$ and $D_1$ are as given above and $A_{(y^{n-2})}$ is the row of the B\'ezout matrix $A$ corresponding to the basis element $y^{n-2}$ of $H^0(X,\Ocal(n-2))$, presents a module isomorphic on the open affine set $U_y$ to the open swallowtail $\Scal_n$.
\end{theorem}
We may also use this construction to count the minimal number of generators of $\Scal_n$ on the affine piece $\{a_0\neq 0\}$
\begin{proposition}
\label{PropMinGenerators}
On the affine piece $\{a_0\neq 0\}$, the open swallowtail $\Scal_n$ is minimally generated by $n-2$ elements. In particular, it is not isomorphic to the normalization of $\Delta_n$ and, when $n>3$, not free.
\end{proposition}
\begin{proof}
After restricting to the affine piece $\{a_0\neq 0\}$, the now invertible variable $a_0$ appears in exactly $n-2$ of the $2(n-2)+(n-1)=3n-5$ columns of \eqref{EqPresentOS}. Furthermore, there are invertible elements in each of the $n-1$ columns of $D_1$. None of the other columns has an invertible element. Thus a minimal presentation matrix of $\Scal_n$ is of size $(n-2)\times (n-2)$. On the other hand, since the B\'ezout formula contains no units and is $(n-1)\times (n-1)$, the normalization $\bar{\Delta}$ is minimally $n-1$ generated.
\end{proof}
\begin{example}
We construct a presentation matrix of the open swallowtail for the degree 4 discriminant. In accordance with the above discussion, we construct a presentation of the open swallowtail over the affine piece $\{y\neq 0\}$. The matrix representing $\partial_2$ is
\[\partial_2=\begin{gmatrix}
12a_0 & 6a_1 & 2a_2 & 0 \\
0 & 12a_0 & 6a_1 & 2a_2 \\
3a_1 & 4a_2 & 3a_3 & 0 \\
0 & 3a_1 & 4a_2 & 3a_3 \\
2a_2 & 6a_3 & 12a_4 & 0 \\
0 & 2a_2 & 6a_3 & 12a_4
\end{gmatrix}.\]
The map $D_1$ is given by the formulae \eqref{EqLiftingD} above. We compute
\begin{eqnarray*}
D_1(x^{-3}y^{-1}) &=& \left(-\frac{1}{3}yx^{-4},0,-\frac{1}{3}x^{-2}y^{-1}\right) \\
D_1(x^{-2}y^{-2}) &=& \left(\frac{2}{9}x^{-3},\frac{1}{9}x^{-2}y^{-1},-\frac{4}{9}x^{-1}y^{-2}\right) \\
D_1(x^{-1}y^{-3}) &=& \left(\frac{1}{9}x^{-2}y^{-1},\frac{2}{9}x^{-1}y^{-2},-\frac{5}{9}y^{-3}\right).
\end{eqnarray*}
Thus $D_1$ has the form
\[D_1=\begin{gmatrix}
0 & 0 & \frac{1}{9} \\
0 & 0 & 0 \\
0 & \frac{1}{9} & 0 \\
0 & 0 & \frac{2}{9} \\
-\frac{1}{3} & 0 & 0 \\
0 & -\frac{4}{9} & 0
\end{gmatrix}.\]
The matrix $A$ is the B\'ezout matrix
\[A=\begin{gmatrix}
a_1a_3-16a_0a_4 & 2a_2a_3-12a_1a_4 & 3a_3^2-8a_2a_4 \\
2a_1a_2-12a_0a_3 & 4a_2^2-8a_1a_3-16a_0a_4 & 2a_2a_3-12a_1a_4 \\
3a_1^2-8a_0a_2 & 2a_1a_2-12a_0a_3 & a_1a_3-16a_0a_4
\end{gmatrix}.\]
Putting these together, $\Scal'$ is presented by
\[\Scal'=\coker\begin{gmatrix}
12a_0 & 6a_1 & 2a_2 & 0 & 0 & 0 & \frac{1}{9} \\
0 & 12a_0 & 6a_1 & 2a_2 & 0 & 0 & 0 \\
3a_1 & 4a_2 & 3a_3 & 0 & 0 & \frac{1}{9} & 0 \\
0 & 3a_1 & 4a_2 & 3a_3 & 0 & 0 & \frac{2}{9} \\
2a_2 & 6a_3 & 12a_4 & 0 & -\frac{1}{3} & 0 & 0 \\
0 & 2a_2 & 6a_3 & 12a_4 & 0 & -\frac{4}{9} & 0 \\
0 & 0 & 0 & 0 & \eta_1 & \eta_2 & \eta_3
\end{gmatrix},\]
where
\begin{align*}
\eta_1 &:= a_1a_3-16a_0a_4, \\
\eta_2 &:= 2a_2a_3-12a_1a_4, \\
\eta_3 &:= 3a_3^2-8a_2a_4.
\end{align*}
After applying necessary row operations, we obtain the following minimal presentation matrix:
\[\Scal'=\coker\bgroup\begin{gmatrix}
0 & 12a_0 & 6a_1 & 2a_2 \\
-24a_0 & -9a_1 & 0 & 3a_3 \\
12a_1 & 18a_2 & 18a_3 & 12a_4 \\
\gamma_1 &
\gamma_2 &
\gamma_3 &
0 \\
\end{gmatrix}\egroup,\]
where
\begin{eqnarray*}
\gamma_1 &=& -9\cdot 12a_0\cdot\eta_3-9\cdot 3a_1\cdot\eta_2+3\cdot 2a_2\cdot \eta_1,\\
\gamma_2 &=& -9\cdot 6a_1\cdot\eta_3-9\cdot 4a_2\cdot\eta_2+3\cdot 6a_3\cdot\eta_1, \\
\gamma_3 &=& -9\cdot 2a_2\cdot\eta_3-9\cdot 3a_3\cdot\eta_2+3\cdot 12a_4\cdot\eta_1.
\end{eqnarray*}
Restricting to monic polynomials by setting $a_0=1$ and making a few simplifications, we get a minimal presentation
\[\Gamma(U_y,\Scal)=\coker\bgroup\begin{gmatrix}
3(2a_3-a_1a_2) & 4a_4-a_2^2 \\
\gamma_3-\frac{1}{2}a_1\gamma_2+\frac{3}{16}a_1^2\gamma_1 & \frac{1}{8}a_3\gamma_1-\frac{1}{6}a_2\gamma_2+\frac{1}{16}a_1a_2\gamma_1
\end{gmatrix}\egroup.\]
\end{example}
\section{\label{SecArnold}The construction of Arnol'd}
The original definition of the open swallowtail is was given by Arnol'd in \cite{Arn81}. In this section, we describe his construction and show that it is equivalent to Definition \ref{DefOpenSwallowtail}.
To do so, we restrict to the affine subset $\{y\neq 0\ \mbox{and}\ a_0\neq 0\}$ of $\Pbf$. This may be identified with the space of monic polynomials of degree $n$ in one variable $x$. It will be convenient to work in different coordinates, namely, those associated to the \textit{divided powers} of $x$. For $1\leq i\leq n$, set $s_i:=(n!/(n-i)!)a_i$. Then $s_1,\dots,s_n$ are identified with the coefficients of the polynomial
\[ x^{(n)}+s_1x^{(n-1)}+s_2x^{(n-2)}+\cdots+s_n, \]
where $x^{(k)}:=x^k/k!$ is the $k$th \textit{divided power} of $x$. For $n\geq k>0$, differentiation of a polynomial in $x$ with respect to $x$ defines a finite map $\Sigma_{n,k}\to\Sigma_{n-1,k-1}$, which in turn defines a tower of varieties terminating at the discriminant $\Delta_n=\Sigma_{n,2}$. With respect to the coordinates $s_1,\dots,s_n$, this map is just projection $(s_1,\dots,s_n)\mapsto(s_1,\dots,s_{n-1})$.
For $n\geq k\geq 2$, we define the $k$th caustic $\Sigma_{n,k}$ to be the locus of polynomials of degree $n$ with a root of multiplicity at least $k$. Differentiation of such a polynomial with respect to the indeterminate gives rise to a polynomial of degree $n-1$ and a root of multiplicity $k$. This defines, for $n\geq k>2$, a finite map $\Sigma_{n,k}\to\Sigma_{n-1,k-1}$. Repeating this process defines a \textit{tower of caustics}
\begin{equation}\label{EqTowerOfCaustics}
\cdots \to \Sigma_{n+i+1,i+3} \to \Sigma_{n+i,i+2} \to \Sigma_{n+i-1,i+1} \to \cdots \to \Sigma_{n,2} = \Delta_n
\end{equation}
terminating at the (affine) classical discriminant. Since each of the maps is finite and birational, the varieties in this tower share a common normalization.
Givental shows in \cite{Giv82} that this tower stabilizes, as in the following proposition.
\begin{proposition}[\cite{Giv82}, Theorem 1]
For $n\geq 2$ and for $i>n-3$, the differentiation map $\Sigma_{n+i,i+2}\to\Sigma_{n+i-1,i+1}$ is an algebraic isomorphism. Thus the tower \eqref{EqTowerOfCaustics} stabilizes at $i=n-3$.
\end{proposition}
This motivates the following definition.
\begin{definition}
The \textit{(geometric) open swallowtail} associated to $\Delta_n$, denoted $\Sigma_n$ (or $\Sigma$ when $n$ is understood), is the variety obtained at the point where the tower \eqref{EqTowerOfCaustics} stabilizes, namely, $\Sigma_{2n-3,n-1}$ in the notation above.
\end{definition}
\begin{figure}
\begin{center}
\includegraphics[width=6cm]{os-picture.pdf}
\end{center}
\caption{\label{FigOpenSwallowtail}A schematic diagram of the open swallowtail $\Sigma_4$}
\end{figure}
The term \textit{open swallowtail} is used because $\Sigma$ is a partial normalization of $\Delta$ in which the self-intersection locus bifurcates, but the caustic remains. This is intuitively clear: a polynomial of degree $2n-3$ cannot have two roots of multiplicity $n-1$. However, it certainly can have a root of multiplicity strictly greater than $n-1$.
Since the differentiation map is finite, the coordinate ring $\Ocal_\Sigma$ of $\Sigma$ is a finite module over $\Ocal_\Delta$ which embeds in $\Ocal_{\bar{\Delta}}$. As such, it agrees with the algebraic open swallowtail introduced above. More precisely, the module $\Gamma(U_y,\Scal)$, to which we shall refer again as $\Scal$, is a module over the affine discriminant $\Ocal_\Delta$ which also by definition embeds in $\Ocal_{\bar{\Delta}}$. We have the following result.
\begin{theorem}
\label{ThmArnoldsOS}
The image of $\Ocal_\Sigma$ in $\Ocal_{\bar{\Delta}}$ equals $\Scal$.
\end{theorem}
To prove Theorem \ref{ThmArnoldsOS}, we need the following technical lemma of Givental which shows how the functions $s_{n-2+i}$ on $\Sigma_{n+k,k+2}$ for $k\geq i>0$ embed in the normalization $\bar{\Sigma}_{n+k,k+2}\cong\bar{\Delta}_n$.
\begin{lemma}[\cite{Giv82}, Lemma 2]
\label{LemmaCharImageSigma}
For $i>0$, $s_{n-2+i}=\pm\int_0^xf''(t)t^{(i-1)}\ dt$.
\end{lemma}
\begin{lemma}
\label{PropDiffIsom}
For $n\geq 2$ and $k\geq 0$, $\Omega^1_{\bar{\Sigma}_{n+k,k+2}/\Sigma_{n+k,k+2}}\cong\Omega^1_{\bar{\Sigma}_{n,2}/\Sigma_{n,2}}$.
\end{lemma}
\begin{proof}
The modules $\Omega^1_{\bar{\Sigma}_{n+k,k+2}/\Sigma_{n+k,k+2}}$ and $\Omega^1_{\bar{\Sigma}_{n,2}/\Sigma_{n,2}}$ are the cokernels of the Jacobian matrices of the normalization maps $\pi:\bar{\Sigma}_{n+k,k+2}\to\Sigma_{n+k,k+2}$ and $\pi':\bar{\Sigma}_{n,2}\to\Sigma_{n,2}$. We use the local coordinates $x,s_1,\dots,s_{n-2}$ for $\bar{\Sigma}_{n+k,k+2}\cong\bar{\Sigma}_{n,2}$ and local coordinates $s_1,\dots,s_{n+k}$, respectively $s_1,\dots,s_n$, for $\Sigma_{n+k,k+2}$, respectively $\Sigma_{n,2}$. It suffices to show that, for $i>1$, the form $ds_{n+i-2}$ is a $\bar{\Sigma}_{n,2}$-linear combination of $ds_1,\dots,ds_{n-1}$. For $i>0$, differentiating the formula for $s_{n+i-2}$ given in Lemma \ref{LemmaCharImageSigma} with respect to the local coordinates on $\bar{\Sigma}_{n,2}$, we obtain the form
\[ ds_{n+i-2} = \pm\left(f''(x)x^{(i-1)}\ dx + \binom{n+i-4}{i-1}x^{(n+i-3)}\ ds_1 + \cdots + \binom{i-1}{i-1}x^{(i)}\ ds_{n-2}\right). \]
Setting $i=1$, we obtain the form
\[ ds_{n-1} = \pm\left(f''(x)\ dx + x^{(n-2)}\ ds_1 + \cdots + x\ ds_{n-2}\right). \]
Therefore, for $i>1$, $ds_{n+i-2}$ is the sum of $\pm x^{(i-1)}ds_{n-1}$ and a suitable $\bar{\Sigma}_{n,2}$-linear combination of $ds_1,\dots,ds_{n-2}$. The claim follows.
\end{proof}
\begin{proof}[Proof of Theorem \ref{ThmArnoldsOS}]
Lemma \ref{PropDiffIsom} shows that $\Omega^1_{\bar{\Sigma}/\Sigma}\cong\Omega^1_{\bar{\Delta}/\Delta}$, which implies that $\Ocal_\Sigma$ is contained in $\Scal$. We claim that the embedding $\Ocal_\Sigma\hookrightarrow\Scal$ is surjective. From Theorem \ref{ThmCharOmega1}, we see that the kernel of $d$ consists of those elements $g\in\Ocal_{\bar{\Delta}}$ which, after being differentiated with respect to $x$, are divisible by $f''$. Such elements are of the form
\[g(x,s_1,\dots,s_{n-2})=\int_0^xh_1(t,s_1,\dots,s_{n-2})f''\ dt+h_2(s_1,\dots,s_{n-2}).\]
Writing $h_1$ as a polynomial in $t$ with coefficients in $\KK[s_1,\dots,s_{n-2}]$, we see that $g-h_2$ is an $\Ocal_\Delta$-linear combination of elements of the form
\[ \int_0^xf''(t)t^{(i-1)}\ dt, \quad i\geq 1 \]
and therefore, by Lemma \ref{LemmaCharImageSigma}, in the image of $\Ocal_\Sigma$. On the other hand, $h_2$ is in the image of $\Ocal_\Delta$ and a fortiori of $\Ocal_\Sigma$. This proves the claim.
\end{proof}
In \cite{Sev04} Sevenheck and van Straten point out that Givental's results in \cite{Giv88} imply that $\Sigma$ is a Cohen-Macaulay variety, and hence that $\Ocal_\Sigma$ is maximal Cohen-Macaulay over $\Ocal_\Delta$. Our results yield a new, algebraic proof that the open swallowtail of Arnol'd is Cohen-Macaulay.
\begin{corollary}
The open swallowtail $\Sigma$ is Cohen-Macaulay.
\end{corollary}
\begin{proof}
Combine Theorem \ref{ThmArnoldsOS} with Proposition \ref{PropOSProps}.
\end{proof}
The following result gives a generating set for $\Ocal_\Sigma$ as an $\Ocal_\Delta$-module. It was first proved by Givental in \cite{Giv88}, but we give an alternative proof using the tools developed here.
\begin{theorem}
\label{ThmOSGens}
The module $\Ocal_\Sigma$ is generated over $\Ocal_\Delta$ by 1 and $s_{n+1},\dots,s_{2n-3}$.
\end{theorem}
\begin{proof}
Clearly $\Ocal_\Sigma$ is generated as an $\Ocal_\Delta$-algebra by the aforementioned elements. From Theorem \ref{ThmArnoldsOS} and Proposition \ref{PropMinGenerators}, $\Ocal_\Sigma$ as an $\Ocal_\Delta$-module has $n-2$ minimal generators. In order to prove the claim, it suffices to show that no element $s_{n+i}$ lies in the submodule generated by the remaining generators $1,s_{n+1},\dots,\hat{s}_{n+i},\dots,s_{2n-3}$. Suppose by way of contradiction otherwise, that
\[ s_{n+i}=\sum_{j=1,\dots,i-1,i+1,\dots,n}f_js_{n+j}. \]
Since $\Ocal_\Sigma$ is graded, we may take the above equation to be quasihomogeneous. Since each $s_{n+i}$ has degree $n+i$, degree considerations indicate that $f_j=0$ for $j>i$, that is
\[ s_{n+i}=\sum_{j=1,\dots,i-1}f_js_{n+j}. \]
But that would imply that the map $\Sigma_{n+i,i+2}\to\Sigma_{n+i-1,i+1}$ were an isomorphism. However, since, for $i\leq n-3$, each map $\Sigma_{n+i,i+2}\to\Sigma_{n+i-1,i+1}$ reduces the dimension of the self-intersection locus, these maps are not isomorphisms. This is a contradiction, and the claim follows.
\end{proof}
\section{\label{SecConductor}The conductor of the open swallowtail}
We now show that the map $\Sigma\to\Delta$ is an isomorphism outside of self-intersection locus of $\Delta$. More precisely, we prove the following result.
\begin{theorem}
\label{ThmConductorOS}
Let $\cfrak$ be the conductor of the map $\Sigma\to\Delta$. Then the closed subset of $\Delta$ defined by $\cfrak$ is the self-intersection locus of $\Delta$.
\end{theorem}
We start with the following immediate corollary of Theorem \ref{ThmSingSigma}.
\begin{proposition}
\label{PropJacODBar}
The closed subset of $\Delta$ defined by the conductor $\dfrak$ of the normalization map $\Ocal_\Delta\hookrightarrow\Ocal_{\bar{\Delta}}$ is the singular locus of $\Ocal_\Delta$. It has two irreducible components: the caustic and the self-intersection locus.
\end{proposition}
We require the following classical result, which describes the behaviour of the discriminant at sufficiently generic points of the caustic.
\begin{lemma}
\label{ThmGenPtCaustic}
Let $p\in\Gamma$ be a point which is not on the self-intersection locus of $\Delta_n$. Then the germ of $\Delta_n$ at $p$ is formally isomorphic to the product of the cuspidal cubic $\Spec\KK[x,y]/(x^3-y^2)$ and a smooth factor.
\end{lemma}
\begin{lemma}
\label{LemmaJacGenRed}
The conductor $\dfrak$ is reduced at points of the caustic which are not in the self-intersection locus.
\end{lemma}
\begin{proof}
Such points correspond to polynomials of degree $n$ with exactly one root of multiplicity exactly three and with all other roots distinct. Lemma \ref{ThmGenPtCaustic} implies that, locally at such a point, $\Delta$ is the product of a smooth factor and the cuspidal cubic. The claim now follows from the equivalent claim for the cuspidal cubic, which is an easy calculation.
\end{proof}
The following lemma indicates that, in the affine setting, $\Omega^1_{\bar{\Delta}/\Delta}$ is a Gorenstein module over $\Ocal_\Delta$.
\begin{lemma}
\label{LemmaOmegaDuality}
We have $\Ext^1_{\Ocal_\Delta}(\Omega^1_{\bar{\Delta}/\Delta},\Ocal_\Delta)\cong\Omega^1_{\bar{\Delta}/\Delta}$.
\end{lemma}
\begin{proof}
Proposition \ref{PropGammaBarCM} and Theorem \ref{ThmCharOmega1} imply that $\Omega^1_{\bar{\Delta}/\Delta}$ is presented as a quotient of $\Ocal_{\bar{\Delta}}$ by a principal ideal thereof. That is, we have an exact sequence
\[ \begin{diagram} 0 & \rTo & \Ocal_{\bar{\Delta}} & \rTo & \Ocal_{\bar{\Delta}} & \rTo & \Omega^1_{\bar{\Delta}/\Delta} & \rTo & 0 \end{diagram} \]
of $\Ocal_{\bar{\Delta}}$-modules. Treating it as an exact sequence of $\Ocal_\Delta$ modules and applying $\Hom_{\Ocal_\Delta}(-,\Ocal_\Delta)$, we obtain the sequence
\[ \begin{diagram} 0 & \rTo & \Hom_{\Ocal_\Delta}(\Ocal_{\bar{\Delta}},\Ocal_\Delta) & \rTo_\eta & \Hom_{\Ocal_\Delta}(\Ocal_{\bar{\Delta}},\Ocal_\Delta) & \rTo & \Ext^1_{\Ocal_\Delta}\left(\Omega^1_{\bar{\Delta}/\Delta},\Ocal_\Delta\right) \\ & \rTo & \Ext^1_{\Ocal_\Delta}(\Ocal_{\bar{\Delta}},\Ocal_\Delta) = 0, \end{diagram} \]
where the vanishing on the right follows from $\Ocal_{\bar{\Delta}}$ being maximal Cohen-Macaulay over the Gorenstein ring $\Ocal_\Delta$. Since $\Ocal_{\bar{\Delta}}$ is a maximal Cohen-Macaulay module on a hypersurface and is presented by a symmetric matrix, it is self-dual. The map $\eta$ is just multiplication by the same non-zerodivisor which presents $\Omega^1_{\bar{\Delta}/\Delta}$. Thus both $\Omega^1_{\bar{\Delta}/\Delta}$ and $\Ext^1_{\Ocal_\Delta}(\Omega^1_{\bar{\Delta}/\Delta},\Ocal_\Delta)$ have the same presentations as $\Ocal_\Delta$-modules, and the claim follows.
\end{proof}
We shall require the following technical lemma, whose easy proof is left to the reader.
\begin{lemma}
\label{LemmaCharConductor}
Suppose that $X\to Y$ is a finite, birational map of irreducible affine varieties with conductor $\cfrak$. Then the map $\Hom_{\Ocal_Y}(\Ocal_X,\Ocal_Y)\to\Ocal_Y$ sending $\alpha$ to $\alpha(1)$ is an isomorphism of $\Hom_{\Ocal_Y}(\Ocal_X,\Ocal_Y)$ onto $\cfrak$.
\end{lemma}
\begin{proof}[Proof of Theorem \ref{ThmConductorOS}]
We begin with the short exact sequence
\[ \begin{diagram} 0 & \rTo & \Ocal_\Sigma & \rTo & \Ocal_{\bar{\Delta}} & \rTo^d & \Omega^1_{\bar{\Delta}/\Delta} & \rTo & 0 \end{diagram} \]
which results from combining the definition of the open swallowtail $\Scal$ with Theorem \ref{ThmArnoldsOS}. Applying $\Hom_{\Ocal_\Delta}(-,\Ocal_\Delta)$, we obtain
\begin{equation}
\label{EqHomExt}
\begin{diagram}
0 & \rTo & \Hom_{\Ocal_\Delta}(\Ocal_{\bar{\Delta}},\Ocal_\Delta) & \rTo^j & \Hom_{\Ocal_\Delta}(\Ocal_\Sigma,\Ocal_\Delta) & \rTo & \Ext^1_{\Ocal_\Delta}\left(\Omega^1_{\bar{\Delta}/\Delta},\Ocal_\Delta\right) & \rTo & 0
\end{diagram},
\end{equation}
where exactness on the right follows from $\Ocal_{\bar{\Delta}}$ being maximal Cohen-Macaulay and $\Ocal_\Delta$ being Gorenstein. Now let $\cfrak$ be the conductor of $\Ocal_\Delta\hookrightarrow\Ocal_\Sigma$ and $\dfrak$ be the conductor of $\Ocal_\Delta\hookrightarrow\Ocal_{\bar{\Delta}}$. Lemma \ref{LemmaCharConductor} implies that $\cfrak\cong\Hom_{\Ocal_\Delta}(\Ocal_\Sigma,\Ocal_\Delta)$ and $\dfrak\cong\Hom_{\Ocal_\Delta}(\Ocal_{\bar{\Delta}},\Ocal_\Delta)$ and that the following diagram commutes:
\[ \begin{diagram}
\dfrak & \rInto^i & \cfrak \\
\dEquals_\sim & & \dEquals_\sim \\
\Hom_{\Ocal_\Delta}(\Ocal_{\bar{\Delta}},\Ocal_\Delta) & \rTo^j & \Hom_{\Ocal_\Delta}(\Ocal_\Sigma,\Ocal_\Delta),
\end{diagram} \]
where $i:\dfrak\to\cfrak$ is the natural inclusion and $j$ is the same map as given in \eqref{EqHomExt}.
Applying these identifications, Lemma \ref{LemmaOmegaDuality}, and Theorem \ref{ThmCharOmega1} to \eqref{EqHomExt}, we obtain a commutative diagram
\begin{equation}
\label{EqCondDiagram}
\begin{diagram}[height=.5cm]
& & 0 & & 0 \\
& & \dTo & & \dTo \\
0 & \rTo & \dfrak & \rTo^i & \cfrak & \rTo & \Ocal_{\bar{\Gamma}} & \rTo & 0 \\ \\
& & \dTo & & \dTo \\ \\
& & \Ocal_\Delta & \rEquals & \Ocal_\Delta \\ \\
& & \dTo & & \dTo \\ \\
& & \Ocal_\Delta/\dfrak & \rTo & \Ocal_\Delta/\cfrak \\ \\
& & \dTo & & \dTo \\
& & 0 & & 0.
\end{diagram}
\end{equation}
The map $i$ in \eqref{EqCondDiagram} is an isomorphism outside of the caustic $\Gamma$. Thus, outside of $\Gamma$, the support of $\cfrak$ equals that of $\dfrak$. Proposition \ref{PropJacODBar} implies that this support is precisely the self-intersection locus.
It remains to show that, among points on $\Gamma$, $\cfrak$ is supported only at the intersection of $\Gamma$ and the self-intersection locus. The snake lemma applied to \eqref{EqCondDiagram} implies the existence of an exact sequence
\[ \begin{diagram}
0 & \rTo & \Ocal_{\bar{\Gamma}} & \rTo & \Ocal_\Delta/\dfrak & \rTo & \Ocal_\Delta/\cfrak & \rTo & 0.
\end{diagram} \]
Let $p$ be a point of $\Gamma$ not in the self-intersection locus. Then, by Theorem \ref{ThmSingSigma}, $p$ is a smooth point of $\Gamma$, so the map $\bar{\Gamma}\to\Gamma$ is an isomorphism at $p$. Also, at $p$, by Lemma \ref{LemmaJacGenRed}, $\Ocal_\Delta/\dfrak\cong\Ocal_\Gamma$. Thus $\Ocal_\Delta/\cfrak$ is not supported at $p$. This proves the claim.
\end{proof}
\section{\label{SecApplication}Application to the root structure of a univariate polynomial}
We now give a compelling application of the matrix of the open swallowtail. The rank of a minimal presentation $A$ of the normalization of $\Delta_n$, specialized to a particular polynomial $f$, is the number of distinct roots of $f$ minus one. This follows from the description of the normalization of $\Delta$ given in Section \ref{SecPreliminaries}. The nullity of the specialization of $A$ to $f$ is the length of the fibre of the normalization map over $f$. The fibre of $f$ consists of pairs $(f,x)$ where $x$ is a repeated root of $f$. The multiplicity of the point $(f,x)$ in the fibre is, in turn, one less than the multiplicity of $x$ as a root of $f$.
However, the rank of the matrix of the normalization is not able to distinguish between degenerate repeated roots and multiple repeated roots. For example, it cannot detect whether a polynomial has $n-2$ distinct roots because it has two distinct pairs of double roots or because it has one root of multiplicity 3. We show here that the matrix of the open swallowtail can make this distinction.
\begin{theorem}
\label{ThmOSRanks}
Let $B$ be a minimal presentation of $\Ocal_\Sigma$ over the ambient ring of $\Ocal_\Delta$. Suppose $B$ is specialized to some polynomial $f(x)=x^n+a_1x^{n-1}+\cdots+a_n$. The nullity of the resulting matrix is at least 2 if and only if $f(x)$ has more than one distinct pair of double roots.
\end{theorem}
\begin{proof}
Fix $i\geq 0$. The ideal defining the locus of polynomials $f(x)$ for which the specialized matrix $B$ has nullity at least $2$ is the radical of the Fitting ideal $F_1(\Sigma)$. By \cite{Eis95}, Proposition 20.6, the points defined by $F_1(\Sigma)$ are those where $\Ocal_\Sigma$ cannot be generated by one element, that is, where the map $\Sigma\to\Delta$ is not an isomorphism. The locus of such points is precisely the zero locus of the conductor of the map $\Sigma\to\Delta$, which, by Theorem \ref{ThmConductorOS}, is precisely the self-intersection locus, whence the claim.
\end{proof}
It is natural to ask what would be the meaning of the nullity of the matrix of the open swallowtail being strictly greater than two. It is likely that, for $i\geq 0$, the nullity of this matrix is at least $i+2$ if and only if the polynomial $f$ is the $i$th derivative of a polynomial with more than one root of multiplicity $i+2$. However, we do not have a proof of this.
\bibliographystyle{amsalpha}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 1,496
|
Kell's was recently sought after by Roswell, GA City Hall to refinish the pews inside the main city hall area. See how Kell's transformed the interior of City Hall.
We'd love to speak with you about your next furniture restoration project.
Or, send us an email to get started.
We're conveniently located in historic Roswell, GA, just minutes from Atlanta, Sandy Springs, Buckhead, Alpharetta, Marietta, Johns Creek — just off Ga. 400, Holcomb Bridge exit.
Copyright © 2019 Kell's Furniture Restoration. All Rights Reserved.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 4,067
|
//
// UIView+Animation.h
// LXFCommonCode
//
// Created by 林洵锋 on 2017/3/2.
// Copyright © 2017年 LXF. All rights reserved.
//
// GitHub: https://github.com/LinXunFeng
// 简书: http://www.jianshu.com/users/31e85e7a22a2
#import <UIKit/UIKit.h>
@interface UIView (Animation)
/** 动画回调方法 */
@property(nonatomic,copy)void(^completeBlock)();
/** 摇动动画 */
- (void) shakeAnimation;
/** 弹跳动画 */
- (void) springingAnimation;
/** 旋转180°动画 */
- (void) trans180DegreeAnimation;
/** 抛物线动画(起始、高度、时间、执行回调方法) */
- (void) throwFrom:(CGPoint)start to:(CGPoint)end height:(CGFloat)height
duration:(CGFloat)duration completedBlock:(void(^)())completedBlock;
/** 点攒动画 */
- (void) praiseAnimation;
#pragma mark - other
// Moves
- (void)moveTo:(CGPoint)destination duration:(float)secs option:(UIViewAnimationOptions)option;
- (void)moveTo:(CGPoint)destination duration:(float)secs option:(UIViewAnimationOptions)option delegate:(id)delegate callback:(SEL)method;
- (void)raceTo:(CGPoint)destination withSnapBack:(BOOL)withSnapBack;
- (void)raceTo:(CGPoint)destination withSnapBack:(BOOL)withSnapBack delegate:(id)delegate callback:(SEL)method;
// Transforms
- (void)rotate:(int)degrees secs:(float)secs delegate:(id)delegate callback:(SEL)method;
- (void)scale:(float)secs x:(float)scaleX y:(float)scaleY delegate:(id)delegate callback:(SEL)method;
- (void)spinClockwise:(float)secs;
- (void)spinCounterClockwise:(float)secs;
// Transitions
- (void)curlDown:(float)secs;
- (void)curlUpAndAway:(float)secs;
- (void)drainAway:(float)secs;
// Effects
- (void)changeAlpha:(float)newAlpha secs:(float)secs;
- (void)pulse:(float)secs continuously:(BOOL)continuously;
//add subview
- (void)addSubviewWithFadeAnimation:(UIView *)subview;
@end
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 1,746
|
\section{Introduction}
Markov random fields (MRFs) \cite{Besag-74,Geman-Geman84,Lauritzen96}
are popular probabilistic graphical representation for encoding the
object's state space using sites and the correlation between local
objects using edges. For example, a grid is a powerful image representation
for pixels, where each site represents a pixel state (e.g., intensity
or label) and an edge represents local relations between neighboring
pixels (e.g., smoothness). In other words, we can encode prior knowledge
about the nature of interaction between objects in a MRF. Once the
model has been built, we can perform inference in a principled manner.
One of the most important MRF inference problems in many applications
is finding \emph{maximum a posteriori} (MAP) assignment. The goal
is to search for the the most probable state configuration of all
objects, or equivalently, the lowest energy of the model. The problem
is known to be NP-complete \cite{Boykov-et-al01}. Given a MRF of
$N$ objects each of which has $S$ states, a brute-force search must
explore $S^{N}$ state configurations. In image denoising, for example,
$N$ is the number of pixels, which can range from $10^{4}-10^{7}$,
and $S$ is the number of pixel intensity levels, which are in the
order of $2^{8}-2^{32}$. This calls for heuristic methods which can
find reasonable solutions in practical time.
There have been a great number of attempts to solve this problem.
An early approach was based on simulated annealing (SA), where the
convergence is also guaranteed for log-time cooling schedule \cite{Geman-Geman84}.
The main drawback of this approach is its low speed -- it takes long
time to achieve reasonably good solutions. Another early attempt involves
local greedy search, and the iterated conditional mode (ICM) \cite{Besag-86}
is probably the most well-known method. In probabilistic terms, it
iteratively seeks for the mode of the local distribution of states
of an object conditioned on the states of nearby objects. Translated
in combinatorial terms, it greedily searches for the local valley
- here the neighborhood size is limited to $S$ - the number of possible
states per object. Not surprisingly, this method is prone to getting
stuck at poor local minima.
A more successful approach is belief-propagation (BP) \cite{Pearl88},
which exploits the \emph{problem structure} better than the ICM. The
main idea is that we maintain a set of messages sending simultaneously
along all edges of the MRF network. A message carries the information
of the state of the sites it originates from, and as a result, any
update of a particular site is informed by messages from all nearby
sites. However, this method can only be guaranteed to work for a limited
class of network structures -- when the network reduces to a tree,
where there are no loops in the network. Another drawback is that
the memory requirement for BP is high - this is generally linear in
the number of edges in the network. More recently, efficient algorithms
with theoretical guarantees have been introduced based on the theory
of graph cuts \cite{Boykov-et-al01}. This class of algorithms, while
being useful in certain computer vision problems, has limitation in
the range of problems it can solve -- the energy formulation must
admits a certain \emph{metric} form \cite{Boykov-et-al01,szeliski2007comparative}.
In effect, these algorithms are not applicable to problems where energy
functions are estimated from data and their functional forms are not
known in priori.
Given this ground, it is desirable to have an approximate algorithm
which is fast enough (better than ICM - for example), consumes little
memory and does not have any specific requirements of network structures
or energy functionals. A meta-heuristic solution has already been
proposed in the combinatorial optimization literature - the Iterated
Local Search (ILS) (e.g. see \cite{Lourenco-et-al03}). Typically,
ILS encourages jumping between local minima, which can be found by
local search methods such as ICM. This algorithm, however, does not
exploit any model-specific information, and thus could be inefficient
for the MAP assignment in MRFs. To this end, we propose a novel algorithm
called \emph{Tree-based Iterated Local Search} (T-ILS), which combines
the strength of BP and ILS. This algorithm exploits the fact that
BP works efficiently on tree structures, in which the time complexity
is linear in the number of edges in the tree, and thus BP is an effective
candidate for locating good local minima. The main difference from
standard tree-based BP is that our trees are \emph{conditional} trees
which are built upon fixing states of neighbor leaves. When combined
with ILS, we have a heuristic algorithm that is less likely to get
stuck in poor local minima, and has better chance to reach high quality
solution, or even global minima.
We evaluate our tree-based inference methods on three benchmark problems:
Ising model, stereo correspondence and image denoising. We empirically
demonstrate that T-ILS attains good performance, while requiring less
training time and memory than the loopy BP, which is one the state-of-the-arts
for these problems.
To summarize, our main contributions are the proposal and evaluation
of fast and lightweight tree-based inference methods in MRFs. Our
choice of trees on $N=W\times H$ images requires only $\mathcal{O}(2D)$
memory where $D=\max\{W,H\}$ and two passes over all sites in the
MRFs per iteration. These are much more economical than $\mathcal{O}(4WH)$
memory and many passes needed by the traditional loopy BP.
This paper is organized as follows. Section~\ref{sec:Problem-Setting}
describes MRFs, the MAP assignment problem, and belief propagation
for trees. In Section~\ref{sec:Iterated-Strong-Local}, the concept
of conditional trees is defined, followed by two algorithms: the strong
local search T-ICM and the global search T-ILS. Section~\ref{sec:exp}
provides empirical support for the performance of the T-ICM and T-ILS.
Finally, Section~\ref{sec:conclusion} concludes the paper.
\section{Related work \label{sec:Related-Work}}
The MAP assignment for Markov random fields (MRFs) as a combinatorial
search problem has attracted a great amount of research in the past
several decades, especially in the area of computer vision \cite{li1995markov}
and probabilistic artificial intelligence \cite{Pearl88}. The problem
is known to be NP-hard \cite{shimony1994finding}. For example, in
labeling of an image of size $W\times H$, the problem space is $S^{WH}$
large, where $S$ is the number of possible labels per pixel.
Techniques for solving the MAP assignment can be broadly classified
into stochastic and deterministic classes. In early days, the first
stochastic algorithms were based on simulated annealing (SA) \cite{Kirkpatrick-et-al83}.
The first application of SA to Markov random fields (MRFs) with provable
convergence was perhaps the work of \cite{Geman-Geman84}. The main
drawback of this method is slow convergence toward good solutions
\cite{szeliski2007comparative}. Nature-inspired algorithms were also
popular, especially the family of genetic algorithms \cite{brown2002markov,kim1998mrf,kim2009markov,maulik2009medical,tseng1999genetic}.
Some attempts using ant colony optimization and tabu-search have also
been made \cite{ouadfel2003mrf,yousefi2012brain}.
Deterministic algorithms started in parallel with iterated conditional
model (ICM) \cite{Besag-86}. It is a simple greedy search strategy
that updates one label at a time. Thus it is very slow and sensitive
to bad initialization. A more successful approach is based on Pearl's
loopy belief propagation (BP) \cite{Pearl88}. Due to its nature of
using local information (called ``messages'') to update ``belief''
about the optimal solution, loopy BP is also called a \emph{message
passing} algorithm. Although loopy BP is neither guaranteed to converge
at all nor to reach global optima, empirical evidences so far have
indicated that it is very competitive against state-of-the-arts in
a variety of image analysis problems \cite{Felzenszwalb-Huttenlocher-IJCV06,szeliski2007comparative}.
Research on improving loopy BP is currently a very active topic in
a range of disciplines, from artificial intelligence, statistical
physics, computer visions to social network analysis \cite{duchi2007uco,Felzenszwalb-Huttenlocher-IJCV06,hazan2010norm,jojic2010accelerated,Kolmogorov-PAMI06,kumar2012message,meltzer2009convergent,zheng2012map,Wainwright-et-al-TR03}.
The most recent development centers around convex analysis \cite{johnson2007lrm,kumar2009analysis,ravikumar2006qpr,Wainwright-et-al05TIT,werner2007linear}.
In particular, the MAP is converted into linear programming with relaxed
constraints from which a mixture of convex optimization and message
passing can be used. Loopy BP also plays role in improving evolutionary
algorithms under probabilistic graphical model representation \cite{larranaga2012review}.
Another powerful class of algorithms in computer vision is graph cuts
\cite{Boykov-et-al01,szeliski2007comparative}. They are, nevertheless,
designed with specific cost functions in mind (i.e. \emph{metric}
and \emph{semi-metric}) \cite{kolmogorov2004energy}, and therefore
inapplicable for generic cost functions such as those resulting from
learning. Again, research in graph cuts is an active area in computer
vision \cite{bhusnurmath2008graph,boykov2004experimental,kohli2010dynamic,kolmogorov2007minimizing,kumar2009map,lempitsky2007logcut}.
Interestingly, it has been recently proved that graph cuts are in
fact loop BP \cite{tarlow2011graph}.
It is fair to say that the deterministic approach has become dominant
due to their performance and theoretical guarantee for certain classes
of problems \cite{kappes2014comparative}. However, the problem is
still unsolved for general settings, thus motivates this paper. Our
approach has both the deterministic and heuristic nature. It relies
on the concept of \emph{strong local search} using the deterministic
method of BP, which is efficient in trees. The local search is strong
because it covers a significant number of sites, rather than just
one, which is often found in other local search methods such as ICM
\cite{Besag-86}. The neighborhood size in our method is very large
\cite{ahuja2002survey}. For typical image labeling problems, the
size is $S^{0.5WH}$ for an image of height $H$ and width $W$ and
label size of $S$. Standard local search like ICM only explores the
neighborhood of size $S$ at a time. Once a strong local minimum is
found, a stochastic procedure based on iterated local search \cite{Lourenco-et-al03}
is applied to escape from it and explores a better local minimum.
The idea of exploiting the trees in MRF in image analysis is not entirely
new. In early days, a spanning tree is used to approximate the entire
MRF \cite{chow1968adp,Wu-Doerschuk-PAMI95}. This method is efficient
but the approximation quality may hurt because the number of edges
in tree is far less than that in the original MRF. Another way is
to built a hierarchical MRF with multiple resolutions \cite{Willsky-IEEE02},
but this is less applicable for flat image labeling problems. Our
method differs from these efforts in that we use trees embedded in
the original graph rather than building an approximate tree. Second,
our trees are conditional -- trees are defined on the values of its
leaves. Third, trees are selected as we go during the search process.
More recently, trees are used in variants of loop BP to specify the
orders which messages are scheduled \cite{Wainwright-et-al05TIT,sontag2009tree}.
Our method can also viewed along this line by differs in the way trees
are built and messages are updated. In particular, our trees are conditional
on neighbor labeling, which is equivalent to collapsing an associated
message to a single value.
Iterated Local Search (ILS), also known as basin hopping \cite{wales1997global},
has been used in related applications such as image registration \cite{cordon2006image},
and structure learning in probabilistic graphical models \cite{biba2008discriminative}.
The success of ILS depends critically on the local search and the
perturbation (basin hopping) strategy \cite{lourencco2010iterated}.
In \cite{wales1997global}, for example, a powerful local search based
on conjugate gradients is essential to reach global solution for the
Lennard-Jones clusters problem. Our work builds strong local search
using tree-based BP on the discrete spaces rather than continuous
ones.
\section{Markov random fields for image labeling \label{sec:Problem-Setting}}
In this section we introduce Markov random fields (MRFs) and the MAP
assignment problem with application to image labeling. A MRF is a
probabilistic way to express the uncertainty in the discrete system
of many interacting variables each of which is characterized by a
set of possible states \cite{Pearl88}. In what follows, we briefly
describe the MRF and its MAP assignment problem and focus on the minimization
of model energy.
Formally, a MRF specifies a random field $\mathbf{x}=\{x_{i}\}_{i=1}^{N}$
over a graph $\mathcal{G}=(\mathcal{V},\mathcal{E})$, where $\mathcal{V}$
is the collection of $N$ sites $\{i\}$, $\mathcal{E}$ is the collection
of edges $\{(i,j)\}$ between sites, and $x_{i}\in L$ represents
states at site $i$. The entire system is random because the uncertainty
in specifying the exact state of each site. One of the main objectives
is to compute the most probable specification, also known as MAP assignment,
which is the main focus of the paper.
\subsection{Image labeling as energy minimization and MAP assignment}
In image labeling problem, an image $\mathbf{y}$ is a collection of pixels
arranged in a particular geometrical way, as defined by the graph
$\mathcal{G}$. Typically, we assume a grid structure over pixels,
where every inner pixel has exactly four nearby pixels. A labeling
$\mathbf{x}$ is the assignment of each pixel $y_{i}$ a corresponding label
$x_{i}$ for all $i=1,2,...,N$.
A full specification of an MRF over the labeling $\mathbf{x}$ given the
image $\mathbf{y}$ can be characterized by its energy. Assuming pairwise
interaction between connected sites, the energy is the sum of local
energies as follows:
\begin{eqnarray}
E(\mathbf{x},\mathbf{y}) & = & \sum_{i\in\mathcal{V}}E_{i}(x_{i},\mathbf{y})+\sum_{(i,j)\in\mathcal{E}}E_{ij}(x_{i},x_{j})\label{eq:energy-decompose}
\end{eqnarray}
The singleton energy $E_{i}(x_{i},\mathbf{y})$ encodes the disassociation
between the label $x_{i}$ and the features of image $\mathbf{y}$ at site
$i$. In image denoising, for example, where $y_{i}$ is the corrupted
pixel and $x_{i}$ is the true pixel we may use $E_{i}(x_{i},\mathbf{y})=\left|x_{i}-y_{i}\right|$
as the cost due to corruption. The pairwise energy $E_{ij}(x_{i},x_{j})$
often captures the smoothness nature of image, that is, two nearby
pixels tend to be similar. For example, $E_{ij}(x_{i},x_{j})=\lambda\left|x_{i}-x_{j}\right|$
is a cost of difference between two labels, where $\lambda>0$ is
a problem-specific parameter.
In image labeling, the task is to find the optimal $\mathbf{x}^{map}$ that
minimizes the energy $E(\mathbf{x},\mathbf{y})$, which now plays the role of the
\emph{cost function:}
\begin{eqnarray}
\mathbf{x}^{map} & = & \arg\min_{\mathbf{x}}E(\mathbf{x},\mathbf{y})\label{eq:MAP}
\end{eqnarray}
For example, in image denoising, this translates to finding a map
of intensity that admits both the low cost of corruption and high
smoothness.
The formal justification for the energy minimization in MRF can be
found through the probability of the labeling defined as
\begin{equation}
P(\mathbf{x}\mid\mathbf{y})=\frac{1}{Z(\mathbf{y})}e^{-E(\mathbf{x},\mathbf{y})}\label{eq:Boltzmann-distribution}
\end{equation}
where $Z(\mathbf{y})$ is the normalization term. Thus minimizing the energy
is equivalent to finding the most probable labeling $\mathbf{x}^{map}$.
As $P(\mathbf{x}\mid\mathbf{y})$ is often called the \emph{posterior} distribution
in computer vision%
\footnote{The term \emph{posterior} comes from the early practice in computer
vision in which $P(\mathbf{y}\mid\mathbf{x})$ is first defined then linked to $P(\mathbf{x}\mid\mathbf{y})$
through the Bayes rule:
\[
P(\mathbf{x}\mid\mathbf{y})=\frac{P(\mathbf{x})P(\mathbf{y}\mid\mathbf{x})}{P(\mathbf{y})}
\]
where $P(\mathbf{x})$ is called the \emph{priori}. However in this paper
we will work directly with $P(\mathbf{x}\mid\mathbf{y})$ for simplicity. The posterior
is recently called conditional random fields in machine learning \cite{lafferty01conditional,truyen-thesis08}%
}, the energy minimization problem is also referred to as \emph{maximum
a posteriori} (MAP) assignment.
\subsection{Local search: Iterated conditional mode \label{sub:Iterated-Conditional-Mode}}
Iterated conditional mode (ICM) \cite{Besag-86} is a simple local
search algorithm. It iteratively finds the local optimal labeling
for each site $i$ as follows
\begin{eqnarray}
x_{i}^{*} & =\arg\min_{x_{i}} & \left\{ E_{i}(x_{i},\mathbf{y})+\sum_{j\in\mathcal{N}(i)}E_{ij}(x_{i},x_{j})\right\} \label{eq:ICM-energy}
\end{eqnarray}
where $\mathcal{N}(i)$ is the set of sites connected to the site
$i$, often referred to as \emph{Markov blanket}. The Markov blanket
shields a site from the long-range interactions with remote sites,
due to a special property of MRF known as \emph{Markov property,}
which states that probability of a label assignment at site $i$ given
all other assignments depends only on the nearby assignments \cite{Hammersley-Clifford71,Lauritzen96}.
The probabilistic interpretation of Eq.~(\ref{eq:ICM-energy}) is
\[
x_{i}^{*}=\arg\max_{x_{i}}P\left(x_{i}\mid\{x_{j}\}_{j\in\mathcal{N}(i)},\mathbf{y}\right)
\]
The local update in Eq.~(\ref{eq:ICM-energy}) is repeated for all
sites until no more improvement can be made. This procedure is guaranteed
to find a local minimum energy in a finite number of steps. However,
the solutions found by the ICM are sensitive to initialization and
often unsatisfactory for image labeling \cite{szeliski2007comparative}.
\subsection{Exact global search on trees: Belief-propagation \label{sec:Belief-Propagation}}
\begin{figure}[htb]
\begin{centering}
\begin{tabular}{c}
\includegraphics[width=0.7\textwidth]{BP.pdf}\tabularnewline
\end{tabular}
\par\end{centering}
\caption{Belief propagation on trees: the two-pass procedure.\label{fig:The-two-pass-procedure:}}
\label{fig:bgr-mrf-tree-2pass}
\end{figure}
Belief-propagation (BP) was first proposed as an inference method
on MRF with tree-like structures in the field of artificial intelligence
\cite{Pearl88}. BP operates by sending \emph{messages} between connecting
sites. For this reason, it is also called \emph{message passing} algorithm.
It is efficient because instead of dealing with all the sites simultaneously,
we need to compute messages passing between two local sites. At each
site, local information modifies the incoming messages before sending
out to neighbor sites.
\paragraph{General BP.}
The general rule is that the message sent from site $j$ to site $i$
in the tree is computed as follows
\begin{eqnarray}
\mu_{j\rightarrow i}(x_{i}) & = & \min_{x_{j}}\left(E_{j}(x_{j},\mathbf{y})+E_{ij}(x_{i},x_{j})+\sum_{k\in\mathcal{N}(j),k\ne i}\mu_{k\rightarrow j}(x_{j})\right)\label{bgr-BP-update}
\end{eqnarray}
That is, the outgoing message is aggregated from all incoming messages,
except for the one in the opposite direction. Messages can be initialized
arbitrarily, and the procedure is guaranteed to stop after finite
steps on trees \cite{Pearl88}. The optimal labeling could be estimated
as follows
\begin{equation}
x_{i}^{map}=\arg\min_{x_{i}}\left(E_{i}(x_{i},\mathbf{y})+\sum_{k\in\mathcal{N}(i)}\mu_{k\rightarrow i}(x_{i})\right)\label{eq:BP-max-marginal}
\end{equation}
It has been proved that the labeling obtained in this way is indeed
globally optimal \cite{Pearl88}, i.e.,
\[
\mathbf{x}^{map}=\arg\min_{\mathbf{x}}E(\mathbf{x},\mathbf{y})
\]
\paragraph{2-pass BP.}
A more efficient variant of BP is the 2-pass procedure, as summarized
in Fig.~\ref{fig:The-two-pass-procedure:}. First we pick one particular
site as the root. Since the graph has no loops, there is a single
path from a site to any other sites in the graph, and each site, except
for the root, has exactly one parent. The procedure consists of two
passes:
\begin{itemize}
\item \emph{Upward pass}: Messages are first initiated at the leaves, and
are set to $0$. Then all messages are sent upward and updated as
messages converging at common parents along the paths from leaves
to the root. The pass stops when all the messages reach the root.
\item \emph{Downward pass}: Messages are combined and re-distributed downward
from the root back to the leaves. The messages are then terminated
at the leaves.
\end{itemize}
The 2-pass BP procedure is a remarkable algorithm: it searches through
the combinatorial space of $S^{N}$ using only $\mathcal{O}\left(2NS^{2}\right)$
operations and $\mathcal{O}\left(2NS\right)$ memory to store all
the messages.
\paragraph{Remark.}
We note in passing that this procedure may be known as \emph{min-sum},
\emph{max-product}, or simply BP. The term max-product comes from
the fact that we can operate in the potential domain by taking the
exponential of negative energies in Eqs.~(\ref{bgr-BP-update},\ref{eq:BP-max-marginal}),
and turn mins into maxes and sums into products.
\subsection{Approximate global search on general graphs: Loopy belief-propagation
\label{sec:Loopy-BP}}
Standard MRFs in image analysis are usually not tree-structured. A
common topology is a grid in which each site represents a pixel and
has four neighbors. Thus the resulting graph has many cycles, rendering
the standard 2-pass BP algorithm useless.
However, an approximation to exact BP has been suggested. Using the
general BP described above, messages are sent across all edges without
worrying about the order \cite{Pearl88}. At each step, the messages
are updated using Eq.~(\ref{bgr-BP-update}). After some stopping
criteria are met, we still use Eq.~(\ref{eq:BP-max-marginal}) to
find the best labeling. This procedure is often called \emph{loopy
BP} due to the presence of loops in the graph. The heuristic has been
shown to be useful in several applications \cite{Murphy-et-al-UAI99}
and this has triggered much research on improving it \cite{duchi2007uco,Felzenszwalb-Huttenlocher-IJCV06,kolmogorov2005otr,Sun-et-alPAMI03,sanghavi2007elr,Wainwright-et-al05TIT,Wainwright-et-al04,weiss2001osm,yanover2003fmm,yanover2006lpr}.
The main drawback of loopy BP is lack of convergence guarantee for
general problems. In our simulation of Ising models (Sec.~\ref{sub:Simulated-Ising-model}),
loop BP clearly fails in the cases where interaction energies dominate
singleton energies, that is $\left|E_{ij}(x_{i},x_{j})\right|\gg\left|E_{i}(x_{i},\mathbf{y})\right|$
for all $i,j$ (see Fig.~\ref{fig:Ising}). Another drawback is that
the memory will be very demanding for large images. For grid-image,
the memory needed is $\mathcal{O}\left(4HWS\right)$ which in the
order of gigabytes, and thus may not be suitable for devices with
small footprint.
\section{Iterated strong local search \label{sec:Iterated-Strong-Local}}
In this section we present a method to exploit the efficiency of the
BP on trees to build strong local search for the MAP assignment problem
in Markov random fields. By `strong', we mean the quality of the local
solution found by the procedure is often much better than standard
greedy local search. Although a typical MRF in computer vision is
not a tree, we observe that it can be thought as a super-imposition
of trees. Second, due to the Markov property of MRFs, described in
Sec.~\ref{sub:Iterated-Conditional-Mode}, variables in a tree can
be shielded from other variables through the Markov blanket of the
tree. This gives rise to the concept of \emph{conditional trees},
which we present subsequently.
\subsection{Conditional trees \label{sec:Conditional-trees} }
\begin{figure}[htb]
\begin{centering}
\begin{tabular}{cc}
\includegraphics[width=0.45\textwidth]{cond_trees} & \includegraphics[width=0.45\textwidth]{cond_trees2}\tabularnewline
\end{tabular}
\par\end{centering}
\caption{Examples of conditional trees on grid (connecting empty sites). Filled
nodes are labeled sites. Arrows indicate absorbing direction, dashes
represent unused interactions. Dotted lines in (c,d) are dummy edge
(with zeros interacting energy) that connects separate sub-trees together
to form a full tree. \label{fig:conditional}}
\end{figure}
For concreteness, let us consider grid-structured MRFs. There are
more than one way to extract a tree out of the grid, as shown in Fig~\ref{fig:conditional}.
In particular, we fix some labeling to some sites, leaving the rest
forming a tree. Consider a tree $\tau$ and let $\mathbf{x}_{\tau}=\{x_{i}\mid i\in\tau\}$,
and $\mathbf{x}_{\neg\tau}=\{x_{i}\mid i\notin\tau\}$. Denote by $\mathcal{N}(\tau)$
the set of sites connecting to $\tau$ but do not belong to $\tau$.
This is essentially the Markov blanket of the tree $\tau$. Thus the
collection of sites $\left(\tau,\mathcal{N}(\tau)\right)$ and the
partial labeling of the neighbor sites $\mathbf{x}_{\mathcal{N}(\tau),}$
forms a conditional tree. The energy of the conditional tree can be
written as:
\begin{eqnarray}
E_{\tau}\left(\mathbf{x}_{\tau},\mathbf{x}_{\mathcal{N}(\tau)},\mathbf{y}\right) & = & \sum_{i\in\tau}E_{i}^{*}(x_{i},\mathbf{y})+\sum_{i,j\in\tau}E_{ij}(x_{i},x_{j})\label{eq:cond-tree-energy}
\end{eqnarray}
where
\begin{equation}
E_{i}^{*}(x_{i},\mathbf{y})=E_{i}(x_{i},\mathbf{y})+\sum_{(i,j)\in\mathcal{E},j\in\mathcal{N}(\tau)}E_{ij}(x_{i},x_{j})\label{eq:absorbing}
\end{equation}
In other words, the interacting energies at the tree border are \emph{absorbed}
into the singleton energy of the ordering sites. In Fig.~\ref{fig:conditional}
the absorbing direction is represented by an arrow.
The minimizer of this conditional tree energy can be found efficiently
using the BP:
\begin{equation}
\hat{\mathbf{x}}_{\tau}=\arg\min_{\mathbf{x}_{\tau}}E_{\tau}\left(\mathbf{x}_{\tau},\mathbf{x}_{\mathcal{N}(\tau)},\mathbf{y}\right)\label{eq:MAP-cond-tree-energy}
\end{equation}
This is due to the fact that Eq.~(\ref{eq:cond-tree-energy}) now
has the form of Eq.~(\ref{eq:energy-decompose}).
One may wonder how the minima of the energy of conditional trees $E_{\tau}\left(\mathbf{x}_{\tau},\mathbf{x}_{\mathcal{N}(\tau)},\mathbf{y}\right)$
relate to the minima of the entire systems $E\left(\mathbf{x},\mathbf{y}\right)$.
We present here two theoretical results of this connection. First,
the local minimum found by Eq.~(\ref{eq:MAP-cond-tree-energy}) is
also a local minimum of $E\left(\mathbf{x},\mathbf{y}\right)$:
\begin{proposition} \label{prop:T-ICM-local-min}
Finding the mode $\hat{\mathbf{x}}_{\tau}$ as in Eq.~(\ref{eq:MAP-cond-tree-energy})
guarantees a local minimization of model energy over all possible
tree labelings. That is
\[
E(\hat{\mathbf{x}}_{\tau},\mathbf{x}_{\neg\tau},\mathbf{y})\le E(\mathbf{x}_{\tau},\mathbf{x}_{\neg\tau},\mathbf{y})
\]
for all $\mathbf{x}_{\tau}\ne\hat{\mathbf{x}}_{\tau}$.
\end{proposition}
\paragraph{Proof:}
The proof is presented in Appendix~\ref{sub:Proof-of-T-ICM-local-opt}.
The second theoretical result is that the local minimum found by Eq.~(\ref{eq:MAP-cond-tree-energy})
is indeed the global minimum of the entire system if all other labels
outside the tree happen to be part of the optimal labeling:
\begin{proposition} \label{prop:MAP-property}
If $\mathbf{x}_{\neg\tau}\in\mathbf{x}^{map}$ then $\hat{\mathbf{x}}{}_{\tau}\in\mathbf{x}^{map}$.
\end{proposition}
\paragraph{Proof:}
We first observe that since $E(\mathbf{x}^{map},\mathbf{y})$ is the lowest energy
then
\begin{eqnarray}
E(\mathbf{x}^{map},\mathbf{y}) & \le & E(\hat{\mathbf{x}}_{\tau},\mathbf{x}_{\neg\tau},\mathbf{y})\label{E-upperboud}
\end{eqnarray}
Now assume that $\hat{\mathbf{x}}_{\tau}\notin\mathbf{x}^{map}$, so there must exist
$\mathbf{x}'_{\tau}\in\mathbf{x}^{map}$ that $\hat{\mathbf{x}}_{\tau}\ne\mathbf{x}'_{\tau}$ and
$E(\mathbf{x}'_{\tau},\mathbf{x}_{\neg\tau},\mathbf{y})>E(\hat{\mathbf{x}}_{\tau},\mathbf{x}_{\neg\tau},\mathbf{y})$,
or equivalently $E(\mathbf{x}^{map},\mathbf{y})>E(\hat{\mathbf{x}}_{\tau},\mathbf{x}_{\neg\tau},\mathbf{y})$,
which contradicts with Eq.~(\ref{E-upperboud}) $\blacksquare$
The derivation in Eq.~(\ref{eq:cond-tree-energy}) from the probabilistic
formulation is presented in Appendix.~\ref{sub:Distribution-over-conditional}.
\subsection{Tree-based ICM (T-ICM): conditional trees for strong local search
\label{sub:Tree-based-ICM-(T-ICM)}}
As conditional trees can be efficient to estimate the optimal labeling,
we propose a method in the spirit of the simple local search ICM \cite{Besag-86}
(Section~\ref{sub:Iterated-Conditional-Mode}). First of all, a set
of conditional trees $\mathcal{T}$ is constructed. At each step,
a tree $\tau\in\mathcal{T}$ is picked according to predefined rules.
Using the 2-step procedure of BP, we find the optimal labeling for
$\tau$ using Eq.~(\ref{eq:MAP-cond-tree-energy}). This method includes
the ICM as a special case when the tree is reduced to a single site,
so we call it the tree-based ICM (T-ICM) algorithm, which is presented
in pseudo-code in Algorithm~\ref{alg:Tree-based-ICM}.
\begin{algorithm}
\textbf{Function}: T-ICM()
\textbf{Input}:
\begin{itemize}
\item Graph $\mathcal{G}=(\mathcal{V},\mathcal{E})$.
\item Local cost/energy functions $E_{i}(x_{i},\mathbf{y})$ and $E_{ij}(x_{i},x_{j})$.
\item A set of trees $\mathcal{T}$, and an update schedule.
\item Maximum number of iterations $T$.
\item Initial labeling $\mathbf{x}^{0}$.
\end{itemize}
\textbf{Procedure:}
\textbf{$\quad$For $t=1,2,...,T$}
\textbf{$\quad$$\quad$}1. \emph{Pick} a conditional tree $\tau$
from the tree set $\mathcal{T}$ according to the update schedule.
\textbf{$\quad$$\quad$}2. \emph{Absorb} neighboring energies according
to Eq.~(\ref{eq:absorbing}).
\textbf{$\quad$$\quad$}3. \emph{Run} $2$-pass BP on the conditional
tree (Section~\ref{sec:Belief-Propagation}): $\mathbf{x}_{\tau}^{t}\leftarrow BP(\mathbf{x}_{\tau}^{t-1})$.
\textbf{$\quad$$\quad$}4. \emph{Update} the labeling of the tree:
$\mathbf{x}_{\tau}^{t}\leftarrow\mathbf{x}{}_{\tau}^{t-1}$.
\textbf{$\quad$$\quad$}5. \emph{Stop} if $E_{\tau}\left(\mathbf{x}_{\tau}^{t},\mathbf{x}_{\mathcal{N}(\tau)}^{t},\mathbf{y}\right)$
no longer decreases for all trees $\tau\in\mathcal{T}$.
\textbf{Output}: A local optimal labeling.
\caption{Tree-based iterated conditional mode (T-ICM).\label{alg:Tree-based-ICM}}
\end{algorithm}
\subsubsection{Specification of T-ICM \label{sub:Specification-of-T-ICM}}
\paragraph{Tree set and update schedule.}
For a given graph, there are exponentially many ways to build conditional
trees, and thus defining the tree set is itself a nontrivial task.
However, for grids used in image labeling with height $H$ and width
$W$, we suggest two simple ways:
\begin{itemize}
\item The set of $H$ rows and $W$ columns. The neighborhood of size is
$HS^{W}+WS^{H}$.
\item The set of $2$ alternative rows and $2$ alternative columns (Figs.~\ref{fig:conditional}c,d).
Since alternative rows (or columns) are separated, they can be connected
by \emph{dummy edges} to form a tree (e.g., see Figs.~\ref{fig:conditional}c,d).
A dummy edge has the interacting energy of zero, thus does not affect
search operations on individual components. The neighborhood size
is $4S^{0.5HW}$.
\end{itemize}
These two sets lead to much more efficient T-ICM compared to the standard
ICM which only covers the neighborhood of size $SHW$ using the same
running time. Once the set has been defined, the update order for
trees can be predefined (e.g., rows from-top-to-bottom then columns
from-left-to-right), or random.
\subsubsection{Properties of T-ICM}
Due to Proposition~\ref{prop:T-ICM-local-min}, at each step of Algorithm~\ref{alg:Tree-based-ICM},
the total energy $E(\mathbf{x},\mathbf{y})$ will be either reduced or the algorithm
will terminate. Since the model is finite and the energy reduction
is discrete (hence non-vanishing), the algorithm is guaranteed to
reach a local minimum after finite steps.
Although the T-ICM only finds local minima of the energy, we can expect
the quality to be better than the original ICM because each tree covers
many sites. For example, as shown in Figs.~\ref{fig:conditional}a,b,
a tree in the grid can account for half of all the sites, which is
overwhelmingly large compared to a single site used by the ICM. The
number of configurations of the tree $\tau$, or equivalently the
neighborhood size, is $S^{N_{\tau}}$, where $N_{\tau}$ is the number
of sites on the tree $\tau$. The neighborhood size of the ICM, on
the other hands, is just $S$.
For the commonly used $4$-neighbor grid MRF in image labeling, and
the tree set of alternative rows and columns, the BP takes $\mathcal{O}(4HW)$
time to pass messages, each of which cost $3S^{2}$ time to compute.
Thus, the time complexity per iteration of T-ICM is only $S$ times
higher than that of ICM and about the same as that of loop BP (Sec.~\ref{sec:Loopy-BP}).
However, the memory in our case is still $\mathcal{O}\left(2\times\max\{H,W\}\right)$,
which is much smaller than the $\mathcal{O}(4HW)$ memory required
by loopy BP. In addition, each step in T-ICM takes exactly 2 passes,
while the number of iterations of loopy BP for the whole image, if
the method does converge, is unknown and parameter dependent.
\subsection{Tree-based ILS: global search \label{sub:Tree-based-ILS}}
\begin{algorithm}
\textbf{Function:} T-ILS()
\textbf{Input:}
\begin{itemize}
\item Max jump step-size: $\rho_{max}\in(0,100)$.
\item Max number of iterations $T_{outter}$; max number of iterations for
the inner T-ICM $T_{inner}$.
\item Max number of backtracks.
\end{itemize}
\textbf{Procedure:}
$\quad$\emph{Initialize} some labelings: $\tilde{\mathbf{x}}^{0}$.
$\quad$\emph{Find} the first local minimum: $\mathbf{x}^{1}\leftarrow\mbox{T-ICM}\left(\tilde{\mathbf{x}}^{0},T_{inner}\right)$.
$\quad$\emph{Initialize} variables: $n=0$; $\beta=1$.
$\quad$\textbf{For }$t=1,2,...,T_{outter}$
$\quad$$\quad$1. \emph{Jump} to a new place: $\tilde{\mathbf{x}}^{t}\leftarrow\mathbf{x}^{t}$
by randomly resetting $\mathcal{U}\left(0,\rho_{max}\right)\%$ of
labels.
$\quad$$\quad$2. \emph{Find} a local minimum: $\hat{\mathbf{x}}^{t+1}\leftarrow\mbox{T-ICM}\left(\tilde{\mathbf{x}}^{t},T_{inner}\right)$.
$\quad$$\quad$3. \emph{Accept}: $\mathbf{x}^{t+1}\leftarrow\hat{\mathbf{x}}^{t+1}$
with probability of
$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$a=\min\left\{ 1,\exp\left(-\beta\left\{ E(\hat{\mathbf{x}}^{t+1},\mathbf{y})-E(\mathbf{x}^{t},\mathbf{y})\right\} \right)\right\} $
$\quad$$\quad$$\quad$otherwise \emph{backtrack}: $\mathbf{x}^{t+1}\leftarrow\mathbf{x}^{t}$
.
$\quad$$\quad$4. \emph{Adjust} the temperature:
$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$n\leftarrow n+1$
if $\mathbf{x}^{t+1}=\hat{\mathbf{x}}^{t+1}$;
$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$r\leftarrow0.9n/t+0.1\mathbb{I}\left[\mathbf{x}^{t+1}=\hat{\mathbf{x}}^{t+1}\right]$
;
$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$if $r<0.45$ then
$\beta\leftarrow0.8\beta$ else if $r>0.55$ then $\beta\leftarrow\beta/0.8$.
$\quad$$\quad$5. \emph{Stop} if number of backtracks has been reach.
\textbf{Output}: A near global optimal labeling.
\caption{Tree-based iterated local search (T-ILS). \label{alg:Tree-based-ILS}}
\end{algorithm}
As T-ICM is still a local search procedure, inherent drawbacks still
remain: (i) it is sensitive to initialization, and (ii) it can get
stuck in suboptimal solutions. To escape from the local minima, global
search strategies must be employed. We can consider the entire T-ICM
as a single super-move in an \emph{exponentially large neighborhood}.
\begin{figure}
\begin{centering}
\includegraphics[width=0.8\linewidth]{T-ILS}
\par\end{centering}
\caption{Search behavior of T-ICM and T-ILS. The use of T-ICM creates a smoother
energy landscape for T-ILS (the surrogate dotted curve). ICM gets
stuck on the first local minimum it finds, but T-ICM could find a
much better solution by operating on an exponentially large neighborhood.
\label{fig:basin-hop}}
\end{figure}
Since it is not our intention to create a totally new escaping heuristic,
we draw from the rich pool of metaheuristics in the literature and
adapt to the domain of image labeling. In particular, we choose an
effective heuristic, commonly known as iterated local search (ILS)
\cite{Lourenco-et-al03} for escaping from the local minima. ILS advocates
\emph{jumps} from one local minimum to another with the hope that
we can eventually find better local minima after multiple tries. If
a jump fails to lead to a better solution, it can still be accepted
according to an \emph{acceptance} scheme, following the spirit of
simulated annealing (SL). However, we do not decrease the temperature
as in the SL, but rather, the temperature is adjusted so that on average
the acceptance probability is roughly $0.5$. The process is repeated
until the stopping criteria are met. We term the resulting metaheuristic
the \emph{Tree-based Iterated Local Search} (T-ILS) whose pseudo-code
is presented in Algorithm~\ref{alg:Tree-based-ILS}, and behavior
is illustrated in Fig.~\ref{fig:basin-hop}. In what follows we specify
the algorithm in more details.
\subsubsection{Specification of T-ILS \label{sub:Specification-of-T-ILS}}
\paragraph{Jump.}
The jump step-size has to be large enough to successfully escape from
the \emph{basin} that traps the local search. In this study, we design
a simple jump by randomly changing labels of $\rho\%$ of sites. The
step-size $\rho$ is drawn randomly in the range $(0,\rho_{max})$,
i.e., $\rho\sim\mathcal{U}\left(0,\rho_{max}\right)$, where $\rho_{max}$
is an user-specified parameter.
\paragraph{Acceptance.}
After a jump, the local search is invoked, followed by an acceptance
decision to accept or reject the jump. Convergence guaranteed acceptance
criteria such as those used in simulated annealing can be used, but
it is likely to be slow. We consider the following acceptance probability:
\[
a=\min\left\{ 1,\exp(-\beta\Delta E)\right\}
\]
where $\Delta E=E(\hat{\mathbf{x}}^{t+1},\mathbf{y})-E(\mathbf{x}^{t},\mathbf{y})$ is the change
in energy between two consecutive minima, and $\beta>0$ is the adjustable
``inverse temperature''. Large $\beta$ lowers the acceptance rate
but small $\beta$ increases the rate. This fact will be used to adjust
the acceptance rate, as detailed below.
\paragraph{Adjusting inverse temperature.}
We wish to maintain an average acceptance probability of $0.5$, following
the success of \cite{wales1997global}. However, unlike the work in
\cite{wales1997global}, we do not change the step-size, but rather
adjusting the inverse temperature. The estimation of acceptance rate
is $r\leftarrow r/t$, where $n$ is the total number of accepted
jumps up to step $t$. To introduce short-term effect, we use the
last event:
\[
r\leftarrow0.9r+0.1\mathbb{I}\left[\mathbf{x}^{t+1}=\hat{\mathbf{x}}^{t+1}\right]
\]
If the acceptance rate is within the range $[0.45,0.55]$ we do nothing.
A lower rate will lead to decrease of the inverse temperature: $\beta\leftarrow0.8\beta$,
and a higher rate will lead to increase: $\beta\leftarrow\beta/0.8$.
\subsubsection{Properties of T-ILS}
Fig.~\ref{fig:basin-hop} illustrates the behavior of the T-ILS.
Through the T-ICM component, the energy landscape is smoothed out,
helping the T-ICM to locate good local minima. When the jump is not
large, the search trajectory can be tracked to avoid self-crossing
walks. If the jump is far enough (with large $\rho_{max}$), the resulting
algorithm will behave like the well-known multistart procedures.
When the inverse temperature $\beta$ is set to $0$, the acceptance
become deterministic, that is, we only accept the jump if it improves
the current solution. In other words, the T-ILS becomes a greedy algorithm.
Alternatively, when $\beta$ is set to a very large number and no
adjustment is made, we would accept all the jumps, allowing memoryless
foraging behavior.
\section{Experiments\label{sec:exp}}
In this section, we evaluate our proposed algorithms on a simulated
\emph{Ising model} and two standard vision labeling problems: \emph{stereo
correspondence }and\emph{ image denoising}. In all settings, we employ
MRFs with grid-structure (e.g. each inner pixel is connected to exactly
4 nearby pixels). Trees are composed of rows and columns as specified
in Sec.~\ref{sub:Specification-of-T-ICM}. Unless specified otherwise,
the initial labeling is randomly assigned. Max step-size is $\rho_{max}=10\%$
(Sec.~\ref{sub:Specification-of-T-ILS}). For T-ILS, the inner loop
has $T_{inner}=1$, i.e., the full local minima may not be reached
by the T-ICM, as does not seem to hurt the final performance.
\subsection{Simulated Ising model \label{sub:Simulated-Ising-model}}
In this subsection, we validate the robustness of our proposed algorithms
on Ising models, which have wide applications in magnetism, lattice
gases, and neuroscience \cite{mccoy1973two}. Within the MRF literature,
Ising lattice is often used as a benchmark to test inference algorithms
(e.g., see \cite{Wainwright-et-al05TIT}). Following \cite{Wainwright-et-al05TIT},
we simulate a 500$\times$500 grid Ising model where labels are binary
spin orientations (up or down): $x_{i}\in\pm1$, and local energy
functions are: $E_{i}(x_{i})=\theta_{i}x_{i}$; $E_{ij}(x_{i},x_{j})=\theta_{ij}x_{i}x_{j}$.
The parameter $\theta_{i}$ specifies the influence of external field
on the spin orientation and $\theta_{ij}$ specifies the interaction
strength and direction (impulsive or repulsive) between sites. For
this experiment, the parameters $\left\{ \theta_{i},\theta_{ij}\right\} $
are set as follows
\begin{eqnarray*}
\theta_{i},\theta_{ij} & \sim & \mathcal{U}(-1,1)
\end{eqnarray*}
where $\mathcal{U}(-1,1)$ denotes the uniform distribution in the
range $(-1,1)$, and $\lambda>0$ specifies the interaction strength.
When $\lambda$ is small, the interaction is weak, and thus the external
field has more effect on the spin arrangement. However, when $\lambda$
is large, the spin arrangement depends more on the interacting nature.
A stable arrangement in nature would be of the minimum energy.
The result of minimizing energy is shown in Fig.~\ref{fig:Ising}.
When the interaction is weak (e.g. $\lambda=0.5$), the loopy BP performs
well, but when the interaction is strong (e.g. $\lambda=1.0$), the
T-ILS has a clear advantage. Thus T-ILS is more robust since it is
less sensitive to $\lambda$.
\begin{figure}
\begin{centering}
\begin{tabular}{cc}
\includegraphics[width=0.45\linewidth]{Ising_mix_edge_strength0. 5.eps} & \includegraphics[width=0.45\linewidth]{Ising_mix_edge_strength1.eps} \tabularnewline
\end{tabular}
\par\end{centering}
\caption{Performance of T-ILS and loopy BP algorithm in minimizing Ising energy
with $\lambda=0.5$ (left) and $\lambda=1.0$ (right). \label{fig:Ising}}
\end{figure}
\subsection{Stereo correspondence \label{sub:Stereo-correspondence}}
The problem in stereo correspondence is to estimate the depth of the
field (DoF) given two or more 2D images of the same scene taken from
two or more cameras arranged horizontally. This is used in 3D reconstruction
of a scene using standard 2D cameras. The problem is often translated
into estimating \emph{disparit}y between images -- how much two images
differ and this reflects the depth at any pixel locations. For simplicity,
we only investigate the two-cameras setting. In the MRF-based stereo
framework, a configuration of $\mathbf{x}\in\mathbb{N}^{W\times H}$ realizes
the \emph{disparity map}, which in this case is represented by a grid
network. The disparity set (or the label set) is often predefined.
For example, in the two standard datasets%
\footnote{Available at: http://vision.middlebury.edu/stereo/%
} used in this experiment, the Tsukuba has $16$ labels (Fig.~\ref{fig:tsukuba}),
and the Venus has $20$ (Fig.~\ref{fig:venus}).
\begin{figure}
\begin{centering}
\begin{tabular}{ccc}
\includegraphics[width=0.297\linewidth]{Tsukuba_left} & \includegraphics[width=0.297\linewidth]{Tsukuba_right} & \includegraphics[width=0.297\linewidth]{Tsukuba_truedisp}\tabularnewline
\includegraphics[width=0.3\linewidth]{Tsukuba_SL} & \includegraphics[width=0.3\linewidth]{Tsukuba_LBP} & \includegraphics[width=0.3\linewidth]{Tsukuba_ILS_scanline_init_jump0. 1}\tabularnewline
\end{tabular}
\par\end{centering}
\caption{Stereo results on the Tsukuba dataset. (Top-left): left image, (top-middle):
right image, (top-right): groundtruth; (bottom-left): scan-line, (bottom-middle):
loop BP, and (bottom-right): T-ILS (initialized from scan-line). \label{fig:tsukuba}}
\end{figure}
\begin{figure}
\begin{centering}
\begin{tabular}{ccc}
\includegraphics[width=0.297\linewidth]{Venus_left} & \includegraphics[width=0.297\linewidth]{Venus_right} & \includegraphics[width=0.297\linewidth]{Venus_truedisp}\tabularnewline
\includegraphics[width=0.3\linewidth]{Venus_SL} & \includegraphics[width=0.3\linewidth]{Venus_LBP} & \includegraphics[width=0.3\linewidth]{Venus_ILS_scanline_init_jump0. 1}\tabularnewline
\end{tabular}
\par\end{centering}
\caption{Stereo results on the Venus dataset. (Top-left): left image, (top-middle):
right image, (top-right): groundtruth; (bottom-left): scan-line, (bottom-middle):
loop BP, and (bottom-right): T-ILS (initialized from scan-line). \label{fig:venus}}
\end{figure}
The singleton energy $E_{i}(x_{i},\mathbf{y})$ at each pixel location usually
measures the dissimilarity of pixel intensity between the left/right
images, and the interaction energy $E_{ij}(x_{i},x_{j})$ ensures
the smoothness of the disparity map. In this set of experiments, we
use the simple linear Potts cost model as often used in testing stereo
correspondence algorithms \cite{Scharstein-Szeliski02}. Let $\mathbf{y}=(I^{l},I^{r})$
where $I^{l}$ and $I^{r}$ are intensities of the left and right
images respectively, and $i=(i_{X},i_{Y})$ where $i_{X}$ and $i_{Y}$
are horizontal and vertical coordinates of the pixel $i$. The local
energies are defined as \cite{Scharstein-Szeliski02}:
\begin{eqnarray*}
E_{i}(x_{i},\mathbf{y}) & = & \Delta I(i,x_{i})\\
E_{ij}(x_{i},x_{j}) & = & \lambda\times\mathbb{I}[x_{i}\ne x_{j}]
\end{eqnarray*}
where $\mathbb{I}[\cdot]$ is the indicator function, $\lambda>0$
is the smoothness parameter, and$\Delta I(i,x_{i})=\left|I^{l}(i_{X},i_{Y})-I^{r}(i_{X}-x_{i},i_{Y})\right|$
is the difference in pixel intensity in two images when pixel positions
are $x_{i}$ pixels apart in the horizontal dimension. Due to the
optical properties of two nearby cameras, a small $x_{i}$ would result
in large $\Delta I(i,x_{i})$ if the true DoF is small. Thus by minimizing
the singleton energy with respect to $x_{i}$, a small DoF would leads
to stronger reduction of $x_{i}$ than a large DoF. For this set of
experiments, we choose $\lambda=20$ following \cite{Scharstein-Szeliski02}.
Our implementation is based on the software framework of \cite{szeliski2007comparative}%
\footnote{The C++ code is available at http://vision.middlebury.edu/MRF/%
}.
There is a wide range of techniques available for stereo estimation,
and loopy BP is one of the winning methods \cite{Scharstein-Szeliski02}\cite{szeliski2007comparative}.
Fast methods like \emph{scan-line }(SL) optimization are still widely
used for real-time implementation. The scan-line is equivalent to
taking independent 1D rows of the MRF and running the chain BP. Since
the SL does not admit the original 2D structure, we need to adapt
the singleton energy as: $\bar{E}_{i}(x_{i},\mathbf{y})=\nu E_{i}(x_{i},y)$
where $\nu\in[0,1]$ to account for the lack of inter-row interactions.
\begin{table}[htb]
\begin{centering}
\begin{tabular}{|l|rr|}
\hline
Method & Tsukuba & Venus\tabularnewline
\hline
SL($\nu=1.0$) & 814,121 & 1,362,067\tabularnewline
SL($\nu=0.4$) & 658,946 & 1,198,324\tabularnewline
Random$\rightarrow$T-ICM($T=1)$ & 739,370 & 1,048,587\tabularnewline
SL($\nu=0.4$)$\rightarrow$T-ICM($T=1)$ & 427,860 & 669,973\tabularnewline
Loopy BP($T=1,000$) & 413,269 & 640,385 \tabularnewline
SL($\nu=0.4$)$\rightarrow$T-ILS($T_{outter}=1,000$) & \textbf{403,129} & \textbf{635,305} \tabularnewline
\hline
\end{tabular}
\par\end{centering}
\caption{Stereo energy found by algorithms. SL=Scan-line.\label{tab:stereo-energy-time} }
\end{table}
\begin{figure}
\begin{centering}
\begin{tabular}{cc}
\includegraphics[width=0.48\textwidth]{Tsukuba_LBP_versus_T-ILS} & \includegraphics[width=0.48\textwidth]{Venus_LBP_versus_T-ILS}\tabularnewline
Tsukuba (Fig\@.~\ref{fig:tsukuba}) & Venus (Fig\@.~\ref{fig:venus})\tabularnewline
\end{tabular}
\par\end{centering}
\caption{Stereo energy minimization by Loopy BP (dashed line) and T-ILS (line)
on Tsukuba (left) and Venus (right) images. \label{fig:Stereo-energy-minimization}}
\end{figure}
Table~\ref{tab:stereo-energy-time} shows the effect of changing
from $\nu=1.0$ to $\nu=0.4$ in term of reducing 2D energy and error.
The result, however, has the inherent horizontal `streaking' effect
since no 2D constraints are ensured (Figs.~\ref{fig:tsukuba},\ref{fig:venus},
bottom-left). The randomly initialized T-ICM with one iteration ($T=1$
in Algorithm~\ref{alg:Tree-based-ICM}) performs comparably with
the best of SL ($\nu=0.4$). The performance of T-ICM improves significantly
by initializing from the result of SL. T-ILS initialized from SL finds
better energy than the loopy BP given the same number of iterations,
as shown in Fig.~\ref{fig:Stereo-energy-minimization}.
\subsection{Image denoising \label{sub:Image-denoising}}
In image denoising, we are given an image corrupted by noise, and
the task is to reconstruct the original image. For this set of experiments
we use the $122\times179$ noisy gray Penguin image%
\footnote{Available at: http://vision.middlebury.edu/MRF/%
} (Fig.~\ref{fig:penguin-restore}). The labels of the MRF correspond
to $S=256$ intensity levels ($8$ bits depth). Similar to the stereo
correspondence problem, we use a simple truncated Potts model for
the energy as follows
\begin{eqnarray*}
E_{i}(x_{i},\mathbf{y}) & = & \min\left\{ |x_{i}-y_{i}|,\tau\right\} \\
E_{ij}(x_{i},x_{j}) & = & \lambda\times\delta[x_{i}\ne x_{j}]
\end{eqnarray*}
where $\tau=100$ prevents the effect of extreme noise, and $\lambda=25$
is smoothness parameter, following \cite{szeliski2007comparative}.
In addition, the optimized loopy BP for Potts models from \cite{Felzenszwalb-Huttenlocher-IJCV06}
is used. Figs~\ref{fig:penguin-restore}(b,c) demonstrates that T-ILS
runs faster than the optimize loopy BP, yielding lower energy and
smoother restoration.
\begin{figure}
\begin{centering}
\begin{tabular}{>{\centering}p{0.2\textwidth}>{\centering}p{0.15\textwidth}>{\centering}p{0.15\textwidth}c}
\multicolumn{3}{c}{\includegraphics[height=0.28\textwidth]{penguin_changed2} \includegraphics[height=0.28\textwidth]{penguin_ILS}~\includegraphics[height=0.28\textwidth]{penguin_BP}} & \includegraphics[height=0.28\textwidth]{penguin_runtime}\tabularnewline
(a) & (b) & (c) & (d)\tabularnewline
\end{tabular}
\par\end{centering}
\caption{Penguin images: (a) noisy, (b) restored with T-ILS, (b) restored with
loopy BP; (d) running time. Algorithms stop after $5$ unsuccessful
iterations. \label{fig:penguin-restore}}
\end{figure}
\section{Discussion \label{sec:conclusion} }
We have proposed a fast method for inference in Markov random fields
by exploiting tree structures embedded in the network. We proposed
a strong local search operator (T-ICM) based on Belief-Propagation
and a global stochastic search operator T-ILS based on the iterated
local search framework. We have shown in both simulation and two real-world
image analysis tasks (stereo correspondence and image denoising) that
the T-ILS is competitive against state-of-the-art algorithms. We have
demonstrated that by exploiting the structure of the domains, we can
derive strong local search operators which can be exploited in a metaheuristic
strategy such as ILS.
\subsection{Future work}
The line of current work could be extended in several directions.
First, we could adapt the T-ILS for certain cost functions. Currently,
the T-ILS is designed as a generic optimization method, making no
assumptions about the the nature of optimal solution. In contrast,
label maps in vision are often smooth almost everywhere except for
sharp boundaries. Second, the MRFs may offer a more informative way
to perform the jump steps, e.g., by relaxing the messages in the local
edges or by keeping track of the hopping trajectories. Third, we have
limited the T-ILS to uniform distribution of step-sizes, but it needs
not be the case. One useful heuristic is L\'{e}vy flights \cite{tran2004global,yang2009cuckoo}
in which the step-size $\rho$ is drawn from the power-law distribution:
$\rho^{-\alpha}$ for $\alpha>0$. This distribution allows the step-size
to usually stay within a certain narrow range but also allows occasional
big jump (which might behave like a total restart). Alternatively,
we can use Beta distribution due to its richness in distribution shape
and the boundedness of $\rho$. Fourth, since a MRF typically contain
many separated conditional trees, it could be interesting to explore
the parallel jump strategies.
As our development is based on the recognition that we can exploit
conditional trees in MRFs to obtain fast strong local search. The
metaheuristics thus need not be limited to ILS. In fact, conditional
trees open up a new direction of research in the MAP assignment by
investigating the use of other metaheuristics. For example, we can
use genetic algorithms in conjunction with the conditional trees as
follows. Each individual in the GA population can be represented by
a string of $N$ characters, each of which has one of $S$ values
in the label alphabet. For each individual, we run the 2-pass BP to
obtain a strong local solution. Then the crossover operator can be
applied character-wise on a selected subset to generate a new population.
Finally, although we have limited ourselves to applications in image
analysis, the proposed algorithm is generic to any problems where
MRFs are applicable.
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 9,745
|
Q: Prevent PostGIS Topology from splitting edges on line insert I'm dealing with a large amount of road data represented with PostGIS Topology types. Anytime I add an edge over another edge, the edge is automatically split and a new node is created at the intersection of the two lines. This creates a problem when I have roads that overlap other roads at bridges or underpasses. Is it possible to prevent edges from automatically being split when inserting an edge using TopoGeo_AddLineString? Or is this an incorrect usage of Topology?
A: PostGIS Topology is not good for modeling road networks. The ISO/IEC 13249-3 (SQL/MM) standard has a different API for that (Network Topology) which is not implemented in PostGIS yet.
But, if it may help, it's now implemented in spatialite:
https://www.gaia-gis.it/fossil/libspatialite/wiki?name=topo-intro
A: I figure it out, PostGIS Topology supports a z-index. If you want to prevent new lines from splitting other lines in the topology, they need to have different z-indexes. The CreateTopology function has a parameter hasz that allows support for this but it is false by default.
http://postgis.net/docs/CreateTopology.html
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 2,423
|
\section{Introduction}
These notes arise from the attempt to extend the results of \cite{marcello-bolo-conicbd} to a wider class of complex threefolds with
negative Kodaira dimension. If $Y \to S$ is a conic bundle and $S$ is rational, a semiorthogonal decomposition of ${\rm D}^{\rm b}(Y)$
by derived categories of curves and exceptional objects gives a splitting of the intermediate Jacobian as the direct
sum of the Jacobians of the curves \cite[Thm 1.1]{marcello-bolo-conicbd}. This result is based on the relation between fully
faithful functors ${\rm D}^{\rm b}(\Gamma) \to {\rm D}^{\rm b}(Y)$ (where $\Gamma$ is a smooth projective curve) and algebraic cycles on $Y$.
First of all, using the Chow--K\"unneth decompositions of the motives of $\Gamma$ and $Y$, we get from such functor an isogeny
between $J(\Gamma)$ and an abelian subvariety of $J(Y)$. Secondly, using the universal isomorphism between $A^2_{\mathbb{Z}}(Y)$ and a Prym variety
and the incidence property, we prove that such an isogeny is indeed an injective morphism of principally polarized
abelian varieties. Finally, the existence of the mentioned semiorthogonal decomposition assures the splitting of the intermediate Jacobian.
It turns out that the properties needed to prove this result are enjoyed also by threefolds other than conic bundles. One of the aims of this paper is to describe certain varieties satisfying those representability assumptions.
In a generalization attempt, we define a new notion of representability based on semiorthogonal decompositions, which we expect to
carry useful geometrical insights also in higher dimensions.
Let $X$ be a smooth projective variety of dimension $n$. We define \it categorical representability in
(co)dimension $m$ \rm for $X$, roughly by requiring that the derived category ${\rm D}^{\rm b}(X)$ admits a semiorthogonal decomposition
by categories appearing in smooth projective varieties of dimension $m$ (resp. $n-m$).
The easiest case is of course representability in dimension 0. This is equivalent to say that $X$ admits
a full exceptional sequence of a finite number, say $l$, of objects. In this case we have $K_0(X) = \mathbb{Z}^l$. This
is indeed a very strong notion and gives rise to intriguing questions to explore even for surfaces.
Various notions of representability of the group $A^i_{\mathbb{Z}}(X)$ of algebraically trivial cycles of codimension
$i$ on $X$ have appeared throughout the years in the literature, and it seems interesting to understand
their interactions with categorical representability, as our examples suggest.
Roughly speaking, \it weak representability \rm for $A^i_{\mathbb{Z}}(X)$ is given by an algebraic map
$J(\Gamma) \to A^i_{\mathbb{Z}}(X)$ whose kernel is an algebraic group, for an algebraic curve $\Gamma$. Working
with rational coefficients (that is, with $A^i_{\mathbb{Q}}$) gives the notion of \it rational representability.
Algebraic representability \rm
requires the existence of a universal regular isomorphism $A^i_{\mathbb{Z}}(X) \to A$ onto an abelian variety $A$.
Finally, if $\dim(X)=2n+1$ is odd, $A$ is the algebraic representative of $A^n_{\mathbb{Z}}(X)$, and the principal polarization
of $A$ is ``well behaved`` with respect to this regular isomorphism
we say that $A$ carries an \it incidence polarization. \rm
The definition of categorical representability could seem rather disjoint from the classical ones.
It is nevertheless clear that rational representability is strongly related to the structure of the motive of $X$.
For example, if $X$ is a threefold, then rational representability of all the $A^i_{\mathbb{Q}}(X)$ is equivalent to the existence of
a specific Chow--K\"unneth decomposition \cite{gorch-gul-motives-and-repr}.
A first point to note is then that fully faithful functors should hold motivic maps, as stated in the following conjecture by Orlov.
\begin{conjecture}[\cite{orlov-motiv}]\label{orlov-conj}
Let $X$ and $Y$ be smooth projective varieties and $\Phi: {\rm D}^{\rm b}(Y) \to {\rm D}^{\rm b}(X)$ be a fully faithful functor. Then
the motive $h(Y)$ is a direct summand of the motive $h(X)$.
\end{conjecture}
In order to get a link between categorical and rational representability, we should consider the former in
dimension 1. Note that being categorically representable in dimension 1 is equivalent to the existence
of a semiorthogonal decomposition by exceptional objects and derived categories of curves.
Orlov conjecture would then imply that if $X$ is categorically representable in dimension 1, then
its motive is a finite sum of abelian and discrete motives, and this would give informations about rational representability
for $A^i_{\mathbb{Q}}(X)$. Being categorically representable in dimension 1
seems to be in fact a very strong condition. For example a smooth cubic threefold is strongly representable
with incidence property but not categorically representable, otherwise we would have the splitting
of the intermediate Jacobian (see Corollary \ref{cor-no-split-no-fm}).
Notice that in \cite{kuzne-manivel-marku} the study of the Abel--Jacobi map for some hypersurfaces and
its link with categorical constructions were already treated.
Algebraic representability and the incidence property can have deep interactions with
categorical representability, and this is indeed the heart of the proof of Theorem 1.1 in \cite{marcello-bolo-conicbd}.
Consider a smooth projective threefold $X$ and assume it to be
rationally representable, with $h^1(X)=h^5(X)=0$, and with $A^2_{\mathbb{Z}}(X)$ algebraically representable with the incidence property. The arguments
in \cite{marcello-bolo-conicbd} show that if $X$ is categorically representable in dimension 1, then
the intermediate Jacobian $J(X)$ splits into Jacobians of curves, namely of those curves of positive genus appearing in the
semiorthogonal decomposition. This result can then be applied to a large class of complex threefolds with negative
Kodaira dimension (see a list in Remark \ref{remark-list-of-3folds}).
We can then reasonably raise the following question, which also points out how this new definition could be useful
in higher dimensions: is categorical representability in codimension 2 a necessary condition
for rationality? This is true for curves (where we have to replace codimension 2 with dimension 0) and
for surfaces, since any rational smooth projective surface admits a full exceptional sequence.
Remark \ref{list-of-iff} shows that this is true for a wide class of complex threefods with negative Kodaira dimension, but we can only
argue so far by a case by case analysis. Categorical representability should moreover hold the
vanishing of the Clemens--Griffiths component of ${\rm D}^{\rm b}(X)$ mentioned in \cite{kuznetcubicfourfold}.
We can wonder if Kuznetsov's conjecture about rationality of cubic fourfold (\cite[Conj. 1.1]{kuznetcubicfourfold}) could then
be restated as follows: a cubic fourfold is rational if and only if it is categorically representable in
codimension 2. Finally, we can argue some conjectural relation between
categorical representability and the existence of gaps in the Orlov spectrum defined
in \cite{katza-favero-ballard-generation-time}.
\subsection*{Notations}
Any triangulated category is assumed to be essentially small.
Given a smooth projective variety $X$, we denote $\kappa_X$ its Kodaira dimension, ${\rm D}^{\rm b}(X)$ the bounded derived
category of coherent sheaves on it, $K_0(X)$ its Grothendieck group, $CH_{\mathbb{Z}}^d(X)$ the Chow group of
codimension $d$ cycles, and $A_{\mathbb{Z}}^d(X)$ the subgroup of algebraically trivial cycles in $CH_{\mathbb{Z}}^d(X)$.
If is $X$ pure $d$-dimensional, and $Y$ any smooth projective variety,
we denote by ${\rm Corr}^i(X,Y):= CH_{\mathbb{Q}}^{i+d}(X\times Y)$ the group of correspondences with rational
coefficients. If $X=\coprod X_j$, with $X_j$ connected, then
${\rm Corr}^i(X,Y) = \oplus {\rm Corr}^i(X_j,Y)$.
\section{Categorical and classical representabilities for smooth projective varieties}
\subsection{Semiorthogonal decompositions and categorical representability}
We start by recalling some categorical definitions which are necessary to define representability.
Let $K$ be a field and $\cat{T}$ a $K$-linear triangulated category. A full triangulated category $\cat{A}$ of
$\cat{T}$ is called \it admissible \rm if the embedding functor admits a left and a right adjoint.
\begin{definition}[\cite{bondalkap,bondalorlov}]\label{def-semiortho}
A \it semiorthogonal decomposition \rm of $\cat{T}$ is a sequence of admissible subcategories
$\cat{A}_1, \ldots, \cat{A}_l$ of $\cat{T}$ such that ${\rm Hom}_{\cat{T}}(A_i,A_j) = 0$ for all $i>j$ and for
all objects $A_i$ in $\cat{A}_i$ and $A_j$ in $\cat{A}_j$, and for every object $T$ of $\cat{T}$, there is a chain
of morphisms $0=T_n \to T_{n-1} \to \ldots \to T_1 \to T_0 = T$ such that the cone of $T_k \to T_{k-1}$ is
an object of $\cat{A}_k$ for all $k=1,\ldots,l$. Such a decomposition will be written
$$\cat{T} = \langle \cat{A}_1, \ldots, \cat{A}_l \rangle.$$
\end{definition}
\begin{definition}[\cite{bondal}]\label{def-except}
An object $E$ of $\cat{T}$ is called \it exceptional \rm if ${\rm Hom}_{\cat{T}} (E,E) = K$, and ${\rm Hom}_{\cat{T}}(E,E[i])=0$
for all $i \neq 0$. A collection $\{E_1,\ldots,E_l\}$ of exceptional objects is called \it exceptional \rm if
${\rm Hom}_{\cat{T}}(E_j,E_k[i])=0$ for all $j>k$ and for all integer $i$.
\end{definition}
If $E$ in $\cat{T}$ is an exceptional object, the triangulated category generated by $E$ (that is, the smallest full
triangulated subcategory of $\cat{T}$ containing $E$) is equivalent to the derived category of a point, seen as a smooth projective
variety. The equivalence ${\rm D}^{\rm b}(pt) \to \langle E \rangle \subset \cat{T}$ is indeed given by sending ${\cal O}_{pt}$ to $E$.
Given an exceptional collection $\{E_1,\ldots,E_l\}$ in the derived category ${\rm D}^{\rm b}(X)$ of a smooth projective variety,
there is a semiorthogonal decomposition \cite{bondalorlov}
$${\rm D}^{\rm b}(X) = \langle \cat{A}, E_1, \ldots, E_l\rangle,$$
where $\cat{A}$ is the full triangulated subcategory whose objects are all the $A$ satisfying ${\rm Hom}(E_i,A)=0$
for all $i=1,\ldots,l,$ and we denote by $E_i$ the category generated by $E_i$.
We say that the exceptional sequence is \it full \rm if the category $\cat{A}$ is trivial.
\begin{definition}\label{def-rep-for-cat}
A triangulated category $\cat{T}$ is \it representable in dimension $m$ \rm
if it admits a semiorthogonal decomposition
$$\cat{T} = \langle \cat{A}_1, \ldots, \cat{A}_l \rangle,$$
and for all $i=1,\ldots,l$ there exists a smooth projective variety $Y_i$ with $\dim Y_i \leq m$, such that $\cat{A}_i$
is equivalent to an admissible subcategory of ${\rm D}^{\rm b}(Y_i)$.
\end{definition}
\begin{remark}\label{connectd}
Notice that we can assume that the categories $\cat{A}_i$ to be indecomposable, and
then the varieties $Y_i$ in the definition to be connected. Indeed, the derived category
${\rm D}^{\rm b}(Y)$ of a scheme $Y$ is indecomposable if and only if $Y$ is connected (see \cite[Ex. 3.2]{bridg-equiv-and-FM}).
\end{remark}
\begin{definition}
Let $X$ be a smooth projective variety of dimension $n$. We say that $X$ is \it categorically representable \rm
in dimension $m$ (or equivalently in codimension $n-m$) if ${\rm D}^{\rm b}(X)$ is representable in dimension $m$.
\end{definition}
\begin{remark}\label{rem-def-for-non-smooth}
Suppose that $X$ is not smooth. Then to define categorical representability for it, we need to use
categorical resolution of singularities, as defined by Kuznetsov \cite{kuznet-singul}. He constructs,
provided that $X$ has rational singularities, and given a resolution $\widetilde{X} \to X$,
an admissible subcategory $\widetilde{\cat{D}}$ of ${\rm D}^{\rm b}(\widetilde{X})$ which is the \it categorical
resolution of singularities \rm of ${\rm D}^{\rm b}(X)$. Then we can say that $X$ is categorically representable
in dimension $m$ if $\widetilde{\cat{D}}$ is.
\end{remark}
Notice that if any fully faithful functor between smooth projective varieties is of Fourier--Mukai type \cite{orlovequivk3,orlovequivall}.
It is moreover worth noting and recalling the following facts, which are well-known in the derived categorical setting.
\begin{remark}[\cite{beilinson}]
The derived category of $\mathbb{P}^n$ admits a full exceptional sequence.
\end{remark}
\begin{remark}
If $\Gamma$ is a smooth connected projective curve of positive genus, then ${\rm D}^{\rm b}(\Gamma)$ has no proper
admissible subcategory. Indeed any fully faithful functor
$\cat{A} \to {\rm D}^{\rm b}(\Gamma)$ is an equivalence, unless $\cat{A}$ is trivial. Then being categorically representable in dimension
1 is equivalent to admit a semiorthogonal decomposition by exceptional objects and derived
categories of smooth projective curves.
\end{remark}
\begin{remark}\label{rem-grr-decomp}
If $X$ and $Y_i$ are smooth projective and
$${\rm D}^{\rm b}(X) = \langle {\rm D}^{\rm b}(Y_1), \ldots, {\rm D}^{\rm b}(Y_k) \rangle,$$
then
$$K_0(X) = \bigoplus_{i=1}^k K_0(Y_i)$$
and the Grothendieck--Riemann--Roch Theorem gives
$${\rm CH}^*_{\mathbb{Q}}(X) = \bigoplus_{i=1}^k {\rm CH}^*_{\mathbb{Q}}(Y_i).$$
\end{remark}
\begin{proposition}[\cite{orlovprojbund}]\label{blow-up-formula}
Let $X$ be smooth projective and $Z \subset X$ a smooth subvariety of codimension $d > 1$. Denote by
$\varepsilon:\widetilde{X} \to X$ the blow up of $X$ along $Z$. Then
$${\rm D}^{\rm b}(\widetilde{X}) = \langle \varepsilon^* {\rm D}^{\rm b}(X), {\rm D}^{\rm b}(Z)_1, \ldots, {\rm D}^{\rm b}(Z)_{d-1} \rangle,$$
where ${\rm D}^{\rm b}(Z)_i$ is equivalent to ${\rm D}^{\rm b}(Z)$ for all $i=1,\ldots,d-1$.
\end{proposition}
\subsection{Classical representabilities and motives}
In this Section we outline a list of definitions of representabilities for the groups $A^i_{\mathbb{Z}}(X)$. This is
far for being exhaustive, especially in the referencing.
Indeed, giving a faithful list of all contributions
to these questions is out of the aim of these notes. Chow motives and their properties could give, through Conjecture
\ref{orlov-conj}, a way to connect categorical and classical representabilities. We also outline the basic
facts needed to stress the possible interplay between new and old definitions.
Let $X$ as usual be a smooth projective variety over an algebraically closed field $K$.
\begin{definition}[\cite{blochmurreFano}]
The group $A_{\mathbb{Z}}^i(X)$ is said to be \it weakly representable \rm if there exists a smooth projective curve $\Gamma$, a class
$z$ of a cycle in $CH_{\mathbb{Z}}^i(X\times \Gamma)$ and an algebraic subgroup $G \subset J(\Gamma)$ of the Jacobian variety
of $\Gamma$, such that the induced morphism
$$z_*:J(\Gamma) \rightarrow A^i_{\mathbb{Z}}(X)$$
is surjective with kernel $G$.
\end{definition}
When working with coefficients in $\mathbb{Q}$, we have the following definition.
\begin{definition}\label{rat}
The group $A^i_{\mathbb{Q}}(X)$ is \it rationally representable \rm if
there exists a regular surjective morphism
$$z_*:J_{\mathbb{Q}}(\Gamma) \rightarrow A^i_{\mathbb{Q}}(X).$$
\end{definition}
Rational representability is a name that has been used several times in the literature, so it might lead to some misunderstanding.
We underline that Definition \ref{rat} is exactly the one from (\cite{gorch-gul-motives-and-repr}, page 5).
In the complex case, we have also a
stronger notion, which is called the \it Abel--Jacobi property \rm \cite{blochmurreFano}, which requires the existence
of an isogeny (i.e. a regular surjective morphism) $A^i_{\mathbb{Z}}(X) \to J^i(X)$ onto the $i$-th intermediate Jacobian.
The Abel-Jacobi property implies weak representability for smooth projective varieties defined on $\mathbb{C}$.
\begin{definition}[\cite{beauvilleprym}]
An abelian variety $A$ is said to be the algebraic representative of $A^i_{\mathbb{Z}}(X)$ if there exists an isomorphism
$G:A^i_{\mathbb{Z}}(X) \rightarrow A$ which is universal. That is: for any morphism $g$ from $A^i_{\mathbb{Z}}(X)$ to an abelian variety $B$,
there exists a unique morphism $u:A \rightarrow B$ such that $u\circ G=g$. In this case we say that $A^i_{\mathbb{Z}}(X)$ is
\it algebraically representable. \rm
\end{definition}
The first examples of algebraic representatives are the Picard variety ${\rm Pic}^0(X)$ or the Albanese variety
${\rm Alb}(X)$ if $n=1$ or, respectively, $n=\dim(X)$.
\begin{definition}
Let $X$ be a smooth projective variety of odd dimension $2n + 1$
and $A$ the algebraic representative of $A_{\mathbb{Z}}^{n+1}(X)$ via the canonical map $G:
A_{\mathbb{Z}}^{n+1}(X)\rightarrow A$. A polarization of $A$ with associated correspondence $\theta_A$ in ${\rm Corr}(A)$, is the \it incidence polarization \rm with respect
to $X$ if for all algebraic maps $f : T \rightarrow A_{\mathbb{Z}}^{n+1}(X)$ defined by a cycle $z$ in $CH_{\mathbb{Z}}^{n+1}(X\times T)$, we have
$$(G\circ f)^*\theta_A = (-1)^{n+1}I(z);$$
where $I(z)$ in ${\rm Corr}(T)$ is the composition of the correspondences $z \in {\rm Corr}(T,X)$ and $z\in {\rm Corr}(X,T)$.
\end{definition}
There are many complex threefolds $X$ with negative Kodaira dimension, for which $A^2_{\mathbb{Z}}(X)$ is strongly represented by a generalized
Prym with incidence polarization. For these threefolds, we will show how categorical representability in dimension
1 gives a splitting of the intermediate Jacobian. A list of the main cases will be given in Section \ref{section-reconstr}.
\smallskip
A more modern approach to representability questions has to take Chow motives into account.
Let us recall their basic definitions and notations.
The category ${\cal M}_K$ of Chow motives over $K$
with rational coefficients is defined as follows: an object of ${\cal M}_K$ is a triple $(X,p,m)$, where $X$
is a variety, $m$ an integer and $p \in {\rm Corr}^0(X,X)$ an idempotent,
called a \it projector\rm. Morphisms from $(X,p,m)$ to $(Y,q,n)$ are given by elements of ${\rm Corr}^{n-m}(X,Y)$
precomposed with $p$ and composed with $q$.
There is a natural functor $h$ from the category of smooth projective schemes to the category of motives,
defined by $h(X) = (X,{\rm id},0)$, and, for any morphism $\phi: X \to Y$, $h(\phi)$ being the correspondence given
by the graph of $\phi$. We write $\mathbf{1}:=({\rm Spec} \, K, {\rm id}, 0)$ for the unit motive and $\mathbb{L} := ({\rm Spec} \, K, {\rm id}, -1)$
for the Lefschetz motive,
and $M(-i) := M \otimes \mathbb{L}^i$. Moreover, we have
${\rm Hom}(\mathbb{L}^d,h(X))= CH_{\mathbb{Q}}^d(X)$ for all smooth projective schemes $X$ and all integers $d$.
If $X$ is irreducible of dimension $d$, the embedding $\alpha: pt \to X$ of the point defines a motivic map $\mathbf{1} \to h(X)$. We denote
by $h^0(X)$ its image and by $h^{\geq 1}(X)$ the quotient of $h(X)$ via $h^0(X)$. Similarly, $\mathbb{L}^d$ is a quotient of $h(X)$,
and we denote it by $h^{2d}(X)$.
In the case of smooth projective curves of positive genus there exists another factor which corresponds to the Jacobian variety of the
curve. Let $C$ be a smooth projective connected curve, let us define a motive $h^1(C)$ such that we have a direct sum:
$$h(C) = h^0(C) \oplus h^1(C) \oplus h^2(C).$$
The upshot is that the theory of the motives $h^1(C)$ corresponds to that of Jacobian varieties (up to isogeny), in fact we have
$${\rm Hom}(h^1(C),h^1(C')) = {\rm Hom}(J(C),J(C'))\otimes \mathbb{Q}.$$
In particular, the full subcategory of ${\cal M}_K$ whose objects are direct summands of the motive $h^1(C)$ is equivalent
to the category of abelian subvarieties of $J(C)$ up to isogeny. Such motives can be called \it abelian. \rm We will say
that a motive is \it discrete \rm if it is the direct sum of a finite number of Lefschetz motives.
The strict interplay between motives and representability for threefolds is shown by Gorchinskiy and Guletskii.
In this case, the rational representability of $A^i_{\mathbb{Q}}(X)$ for $i \geq 2$ is known (\cite{murre-resultat}).
In \cite{gorch-gul-motives-and-repr} it is proved that
$A^3_{\mathbb{Q}}(X)$ is rationally representable if and only if the Chow motive of $X$ has a given
Chow-K\"{u}nneth decomposition.
\begin{theorem}[\cite{gorch-gul-motives-and-repr}, Thm 8]\label{theo-gor-gul}
Let $X$ be a smooth projective threefold. The group $A^3_{\mathbb{Q}}(X)$ is rationally representable if and only if the motive $h(X)$
has the following Chow-K\"{u}nneth decomposition:
$$h(X) \cong \mathbf{1} \oplus h^1(X) \oplus \mathbb{L}^{\oplus b} \oplus (h^1(J)(-1)) \oplus
(\mathbb{L}^2)^{\oplus b} \oplus h^5(X) \oplus \mathbb{L}^3,$$
where $h^1(X)$ and $h^5(X)$ are the Picard and Albanese motives respectively,
$b = b^2(X) = b^4(X)$ is the Betti number, and $J$ is a certain abelian
variety, which is isogenous to the intermediate Jacobian $J(X)$ if $K = \mathbb{C}$.
\end{theorem}
\section{Interactions between categorical and classical representabilities}\label{tre}
In this section, we will consider varieties defined over the complex numbers. This restriction
is not really necessary, since most of the constructions work over any algebraically closed
field. Anyway, in the complex case, we can simplify our treatment by dealing with
intermediate Jacobians. Moreover, it will be more simple to list examples without the need
to make the choice of the base field explicit for any case.
\subsection{Fully faithful functors and motives}\label{sec-fff-and-mot}
At the end of the last section we have seen that, in the case of threefolds, rational representability of $A^3_{\mathbb{Q}}(X)$ is equivalent
to the existence of some Chow-K\"unneth decomposition.
The first step in relating categorical and rational representability is exploiting an idea of Orlov about the
motivic decomposition which should be induced by a fully faithful functor between the derived categories of
smooth projective varieties. Assuming this conjecture we get that for threefolds categorical representability in
dimension 1 is a stronger notion than rational representability.
Let us sketch Orlov's idea \cite{orlov-motiv}. If $X$ and $Y$ are smooth projective varieties
of dimension respectively $n$ and $m$,
and $\Phi: {\rm D}^{\rm b}(Y) \to {\rm D}^{\rm b}(X)$ is a fully faithful functor, then it is of Fourier--Mukai type \cite{orlovequivk3,orlovequivall}.
Let ${\cal E}$ in ${\rm D}^{\rm b}(X \times Y)$ be its kernel and ${\cal F}$ in ${\rm D}^{\rm b}(X \times Y)$ the kernel
of its right adjoint $\Psi$, we have ${\cal F} \simeq {\cal E}^{\vee} \otimes pr_X^{*}\omega_X [\dim X]$ (see \cite{mukaiabelian}).
Consider $e:= ch({\cal E}) {\rm Td}(X)$ and $f:= ch({\cal F}) {\rm Td}(Y)$, two mixed rational cycles in ${\rm CH}^*_{\mathbb{Q}}(X \times Y)$. We
denote by $e_i$ (resp. $f_i$) the $i$-th codimensional component of $e$ (resp. $f$), that is
$e_i, f_i \in {\rm CH}_{\mathbb{Q}}^i (X \times Y)$. As correspondences they induce
motivic maps $e_i: h(Y) \to h(X)(i-n)$ and $f_j: h(X)(m-j) \to h(Y)$. The Grothendieck--Riemann--Roch
Theorem implies that $f.e := \bigoplus_{i=0}^{n+m} f_{n+m-i} e_i = {\rm id}_{h(Y)}$.
\begin{orlconj}
Let $X$ and $Y$ be smooth projective varieties and $\Phi: {\rm D}^{\rm b}(Y) \to {\rm D}^{\rm b}(X)$ be a fully faithful functor. Then
the motive $h(Y)$ is a direct summand of the motive $h(X)$.
\end{orlconj}
The Conjecture is trivially true for $Y$ a smooth point, in which case $\Phi({\rm D}^{\rm b}(Y))$ is generated
by an exceptional object of ${\rm D}^{\rm b}(X)$.
In \cite{orlov-motiv}, it is proven that the Conjecture holds if $X$ and $Y$ have the same dimension $n$
and ${\cal E}$ is supported in dimension $n$. This already covers some interesting example: if $X$ is a smooth
blow-up of $Y$, or if there is a standard flip from $X$ to $Y$. Using the same methods as in \cite{marcello-bolo-conicbd}
we will show that the conjecture holds (up to restricting to all direct summand of $h(Y)$) for some more examples, namely the
case of $Y$ a curve and $X$ a rationally representable threefold (i.e., $A^i_{\mathbb{Q}}(X)$ is rationally representable for
all $i$) with $h^1(X) = h^5(X) = 0$.
But let us first take a look to the simplest case, that is relating categorical representability in dimension 0 and
discreteness of the motive.
\begin{remark}\label{prop-categorical-repr-in-dim-0}
If a smooth projective variety $X$ is categorically representable in dimension $0$, then the motive
$h(X)$ is discrete.
\end{remark}
\begin{proof}
Being representable in dimension $0$ is equivalent to having a full exceptional sequence. Then the
proof is straightforward, we actually have more, that is $K(X) = \mathbb{Z}^l$, where $l$ is the number of
objects in the sequence.
\end{proof}
A way more interesting case relates categorical representability in dimension 1 and rational representability
for threefolds.
In this case, in light of Theorem \ref{theo-gor-gul}, we have a more specific conjecture.
\begin{conjecture}
If a smooth projective threefold $X$ is categorically representable in dimension $1$, then it is rationally
representable.
\end{conjecture}
If $X$ is a standard conic bundle over a rational surface and $\Gamma$ a smooth projective curve, the Chow-K\"unneth decomposition of $h(X)$
(see \cite{nagel-saito}) can be used to show that a fully faithful functor ${\rm D}^{\rm b}(\Gamma) \to
{\rm D}^{\rm b}(X)$ gives $h^1(\Gamma)(-1)$ as a direct summand of $h(X)$. In particular, this
gives an isogeny between $J(\Gamma)$ and an abelian subvariety of $J(X)$, and proves
(up to codimensional shfit for each direct summand of $h(\Gamma)$) Conjecture \ref{orlov-conj}
in this case. The proof in \cite{marcello-bolo-conicbd} is based on the fact that
the motive $h(X)$ splits into a discrete motive and in a unique abelian motive which
corresponds to $J(X)$. Let us make a first assumption
\begin{itemize}
\item[($\star$)] $X$ is a smooth projective rationally representable threefold with $h^1(X) = 0$ and $h^5(X) = 0$.
\end{itemize}
\begin{theorem}\label{from-Db-to-isogeny}
Suppose $X$ satisfies $\star$. If there is a smooth projective curve $\Gamma$ and
a fully faithful functor ${\rm D}^{\rm b}(\Gamma) \to {\rm D}^{\rm b}(X)$, then there exists an integer $j_i$ such that $h^i(\Gamma)(j_i)$ is
a direct summand of $h(X)$ for $i=0,1,2$, and there is an injective
morphism $J(\Gamma)_{\mathbb{Q}} \to J(X)_{\mathbb{Q}}$, that is an isogeny between $J(\Gamma)$ and an abelian subvariety
of $J(X)$.
\end{theorem}
\begin{proof}
Let ${\cal E}$ and ${\cal F}$, and $e$ and $f$ as before. Consider $h^0(\Gamma)= \mathbf{1}$, we have
$f.e_{\vert h^0(\Gamma)} = {\rm id}_{h^0(\Gamma)}$, which gives the claim, but not an
explicit value of $i_0$. The same argument works for $h^2(\Gamma) = \mathbb{L}$.
For $h^1(\Gamma)$, we only need the case where $g(\Gamma) >0$, and
we can use the same argument as in \cite{marcello-bolo-conicbd} Lemma 4.2 : since
all but one addendum of $h(X)$ are discrete, the map $f.e_{\vert h^1(\Gamma)} = {\rm id}_{h^1(\Gamma)}$ is given
by $f_2.e_2$, which proves that $h^1(\Gamma)(-1)$ is a direct summand of $h^3(X)=M^1(J)(-1)$.
\end{proof}
\begin{corollary}\label{corollary-cat-rep-and-isogeny}
Suppose $X$ satisfies $\star$ and let $\{\Gamma_i\}_{i=1}^k$ be smooth projective curves
of positive genus. If ${\rm D}^{\rm b}(X)$ is categorically representable
in dimension 1 by the categories ${\rm D}^{\rm b}(\Gamma_i)$ and by exceptional objects, then $J(X)$ is isogenous
to $\oplus_{i=1}^k J(\Gamma_i)$.
\end{corollary}
\begin{proof}
Use remark \ref{rem-grr-decomp}.
\end{proof}
\begin{remark}\bf{(Threefolds satisfying $\star$).} \rm
By \cite{gorch-gul-motives-and-repr, nagel-saito} Fano threefolds, threefolds fibered in Del Pezzo or Enriques surfaces over $\mathbb{P}^1$
with discrete Picard group,
and standard conic bundles over rational surfaces satisfy assumptions of Theorem \ref{from-Db-to-isogeny}.
\end{remark}
\subsection{Reconstruction of the intermediate Jacobian}\label{section-reconstr}
The aim of this section is to show how, under appropriate hypothesis,
categorical representability in dimension 1 for a threefold $X$ gives a splitting of the intermediate Jacobian $J(X)$.
Notice that in the case of curves the derived category carries the information about the principal polarization
of the Jacobian \cite{marcellocurves}.
In the case of threefolds, we need first of all the hypothesis of Theorem \ref{from-Db-to-isogeny}.
As we will see, the crucial hypothesis that will allow us to recover also the principal polarization
is that the polarization on $J(X)$ is an \textit{incidence polarization}.
\begin{itemize}
\item[($\natural$)] $X$ is a smooth projective rationally and algebraically representable threefold with $h^1(X) = 0$ and $h^5(X) = 0$
and the algebraic representative of $A^2_{\mathbb{Z}}(X)$ carries an incidence polarization.
\end{itemize}
\begin{theorem}\label{reconstr-of-interm}
Suppose $X$ satisfies $\natural$. Let
$\Gamma$ be smooth projective curve and ${\rm D}^{\rm b}(\Gamma) \to {\rm D}^{\rm b}(X)$ fully faithful. Then there is an injective
morphism $J(\Gamma) \hookrightarrow J(X)$ preserving the principal polarization, that is $J(X) = J(\Gamma) \oplus A$ for
some principally polarized abelian variety $A$.
\end{theorem}
\begin{proof}
From Theorem \ref{from-Db-to-isogeny} we get an isogeny. As in the proof of \cite[Prop. 4.4]{marcello-bolo-conicbd},
the incidence property shows that this isogeny is an injective morphism respecting the principal polarizations.
\end{proof}
\begin{corollary}\label{ortjac}
Suppose $X$ satisfies $\natural$ and let $\{\Gamma_i\}_{i=1}^k$ be smooth projective curves
of positive genus. If ${\rm D}^{\rm b}(X)$ is categorically representable
in dimension 1 by the categories ${\rm D}^{\rm b}(\Gamma_i)$ and by exceptional objects, then $J(X)$ is isomorphic
to $\oplus_{i=1}^k J(\Gamma_i)$ as principally polarized variety.
\end{corollary}
\begin{remark}\label{remark-list-of-3folds}\bf{(Threefolds satisfying $\natural$).} \rm
The assumptions of Theorem \ref{reconstr-of-interm} seem rather restrictive. Anyway, they are satisfied by
a quite big class of smooth projective threefolds with $\kappa_X < 0$. The Chow-K\"unneth decomposition
for the listed varieties
is provided by \cite{nagel-saito} for conic bundles and by \cite{gorch-gul-motives-and-repr} in any other case.
In the following list the references
point out the most general results about strong representability and incidence property.
Giving an exhaustive list of all the results and contributors would be out of reach
(already in the cubic threefold case). We will consider Fano threefolds with Picard number one only. The
interested reader could find an exhaustive treatment in \cite{isko-prok-fano}.
\begin{itemize}
\item[1)] Fano of index $>2$: $X$ is either $\mathbb{P}^3$ or a smooth quadric.
\item[2)] Fano of index $2$: $X$ is a quartic double solid \cite{tihoquarticsolid} , or a smooth cubic in $\mathbb{P}^4$
\cite{clemensgriffiths}, or an intersection of two quadrics in $\mathbb{P}^5$ \cite{reidphd}, or a $V_5$ (in the last case $J(X)$ is trivial).
\item[3)] Fano of index $1$: $X$ is a general sextic double solid \cite{ceresaverra}, or
a smooth quartic in $\mathbb{P}^4$ \cite{blochmurreFano},
or an intersection of a cubic and a quadric in $\mathbb{P}^5$ \cite{blochmurreFano}, or the intersection of three
quadrics in $\mathbb{P}^6$ \cite{beauvilleprym}, or a $V_{10}$ \cite{logachevV10,iliev10}, or a $V_{12}$ \cite{ilievmarkuV12} ($J(X)$
is the jacobian of a genus 7 curve),
or a $V_{14}$ \cite{iliev-marku-v14} (in which case the representability is related to the birational map to a smooth cubic threefold),
or a general $V_{16}$ \cite{ilievV16, mukaigranmisto}, or a general $V_{18}$ \cite{ilievamanovella,isko-prok-fano}
($J(X)$ is the jacobian of a genus 2 curve), or a $V_{22}$ (and the Jacobian is trivial).
\item[4)] Conic bundles: $X \to S$ is a standard conic bundle over a rational surface \cite{beauvilleprym,beltrachow}, this is the case examined in
\cite{marcello-bolo-conicbd}.
\item[5)] Del Pezzo fibrations: $X \to \mathbb{P}^1$ is a Del Pezzo fibration with $2\leq K_X^2 \leq 5$ \cite{kanevdp1,kanevdp2}.
\end{itemize}
\end{remark}
From the unicity of the splitting of the intermediate Jacobian we can easily infer the following.
\begin{corollary}
Suppose $X$ satisfies $\natural$ and is categorically representable in dimension 1, with semiorthogonal decomposition
$${\rm D}^{\rm b}(X)= \langle {\rm D}^{\rm b}(\Gamma_1),\ldots,{\rm D}^{\rm b}(\Gamma_k),E_1,\ldots,E_l\rangle.$$
Then there is no fully faithful functor ${\rm D}^{\rm b}(\Gamma) \to {\rm D}^{\rm b}(X)$ unless $\Gamma \simeq \Gamma_i$ for some $i \in \{ 1,\ldots,k\}$.
Moreover, the semiorthogonal decomposition is essentially unique, that
is any semiorthogonal decomposition of ${\rm D}^{\rm b}(X)$ by smooth projective curves and exceptional objects is
given by all and only the curves $\Gamma_i$ and $l$ exceptional objects.
\end{corollary}
\begin{corollary}\label{cor-no-split-no-fm}
Suppose $X$ satisfies $\natural$, $\Gamma$ is a smooth projective curve of positive genus
and there is no splitting $J(X) = J(\Gamma) \oplus A$. Then there is no fully faithful functor
${\rm D}^{\rm b}(\Gamma) \to {\rm D}^{\rm b}(X)$.
\end{corollary}
The assumptions of Corollary \ref{cor-no-split-no-fm} are trivially satisfied if the
threefold satisfying $\natural$ has $J(X)=0$. A way more interesting case is when
the intermediate Jacobian is not trivial and has no splitting at all, in which case the
variety is not representable in dimension $<2$.
\begin{remark}\label{list-three-not-rep}\bf{(Threefolds not categorically representable in dimension $<2$)}. \rm
The assumptions of Corollary \ref{cor-no-split-no-fm} are satisfied by smooth threefolds with $J(X) \neq 0$
for all curve $\Gamma$ of positive genus in the following cases:
\smallskip
Either $X$ is a smooth cubic \cite{clemensgriffiths}, or a generic quartic threefold \cite{letiziamoratti}, or a generic complete intersection of type $(3,2)$
in $\mathbb{P}^5$ \cite{beauvilleprym} or a symmetric one \cite{bovesym}, or the intersection of three quadrics in $\mathbb{P}^7$ \cite{beauvilleprym},
or a standard conic bundle $X \to \mathbb{P}^2$ degenerating along a curve
of degree $\geq 6$ \cite{beauvilleprym}, or a non-rational standard conic bundle $X \to S$ on a Hirzebruch surface
\cite{shokuprym}, or a non-rational Del Pezzo fibration $X \to \mathbb{P}^1$ of degree four \cite{aleks-dp4}.
There are some other cases of Fano threefolds of specific type satisfying geometric assumptions. For a detailed treatment, see
\cite[Chapt. 8]{isko-prok-fano}.
\end{remark}
Notice that if $X$ is a smooth cubic threefold, the equivalence class of a notable admissible subcategory $\cat{A}_X$
(the orthogonal complement of $\{{\cal O}_X,{\cal O}_X(1)\}$) corresponds to the isomorphism class of $J(X)$ as principally polarized
abelian variety \cite{noicubic}; the proof is based on the reconstruction of the Fano variety and the techniques used
there are far away from the subject of this paper.
A natural question is if, under some hypothesis, one can give the inverse statement of Corollaries \ref{corollary-cat-rep-and-isogeny}
and \ref{ortjac}, that is: suppose that $X$ is a threefold satisfying either $\star$ or $\natural$, such
that $J(X) \simeq \oplus J(\Gamma_i)$. Can one describe a semiorthogonal decomposition of ${\rm D}^{\rm b}(X)$ by
exceptional objects and the categories ${\rm D}^{\rm b}(\Gamma_i)$? Notice that a positive
answer for $X$ implies a positive answer for all the smooth blow-ups of $X$.
\begin{remark}\label{list-of-iff}\bf(Threefolds with $\kappa_X <0$ categorically representable in dimension $\leq 1$). \rm
Let $X$ be a threefold satisfying $\star$ or $\natural$ and with $J(X) = \oplus J(\Gamma_i)$. Then if $X$
is in the following list (or is obtained by a finite number of smooth blow-ups from a variety in the list)
we have a semiorthogonal decomposition
$${\rm D}^{\rm b}(X) = \langle {\rm D}^{\rm b}(\Gamma_1), \ldots, {\rm D}^{\rm b}(\Gamma_k), E_1, \ldots, E_l \rangle,$$
with $E_i$ exceptional objects.
\begin{itemize}
\item[1)] Threefolds with a full exceptional sequence: $X$ is $\mathbb{P}^3$ \cite{beilinson},
or a smooth quadric \cite{kapranovquadric},
or a $\mathbb{P}^1$-bundle over a rational surface or a $\mathbb{P}^2$-bundle over $\mathbb{P}^1$ \cite{orlovprojbund},
or a $V_5$ \cite{orlov-v5}, or a $V_{22}$ Fano threefold \cite{kuznev22}.
\item[2)] Fano threefolds without any full exceptional sequence: $X$ is the complete intersection of two quadrics or a Fano
threefold of type $V_{18}$, and $J(\Gamma) \simeq J(X)$ with $\Gamma$ hyperelliptic.
The semiorthogonal decompositions are described in \cite{bondalorlov,kuznetHyperplane}, and are strikingly
related (as in the cases of $V_5$ and $V_{22}$ and of the cubic and $V_{14}$) by a correspondence in
the moduli spaces, as described in \cite{kuznetfanothreefolds}. $X$ is a $V_{12}$ Fano threefold
\cite{kuznetv12}, or a $V_{16}$ Fano threefold \cite{kuznetHyperplane}.
\item[3)] Conic bundles without any full exceptional sequence: $X \to S$ is a rational conic bundle over a minimal surface
\cite{marcello-bolo-conicbd}. If the degeneration locus of $X$ is either empty or a cubic in $\mathbb{P}^2$, then $X$ is a
$\mathbb{P}^1$-bundle and is listed in 1).
\item[4)] Del Pezzo fibrations: $X \to \mathbb{P}^1$ is a quadric fibration with at most simple degenerations, in which case the
hyperelliptic curve $\Gamma \to \mathbb{P}^1$ ramified along the degeneration appears naturally as the orthogonal complement of
an exceptional sequence of ${\rm D}^{\rm b}(X)$ \cite{kuznetconicbundles}. $X \to \mathbb{P}^1$ is a rational Del Pezzo fibration of degree four.
In this case $X$ is birational to a conic bundle over a Hirzebruch surface
\cite{aleks-dp4} and the semiorthogonal decomposition will be described in a forthcoming paper \cite{asher-marcello-bolo}.
\end{itemize}
Notice that the first two items cover all classes of Fano threefolds with Picard number one whose members are all rational.
\end{remark}
\section[Developments and Questions]{Categorical representability and rationality: \\
further developments and open questions}
This last Section is dedicated to speculations and open questions about categorical representability and rationality.
The baby example of curves is full understood. A smooth projective curve $X$ over a field $K$ is categorically representable in
dimension 0 if and only if it is rational. Indeed, the only case where ${\rm D}^{\rm b}(X)$ has exceptional objects is
$X=\mathbb{P}^1$, and ${\rm D}^{\rm b}(X) = \langle {\cal O}_X,{\cal O}_X(1) \rangle$.
Let us start with a trivial remark: the projective space $\mathbb{P}^n$ over $K$ is categorically representable in dimension 0.
Then if $X$ is given by a finite number of smooth blow-ups of $\mathbb{P}^n$, it is categorically representable in
codimension $\geq 2$. This is easily obtained from Orlov's blow-up formula (see Prop. \ref{blow-up-formula}).
More generally, if a smooth projective variety $X$ of dimension $\geq 2$ is categorically representable in
codimension $m$, then any finite chain of smooth blow-ups of $X$ is categorically representable in
codimension $\geq {\rm min}(2,m)$.
One could naively wonder about the inverse statement: if $X \to Y$
is a finite chain of smooth blow-ups and $X$ is categorically representable in codimension $m$, what can
we say about $Y$? Unfortunately, triangulated categories do not have enough structure to let us
compare different semiorthogonal decomposition. For example, the theory of mutations allows to do this only
in a few very special cases.
In this Section we present some more example to stress how the interaction between categorical representability
and rationality can be devloped further, and we point out some open question.
We deal with surfaces in \ref{surf} and with threefolds in \ref{threefolds}.
Then we will discuss in \ref{noncommutative} how categorical
representability for noncommutative varieties plays an important role in this frame, to deal with
varieties of dimension bigger than 3 in \ref{higherdim}. Finally, we compare in \ref{approaches}
our methods with recent approaches to birationality
problems via derived categories. We will work over the field $\mathbb{C}$ for simplicity, even if many
problems and arguments do not depend on that.
\subsection{Surfaces}\label{surf}
If $X$ is a smooth projective rational surface,
then it is categorically representable in codimension 2. Indeed,
$X$ is the blow-up in a finite number of smooth points of a minimal rational surface, that is either $\mathbb{P}^2$ or
$\mathbb{F}_n$. Are there any other example of surfaces categorically representable in codimension 2? Notice that by
Proposition \ref{prop-categorical-repr-in-dim-0} such a surface would have a discrete motive, and even more:
we would have $K_0(X) = \mathbb{Z}^l$. In particular, if $K_0(X)$ is not locally free, then
$X$ is not categorically representable in dimension 0.
In general, an interesting problem is to construct exceptional sequences on surfaces with $p_g=q=0$, and to study their
orthogonal complement. Suppose for example that $X$ is an Enriques surface: a (non-full) exceptional collection of 10
vector bundles on $X$ is described in \cite{zube-enriques}. Since $K_0(X)$ is not locally free, we do not expect any
full exceptional collection. The orthogonal complement $\cat{A}_X$ turns then out to be a very interesting
object, related also to the geometry of some singular quartic double solid \cite{kuzne-ingalls}.
Using a motivic trick, we can prove that, under some assumption, a surface with $p_g=q=0$ is
either categorically representable in codimension 2 or not categorically representable in positive codimension.
\begin{proposition}\label{prop-surf-p=q=0}
Let $X$ be a surface with $h(X)$ discrete. Then for any curve $\Gamma$ of positive genus, there is no fully faithful
functor ${\rm D}^{\rm b}(\Gamma) \to {\rm D}^{\rm b}(X)$.
\end{proposition}
\begin{proof}
Suppose there is such a curve and such a functor $\Phi: {\rm D}^{\rm b}(\Gamma) \to {\rm D}^{\rm b}(X)$. Let ${\cal E}$ denote the kernel of
$\Phi$ (which has to be of Fourier--Mukai type) and ${\cal F}$ the kernel of its adjoint. Consider the cycles $e$ and $f$ described
in Section \ref{sec-fff-and-mot}, and recall that $f.e = \oplus_{i=0}^3 f_{3-i}.e_i = {\rm id}_{h(\Gamma)}$. Restricting now
to $h^1(\Gamma)$ we would have that ${\rm id}_{h^1(\Gamma)}$ would factor through a discrete motive, which is impossible.
\end{proof}
\begin{corollary}\label{cor-surf-non-rep}
Let $X$ be a surface with $h(X)$ discrete and $K_0(X)$ not locally free. Then $X$ is not categorically representable in codimension
$>0$.
\end{corollary}
\begin{remark}\bf(Surfaces with $p_g=q=0$ not categorically representable in positive codimension). \rm
Proposition \ref{prop-categorical-repr-in-dim-0} could be an interesting tool in the study of derived categories of surfaces
with $p_g=q=0$: notice that many of them have torsion in $H_1(X, \mathbb{Z})$ (for an exhaustive treatment and referencing, see
\cite{bauer-cata-pigna-survey}). Anyway the discreteness of the motive is a rather strong assumption, which for
example implies the Bloch conjecture. There are few cases where this is known.
\begin{itemize}
\item[1)] $X$ is an Enriques surface \cite{coombes}.
\item[2)] $X$ is a Godeaux surface obtained as a quotient of a quintic by an action of $\mathbb{Z}/5\mathbb{Z}$ \cite{gul-pedr-godeaux}.
\end{itemize}
\end{remark}
These observations lead to state some deep question about categorical representability of
surfaces.
\begin{question}\label{exc-obj-on-surf}
Let $X$ be a smooth projective surface with $p_g = q = 0$.
\begin{itemize}
\item[1)] Does ${\rm D}^{\rm b}(X)$ admit an exceptional sequence?
\item[2)] Is the exceptional sequence full? That is, is $X$ representable in codimension 2?
\item[3)] If $X$ is representable in codimension 2, is $X$ rational?
\end{itemize}
\end{question}
\subsection{Threefolds}\label{threefolds}
Remark that there are examples
of smooth projective non-rational threefolds $X$ which are categorically representable in codimension 2:
just consider a rank three vector bundle ${\cal E}$ on a curve $C$ of positive genus and take $X:=\mathbb{P}({\cal E})$.
In \cite[Sect. 6.3]{marcello-bolo-conicbd} we provide a conic bundle example. Anyway, Corollary
\ref{ortjac} somehow suggests that categorical representability in codimension 2 should be a necessary condition
for rationality.
A reasonable idea is to restrict our
attention to minimal threefolds with $\kappa_X <0$ (recall that this is a necessary condition for rationality),
in particular to the ones we expect to satisfy assumption $\natural$, in order to have interesting information about the intermediate Jacobian from semiorthogonal decompositions.
The three big families of such threefolds are:
Fano threefolds, conic bundles over rational surfaces and del Pezzo fibrations over $\mathbb{P}^1$.
Remark \ref{list-of-iff} gives a list of rational threefolds which are categorically representable in codimension 2,
and Remark \ref{remark-list-of-3folds} a list of families whose generic term is non-rational and cannot be categorically
representable in codimension $> 1$.
\begin{question}\label{question-on-3folds}
Let $X$ be a smooth projective threefold with $\kappa_X <0$.
\begin{itemize}
\item[1)] If $X$ is rational, is $X$ categorically representable in codimension 2?
\item[2)] Is $X$ categorically representable in codimension 2 if and only if $X$ is rational?
\end{itemize}
\end{question}
A positive answer to the second question is provided for standard conic bundles over minimal surfaces \cite{marcello-bolo-conicbd},
but it seems to be quite a strong fact to hold in general: recall that having a splitting $J(X) \simeq \oplus J(\Gamma_i)$ is only a necessary
condition for rationality, and Corollary \ref{ortjac} shows that if $X$ satisfies $\natural$, categorical representability
in codimension 2 would give the splitting of the Jacobian.
Remark \ref{list-of-iff} provides a large list of rational threefolds categorically representable in codimension 2.
Is it possible to add examples to this list? In particular in the case of Del Pezzo fibrations over $\mathbb{P}^1$
only the quadric and the degree 4 fibration are described.
A good way to understand these questions is by studying some special rational or non-rational (that is non generic in their
family) threefold. This forces to consider non smooth ones, but we can use Kuznetsov's theory of categorical resolution of singularities \cite{kuznet-singul}
and study the categorical resolution of ${\rm D}^{\rm b}(X)$, as we pointed out in Remark \ref{rem-def-for-non-smooth}.
For example, let $X \subset \mathbb{P}^4$ be nodal cubic threefold with a double point, which is known to be rational.
\begin{proposition}
Let $X \subset \mathbb{P}^4$ be a cubic threefold with a double point and $\widetilde{X} \to X$ the blow-up of the singular point. The categorical
resolution of singularities $\widetilde{\cat{D}} \subset {\rm D}^{\rm b}(\widetilde{X})$ of ${\rm D}^{\rm b}(X)$ is representable in codimension two.
Indeed there is a semiorthogonal decomposition
$$\widetilde{\cat{D}} = \langle {\rm D}^{\rm b}(\Gamma), E \rangle,$$
where $E$ is an exceptional object and $\Gamma$ a complete intersection of a quadric and a cubic in $\mathbb{P}^3$.
\end{proposition}
\begin{proof}
This is shown following step by step \cite[Section 5]{kuznetcubicfourfold}, where the four dimensional case is studied.
Let us give a sketch of the proof. Let $P$ be the singular point of $X$, and $\sigma: \widetilde{X} \to X$ its blow-up.
The exceptional locus $\alpha: Q \hookrightarrow \widetilde{X}$ of $\sigma$ is a quadric surface.
The projection of $\mathbb{P}^4$ to $\mathbb{P}^3$ from the point $P$ restricted to $X$ gives the birational map $X \dashrightarrow \mathbb{P}^3$.
The induced map $\pi: \widetilde{X} \to \mathbb{P}^3$ is the blow-up of a smooth curve $\Gamma$ of genus 4, given by the complete intersection
of a cubic and a quadric surface.
If we denote $h:= \pi^* {\cal O}_{\mathbb{P}^3}(1)$ and $H:= \sigma^* {\cal O}_X (1)$, we have that $Q=2h-D$, $H=3h-D$, then $h=H-Q$ and $D=2H-3Q$
as in \cite[Lemma 5.1]{kuznetcubicfourfold}. The canonical bundle $\omega_{\widetilde{X}} = -4h+D= -2H+Q$ can be calculated
via the blow-up $\pi$.
The same arguments as in \cite{kuznetcubicfourfold} give the decomposition
$${\rm D}^{\rm b}(\widetilde{X}) = \langle \alpha_* {\cal O}_Q (-h), \widetilde{\cat{D}} \rangle.$$
Indeed the conormal bundle of $Q$ is ${\cal O}_Q(h)$ and the Lefschetz decomposition with respect to it is:
$$\langle {\cal A}_1(-h),{\cal A}_0\rangle,$$
where ${\cal A}_1 = \langle{\cal O}_Q\rangle$ and ${\cal A}_0 = \langle {\cal O}_Q, S_1, S_2 \rangle$, with $S_1$ and $S_2$ the two spinor bundles.
We obtain then the semiorthogonal decomposition:
\begin{equation}\label{semiorth1}
{\rm D}^{\rm b}(\widetilde{X}) = \langle \alpha_* {\cal O}_Q (-h), \widetilde{\cat{A}}_X, {\cal O}_{\widetilde{X}}, H \rangle,
\end{equation}
where $\widetilde{\cat{A}}_X$ is the categorical resolution of $\cat{A}_X$, as in \cite[Lemma 5.8]{kuznetcubicfourfold}.
The representability of $\widetilde{\cat{D}}$ relies then on the representability of $\widetilde{\cat{A}}_X$.
On the other side, applying the blow-up formula (see Prop. \ref{blow-up-formula}) to $\pi: \widetilde{X} \to \mathbb{P}^3$,
and choosing $\{ {\cal O}_{\mathbb{P}^3}(-3), \ldots, {\cal O}_{\mathbb{P}^3} \}$ as full exceptional sequence for ${\rm D}^{\rm b}(\mathbb{P}^3)$, we obtain:
$${\rm D}^{\rm b}(\widetilde{X}) = \langle \Phi {\rm D}^{\rm b}(\Gamma), -3h,-2h-h,{\cal O}_{\widetilde{X}} \rangle,$$
where $\Phi: {\rm D}^{\rm b}(\Gamma) \to {\rm D}^{\rm b}(\widetilde{X})$ is fully faithful. Now as in \cite[Lemma 5.3]{kuznetcubicfourfold},
if we mutate $-3h$ and $-2h$ to the left with respect to $\Phi {\rm D}^{\rm b}(\Gamma)$, we get
\begin{equation}\label{semiorth2}
{\rm D}^{\rm b}(\widetilde{X}) = \langle -3h+D, -2h+D, \cat{B}, {\cal O}_{\widetilde{X}} \rangle,
\end{equation}
where $\cat{B} = \langle \Phi {\rm D}^{\rm b}(\Gamma), -h \rangle$ is an admissible subcategory of ${\rm D}^{\rm b}(\widetilde{X})$.
Finally, one can show that $\cat{B}$ and $\widetilde{\cat{A}}_X$ are equivalent,
following exactly the same path of mutations as in \cite[Sect. 5]{kuznetcubicfourfold} to compare the
decompositions (\ref{semiorth1}) and (\ref{semiorth2}). Notice that one can calculate explicitely the
exceptional object $E$ by following the mutations of $-h$.
\end{proof}
Another special very interesting example is described in \cite{kuzne-ingalls}: a singular double solid $X \to \mathbb{P}^3$
ramified along a quartic symmetroid. This threefold is non-rational thanks to \cite{artin-mumford}, because $H^3(X, \mathbb{Z})$
has torsion. A rough account
(skipping the details about the resolution of singularities) of Ingalls and Kuznetsov's result is the following:
if $X'$ is the small resolution of $X$, there is an Enriques surface $S$ and a semiorthogonal decomposition
\begin{equation}\label{decomp-double-solid}
{\rm D}^{\rm b}(X') = \langle \cat{A}_S, E_1,E_2 \rangle,
\end{equation}
where $E_i$ are exceptional objects and $\cat{A}_S$ is the orthogonal complement in ${\rm D}^{\rm b}(S)$ of 10 exceptional vector bundles on $S$
(\cite{zube-enriques}). Then we can apply to this set Corollary \ref{cor-surf-non-rep}.
\begin{corollary}
The threefold $X'$ is not categorically representable in codimension $>1$.
\end{corollary}
\begin{proof}
Consider the Enriques surface $S$ and the semiorthogonal decomposition
$${\rm D}^{\rm b}(S) = \langle \cat{A}_S, E_1, \ldots, E_{10} \rangle,$$
where $E_i$ are the exceptional vector bundles described in \cite{zube-enriques}. Then the non-representability
of $S$ in codimension $>0$ is equivalent to the non-representability of $\cat{A}_S$ in dimension $<2$.
The statement follows then from (\ref{decomp-double-solid}).
\end{proof}
Remark that the
lack of categorical representability of $X'$ (and presumably of $X$, thinking about the categorical resolution of
singularities) is due to the presence of torsion in $K_0(S)$ and in particular in $H_1(S,\mathbb{Z})$, whereas the non-rationality
of $X$ is due to the presence of torsion in $H^3(X,\mathbb{Z})$. The relation between torsion in $H^3(X,\mathbb{Z})$ and categorical
representability needs a further investigation, for example in the case recently described in \cite{katza-iliev-pry-nonrational}.
\subsection{Noncommutative varieties}\label{noncommutative}
The previous speculations and partial results give rise to the hope of extending fruitfully the study of categorical representability
to higher dimensions and to the noncommutative setting. By the latter, we mean, following Kuznetsov
\cite[Sect. 2]{kuznetconicbundles}, an algebraic variety $Y$ with a sheaf ${\cal B}$ of ${\cal O}_Y$-algebras of finite type.
Very roughly, the corresponding noncommutative variety $\bar{Y}$ would have a category of coherent sheaves ${\cat{Coh}}(\bar{Y}) = {\cat{Coh}}(Y,
{\cal B})$ and a bounded derived category ${\rm D}^{\rm b}(\bar{Y}) = {\rm D}^{\rm b}(Y,{\cal B})$. The examples
which appear very naturally in our setting
are the cases where ${\cal B}$ is an Azumaya algebra or the even part of the Clifford algebra associated to some quadratic form over $Y$.
Finally, if a triangulated category $\cat{A}$ has
Serre functor such that $S_{\cat{A}}^m = [n]$, for some integers $n$ and $m$, with $m$ minimal with this property,
we will call it a \it $\frac{n}{m}$-Calabi--Yau category. \rm
If $m=1$, these categories deserve the name of noncommutative Calabi--Yau $n$-folds, even if they are not a priori given
by the derived category of some Calabi--Yau $n$-fold with a sheaf of algebras.
If $S$ is any smooth projective variety, $X \to S$ a Brauer--Severi variety of relative dimension $r$, and ${\cal A}$ the
associated Azumaya algebra in ${\rm Br}(S)$, then \cite{marcellobrauer}
$${\rm D}^{\rm b}(X) = \langle {\rm D}^{\rm b}(S), {\rm D}^{\rm b}(S,{\cal A}^{-1}), \ldots, {\rm D}^{\rm b}(S,{\cal A}^{-r}) \rangle.$$
The categorical representability of $X$ would then
rely on the categorical representability of $(S,{\cal A})$, which is an interesting object in itself. For example,
if $Y$ is a generic cubic fourfold containing a plane, there are a K3 surface $S$ and an Azumaya algebra
${\cal A}$ such that the categorical representability of $(S,{\cal A})$ is the subject of Kuznetsov's Conjecture \cite{kuznetcubicfourfold} about the rationality of cubic fourfolds.
\smallskip
If $S$ is a smooth projective variety and $Q \to S$ a quadric fibration of relative dimension $r$, we
can consider the sheaf ${\cal B}_0$ of the even parts of the Clifford algebra associated to the quadratic form defining
$Q$. There is a semiorthogonal decomposition:
$${\rm D}^{\rm b}(Q) = \langle {\rm D}^{\rm b}(S,{\cal B}_0), {\rm D}^{\rm b}(S)_1, \ldots, {\rm D}^{\rm b}(S)_{r-1}\rangle,$$
where ${\rm D}^{\rm b}(S)_i$ are equivalent to ${\rm D}^{\rm b}(S)$ \cite{kuznetconicbundles}. The categorical representability of $(S,{\cal B}_0)$ should then
be a very important tool in studying birational properties of $Q$. This is indeed the case for conic bundles over rational
surfaces \cite{marcello-bolo-conicbd}.
\smallskip
Finally, let $\cat{A}$ be an $\frac{n}{m}$-Calabi--Yau category. Such categories appear as orthogonal complements
of an exceptional sequence on Fano hypersurfaces in projective spaces \cite[Cor. 4.3]{kuznetv14}. It is then natural
to wonder about their representability. For example, if $X$ is a cubic or a quartic threefold,
it follows from Remark \ref{list-three-not-rep} that these orthogonal complements (which are, respectively, $\frac{5}{3}$ and
$\frac{10}{4}$-Calabi--Yau)
are not representable in dimension 1.
\begin{question}\label{question-cycat}
Let $\cat{A}$ be a $\frac{n}{m}$-Calabi--Yau category.
\begin{itemize}
\item[1)] Is $\cat{A}$ representable in some dimension?
\item[2)] If yes, is there an explicit lower bound for this dimension?
\item[3)] If $m=1$, is $\cat{A}$ representable in dimension $n$ if and only if there exist a smooth
$n$-dimensional variety $X$ and an equivalence ${\rm D}^{\rm b}(X) \simeq \cat{A}$?
\end{itemize}
\end{question}
\subsection{Higher dimensional varieties}\label{higherdim}
Unfortunately, it looks like the techniques used for threefolds in \cite{marcello-bolo-conicbd} hardly extend to
dimension bigger than $3$. The examples and supporting evidences provided so far lead anyway
to suppose that categorical representability can give useful informations on the birational properties of
any projective variety. The main case is a challenging Conjecture by Kuznetsov \cite{kuznetcubicfourfold}. Let $X \subset \mathbb{P}^5$ be
a smooth cubic fourfold, then there is a semiorthogonal decomposition
$${\rm D}^{\rm b}(X) = \langle \cat{A}_X, {\cal O}_X, {\cal O}_X(1), {\cal O}_X(2) \rangle.$$
The category $\cat{A}_X$ is 2-Calabi--Yau.
\begin{conjecture}\label{kuz-conj}\bf(Kuznetsov). \rm
The cubic fourfold $X$ is rational if and only if $\cat{A}_X \simeq {\rm D}^{\rm b}(Y)$ for a smooth projective K3 surface $Y$.
\end{conjecture}
This conjecture has been verified in \cite{kuznetcubicfourfold} for singular cubics, pfaffian cubics and
Hassett's \cite{hassett-special} examples.
When $X$ contains a plane $P$
there is a way more explicit construction: blowing up $P$ we obtain a quadric bundle $\widetilde{X} \to \mathbb{P}^2$ of
relative dimension 2, degenerating along a sextic. If the sextic is smooth, let $S \to \mathbb{P}^2$ be the double
cover, which is a K3 surface. Then
$$\cat{A}_X \simeq {\rm D}^{\rm b}(\mathbb{P}^2,{\cal B}_0) \simeq {\rm D}^{\rm b}(S,{\cal A}),$$
where ${\cal B}_0$ is associated to the quadric fibration and ${\cal A}$ is an Azumaya algebra, obtained lifting ${\cal B}_0$
to $S$. The questions about categorical
representability of noncommutative varieties arise then very naturally in this context.
Notice that if $\cat{A}_X$ is representable in dimension 2, then we know something weaker than Kuznetsov conjecture:
we would have a smooth projective surface $S'$ and a fully faithful functor $\cat{A}_X \to {\rm D}^{\rm b}(S')$. Point
3) of Question \ref{question-cycat} appears naturally in this context.
\begin{question}\label{quest-kuz-conj}
One can then wonder if the Kuzentsov conjecture may be stated in the following form: the cubic fourfold $X$ is rational if and only if
it is categorically representable in codimension 2. This is equivalent to proving that the 2-Calabi--Yau category $\cat{A}_X$
is representable in dimension 2 if and only if there exist a K3 surface $Y$ and an equivalence ${\rm D}^{\rm b}(Y) \simeq \cat{A}_X$.
\end{question}
We can propose some more examples of fourfolds for which a Kuznetsov-type conjecture seems natural: if $X$ is the complete intersection
of three quadrics $Q_1$, $Q_2$, $Q_3$ in $\mathbb{P}^7$, then Homological Projective Duality (\cite{kuznetHPD,kuznetconicbundles}) gives an exceptional
sequence on $X$ and its complement $\cat{A}_X \simeq {\rm D}^{\rm b}(\mathbb{P}^2,{\cal B}_0)$, where ${\cal B}_0$ is the even Clifford algebra associated to the net
of quadrics generated by $Q_1,Q_2,Q_3$. Similarly, if we consider two quadric fibrations $Q_1, Q_2 \to \mathbb{P}^1$ of relative dimension
$4$ and their complete intersection $X$, there is an exceptional sequence
on $X$, and let $\cat{A}_X$ be its orthogonal complement. A realtive version of Homological Projective Duality shows that $\cat{A}_X$
equivalent to ${\rm D}^{\rm b}(S,{\cal B}_0)$, where $S$ is a $\mathbb{P}^1$-bundle over $\mathbb{P}^1$ and ${\cal B}_0$ the
even Clifford algebra associated to the net of quadrics generated by $Q_1$ and $Q_2$. It is natural to wonder if representability in dimension
2 of the noncommutative varieties is equivalent or is a necessary condition for rationality of $X$. A partial answer to the last
example will be provided in a forthcoming paper \cite{asher-marcello-bolo}.
Other examples in dimension 7 are provided in \cite{iliev-manivel-cubic-7-8folds}.
If $X$ is a cubic sevenfold, there is a distinguished subcategory $\cat{A}_X$ of ${\rm D}^{\rm b}(X)$,
namely the orthogonal complement of the exceptional sequence $\{{\cal O}_X, \ldots, {\cal O}_X(5)\}$. This
is a 3-Calabi--Yau category. If $X$ is Pfaffian, it is shown in \cite{iliev-manivel-cubic-7-8folds}
that $\cat{A}_X$ cannot be equivalent to the derived category of any smooth projective variety.
It is also conjectured that $\cat{A}_X$ is equivalent to the orthogonal complement of an exceptional
sequence in the derived category ${\rm D}^{\rm b}(Y)$ of a Fano sevenfold $Y$ of index 3,
birationally equivalent to $X$.
\subsection{Other approaches}\label{approaches}
Of course categorical representability is just one among different approaches to the study
of birational geometry of a variety via derived categories. Nevertheless there is some
common ground.
\smallskip
First of all, Kuznetsov mentions in \cite{kuznetcubicfourfold} the notion of Clemens--Griffiths component of ${\rm D}^{\rm b}(X)$, whose
vanishing would be a necessary condition for rationality. It seems reasonable to expect that categorical representability
in codimension 2 implies the vanishing of the Clemens--Griffiths component.
Another recent theory is based on
Orlov spectra and their gaps \cite{katza-favero-ballard-generation-time}. Let us refrain even to sketch a definition of it,
but just notice that \cite[Conj. 2]{katza-favero-ballard-generation-time} draws a link between categorical
representability and gaps in the Orlov spectrum (see, in particular \cite[Cor. 1.11]{katza-favero-ballard-generation-time}).
Finally, conjectures based on homological mirror symmetry are proposed in
\cite{katza-rat-hms-1,katza-rat-hms-2}, but we cannot state a precise relation with our construction. A careful study
of the example constructed in \cite{katza-iliev-pry-nonrational} would be a good starting point.
\bibliographystyle{amsalpha}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 2,510
|
\section{Introduction}
\label{intro}
Newtonian physics is replete with examples of multi-fluid systems, such
as diffusion, ion flow, superfluid Helium, and plasma discharge from the Sun.
\ In fact, large characteristic scattering times between different components
is more the norm than the exception. \ This leads to physical situations
where the various components can move independently of each other, be it
across an interface or through interpenetration. \ In this context, even heat
conduction in systems where all the matter flows together is a two-fluid
problem, \ie there is a heat flux in addition to the matter flux. \ Perhaps
not as widely appreciated is that the relativistic regime has its own set of
multi-fluid scenarios: neutrino streaming during supernovae, superfluid
neutrons and superconducting protons in neutron stars, and heat flow in a
cosmological setting, to name but a few.
A key issue is that relativistic fluids must be causal, meaning
that sound speeds, say, must be less than that of light. \ For fluids, there
are two entry points for causality: the microscopic where particle-particle
interactions are tracked and the macroscopic where fluid elements (large
enough to contain many particles, but small enough to be point-like with
respect to the total system) are monitored. \ Presumably, a fully relativistic
treatment at the microscopic level would lead to a set of fluid coefficients
(describing the equation of state, dissipation, etc.)~that would already
behave appropriately at the macroscopic level. \ However, there is a practical
problem: Equation of state determinations are notoriously difficult. \ This
makes a general analysis of relativistic fluid dynamics prohibitive, if not
impossible. \ Fortunately, one can make progress by imposing causality ``from
above'' and absolute stability (\ie real sound speeds) ``from below'' to
constrain the fluid coefficients.
In this paper, we will do this by analyzing the local propagation of plane
waves on a given (arbitrary) background spacetime. \ Compared to the standard
single-fluid analysis, we have more fluid degrees of freedom and need to
allow for relative flows between the various fluids. \ This is an essential
requirement for two-stream instability. \ Such instabilities are known to
exist for a variety of configurations. \ For shearing motion at an interface,
it is an example of Kelvin-Helmholtz instability. \ However, as far as we are
aware, generic two-stream instability has not been discussed previously in
relativity.
The two-stream instability has been well-documented for plasmas (where
it is known as the ``Farley-Buneman'' instability
\cite{farley63:_2stream,buneman59:_2stream}, see \cite{chen_plasma}
for a text-book discussion). It has also been suggested as the
mechanism behind star formation when two galaxies (whose angular
velocities are more or less anti-aligned) merge
\cite{lovelace1997:_gal_two_strm}. \ In the general relativistic
context, Chandrasekhar, Friedman, and Schutz (CFS)
\cite{chandrasekhar70:_grav_instab,friedman78:_secul_instab} have demonstrated
that oscillation modes in rotating, perfect fluids can become
two-stream unstable due to the emission of gravitational radiation. \
Here, the two ``fluids'' are the rotating mass, and the asymptotically
flat spacetime in which the fluid is embedded. \ Most recently, a
two-stream instability for superfluids has been proposed, with a
natural extension to a mixture of superfluid neutrons and
superconducting protons in neutron star cores
\cite{acp03:_twostream_prl,andersson04:_twostream}. \ Very recent results
suggest that this instability may act as a trigger mechanism for the enigmatic
spin glitches that have been observed in a number of radio pulsars
\cite{glampedakis09:_glitch_prl} (see also \cite{andersson04:_twostream} for
the first suggestion of a link between glitches and two-stream instability).
In what follows we will not restrict the discussion to any specific physical
system. Consequently, the analysis will be somewhat abstract. \ This
strategy can work because the two essential requirements for triggering
two-stream instability is a relative flow between two fluids and a generic
interaction between them. \ This freedom to remain abstract illustrates the
general robustness of the instability and its presence in a diverse collection
of systems. \ Essentially, if the relative velocity is large enough that a
wave moves in one direction with respect to the rest-frame of one fluid, yet
the opposite direction with respect to the other fluid's rest-frame, then the
energy of the wave will be ``negative'' in one of the rest-frames and
therefore unbounded from below. \ Our main aim is to show that a causal and
absolutely stable system of two relativistic fluids can undergo two-stream
instability for a range of relative speeds and equation of state parameter
values.
The presentation of the results is organized as follows: Section \ref{formal}
recalls the multi-fluid formalism, and sets the stage for a plane-wave
analysis of the system. \ Section \ref{singwaves} considers sound waves for a
single fluid. \ The results are not new, but they help establish
basic techniques that carry over to the more complicated two-fluid
calculations discussed in Section \ref{twowaves}. \ The following
sub-sections consider three variations on the two-fluid equation of state:
(i) the ``free'' (where there is no direct coupling between the fluid
densities), (ii) coupled, and (iii) entrained cases. \ Finally, in Section
\ref{conclu}, we make our concluding remarks. \ Spacetime indices are denoted
by the first letters of the roman alphabet ($a, b, c$), constituent indices by
the last (x, y, z), and we adopt ``MTW'' (Misner, Thorne, and Wheeler
\cite{mtw73}) conventions for the metric signature.
\section{The Multi-fluid Formalism}
\label{formal}
We will use the approach to multi-fluid systems that was developed
originally by Carter \cite{carter89:_covar_theor_conduc} (see
\cite{andersson07:_livrev} for a recent review). \ In this description, the
main variables are the various fluxes (for particles and/or entropy),
to be denoted $n^a_{\rm x}$, and the equations of motion follow from a
suitably defined ``master'' function (\ie Lagrangian or equation of
state) $\Lambda$. \ In the single fluid case, $-\Lambda$ is equal to
the rest frame energy density $\rho$ . \ We have here introduced the
convention of attaching a constituent index ${\rm x}$ to each
variable. This index is redundant for a single fluid, but necessary
when there are multiple fluids. \ The master function varies only with
the fluxes.
\ If the fluids are locally isotropic (\ie no preferred direction), as they
should be in the absence of anything else (such as an elastic solid), it is
clear that $\Lambda$ must be a function of only the various scalars that can
be formed from inner products of the fluxes.
We will focus on the case of two fluids (see \cite{andersson07:_livrev} for a
complete description), even though most of the equations in the general
discussion will carry enough constituent indices (${\rm x}$, ${\rm y}$, etc.) to be valid for
any number of fluids. \ In the case of two components, the master function
depends on two distinct particle fluxes $n^a_{\rm x}$ and $n^a_{\rm y}$ and has the
functional dependence~\footnote{It is worth making the following remark on
the notation. \ Throughout the paper we only consider two fluids. \ They are
generally labelled by ${\rm x}$ and ${\rm y}$. \ However, in order to be economic in the
presentation we often treat the constituent index as abstract, meaning that
it can be either ${\rm x}$ or ${\rm y}$. \ That is, an equation written down explicitly
for fluid ${\rm x}$ takes exactly the same form for the other fluid once the index
${\rm x}$ is replaced by ${\rm y}$ (and vice versa). \ We are aware that this
convention may be confusing at first, but it makes sense. \ Especially if one
wants to account for additional fluid components. \ Most of our equations
still remain valid in that case, although in each equation for fluid ${\rm x}$ one
has to sum over all the other fluids (i.e.~the sum runs over ${\rm y} \neq {\rm x}$).}
\beq
\Lambda = \Lambda(\nx,\ny,\nxy) \ , \label{mf2}
\eeq
where $\nxy = - g_{a b} n^a_{\rm x} n^b_{\rm y}$. \ Note that constituent indices are
not summed over when repeated. \ As a matter of convenience repeated indices
are written only once; that is, we write $\nx$ (which is the squared particle
number density of the ${\rm x}^{\rm th}$-fluid) for $n^2_{{\rm x}\x}$ and so on.
The equations of motion become most transparent when expressed in terms of
the momentum $\mu^{\rm x}_a$ which is canonically conjugate to $n_{\rm x}^a$:
\beq
\mu_a^{\rm x} = \BX n^{\rm x}_a + \AXY n^{\rm y}_a \ , \label{mom}
\eeq
where
\beq
\BX \equiv -2 \frac{\partial \Lambda}{\partial \nx}
\quad , \quad
\AXY \equiv -\frac{\partial \Lambda}{\partial \nxy}
\ . \label{bxaxydef}
\eeq
Note that we have simplified the notation by not indicating explicitly
which variables are fixed when partial derivatives are taken. (The
functional dependence of the master function is clear from
\eqref{mf2}.)
\ From \eqref{mom} we see that the momentum $\mu^{\rm x}_a$ is not simply
proportional to its canonical conjugate $n^a_{\rm x}$, but is rather a linear
combination of all the fluxes. \ This is a result of the so-called
entrainment effect (see \cite{andreev75:_three_velocity_hydro} for an example
in superfluid Helium mixtures,
\cite{borumand96:_superfl_neutr_star_matter,comer03:_rel_ent,chamel06:_ent_cold_ns}
for relativistic, nuclear matter, or \cite{andersson08:_ent_ent} for a
treatment of entropy/matter entrainment and its importance for heat flow).
It is convenient at this point to introduce a shorthand notation for
derivatives of these coefficients; namely,
\bea
\Ccc^2 &\equiv& \frac{1}{\BX \BY} \left(2 n_{\rm x} n_{\rm y}
\frac{\partial \BX}{\partial \ny} \right)
\ , \cr
\BX_{, {\rm x} {\rm y}} &\equiv& n_{\rm x} n_{\rm y} \frac{\partial \BX}{\partial \nxy}
\ , \cr
\AXY_{, {\rm x} {\rm y}} &\equiv& n_{\rm x} n_{\rm y} \frac{\partial \AXY}{\partial
\nxy} \ . \label{twoderivs}
\eea
For the same reason we define the ``speed-of-sound'' $c^2_{\rm x}$ of the
${\rm x}^{\rm th}$-fluid as
\beq
c^2_{\rm x} = \frac{\partial \log \BX}{\partial \log n_{\rm x}} + 1 \ . \label{cs1}
\eeq
Finally, we introduce the ``perp'' operator
\beq
\perp^{{\rm x} b}_a = \delta_a{}^b + u^{\rm x}_a u^b_{\rm x}
\quad , \quad
\perp^{{\rm x} b}_a u^a_{\rm x} = 0 \ , \label{perp}
\eeq
which can be used to construct, say, vectors that are orthogonal to $u^a_{\rm x}$.
We have chosen the fluxes $n^a_{\rm x}$ as our primary fields. \ However, there
is no reason why the momenta $\mu^{\rm x}_a$ could not be similarly adopted
\footnote{In fact, the celebrated Landau model for superfluid Helium mixes a
momentum with a flux, see for example, the discussion in
\cite{carter94:_canon_formul_newton_superfl}.}. \ This implies that the
mapping from one set of fields to the other must have an inverse. \ That is,
we see from \eqref{mom} that
\beq
\left[\begin{array}{c} \mu^{\rm x}_a \\ \mu^{\rm y}_a \end{array}\right]
= \left[\begin{array}{cc}
\BX & \AXY \\
\AXY & \BY
\end{array}\right]
\left[\begin{array}{c}
n^{\rm x}_a \\ n^{\rm y}_a
\end{array}\right]
\ , \label{momfluxmat}
\eeq
and thus $\BX \BY - ({\AXY})^2 \neq 0$. \ This will be a useful constraint
later, when we discuss the impact of entrainment on sound modes.
For the purely variational case (\ie no dissipation, imposed constraints,
etc.), the individual constituents are conserved
\cite{andersson07:_livrev,carter06:_crust}, so that we have for each component
\beq
\nabla_a n_{\rm x}^a = 0 \ .
\eeq
The remaining equations of motion take the form
\beq
n^a_{\rm x} \omega^{\rm x}_{a b} = 0 \ , \label{forceeqns}
\eeq
where the vorticity tensor $\omega^{\rm x}_{a b}$ is given by
\beq
\omega^{\rm x}_{a b} \equiv 2 \nabla_{[a}\mu^{\rm x}_{b]} \ . \label{vort}
\eeq
As discussed, {\it eg.~}} \def\etal{{\it et al.}} \def\ie{{\it i.e.~}, in \cite{andersson07:_livrev}, in the single-fluid case
these equations contain the same information as the standard set obtained
from the vanishing of the covariant divergence of the stress-energy-momentum
tensor. \ Eq.~\eqref{forceeqns} illustrates the geometrical significance of
the Euler equation as an integrability condition on the vorticity; \ie that
the particle flux nowhere pierces the surfaces defined by the two-form
$\omega^{\rm x}_{a b}$.
Below we will be analyzing plane-wave propagation on backgrounds such that
$\omega^{\rm x}_{a b} = 0$, the various background quantities are taken to be
constant, and there is a relative flow between the fluids. \ This implies a
linearization of the equations of motion; \ie
\beq
\nabla_a \delta n^a_{\rm x} = 0
\quad , \quad
n_{\rm x}^a \nabla_{[a}\delta \mu^{\rm x}_{b]} = 0 \ . \label{pereqsx}
\eeq
Because there are several fluids, the variation $\delta \mu^{\rm x}_a$ is
significantly more complicated than, say, in the case of the standard perfect
fluid. \ In addition to individual bulk effects for each fluid, there can
also be cross-constituent effects due to coupling between the fluids. \ We
also have to consider the entrainment.
Following \cite{andersson07:_livrev}, we can isolate the various effects in
the variation and write
\beq
\delta \mu_a^{\rm x} = \left(\BXab + \Acalxab\right) \delta n^b_{\rm x} +
\left(\Xcalab + \Acalxyab\right) \delta n^b_{\rm y} \ ,
\label{muvarx}
\eeq
where the bulk effects are captured by
\beq
\BXab = \BX \left(\perp^{\rm x}_{a b} - c^2_{\rm x} u^{\rm x}_a u^{\rm x}_b\right)
\ , \label{bulk}
\eeq
the cross-constituent coupling through
\beq
\Xcalab = - \Ccc \sqrt{\BX \BY} u^{\rm x}_a u^{\rm y}_b \ , \label{crosscoup}
\eeq
and the entrainment via the terms
\bea
\Acalxab &=& - \left[\BX_{, {\rm x} {\rm y}} \left(u^{\rm x}_a u^{\rm y}_b + u^{\rm x}_b u^{\rm y}_a
\right) + \frac{n_{\rm y}}{n_{\rm x}} \AXY_{, {\rm x} {\rm y}} u^{\rm y}_a u^{\rm y}_b
\right] \ , \\
&& \cr
\Acalxyab &=& \AXY \!\!\perp^{\rm x}_{a b} - \left[\left(\AXY + \frac{n_{\rm x}}{n_{\rm y}}
\BX_{, {\rm x} {\rm y}}\right) u^{\rm x}_a u^{\rm x}_b + \frac{n_{\rm y}}{n_{\rm x}}
\BY_{, {\rm x} {\rm y}} u^{\rm y}_a u^{\rm y}_b + \AXY_{, {\rm x} {\rm y}} u^{\rm y}_a
u^{\rm x}_b\right] \ . \label{entraincoup}
\eea
In these expressions the flux $n^a_{\rm x}$ has been decomposed as $n^a_{\rm x} = n_{\rm x}
u^a_{\rm x}$, where $u^a_{\rm x}$ is the unit ($u^{\rm x}_a u^a_{\rm x} = - 1$) four-velocity of
the ${\rm x}$-fluid elements.
\section{Single-fluid Sound Waves}
\label{singwaves}
To set the stage for the general analysis it is useful to first consider the
nature of sound waves in a single, perfect fluid. \ To do this, we perform a
local analysis of linear perturbations of the fluid (keeping the metric fixed)
on a generic background. \ In particular, plane-wave propagation corresponds
to the Ansatz
\beq
\delta n^a_{\rm x} = A^a_{\rm x} \exp(i k_b x^b) \ , \label{plwave}
\eeq
where the amplitude $A^a_{\rm x}$ and wave four-vector $k^a$ have vanishing
covariant derivatives. \ Recall that we assume all unperturbed quantities to
be similarly constant. \ In particular, the background vorticity simply
vanishes. \ From \eqref{muvarx} above we have
\beq
\delta \mu^{\rm x}_a = \Bcalxab \delta n^b_{\rm x} \ . \label{varmu1}
\eeq
Note that we have continued to use a constituent index, even though we are
dealing with a single fluid. \ This allows for some economy of presentation
since many of the formulas will apply later, except that the index ${\rm x}$ will
then range over two fluids. \ Of course, waves in a system are such that the
constant wave vector $k_a$ is the same for all the fluids. \ Hence, it does
not carry a constituent index.
For convenience we will work in the material frame associated with the fluid.
\ This means that $k_a$ and $A^a_{\rm x}$ will each be written as two pieces by
utilizing the ``perp'' operator introduced in \eqref{perp}:
\beq
k_a = k_{\rm x} \left(\sigma_{\rm x} u^{\rm x}_a + \hat{k}^{\rm x}_a\right) \ , \label{kdef}
\eeq
where $\sigma_{\rm x}$ and the wave vector $k^{\rm x}_a$ (with magnitude $k_{\rm x}$)
are
\beq
k_{\rm x} \sigma_{\rm x} = - k_a u^a_{\rm x}
\quad , \quad
k^{\rm x}_a = \perp^b_{{\rm x} a} k_b \equiv k_{\rm x} \hat{k}^{\rm x}_a \ .
\eeq
Similarly, we can decompose the wave amplitude as
\beq
A^a_{\rm x} = A^{\rm x}_{||} u^a_{\rm x} + A_{{\rm x} \perp}^a \ ,
\eeq
where
\beq
A^{\rm x}_{||} = - u^{\rm x}_a A^a_{\rm x} \quad , \quad A_{{\rm x} \perp}^a = \perp^a_{{\rm x} b}
A^b_{\rm x} \ .
\eeq
Note that $\sigma_{\rm x}$ and $\hat{k}_{\rm x}^a$ are measured by an observer moving
with the fluid. \ It will be obvious from the dispersion relation constructed
below that $\sigma_{\rm x}$ measures the phase velocity of the waves as seen in
the fluid frame. \ Furthermore, it is easy to show that evaluating
$\sigma_{\rm x}$ in a frame moving relative to the fluid leads to the standard
Lorentz transformation of velocities.
With these preliminaries, the perturbation equations \eqref{pereqsx} reduce to
\bea
0 &=& k_a A^a_{\rm x} \ , \label{cons1} \\
0 &=& n^a_{\rm x} k_{[a} \BX_{b] c} A^c_{\rm x} \ . \label{euler1}
\eea
The first of these relations shows that the waves are transverse in
the spacetime sense. \ The dispersion relation can be easily obtained
by contracting the second equation with $k^b$. (In the more
complicated two-fluid analysis below, we will in general have to
consider the vanishing of a $4 \times 4$ determinant.) \ Assuming that
$n^{\rm x}_c A^c_{\rm x} \neq 0$, and after several steps of algebra, the
dispersion relation reduces to
\beq
\sigma^2_{\rm x} - c^2_{\rm x} = 0 \ . \label{disper1}
\eeq
In our homogeneous plane-wave setting it is clear that the group and phase
velocities coincide so that we can introduce the speed of sound in the
standard way as $c^2_{\rm x} = \sigma^2_{\rm x}$.
To see that this is equivalent to the usual single-fluid result (as in,
say, \cite{weinberg72:_book}), it will suffice to introduce the pressure and
recall that $\rho = - \Lambda$ in the single fluid case. \ From the
definition above for $\BX$, cf.~\eqref{bxaxydef}, we see that
\beq
{\rm d} \rho = \BX n_{\rm x} {\rm d} n_{\rm x} \ .
\eeq
Moreover, the pressure $p$ is defined by the standard thermodynamic relation, such that
\beq
p = - \rho + n_{\rm x}{ { \rm d} \rho \over {\rm d} n_{\rm x}} = - \rho + \BX n^2_{\rm x} \ .
\eeq
This implies
\beq
{\rm d} p = \left(1 + \frac{\partial \log \BX}{\partial \log n_{\rm x}}\right)
{\rm d} \rho \ ,
\eeq
and we have
\beq
\frac{{\rm d} p}{{\rm d} \rho} = 1 + \frac{\partial \log \BX}{\partial
\log n_{\rm x}} = c^2_{\rm x} \ ,
\eeq
where ${\rm d} p/{\rm d} \rho$ is the usual form of the sound speed squared.
In order to pave the way for the more complicated multi-fluid case to be
discussed below it is useful to examine the properties of the various vectors
we have introduced. \ Starting with the wave vector $k^a$ we see that
\beq
k_a k^a = k_{\rm x}^2 \left(1 - c_{\rm x}^2\right) \ . \label{kmag}
\eeq
Thus, for causal wave propagation ($c_{\rm x}^2 \leq 1$), $k^a$ is spacelike. \
For the wave amplitude we find that, when the force equation
\eqref{euler1} is evaluated in terms of the solution to the
dispersion relation,
\beq
A_{{\rm x} \perp}^a = \sigma_{\rm x} A^{\rm x}_{||} \hat{k}_{\rm x}^a \ .
\eeq
The waves are therefore longitudinal in the normal, three-dimensional sense. \
On the other hand, the transverse nature \eqref{cons1} of the waves in the
four-dimensional sense implies that
\beq
A^2_{\rm x} = A_{{\rm x} \perp}^2 \left(1 - c_{\rm x}^{-2}\right)
\eeq
so that $A^a_{\rm x}$ is timelike (and we can choose it to be future
pointing) for causal waves. \ Note that since the flux $n^a_{\rm x}$ is
also timelike this implies that $n^a_{\rm x} A^{\rm x}_a < 0$ and thus the
degenerate case of \eqref{disper1} is ruled out by causality.
Before we conclude this section, it is useful to consider what constraints
\eqref{cs1} imposes on the equation of state. \ First of all, the causality
requirement leads immediately to
\beq
\frac{\partial \log \BX}{\partial \log n_{\rm x}} + 1 \le 1 \ .
\eeq
In addition, we must have $c_{\rm x}^2 \ge 0$ in order to avoid absolute
instabilities (complex wave speeds). This implies
\beq
\frac{\partial \log \BX}{\partial \log n_{\rm x}} + 1 \ge 0 \ . \label{absstab1}
\end{equation}
Combining the two results we see that we must have
\beq
- 1 \le \frac{\partial \log \BX}{\partial \log n_{\rm x}} \le 0 \ .
\label{stabcaus1}
\eeq
In the next section we will extend this type of analysis to the two-fluid
model.
\section{Sound Waves for the General Two-fluid System}
\label{twowaves}
We want to work out the dispersion relation for wave propagation
in a two-fluid system, using \eqref{plwave} as the starting point. \ An
important addition to the problem of plane waves is a new ``parameter'',
the relative flow between the two fluids. \ We will represent this flow
by the relative velocity $v^a_{{\rm x} {\rm y}}$ of the ${\rm y}^{\rm th}$-fluid with
respect to the frame of the ${\rm x}^{\rm th}$-fluid:
\beq
\gamma_{{\rm x} {\rm y}} v^a_{{\rm x} {\rm y}} = \perp^{{\rm x} a}_b u^b_{\rm y} \ , \label{vxy}
\eeq
where $v_{{\rm x} {\rm y}}$ represents the magnitude of the relative flow and
\beq
\gamma_{{\rm x} {\rm y}} = \gamma_{{\rm y} {\rm x}} = - u^c_{\rm x} u^{\rm y}_c =
\frac{1}{\sqrt{1 - v^2_{{\rm x} {\rm y}}}} \ .
\eeq
This leads to
\beq
u^a_{\rm y} = \gamma_{{\rm x} {\rm y}}\left(u^a_{\rm x} + v^a_{{\rm x} {\rm y}}\right) \ .
\eeq
The mode speed $\sigma_{\rm x}$ and wave (three-) vector $k^{\rm x}_a$ can be defined as
before. \ The insertion of $\gamma_{{\rm x} {\rm y}}$ into \eqref{vxy} makes the
${\rm x}^{\rm th}$-fluid's proper time the standard for setting velocities. \ Since the
dispersion relation below is a scalar equation, we will have in several
places the inner product $\hat{v}^a_{{\rm x} {\rm y}} \hat{k}^{\rm x}_a$ (where
$\hat{v}^a_{{\rm x} {\rm y}} = v^a_{{\rm x} {\rm y}}/v_{{\rm x} {\rm y}}$). \ It is useful to
write this in terms of the angle $\theta_{{\rm x} {\rm y}}$ between the two vectors:
\beq
\hat{v}^a_{{\rm x} {\rm y}} \hat{k}^{\rm x}_a = \cos \theta_{{\rm x} {\rm y}} \ .
\eeq
An important subtlety must be recognized, however: The three quantities
$\sigma_{\rm x}$, $k^{\rm x}_a$, and $v^a_{{\rm x} {\rm y}}$ are what would be measured by an
observer flowing with the ${\rm x}^{\rm th}$-fluid. \ We could have equally as
well chosen the material frame attached to the other fluid (or some other
observer). \ As one might expect, there are well-defined transformations
between the two descriptions (which will be needed later). \ The relative flow
$v^a_{{\rm y} {\rm x}}$ of the ${\rm x}^{\rm th}$-fluid with respect to the
${\rm y}^{\rm th}$-fluid frame is related to $v^a_{{\rm x} {\rm y}}$ via
\beq
v^a_{{\rm y} {\rm x}} = - \gamma_{{\rm x} {\rm y}} \left(v^2_{{\rm x} {\rm y}} u^a_{\rm x} +
v^a_{{\rm x} {\rm y}}\right) \ ,
\eeq
where we have used $v_{{\rm y} {\rm x}} = v_{{\rm x} {\rm y}}$. \ It is also useful to note that
\bea
u^a_{\rm x} &=& - v^{- 2}_{{\rm x} {\rm y}} \left(v^a_{{\rm x} {\rm y}} + \gamma^{- 1}_{{\rm x} {\rm y}}
v^a_{{\rm y} {\rm x}}\right) \ , \cr
u^a_{\rm y} &=& - v^{- 2}_{{\rm x} {\rm y}} \left(v^a_{{\rm y} {\rm x}} + \gamma^{- 1}_{{\rm x} {\rm y}}
v^a_{{\rm x} {\rm y}}\right) \ . \label{423vel}
\eea
Because $k_a$ is not attached to either fluid frame, we must have
\beq
k_a = k_{\rm y} \left(\sigma_{\rm y} u^{\rm y}_a + \hat{k}^{\rm y}_a\right) = k_{\rm x}
\left(\sigma_{\rm x} u^{\rm x}_a + \hat{k}^{\rm x}_a\right) \ . \label{kequal}
\eeq
By contracting each four-velocity in \eqref{423vel} with the wave-vector
$k_a$, we obtain a matrix equation for $[k_{\rm x}~k_{\rm y}]^{\rm T}$; namely,
\beq
\left[\begin{array}{cc}
v_{{\rm x} {\rm y}} \sigma_{\rm x} - \cos \theta_{{\rm x} {\rm y}} & - \gamma^{- 1}_{{\rm x} {\rm y}}
\cos \theta_{{\rm y} {\rm x}} \\
- \gamma^{- 1}_{{\rm x} {\rm y}} \cos \theta_{{\rm x} {\rm y}} &
v_{{\rm x} {\rm y}} \sigma_{\rm y} - \cos \theta_{{\rm y} {\rm x}}
\end{array}\right]
\left[\begin{array}{c}
k_{\rm x} \\
k_{\rm y}
\end{array}\right] =
\left[\begin{array}{c} 0 \\ 0 \end{array}\right]
\ .
\eeq
Obviously the determinant of the $2 \times 2$ matrix must vanish. \ This
leads to
\beq
\sigma_{\rm y} = \cos \theta_{{\rm y} {\rm x}} \frac{\sigma_{\rm x} - v_{{\rm x} {\rm y}} \cos
\theta_{{\rm x} {\rm y}}}{v_{{\rm x} {\rm y}} \sigma_{\rm x} - \cos \theta_{{\rm x} {\rm y}}} \ .
\label{sigtrans}
\eeq
It is not difficult to show that if $\sigma^2_{\rm x} \le 1$ then $\sigma^2_{\rm y} \le
1$. This is natural given that causality is a frame-independent requirement.
Meanwhile, the equation of flux conservation is the same as \eqref{cons1}
(except ${\rm x}$ ranges over two values). \ The conservation of vorticity
equations become
\bea
0 &=& K^{\rm x}_{a b} A^b_{\rm x} + K^{{\rm x} {\rm y}}_{a b} A^b_{\rm y} \ , \cr
0 &=& K^{\rm y}_{a b} A^b_{\rm y} + K^{{\rm y} {\rm x}}_{a b} A^b_{\rm x} \ , \label{pereqns2}
\eea
where the ``dispersion'' tensors are
\bea
K^{\rm x}_{a b} &=& n^c_{\rm x} \left(k_{[c}\BX_{a]b} + k_{[c}\mathcal{A}^{\rm x}_{a]b}
\right) \ , \cr
K^{{\rm x} {\rm y}}_{a b} &=& n^c_{\rm x} \left(k_{[c} \Xcal^{{\rm x} {\rm y}}_{a]b} +
k_{[c}\mathcal{A}^{{\rm x} {\rm y}}_{a]b}\right) \ .
\label{disptens}
\eea
Note that $K^{\rm y}_{a b}$ and $K^{{\rm y} {\rm x}}_{a b}$ are obtained via the interchange
of ${\rm x} \leftrightarrow {\rm y}$ in equation \eqref{disptens}.
In order to solve \eqref{pereqns2}, we obviously need the four inverses
\beq
\tilde{K}^{a c}_{\rm x} K^{\rm x}_{c b} = \delta^a{}_c
\quad , \quad
\tilde{K}^{a c}_{{\rm y} {\rm x}} K^{{\rm x} {\rm y}}_{c b} = \delta^a{}_c \ ,
\eeq
to exist---\ie the determinants of $K^{\rm x}_{a b}$ and $K^{{\rm x} {\rm y}}_{a b}$ do not
vanish---so that we can write
\beq
0 = \left(\tilde{K}^{a c}_{\rm y} K^{{\rm y} {\rm x}}_{c b} - \tilde{K}^{a c}_{{\rm y} {\rm x}}
K^{\rm x}_{c b}\right) A^b_{\rm x} \equiv {\cal M}_{a b} A^b_{\rm x} \ .
\eeq
The only way to get a non-trivial solution is to have a $k_a$ such that
\beq
\epsilon^{a_1 a_2 a_3 a_4} \epsilon^{b_1 b_2 b_3 b_4} {\cal M}_{a_1 b_1}
{\cal M}_{a_2 b_2} {\cal M}_{a_3 b_3} {\cal M}_{a_4 b_4} = 0 \ .
\label{gensol}
\eeq
Written out in full \eqref{gensol} is a quite busy expression. \ This should
come as no surprise since the two-fluid problem is significantly more
complicated than a single fluid having bulk contributions coming from
$\BX_{a b}$, and the cross-coupling from $\Xcal^{{\rm x} {\rm y}}_{a b}$ (in the case
of two, co-moving constituents \cite{andersson07:_livrev}). \ For two-fluid
systems, the two constituents move independently and there are the additional
contributions $\mathcal{A}^{\rm x}_{a b}$ and $\mathcal{A}^{{\rm x} {\rm y}}_{a b}$ coming
from entrainment.
In order to simplify the problem, it is convenient to isolate further the
different contributions that appear in the dispersion matrices. \ The bulk
contribution in $K^{\rm x}_{a b}$ can be reduced to
\bea
b^{\rm x}_{a b} &=& n^c_{\rm x} k_{[c}\BX_{a]b} \cr
&=& - \frac{1}{2} \BX n_{\rm x} \left(k_{\rm x} \sigma_{\rm x} \perp^{\rm x}_{a b}
+ c^2_{\rm x} k^{\rm x}_a u^{\rm x}_b\right) \ , \label{bulkmat}
\eea
while its entrainment piece becomes
\bea
a^{\rm x}_{a b} &=& n^c_{\rm x} k_{[c}\mathcal{A}^{\rm x}_{a]b} \cr
&=& \frac{1}{2} \gamma_{{\rm x} {\rm y}} n_{\rm x} \Bigl\{
\mathcal{B}^{\rm x}_{, {\rm x} {\rm y}} \left[\left(k_{\rm x} \sigma_{\rm x}
v^{{\rm x} {\rm y}}_a - 2 k^{\rm x}_a\right) u^{\rm x}_b - k^{\rm x}_a
v^{{\rm x} {\rm y}}_b\right] \cr
&& + \gamma_{{\rm x} {\rm y}} \frac{n_{\rm y}}{n_{\rm x}}
\mathcal{A}^{{\rm x} {\rm y}}_{, {\rm x} {\rm y}} \left(k_{\rm x} \sigma_{\rm x}
v^{{\rm x} {\rm y}}_a - k^{\rm x}_a\right) \left(u^{\rm x}_b + v^{{\rm x} {\rm y}}_b
\right)\Bigr\} \ . \label{entmat1}
\eea
Meanwhile, the cross-coupling in $K^{{\rm x} {\rm y}}_{a b}$ is simply given by
\bea
x^{{\rm x} {\rm y}}_{a b} &=& n^c_{\rm x} k_{[c} \Xcal^{{\rm x} {\rm y}}_{a]b} \cr
&=& - \frac{1}{2} \mathcal{C}_{cc} \gamma_{{\rm x} {\rm y}} n_{\rm x}
\sqrt{\BX \BY} k^{\rm x}_a \left(u^{\rm x}_b + v^{{\rm x} {\rm y}}_b\right) \ , \label{ccmat}
\eea
but the entrainment has significantly more presence:
\bea
a^{{\rm x} {\rm y}}_{a b} &=& n^c_{\rm x} k_{[c}\mathcal{A}^{{\rm x} {\rm y}}_{a]b} \cr
&=& \frac{n_{\rm x}}{2} \left\{- \AXY k_{\rm x} \sigma_{\rm x}
\perp^{\rm x}_{a b} - \left[\AXY + \frac{n_{\rm x}}{n_{\rm y}} \mathcal{B}^{\rm x}_{, {\rm x} {\rm y}} +
\gamma_{{\rm x} {\rm y}} \left(\gamma_{{\rm x} {\rm y}} \frac{n_{\rm y}}{n_{\rm x}}
\mathcal{B}^{\rm y}_{, {\rm x} {\rm y}} + \mathcal{A}^{{\rm x} {\rm y}}_{, {\rm x} {\rm y}}\right)\right]
k^{\rm x}_a u^{\rm x}_b \right. \cr
&& \left. + \gamma_{{\rm x} {\rm y}} k_{\rm x} \sigma_{\rm x} \left(\gamma_{{\rm x} {\rm y}}
\frac{n_{\rm y}}{n_{\rm x}} \mathcal{B}^{\rm y}_{, {\rm x} {\rm y}} +
\mathcal{A}^{{\rm x} {\rm y}}_{, {\rm x} {\rm y}}\right) v^{{\rm x} {\rm y}}_a u^{\rm x}_b\right\} \ .
\label{entmat2}
\eea
A multi-fluid system must have non-zero bulk properties (unless a fluid
vanishes completely). \ The other terms can be absent, depending on the
equation of state. \ In what follows we will systematically increase the
complexity by considering in turn the different components of two-fluid
physics.
\subsection{Dispersion Relation: Free Case}
\label{DR-free}
Let us first consider the case of two completely uncoupled fluids. \ Then we
have only $b^{\rm x}_{a b}$ non-zero. \ In lieu of \eqref{gensol}, it is easier to
get the dispersion relation by contracting the free indices in
\eqref{pereqns2} with $k_a$. \ This results in the simple $2 \times 2$ matrix
problem
\beq
\left[\begin{array}{cc}
\BX \left(\sigma^2_{\rm x} - c^2_{\rm x}\right) & 0 \\
0 & \BY \left(\sigma^2_{\rm y} - c^2_{\rm y}\right)
\end{array}\right]
\left[\begin{array}{c}
u^{\rm x}_a A^a_{\rm x} \\
u^{\rm y}_a A^a_{\rm y}
\end{array}\right] =
\left[\begin{array}{c} 0 \\ 0 \end{array}\right]
\ , \label{bulkalg}
\eeq
and the dispersion relation is simply
\beq
\left(\sigma^2_{\rm x} - c^2_{\rm x}\right) \left(\sigma^2_{\rm y} - c^2_{\rm y}\right) = 0
\ . \label{freedisp}
\eeq
By construction $\sigma^2_{\rm x}$ is the squared phase (three-) velocity as
measured in the ${\rm x}^{\rm th}$-fluid frame (similarly for $\sigma^2_{\rm y}$).
The outcome of this analysis is that the dispersion relation \eqref{freedisp}
allows four non-trivial solutions consisting of the roots of
\beq
\sigma^2_{\rm x} = c_{\rm x}^2
\eeq
for any ${\rm x}$. \ These roots correspond to $\pm c_{\rm x}$ evaluated in the
${\rm x}^{\rm th}$-fluid frame and are just Lorentz transformed if evaluated in
another frame. \ Thus, as expected in the case of zero coupling between the
fluids, the quantity $c_{\rm x}$ can be interpreted as the sound velocity of the
${\rm x}^{\rm th}$-fluid as measured in its own (background) rest frame. \ This is
the obvious generalisation of the single fluid result. \ It follows that if
$c_{\rm x}$ is subluminal in its own rest-frame it is so in all other frames as
well. \ Also, since absolute instability should be evaluated at zero relative
velocity it is clear that the constraint $0 \le c^2_{\rm x} \le 1$ remains as a
condition for the master function.
The main conclusion from this discussion is that the constraints on the
equation of state are easily generalized to the uncoupled two-fluid
problem. \ We must thus require that the equation of state satisfy
\eqref{stabcaus1} for both fluids in order for the system to be absolutely
stable and give rise to causal wave propagation. \ There are no dynamical
instabilities present in this case. \ In what follows, we caution that the
$c_{\rm x}$ can be understood as ``sound'' speeds only in this completely free
case. \ When fluid couplings are operative, the phase velocities will no
longer simply equal these free sound speeds. \ But in order to make progress,
we will continue to impose \eqref{stabcaus1} throughout.
\subsection{Dispersion Relation: Cross-constituent Coupling}
\label{DR-coup}
We now allow for $x^{{\rm x} {\rm y}}_{a b}$ to be non-zero. \ From \eqref{ccmat}, we
see that this will introduce $\Ccc$ in addition to $\BX$ and $c^2_{\rm x}$. \
Using the same contractions with $k_a$ as in the free case, we again
get a $2 \times 2$ matrix problem; \ie
\beq
\left[\begin{array}{cc}
\BX \left(\sigma^2_{\rm x} - c^2_{\rm x}\right) & - \sqrt{\BX \BY} \Ccc \\
- \sqrt{\BX \BY} \Ccc & \BY \left(\sigma^2_{\rm y} - c^2_{\rm y}\right)
\end{array}\right]
\left[\begin{array}{c}
u^{\rm x}_a A^a_{\rm x} \\
u^{\rm y}_a A^a_{\rm y}
\end{array}\right] =
\left[\begin{array}{c} 0 \\ 0 \end{array}\right]
\ . \label{ccalg}
\eeq
The dispersion relation is now
\beq
\left(\sigma_{\rm x}^2 - c_{\rm x}^2\right) \left(\sigma^2_{\rm y} - c^2_{\rm y}\right) =
\Ccc^2 \ . \label{dispcc}
\eeq
In order for $\Ccc^2$ to be less than zero, the equation of state would have
to allow either of the $\BX$ to be negative. \ For ordinary matter, or
entropy, this is not generally the case. \ Hence, we do not consider this
possibility here. \ We also need to point out that \eqref{sigtrans} must be
used to get a dispersion relation solely in terms of $\sigma_{\rm x}$. \ Clearly,
the cross-coupled case is more complicated than the free problem. \ However, it is also much more
interesting and relevant. \ As we will soon see, the richer phenomenology
allows for two-stream instability.
Addressing first the question of absolute stability we set $v_{{\rm x} {\rm y}} = 0$ to
find
\beq
\sigma^2_{\rm x} = \frac{1}{2} \left(c^2_{\rm x} + c^2_{\rm y} \pm \sqrt{\left(c^2_{\rm x} -
c^2_{\rm y}\right)^2 + 4 \Ccc^2}\right) \ . \label{ccsig}
\eeq
In order to avoid complex $\sigma^2_{\rm x}$, the discriminant of \eqref{ccsig}
must be positive, which is evident for $\Ccc^2 \ge 0$. \ Recall that absolute
stability means $\sigma^2_{\rm x} \ge 0$. \ Clearly, it is sufficient to require
that
\beq
\left(c^2_{\rm x} + c^2_{\rm y}\right)^2 \ge \left(c^2_{\rm x} - c^2_{\rm y}\right)^2 + 4
\Ccc^2 \ .
\eeq
The second term of \eqref{ccsig} will always be less than the
first if
\beq
c^2_{\rm x} c^2_{\rm y} \ge \Ccc^2 \ . \label{ccstab}
\eeq
In other words, since we expect to have $\BX \BY > 0$, absolute stability
constrains the equation of state to satisfy
\beq
\frac{\partial\log\mathcal{B}^{\rm x}}{\partial\log n_{\rm y}}
\frac{\partial\log\mathcal{B}^{\rm y}}{\partial\log n_{\rm x}} \le
\left(1 + \frac{\partial\log\mathcal{B}^{\rm x}}{\partial\log n_{\rm x}}\right)
\left(1 + \frac{\partial\log\mathcal{B}^{\rm y}}{\partial\log n_{\rm y}}\right) \ .
\eeq
The causality constraint requires $\sigma^2_{\rm x} \le 1$. \ For $\Ccc^2 \ge 0$
and satisfying \eqref{ccstab}, we need only make the ``+'' solution in
\eqref{ccsig} causal, since the ``$-$'' solution is always smaller. \ We find
that causality is ensured if
\beq
\Ccc^2 \le \left(1 - c^2_{\rm x}\right) \left(1 - c^2_{\rm y}\right) \ ,
\label{cccaus}
\eeq
which, in terms of the equation of state, translates into
\beq
\frac{\partial\log\mathcal{B}^{\rm x}}{\partial\log n_{\rm y}}
\frac{\partial\log\mathcal{B}^{\rm y}}{\partial\log n_{\rm x}} \le
\frac{\partial\log\mathcal{B}^{\rm x}}{\partial\log n_{\rm x}}
\frac{\partial\log\mathcal{B}^{\rm y}}{\partial\log n_{\rm y}} \ .
\eeq
Note that both \eqref{ccstab} and \eqref{cccaus} restrict $\Ccc^2$ from
above. \ In general, we can show that if $c_{\rm x}^2 + c_{\rm y}^2 \le 1$ then any
absolutely stable equation of state is also causal. \ Conversely, if $c_{\rm x}^2
+ c_{\rm y}^2 \ge 1$, any causal equation of state is absolutely stable.
Given an equation of state that is causal and absolutely stable, we can now
determine if a dynamical two-stream instability is present by solving the
dispersion relation \eqref{dispcc} for some relative flow (as parameterized by
$v_{{\rm x} {\rm y}}$). \ Writing down the general solution is not difficult, but it is
instructive to first focus on the slow velocity limit. \ Assuming
that $v_{{\rm x} {\rm y}}$ and $\sigma_{\rm x}$ are both much smaller than unity (the speed
of light) in \eqref{sigtrans}, the dispersion relation \eqref{dispcc} becomes
\beq
\left(\sigma^2_{\rm x} - c_{\rm x}^2\right) \left[\left(\sigma_{\rm x} - v_{{\rm x} {\rm y}}
\cos \theta_{{\rm x} {\rm y}}\right)^2 - c^2_{\rm y}\right] = \Ccc^2 \ .
\eeq
Introducing new variables
\beq
x = \frac{\sigma_{\rm x}}{c_{\rm y}}
\quad , \quad
y = \frac{v_{{\rm x} {\rm y}} \cos \theta_{{\rm x} {\rm y}}}{c_{\rm y}}
\quad , \quad
b^2 = \left(\frac{c_{\rm x}}{c_{\rm y}}\right)^2
\quad , \quad
a^2 = \frac{\Ccc^2}{c^4_{\rm y}} \ , \label{rescale}
\eeq
we get
\beq
\frac{x^2 - b^2}{a^2} \left[\left(x - y\right)^2 -1\right] = 1 \ .
\eeq
As one might have expected, the problem is now identical to the Newtonian plane-wave
problem discussed by Andersson, Comer, and Prix \cite{andersson04:_twostream}.
Hence, we can learn from their results. \ They demonstrate that a two-stream
instability may operate above a critical relative flow. \ Their particular
example corresponds to $a^2 = 0.0249$ and $b^2 = 0.0379$. \ For this case
they find an instability in the range $0.6 < y < 1.5$. \ This means that the
system becomes unstable for $c_{\rm x} y > 0.6$. \ This flow is clearly
sub-luminal as long as $c_{\rm x} < 1$, but one may suspect that the linear
approximation that we have used is not very accurate. \ Still, this is a
useful first demonstration that the two-stream instability will operate also
in relativistic systems.
Before we turn our attention to the full relativistic case it is useful to
check if the particular example used by Andersson et al.\
\cite{andersson04:_twostream} obeys the causality and absolute stability
criteria derived above. \ First we note that, due to the presence of a
velocity scale given by the speed of light, in relativity we cannot
completely scale out the velocities. \ Thus the relativistic analysis of
stability will in general contain an extra parameter compared to the
Newtonian case. \ Here we shall take that parameter to be $c_{\rm y}$ which,
without loss of generality, can be taken to be larger than $c_{\rm x}$. \ Using
these parameters the absolute stability criterion \eqref{ccstab} becomes just
\beq
\frac{a^2}{b^2} \le 1 \ ,
\eeq
which is satisfied in the model discussed above. \ The causality condition
\eqref{stabcaus1} enters only indirectly as we have been able to re-scale in
terms of $c_{\rm y}$ and thereby get dimensionless variables. \ We conclude that
the Newtonian model of Andersson et al.\ is reasonable also from this
perspective as long as $c_{\rm y}$ is not very close to the speed of light.
We now turn to the relativistic dispersion relation \eqref{ccsig}. \ Written
as an equation for $\sigma_{\rm x}$ it constitutes a non-trivial quartic. \ If
we use the same re-scalings as in \eqref{rescale}, then \eqref{ccsig} becomes
\beq
\frac{x^2 - b^2}{a^2} \left[\frac{\left(x - y\right)^2}{\gamma^{-2}_{{\rm x} {\rm y}}
\left(1 - c^2_{\rm y} x^2 \right) + c^2_{\rm y} \left(x - y\right)^2} - 1\right] =
1 \ . \label{ccquartic}
\eeq
Some immediate insight is obtained by considering the ultra-relativistic
limit for the background flow, where $v_{{\rm x} {\rm y}} \to 1$ or
$\gamma^{- 2}_{{\rm x} {\rm y}} \to 0$, and the limit where the wave vector becomes
perpendicular to the background flow, \ie $\theta_{{\rm x} {\rm y}} \to \pi/2$. \ In
both limits the two-stream instability ceases to operate.
In the ultra-relativisitic limit, the wave-speed tends to
\beq
\sigma_{\rm x} \to \left\{\begin{array}{l}
\pm\sqrt{c^2_{\rm x} + \frac{\Ccc^2}{1 - c^2_{\rm y}}} \\
\cos \theta_{{\rm x} {\rm y}} \quad \mbox{(double root)}
\end{array}\right. \ . \label{ultrarel}
\eeq
If the propagation is to remain causal, we must have $\Ccc^2 \to 0$ as $c_{\rm y}
\to 1$. \ Also there is no two-stream instability since $\Ccc^2 \ge 0$. \ This
might seem surprising, since a two-stream instability requires a ``window'' of
background flows for modes to appear, say, left-moving in one frame but
right-moving in the other. \ But as $v_{{\rm x} {\rm y}} \to 1$ the relative flow is at
its maximum, and yet the instability window is closed. \ In fact, this
behaviour was seen already by Andersson et~al.~\cite{andersson04:_twostream}
in the Newtonian regime. \ From \eqref{rescale} we also see that $y \to 0$
as $\theta_{{\rm x} {\rm y}} \to \pi/2$. \ This turns \eqref{ccquartic} into a
quadratic for $x^2$, and one finds that the discriminant is positive for the
range of values for $\Ccc^2$ that yield absolute stability and causality. \
Obviously, $y$ is the effective ``window'' of the background flow and it is
completely closed for $\theta_{{\rm x} {\rm y}} = \pi/2$.
Although the general solution to \eqref{ccquartic} is readily availiable, it
is quite complicated and offers very little additional insight. \ Instead of
writing it down we will tackle the problem numerically. \ The parameter
values are restricted to those that maintain absolute stability and
causality. \ Figure~\ref{sigcccplt0} provides plots of the real and imaginary
parts for the four solutions to \eqref{ccquartic} in the aligned case. \ The
solutions for $\sigma_{\rm x}$ are taken to be functions of the relative flow
parameter $y$ and the coupling $\Ccc^2$, with $c_{\rm y} = 0.5$, $b^2 = 1$, and
$\theta_{{\rm x} {\rm y}} = 0$. \ Non-zero values for ${\rm Im}\sigma_{\rm x}$ in the
figures indicate the presence of an unstable mode. \ The appearance of
unstable modes is reflected in the real parts wherever two frequencies merge.
\ This behaviour is typical for this kind of dynamical instability. \ The
results for misaligned flows, with $\theta_{{\rm x} {\rm y}} \neq 0$ are very similar
to those shown in Figure~\ref{sigcccplt0}. \ As $\theta_{{\rm x} {\rm y}}$ increases
the $[y,\Ccc^2]$ region of instability moves towards higher relative
velocities, eventually leading to regions that stretch essentially all the
way to $v_{{\rm x} {\rm y}} = 1$.
\begin{figure}
\includegraphics[height=0.6\textwidth,width=0.9\textwidth,clip]
{slnthetaeq0.eps}
\caption{Plots of the real (top) and imaginary (bottom) parts of the mode
frequencies $\sigma_{\rm x}$ as functions of $v_{{\rm x} {\rm y}}$, for $c_y = 0.5$, $b^2
= 1.0$, and $\theta_{{\rm x} {\rm y}} = 0$. \ The merger of two frequencies, and
subsequent non-zero imaginary values, signal the presence of a two-stream
instability.} \label{sigcccplt0}
\end{figure}
\subsection{Dispersion Relation: Aligned or Anti-aligned Flows}
\label{DRalign}
Now that we have established the presence of the two-stream instability for
arbitrary background flows, we will consider the more restricted case of
aligned or anti-aligned background flows. \ This will simplify the dispersion
relation so that analytical insight can be more easily acquired. \ It also
reduces the parameter space, thus allowing a more focused numerical analysis.
By aligned or anti-aligned flow we mean that the wave propagation is
aligned (or anti-aligned) with the relative velocity of the two fluids;
specifically, $\theta_{{\rm x} {\rm y}} = (0,\pi)$ so that
\beq
\hat{k}^{\rm x}_a = \epsilon_{{\rm x} {\rm y}} \hat{v}^{{\rm x} {\rm y}}_a
\quad , \quad
\epsilon_{{\rm x} {\rm y}} \equiv \cos \theta_{{\rm x} {\rm y}} = \pm 1 \ .
\eeq
This leads naturally to the statement that the wave vector is a linear
combination of the background flows:
\bea
k_a &=& \frac{k_{\rm x}}{v_{{\rm x} {\rm y}}} \left[\left(v_{{\rm x} {\rm y}} \sigma_{\rm x} -
\epsilon_{{\rm x} {\rm y}}\right) u^{\rm x}_a + \epsilon_{{\rm x} {\rm y}}
\gamma^{- 1}_{{\rm x} {\rm y}} u^{\rm y}_a\right] \cr
&=& \frac{k_{\rm y}}{v_{{\rm x} {\rm y}}} \left[\left(v_{{\rm x} {\rm y}} \sigma_{\rm y} -
\epsilon_{{\rm y} {\rm x}}\right) u^{\rm y}_a + \epsilon_{{\rm y} {\rm x}}
\gamma^{- 1}_{{\rm x} {\rm y}} u^{\rm x}_a\right] \ . \label{alignvecs}
\eea
Equating coefficients in \eqref{alignvecs} leads to
\beq
k_a = \frac{1}{\gamma_{{\rm x} {\rm y}} v_{{\rm x} {\rm y}}} \left(k_{\rm y} \epsilon_{{\rm y} {\rm x}}
u^{\rm x}_a + k_{\rm x} \epsilon_{{\rm x} {\rm y}} u^{\rm y}_a\right) \ . \label{kalign}
\eeq
Because of \eqref{kalign}, our original four-dimensional linear algebra
problem for $(u^{\rm x}_a A^a_{\rm x},u^{\rm x}_a A^a_{\rm y},u^{\rm y}_a A^a_{\rm x},u^{\rm y}_a
A^a_{\rm y})^\mathrm{T}$ has been reduced to a two-dimensional one for
$(u^{\rm x}_a A^a_{\rm x},u^{\rm y}_a A^a_{\rm y})^\mathrm{T}$.
\subsection{Dispersion Relation: Role of Entrainment}
\label{DR-entrain}
Up to this point we have introduced three equation of state parameters
($c_{\rm x}$, $c_{\rm y}$, and $\Ccc$) that are obtained as second derivatives of the
master function. \ When entrainment is included in the model we see from
\eqref{twoderivs} that we need two additional variables to describe the
general case. \ Given that we have established the two-stream instability for
general cross-constituent coupling and arbitrary background flow, the main
reason for discussing the role of the entrainment is to highlight the basic
feature that the instability can be triggered by a variety of interactions. \
We will simplify the entrainment case by assuming that the relative velocity
$v^a_{{\rm x} {\rm y}}$ is much smaller than the speed of light and that the flows are
aligned (in the sense of the previous section). \ This does not mean,
however, that the individual flows $u^a_{\rm x}$ have to be similarly restricted.
Neither do the sound and wave speeds $c_{\rm x}$ and $\sigma_{\rm x}$ have to be small.
If we keep the relative flow to $\mathcal{O}(v^2_{{\rm x} {\rm y}})$, the master
function can be approximated as
\cite{andersson02:_oscil_GR_superfl_NS,andersson01:_dyn_superfl_ns}
\beq
\Lambda = \lambda_0(\nx,\ny) + \lambda_1(\nx,\ny) \left(\nxy -
\sqrt{\nx \ny}\right) \ ,
\eeq
which immediately implies
\beq
\BX = - 2 \left[\frac{\partial \lambda_0}{\partial \nx} +
\frac{\partial \lambda_1}{\partial \nx} \left(\nxy -
\sqrt{\nx \ny}\right) - \lambda_1 \frac{n_{\rm y}}{2 n_{\rm x}}\right]
\quad , \quad
\BX_{, {\rm x} {\rm y}} = - 2 n_{\rm x} n_{\rm y} \frac{\partial \lambda_1}{\partial \nx} \ ,
\eeq
and
\beq
\AXY = - \lambda_1 \quad , \quad \AXY_{, {\rm x} {\rm y}} = 0 \ .
\eeq
We shall make one further simplifying approximation, which is to take
$\lambda_1$ to be constant so that
\beq
\BX_{, {\rm x} {\rm y}} = 0 \ .
\eeq
This leaves us with the \underline{single} entrainment parameter $\lambda_1$.
With these approximations we find
\beq
\left[\begin{array}{cc}
\BX \left(\sigma^2_{\rm x} - c^2_{\rm x}\right) & - \Ccc \sqrt{\BX \BY} - \AXY
\frac{\epsilon_{{\rm x} {\rm y}} k_{\rm x}}{\epsilon_{{\rm y} {\rm x}} k_{\rm y}} \left(\sigma^2_{\rm x} - 1
\right) \\
- \Ccc \sqrt{\BX \BY} - \AXY \frac{\epsilon_{{\rm y} {\rm x}} k_{\rm y}}
{\epsilon_{{\rm x} {\rm y}} k_{\rm x}} \left(\sigma^2_{\rm y} - 1\right) & \BY \left(
\sigma^2_{\rm y} - c^2_{\rm y}\right)
\end{array}\right]
\left[\begin{array}{c}
u^{\rm x}_a A^a_{\rm x} \\
u^{\rm y}_a A^a_{\rm y}
\end{array}\right] =
\left[\begin{array}{c} 0 \\ 0 \end{array}\right]
\ . \label{ccentalg}
\eeq
From \eqref{kmag} and \eqref{kequal} we have
\beq
\frac{k_{\rm x}}{k_{\rm y}} = \sqrt{\frac{1 - \sigma^2_{\rm y}}{1 - \sigma^2_{\rm x}}} \ ,
\eeq
and thus the dispersion relation becomes
\beq
0 = \left(\sigma^2_{\rm x} - c^2_{\rm x}\right) \left(\sigma^2_{\rm y} - c^2_{\rm y}\right)
- \left[\Ccc + \Cent \sqrt{\left(1 - \sigma^2_{\rm x}\right)
\left(1 - \sigma^2_{\rm y}\right)}\right]^2 \ , \label{dispccent2}
\eeq
where
\beq
\Cent = \epsilon_{{\rm x} {\rm y}} \epsilon_{{\rm y} {\rm x}} \frac{\AXY}{\sqrt{\BX \BY}} \ ,
\eeq
and because the inverse of \eqref{momfluxmat} must exist, $|\Cent|
\neq 1$. Note that, since $\sigma^2_{\rm y}\rightarrow 1$ as $v_{{\rm x}
{\rm y}}\rightarrow 1$, $\Cent$ does not affect the ultra-relativistic limit. Hence,
equation \eqref{ultrarel} [with $\cos(\theta_{{\rm x} {\rm y}})=\pm 1$] is still
valid in this case.
We stress that, unlike the simpler cases, \eqref{dispccent2} does not
hold for arbitrary propagation direction with respect to the relative
velocity. \ This is important qualitatively and quantitatively, since
it mirrors the fact that entrainment enters the master function in a
fundamentally different way: At first-order in the relative velocity
squared. \ In the dispersion relation, however, entrainment
contributes even in the limit of zero relative velocity, because there
are still two sets of interacting sound waves. \ In fact, we will now
follow the earlier analysis of causality and absolute stability by
taking this limit.
From \eqref{sigtrans} we see $\sigma^2_{\rm x} = \sigma^2_{\rm y}$ so that
\beq
\left(\sigma^2_{\rm x} - c_{\rm x}^2\right) \left(\sigma^2_{\rm x} - c^2_{\rm y}\right) -
\left[\Ccc + \Cent \left(1 - \sigma^2_{\rm x}\right)\right]^2 = 0 \ .
\eeq
It is particularly instructive to consider the entrainment alone, \ie set
$\Ccc = 0$. \ The corresponding dispersion relation is a quadratic
in $\sigma^2_{\rm x}$, and has the solutions
\beq
\sigma^2_{\rm x} = \frac{c^2_{\rm x} + c^2_{\rm y} - 2 \Cent^2 \pm \left[\left(c^2_{\rm x} -
c^2_{\rm y}\right)^2 + 4 \Cent^2 \left(1 - c^2_{\rm x}\right) \left(1- c^2_{\rm y}\right)
\right]^{1/2}}{2 \left(1 - \Cent^2\right)} \ . \label{sigxentsln}
\eeq
For $c^2_{{\rm x} , {\rm y}} \le 1$, the discriminant is obviously positive and hence
the $\sigma^2_{\rm x}$ are real. \ In order to analyze absolute stability and
causality we need to consider the ranges $0 \le \Cent^2 < 1$ and $1 <
\Cent^2$ separately. \ We will look at $\Cent^2 > 1$ first.
The first step is to re-write \eqref{sigxentsln} so that the denominator is
positive:
\beq
\sigma^2_{\rm x} = \frac{2 \Cent^2 - c^2_{\rm x} - c^2_{\rm y} \pm \left[\left(c^2_{\rm x} -
c^2_{\rm y}\right)^2 + 4 \Cent^2 \left(1 - c^2_{\rm x}\right) \left(1- c^2_{\rm y}\right)
\right]^{1/2}}{2 \left(\Cent^2 - 1\right)} \ . \label{slnge1}
\eeq
Since we are imposing $c^2_{{\rm x} {\rm y}} \le 1$, and $\Cent^2 > 1$, the terms
outside the square root in the numerator are positive. \ Therefore, the ``+''
solution is absolutely stable. \ But, we can also show that it cannot be
causal. \ As for the ``$-$'' solution, we can easily show that it is
absolutely stable only if $\Cent^2 < 1$, which cannot be satisfied. \ Hence,
$\Cent^2 > 1$ does not lead to both absolute stability and causality, and is
therefore ruled out.
The range $0 \le \Cent^2 < 1$ is a different story, because the terms
outside the radical in the numerator of \eqref{sigxentsln} are not of any
definite sign. \ This affects the absolute stability analysis more than the
determination of causality. \ In fact, the causality analysis is sufficiently
straightforward that we will simply state that this requirement is satisfied
for this range of $\Cent^2$. \ In order to assess absolute stability, it is
useful to introduce
\beq
\tau = \left[\left(c^2_{\rm x} - c^2_{\rm y}\right)^2 + 4 \Cent^2 \left(1 -
c^2_{\rm x}\right) \left(1 - c^2_{\rm y}\right)\right]^{1/2} \ .
\eeq
This allows the numerator of \eqref{sigxentsln} to be rewritten in such a way
that the absolute stability condition becomes
\beq
\tau^2 - \left[\pm 2 \left(1 - c^2_{\rm x}\right) \left(1 - c^2_{\rm y}\right)
\right] + \left[c^2_{\rm x} \left(1 - c^2_{\rm y}\right) + c^2_{\rm y} \left(1 -
c^2_{\rm x}\right)\right] \left[2 - \left(c^2_{\rm x} + c^2_{\rm y}\right)\right] \le 0
\ , \label{tauineq}
\eeq
where the ``$\pm$'' corresponds to that of \eqref{sigxentsln}. \ The final
step is to factorize \eqref{tauineq} and thereby obtain
\beq
\left\{\tau \pm \left[2 - \left(c^2_{\rm x} + c^2_{\rm y}\right)\right]\right\}
\left\{\tau \mp \left[c^2_{\rm x} \left(1 - c^2_{\rm y}\right) + c^2_{\rm y} \left(1 -
c^2_{\rm x}\right)\right]\right\} \le 0 \ ,
\eeq
where if the ``$+$'' is taken from the first factor then the ``$-$'' must be
taken in the second, and vice versa. \ In either case, the factor that has
the ``$+$'' is positive definite, and so the other factor must be less than
zero. \ When the first factor takes the ``$-$'' the inequality leads to
$\Cent^2 \le 1$. \ The other choice leads to the more restrictive condition
of $\Cent^2 \le c^2_{\rm x} c^2_{\rm y}$.
To summarize, we have shown that when $\Cent^2 > 1$, there is either no
absolute stability or causality, which makes this range unphysical. \
Meanwhile, for $0 \le \Cent^2 \le c^2_{\rm x} c^2_{\rm y}$ the system is causal and
absolutely stable. \ In terms of our earlier definitions, this translates into
\beq
({\AXY})^2\ \le \BX \BY \left(\frac{\partial \log \BX}{\partial
\log n_{\rm x}} + 1\right) \left(\frac{\partial \log \BY}{\partial \log n_{\rm y}}
+ 1\right) \label{entconst}
\eeq
as a constraint on the master function, when the relative speed between the
two fluids is sufficiently small.
Finally, we turn to a numerical/graphical analysis for exposing the two-stream
instability due to entrainment coupling. \ As in the cross-constituent
coupling case, we use the re-scalings of \eqref{rescale}, except that
$\Cent^2$ replaces $\Ccc^2$ in $a^2$. \ Equation \eqref{dispccent2} becomes
\beq
\frac{x^2 - b^2}{a^2} \left[\frac{\left(x - y\right)^2}{\left(c^2_{\rm y} y x -
1\right)^2} - 1\right] = \left(c^2_{\rm y} x^2 - 1\right) \left[\frac{c^2_{\rm y}
\left(x - y\right)^2}{\left(c^2_{\rm y} y x - 1\right)^2} - 1\right] \ .
\label{centquartic}
\eeq
The parameter values are restricted to those that maintain absolute stability
and causality. \ Fig.~\ref{entplt} plots the real and imaginary parts of the
four solutions to \eqref{centquartic}. \ As before, the solutions for
$\sigma_{\rm x}$ are taken to be functions of the relative flow parameter $y$ and
the coupling $\Cent^2$, with $c_{\rm y} = 0.5$ and $b^2 = 1.0$. \ Fig.~\ref{entplt}
is not so dissimilar from what we find for cross-constituent coupling, thus
highlighting that the instability is not sensitive to the type of coupling
between the two fluids.
\begin{figure}
\includegraphics[height=0.6\textwidth,width=0.9\textwidth,clip]
{entsln.eps}
\caption{Plots of the real and imaginary parts of the mode frequencies
$\sigma_{\rm x}$ as functions of $y$ and $\Cent^2$, for $c_y = 0.5$, and
$b^2 = 1.0$. \ The lines of intersection and subsequent merger of two
frequencies signal the presence of a two-stream instability.}
\label{entplt}
\end{figure}
\section{Closing Remarks}
\label{conclu}
There are several examples of relativistic systems that require multi-fluid
dynamics for qualitative understanding and quantitative accuracy. \ In such
systems different interpenetrating fluid components (eg.~particles and
entropy in heat conducting situations or a superfluid condensate and finite
temperature excitations) can flow with distinct velocities.
We have examined plane-wave propagation for a generic two-fluid system. \ By
imposing the constraints of absolute stability (necessary in order for the
components not to separate already in the absence of flow) and causality we
have established limits on the equation of state (as represented by the
master function $\Lambda$). \ In particular, we place constraints on the free
sound speeds, the cross-constituent coupling and the entrainment. \ Some of
the obtained results are more or less trivial extensions of the single fluid
result, but others are unique to the two-fluid problem. \ The condition
\eqref{entconst} on the entrainment is a new result, and as such serves as a
new condition on, say, the kind of $\sigma - \omega$ model used by Comer and
Joynt \cite{comer03:_rel_ent} to model entrainment in the outer cores of
neutron stars.
We have demonstrated (for the first time) the existence of a relativistic
two-stream instability. \ This is a generic phenomenon, that does not require
particular fine-tuning to be triggered, nor is it limited to any specific
physical system. \ The only requirement is that there is a relative
(background) flow and some type of coupling between the fluids. \ While it is
true that a single fluid can have an analogous instability, it is only active
at an interface where there is shearing motion. \ Our analysis assumes that
the two fluids are interpenetrating.
In order to exhibit the generic nature of the two-stream instability, we have
kept the analysis rather abstract. \ On the one hand, this means that it
should be relatively straightforward to apply our results to particular
physical systems. \ On the other hand, it means that we have not yet
discussed the relevance of the instability for any particular system. \ A
more detailed consideration of multi-fluid problems in relativity is required
in order to establish whether this mechanism operates in nature. \ There are
already exciting results that hint at this class of instabilities being
associated with pulsar glitches
\cite{andersson04:_twostream,glampedakis09:_glitch_prl}. \ In addition to
exploring possible situations where these instabilities may operate, it would
be very interesting to probe the nonlinear development of the unstable waves.
\ So far, all studies have been at the linear perturbation level. \
The results establish the presence of the instability, but they do not shed
any light on what happens once the unstable oscillation reaches nonlinear
amplitudes. \ Detailed studies of this problem are essential if we
are to understand the actual dynamical role of this instability.
\acknowledgments
NA acknowledges support from STFC via grant number PP/E001025/1.
CLM is supported by CONACyT. GLC acknowledges partial support from NSF via
grant number PHYS-0855558.
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 2,184
|
{"url":"https:\/\/docs.cheddar.vihan.org\/docs\/mathematics\/root","text":"# Syntax\n\nsqrt xcbrt xx root y\n\n# Explanation\n\n## sqrt\/cbrt\n\nsqrt and cbrt, find the square root and the cube root of the given operand respectively. They are aliases of x root 2 and x root 3. There is minimal speed different, if any, and are simply exist for clearer code.\n\n## root\n\nroot finds the $n^{th}$ root of x ($\\sqrt[n]{x}$), where $n = y$. It is equivilent to x ** y ** -1\n\n# Examples\n\nsqrt 16 \/\/ 4cbrt 8 \/\/ 216 root 4 \/\/ 2","date":"2021-01-20 08:57:38","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 3, \"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\": 0.6385524272918701, \"perplexity\": 4904.041145607141}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-04\/segments\/1610703519984.9\/warc\/CC-MAIN-20210120085204-20210120115204-00376.warc.gz\"}"}
| null | null |
Search Česky
The Kellner Family Foundation |
News| Czech students supported by the family foundation...
Board of Trustees and Supervisory Board
Charter and Annual Reports
Grants for the students of the eight-year grammar school of the same name
Financial grants to university students
Helping Schools Succeed
Improving the quality of teaching at public elementary schools
Financial grants to Czech research teams
Other supported projects
For future Open Gate students
For elementary school teachers and principals
Contact for media
I want to join
I want to win a grant at the Open Gate eight-year grammar school
Project Open Gate
I want to win a grant to study at a university
Project Universities
I want to sign up my school for the Helping Schools Succeed program
Project Helping Schools Succeed
Czech students supported by the family foundation of Mrs Renáta Kellnerová and Mr Petr Kellner will study at 36 universities
22. August 2016 In the upcoming academic year, some fifty students will enjoy support from the Universities project: 25 new students who have won a grant for the first time, and other grantees continuing their studies. In addition to the traditional destinations of the United Kingdom and the US, to which Czechs go most frequently to study, the Universities project newcomers will also move to Japan, Sweden and France this year.
The Kellner Family Foundation has been supporting university students since 2009. Students receive grants totalling approximately CZK 10 million every year. Over the time during which the project has been in existence, 126 students (including those receiving grants in the current academic year) have won grants totalling approximately CZK 61 million.
"In the past academic year, 27 of our grantees graduated. We are delighted to watch their continued academic paths and the professional careers they have embarked upon. Some of them will go on to attend master's programmes, for example, at the University of Cambridge, or doctoral programmes at Yale University, while others will start to gather professional experience", said Mrs Hana Halfarová, Director of the Universities and Open Gate projects at The Kellner Family Foundation.
The single largest group of students is heading for schools in the UK (33 students). Others will travel to the Netherlands, the US, France, Japan, and Sweden. Eleven students will enrol at universities and colleges in the Czech Republic with the Foundation's support.
Almost 200 students have vied for grants from the Universities project this year. This academic year, include the largest number of students from Prague (12) and from the Ústí nad Labem Region (6). Other students come from the Central Bohemian region, the Zlín Region, the Olomouc Region, the Plzeň Region, the Vysočina Region, the South Bohemian Region, the Hradec Králové Region and the Moravian-Silesian Region. One student comes from the South Moravian Region and one from the Karlovy Vary Region; one comes from Somalia.
Compared with the past academic year, there are more medical students (their number rose from six to 11), art students (from two to six) and engineering students (from three to five) among the grantees. On the other hand, the group includes a smaller number of mathematics, physics and economics students.
©Nadace The Kellner Family Foundation, 2020
Nadace The Kellner Family Foundation
Evropská 2690/17, P.O. Box 177,<br /> 160 41 Praha 6, Česká republika
on social network
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 6,516
|
\section{Introduction}
Given a number $t \in \mathbb{N}$, a \emph{$K_t$-expansion} is a graph consisting of vertex-disjoint trees $(T_s)_{s=1}^{t}$ and exactly one connecting edge between any pair of trees $T_s, T_{s'}$ for distinct $s,s' \in \{1,\ldots,t\}$. A graph is said to \emph{contain $K_t$ as a minor} or to \emph{contain a $K_t$-minor} if it admits a subgraph which is a $K_t$-expansion. Hadwiger's conjecture, which may well be seen as one of the most central open problems in graph theory, states the following relation between minor containment and the chromatic number of graphs.
\begin{conjecture}[Hadwiger 1943,~\cite{hadwiger}]
If $G$ is a graph which does not contain $K_t$ as a minor, then $\chi(G) \le t-1$.
\end{conjecture}
Hadwiger's conjecture and many variations of it have been studied in past decades, a very good overview of the developments and partial results until about $2$ years ago is given in the survey article~\cite{survey} by Seymour. The best known asymptotic upper bound on the chromatic number of $K_t$-minor free graphs for a long time remained of magnitude $O(t\sqrt{\log t})$, as proved independently by Kostochka~\cite{kostochka} and Thomason~\cite{thomason} in 1984. However, recently there has been progress. First, in 2019, Norine, Postle and Song~\cite{norine} broke the $t \sqrt{\log t}$ barrier by proving an upper bound of the form $O(t (\log t)^\beta)$ for any $\beta>\frac{1}{4}$. Subsequently, there have been several significant improvements of this bound and related results~\cite{norine2},\cite{postle},\cite{postle2}. The following state of the art-bound was proved recently by Delcourt and Postle in~\cite{del}.
\begin{theorem}\label{thm:del}
The maximum chromatic number of $K_t$-minor free graphs is bounded from above by a function in $O(t\log \log t)$.
\end{theorem}
A strengthening of Hadwiger's conjecture to so-called \emph{odd minors} was conjectured by Gerards and Seymour in~\cite{gerards}. A $K_t$-expansion $H$ certified by a corresponding collection of vertex-disjoint trees $(T_s)_{s=1}^{t}$ is said to be \emph{odd}, if there exists an assignment of two colors $\{1, 2\}$ to the vertices of $H$ in such a way that every edge contained in one of the trees $T_s$ with $s \in \{1,\ldots,t\}$ is bichromatic (i.e., has different colors at its endpoints), while every edge joining two distinct trees is monochromatic (i.e., has the same color at its endpoints).
Finally, we say that a graph contains \emph{$K_t$ as an odd minor} or that it contains an \emph{odd $K_t$-minor} if it contains a subgraph which is an odd $K_t$-expansion.
\begin{conjecture}[Gerards and Seymour~\cite{gerards}]\label{oddconjecture}
If $G$ is a graph which does not contain $K_t$ as an odd minor, then $\chi(G) \le t-1$.
\end{conjecture}
Just as for Hadwiger's conjecture, the asymptotic growth of the best-possible upper bound on the chromatic number of graphs without an odd $K_t$-minor has been studied. First, Geelen, Gerards, Reed, Seymour and Vetta proved in~\cite{geelen} that every graph with no odd $K_t$-minor is $O(t \sqrt{\log t})$-colorable. A shorter proof for the same result was given by Kawarabayashi in~\cite{kawarabayashi}. Subsequently, an asymptotical improvement of this upper bound to $O(t(\log \log t)^\beta)$ for any $\beta>\frac{1}{4}$ was achieved by Norine and Song in~\cite{norine3}. This was improved further to $O(t (\log \log t)^6)$ by Postle in~\cite{postle3}. Very recently the exponent of the $\log \log t$ factor was further improved by Delcourt and Postle in~\cite{del}, resulting in an $O(t(\log \log t)^2)$-bound.
Many further results on odd $K_t$-minor free graphs are known, we refer to~\cite{kang,kawarabayashi2,kawarabayashi3,kawarabayashireed,kawarabayashireedwollan,kawarabayashisong} for some additional references.
The purpose of this note is to show that asymptotically, the maximum chromatic number of $K_t$-minor free graphs and the maximum chromatic number of odd $K_t$-minor free graphs differ at most by a multiplicative factor of $2$.
\begin{theorem}\label{thm:main}
Let $t \in \mathbb{N}$ and let $f(t)$ be an integer such that every graph not containing $K_t$ as a minor is $f(t)$-colorable. Then every graph not containing $K_t$ as an odd minor is $2f(t)$-colorable.
\end{theorem}
Theorem~\ref{thm:main} has a very simple proof, given in Section~\ref{sec:proof} below. It is useful in the sense that any progress made towards a better asymptotic upper bound on the chromatic number of $K_t$-minor free graphs carries over, without further work and only at the prize of a constant multiplicative factor, to odd $K_t$-minor free graphs. In particular, Theorem~\ref{thm:del} together with Theorem~\ref{thm:main} directly yields the following (slight) asymptotical improvement of the $O(t(\log \log t)^2)$-upper bound on the chromatic number of odd $K_t$-minor free graphs by Delcourt and Postle.
\begin{corollary}
The maximum chromatic number of odd $K_t$-minor free graphs is bounded from above by a function in $O(t\log \log t)$.
\end{corollary}
\section{Proof of Theorem~\ref{thm:main}}\label{sec:proof}
The proof is based on the following lemma.
\begin{lemma}\label{lemma}
Let $G$ be a graph. Then there exists $n \in \mathbb{N}$ and a partition of $V(G)$ into $n$ non-empty sets $X_1,\ldots,X_n$ such that the following hold:
\begin{itemize}
\item for every $1 \le i \le n$, the graph $G[X_i]$ is bipartite and connected,
\item for every $1 \le i<j \le n$, either there are no edges in $G$ between $X_i$ and $X_j$, or there exist $u_1, u_2 \in X_i$ and $v \in X_j$ such that $u_1v, u_2v \in E(G)$ and $u_1$ and $u_2$ lie on different sides of the bipartition of $G[X_i]$.
\end{itemize}
\end{lemma}
\begin{proof}
Let us define the partition $X_1,X_2,\ldots$ of $V(G)$ inductively as follows:
Suppose that for some integer $i \ge 1$, all the sets $X_k$ with $1 \le k<i$ have been defined already, and do not yet form a partition, i.e., $\bigcup_{1 \le k<i}{X_k} \neq V(G)$. We now choose $X_i$ as an inclusion-wise maximal set among all subsets $X \subseteq V(G) \setminus \bigcup_{1 \le k<i}{X_k}$ which satisfy that $G[X]$ is a bipartite and connected graph. Note that $X_i \neq \emptyset$, since for every vertex $x \in V(G) \setminus \bigcup_{1 \le k<i}{X_k}$, the graph $G[\{x\}]$ is bipartite and connected.
Since we are adding a non-empty set to our collection of pairwise disjoint subsets of $V(G)$ at each step, the above procedure eventually yields a partition $X_1,\ldots,X_n$ of $V(G)$ for some $n \in \mathbb{N}$. By definition, we have that $G[X_i]$ is bipartite and connected for $i=1,\ldots,n$, and hence what remains to show is the second property of the partition stated in the lemma.
So let $i,j$ be given such that $1 \le i <j \le n$, and suppose that there exists at least one edge $e \in E(G)$ between $X_i$ and $X_j$. Denote $e=uv$ with $u \in X_i$ and $v \in X_j$. Let $\{A; B\}$ be the unique bipartition of $G[X_i]$. We claim that $v$ must have a neighbor $u_1 \in A$ and a neighbor $u_2 \in B$, which then yields the statement claimed in the lemma. Indeed, suppose not, and suppose w.l.o.g. that $v$ is not adjacent to any vertex in $A$ (the case that $v$ has no neighbor in $B$ is of course symmetric). Then also the graph $G[X_i \cup \{v\}]$ is bipartite and connected: It is connected since $G[X_i]$ is connected and because of the edge $uv$, and it is bipartite since $\{A \cup \{v\}; B\}$ forms its unique bipartition. However, putting $X:=X_i \cup \{v\} \subseteq V(G) \setminus \bigcup_{1 \le k<i}{X_k}$, this contradicts the definition of $X_i$ as an inclusion-wise maximal subset of $V(G) \setminus \bigcup_{1 \le k<i}{X_k}$ inducing a bipartite and connected subgraph.
\end{proof}
We can now easily deduce Theorem~\ref{thm:main}.
\begin{proof}[Proof of Theorem~\ref{thm:main}]
Let $t \in \mathbb{N}$ and suppose that $f(t)$ is an integer such that every $K_t$-minor free graph is $f(t)$-colorable. Let $G$ be any given graph without an odd $K_t$-minor, and let us prove that $\chi(G) \le 2f(t)$.
We apply Lemma~\ref{lemma} to $G$ and obtain a partition $X_1,\ldots,X_n$ of $V(G)$ with properties as stated in the lemma. Let $H$ be defined as the graph with vertex-set $\{1,\ldots,n\}$ and which has an edge between distinct vertices $i$ and $j$ if and only if there exists at least one edge in $G$ between $X_i$ and $X_j$. It follows from the statement of the lemma that for every edge $ij \in E(H)$ with $i<j$, there exist $u_1, u_2 \in X_i$ and $v \in X_j$ such that $u_1v, u_2v \in E(G)$ and $u_1, u_2$ are on different sides of the bipartition of $G[X_i]$.
We claim that $\chi(G) \le 2\chi(H)$. To see this, let $c_H:\{1,\ldots,n\} \rightarrow \{1,\ldots,\chi(H)\}$ be a proper coloring of $H$, and for every $i \in \{1,\ldots,n\}$ let $c_i:X_i \rightarrow \{1,2\}$ be a proper coloring of the bipartite graph $G[X_i]$. It now follows directly from the definition of $H$ that the coloring $c_G$ of $G$ with color set $\{1,\ldots,\chi(H)\} \times \{1,2\}$, defined by $c_G(x):=(c_H(i),c_i(x))$ for every $x \in X_i$ and $i \in \{1,\ldots,n\}$, is a proper coloring of $G$. Therefore, $\chi(G) \le 2\chi(H)$.
Next, we will show that $\chi(H) \le f(t)$ by proving that $H$ does not contain $K_t$ as a minor. Suppose towards a contradiction that $H$ contains a subgraph which is a $K_t$-expansion, i.e., there exist vertex-disjoint trees $(T_s)_{s=1}^{t}$ contained in $H$ and for every pair $\{s,s'\} \subseteq \{1,\ldots,t\}$ an edge $e(s,s') \in E(H)$ with endpoints in $T_s$ and $T_{s'}$.
For every fixed $s \in \{1,\ldots,t\}$, let us consider the subgraph $G_s:=G\left[\bigcup_{i \in V(T_s)}{X_i}\right]$ of $G$. This is a connected graph because $G[X_i]$ is connected for every $i \in V(T_s)$, since $T_s$ is connected, and since by definition of $H$ for every edge $ij \in E(T_s)$ there exists at least one connecting edge between $X_i$ and $X_j$ in $G$. In particular, $G_s$ contains a spanning tree $T^G_s$ which has the property that $T^G_s[X_i]$ forms a spanning tree of $G[X_i]$, for every $i \in V(T_s)$.
The trees $(T^G_s)_{s=1}^{t}$ in $G$ defined as above are pairwise vertex-disjoint. Let us denote by $c:\bigcup_{s=1}^{t}{V(T^G_s)} \rightarrow \{1,2\}$ a $2$-color-assignment obtained by piecing together proper $2$-colorings of the individual trees $(T^G_s)_{s=1}^{t}$.
\paragraph{Claim.} For every pair $\{s,s'\} \subseteq \{1,\ldots,t\}$, there exists an edge $f(s,s') \in E(G)$ with endpoints in $T^G_{s}$ and $T^G_{s'}$, such that $f(s,s')$ is monochromatic with respect to the coloring $c$.
\begin{proof}[Subproof]
By assumption, there exists $e(s,s') \in E(H)$ which connects a vertex in $i \in V(T_s)$ to a vertex $j \in V(T_{s'})$. Possibly after relabelling assume w.l.o.g. $1 \le i <j \le n$. Then the second property of the partition $X_1,\ldots,X_n$ guaranteed by Lemma~\ref{lemma} yields the existence of vertices $u_1, u_2 \in X_i \subseteq V(T^G_{s})$ and $v \in X_j\subseteq V(T^G_{s'})$ such that $f_1:=u_1v, f_2:=u_2v \in E(G)$, and such that $u_1$ and $u_2$ lie on different sides of the unique bipartition of $G[X_i]$. Since $u_1, u_2 \in X_i \subseteq V(T^G_{s})$ and since by our choice of $T^G_s$ the graph $T^G_s[X_i]$ forms a spanning tree of $G[X_i]$, it follows that $u_1$ and $u_2$ also must be on different sides in the unique bipartition of $T^G_s[X_i]$. In particular, $c(u_1) \neq c(u_2)$, which implies that $c(u_r)=c(v)$ for some $r \in \{1,2\}$. Now the edge $f_r \in E(G)$ connects the vertex $u_r$ in $T^G_s$ with the vertex $v$ in $T^G_{s'}$, and is monochromatic with respect to $c$. This proves the subclaim with $f(s,s'):=f_r$.
\end{proof}
It follows directly from the previous claim that the union of the vertex-disjoint trees $(T^G_s)_{s=1}^{t}$, joined by the edges $f(s,s')$ for every pair $\{s,s'\} \subseteq \{1,\ldots,t\}$, forms an odd $K_t$-expansion contained in $G$. This contradicts our initial assumption that $G$ does not contain $K_t$ as an odd minor. Hence, our initial assumption was wrong, and we have established that $H$ is $K_t$-minor free. It now follows that $\chi(G) \le 2\chi(H)\le 2f(t)$, as required. This concludes the proof of the theorem.
\end{proof}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 3,044
|
Dr. David Livingstone, Missionary
Dr. David Livingstone, Missionary >
David Livingstone was a Scottish Congregationalist pioneer medical missionary and an explorer in Africa. His meeting with H. M. Stanley gave rise to the popular quotation, "Dr. Livingstone, I presume?"
Perhaps one of the most popular national heroes of the late 19th century in Victorian Britain, Livingstone had a mythic status, which operated on a number of interconnected levels: that of Protestant missionary martyr, that of working-class "rags to riches" inspirational story, that of scientific investigator and explorer, that of imperial reformer, anti-slavery crusader, and advocate of commercial empire.
His fame as an explorer helped drive forward the obsession with discovering the sources of the River Nile that formed the culmination of the classic period of European geographical discovery and colonial penetration of the African continent.
• http://en.wikipedia.org/wiki/David_Livingstone
His fame as an explorer helped drive forward the obsession with discovering the sources of the River Nile that formed the culmination of the classic period of European geographical discovery and colonial penetration of the African continent. More...
Related > Activists • Christians • Explorers • Scientists • 1850s • 1860s • Africa • Congo • Exploration • Industrial Revolution • March 19 • Medicine • Missionaries • Physicians • Pisces • Scotland • Slavery • Tanzania • People
Abolition of the Slave Trade Act 1807
The Slave Trade Act sometimes called the Slave Trade Act 1807 or the Abolition of the Slave Trade Act 1807, was an Act of the Parliament of the United Kingdom passed on 25 March 1807, with the title of "An Act for the Abolition of the Slave Trade". T...
Sir Richard Burton, Explorer, etc.
Captain Sir Richard Francis Burton KCMG FRGS was a British geographer, explorer, translator, writer, soldier, orientalist, cartographer, ethnologist, spy, linguist, poet, fencer and diplomat. He was known for his travels and explorations within Asia,...
John Speke, Source of the Nile -1856
John Hanning Speke was an officer in the British Indian Army who made three exploratory expeditions to Africa and who is most associated with the search for the source of the Nile. In 1844 he was commissioned into the British army and posted to I...
Stanley, "Dr. Livingstone, I presume?"
Sir Henry Morton Stanley was a journalist and explorer famous for his exploration of Africa and his search for David Livingstone. Stanley travelled to Zanzibar and outfitted an expedition with the best of everything, requiring no fewer than 200 porte...
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 5,635
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.